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+/*M///////////////////////////////////////////////////////////////////////////////////////
+//
+// IMPORTANT: READ BEFORE DOWNLOADING, COPYING, INSTALLING OR USING.
+//
+// By downloading, copying, installing or using the software you agree to this license.
+// If you do not agree to this license, do not download, install,
+// copy or use the software.
+//
+//
+// License Agreement
+// For Open Source Computer Vision Library
+//
+// Copyright (C) 2000-2008, Intel Corporation, all rights reserved.
+// Copyright (C) 2009, Willow Garage Inc., all rights reserved.
+// Copyright (C) 2013, OpenCV Foundation, all rights reserved.
+// Third party copyrights are property of their respective owners.
+//
+// Redistribution and use in source and binary forms, with or without modification,
+// are permitted provided that the following conditions are met:
+//
+// * Redistribution's of source code must retain the above copyright notice,
+// this list of conditions and the following disclaimer.
+//
+// * Redistribution's in binary form must reproduce the above copyright notice,
+// this list of conditions and the following disclaimer in the documentation
+// and/or other materials provided with the distribution.
+//
+// * The name of the copyright holders may not be used to endorse or promote products
+// derived from this software without specific prior written permission.
+//
+// This software is provided by the copyright holders and contributors "as is" and
+// any express or implied warranties, including, but not limited to, the implied
+// warranties of merchantability and fitness for a particular purpose are disclaimed.
+// In no event shall the Intel Corporation or contributors be liable for any direct,
+// indirect, incidental, special, exemplary, or consequential damages
+// (including, but not limited to, procurement of substitute goods or services;
+// loss of use, data, or profits; or business interruption) however caused
+// and on any theory of liability, whether in contract, strict liability,
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+// the use of this software, even if advised of the possibility of such damage.
+//
+//M*/
+
+#ifndef OPENCV_CALIB3D_HPP
+#define OPENCV_CALIB3D_HPP
+
+#include "opencv2/core.hpp"
+#include "opencv2/core/types.hpp"
+#include "opencv2/features2d.hpp"
+#include "opencv2/core/affine.hpp"
+#include "opencv2/core/utils/logger.hpp"
+
+/**
+ @defgroup calib3d Camera Calibration and 3D Reconstruction
+
+The functions in this section use a so-called pinhole camera model. The view of a scene
+is obtained by projecting a scene's 3D point \f$P_w\f$ into the image plane using a perspective
+transformation which forms the corresponding pixel \f$p\f$. Both \f$P_w\f$ and \f$p\f$ are
+represented in homogeneous coordinates, i.e. as 3D and 2D homogeneous vector respectively. You will
+find a brief introduction to projective geometry, homogeneous vectors and homogeneous
+transformations at the end of this section's introduction. For more succinct notation, we often drop
+the 'homogeneous' and say vector instead of homogeneous vector.
+
+The distortion-free projective transformation given by a pinhole camera model is shown below.
+
+\f[s \; p = A \begin{bmatrix} R|t \end{bmatrix} P_w,\f]
+
+where \f$P_w\f$ is a 3D point expressed with respect to the world coordinate system,
+\f$p\f$ is a 2D pixel in the image plane, \f$A\f$ is the camera intrinsic matrix,
+\f$R\f$ and \f$t\f$ are the rotation and translation that describe the change of coordinates from
+world to camera coordinate systems (or camera frame) and \f$s\f$ is the projective transformation's
+arbitrary scaling and not part of the camera model.
+
+The camera intrinsic matrix \f$A\f$ (notation used as in @cite Zhang2000 and also generally notated
+as \f$K\f$) projects 3D points given in the camera coordinate system to 2D pixel coordinates, i.e.
+
+\f[p = A P_c.\f]
+
+The camera intrinsic matrix \f$A\f$ is composed of the focal lengths \f$f_x\f$ and \f$f_y\f$, which are
+expressed in pixel units, and the principal point \f$(c_x, c_y)\f$, that is usually close to the
+image center:
+
+\f[A = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1},\f]
+
+and thus
+
+\f[s \vecthree{u}{v}{1} = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1} \vecthree{X_c}{Y_c}{Z_c}.\f]
+
+The matrix of intrinsic parameters does not depend on the scene viewed. So, once estimated, it can
+be re-used as long as the focal length is fixed (in case of a zoom lens). Thus, if an image from the
+camera is scaled by a factor, all of these parameters need to be scaled (multiplied/divided,
+respectively) by the same factor.
+
+The joint rotation-translation matrix \f$[R|t]\f$ is the matrix product of a projective
+transformation and a homogeneous transformation. The 3-by-4 projective transformation maps 3D points
+represented in camera coordinates to 2D points in the image plane and represented in normalized
+camera coordinates \f$x' = X_c / Z_c\f$ and \f$y' = Y_c / Z_c\f$:
+
+\f[Z_c \begin{bmatrix}
+x' \\
+y' \\
+1
+\end{bmatrix} = \begin{bmatrix}
+1 & 0 & 0 & 0 \\
+0 & 1 & 0 & 0 \\
+0 & 0 & 1 & 0
+\end{bmatrix}
+\begin{bmatrix}
+X_c \\
+Y_c \\
+Z_c \\
+1
+\end{bmatrix}.\f]
+
+The homogeneous transformation is encoded by the extrinsic parameters \f$R\f$ and \f$t\f$ and
+represents the change of basis from world coordinate system \f$w\f$ to the camera coordinate sytem
+\f$c\f$. Thus, given the representation of the point \f$P\f$ in world coordinates, \f$P_w\f$, we
+obtain \f$P\f$'s representation in the camera coordinate system, \f$P_c\f$, by
+
+\f[P_c = \begin{bmatrix}
+R & t \\
+0 & 1
+\end{bmatrix} P_w,\f]
+
+This homogeneous transformation is composed out of \f$R\f$, a 3-by-3 rotation matrix, and \f$t\f$, a
+3-by-1 translation vector:
+
+\f[\begin{bmatrix}
+R & t \\
+0 & 1
+\end{bmatrix} = \begin{bmatrix}
+r_{11} & r_{12} & r_{13} & t_x \\
+r_{21} & r_{22} & r_{23} & t_y \\
+r_{31} & r_{32} & r_{33} & t_z \\
+0 & 0 & 0 & 1
+\end{bmatrix},
+\f]
+
+and therefore
+
+\f[\begin{bmatrix}
+X_c \\
+Y_c \\
+Z_c \\
+1
+\end{bmatrix} = \begin{bmatrix}
+r_{11} & r_{12} & r_{13} & t_x \\
+r_{21} & r_{22} & r_{23} & t_y \\
+r_{31} & r_{32} & r_{33} & t_z \\
+0 & 0 & 0 & 1
+\end{bmatrix}
+\begin{bmatrix}
+X_w \\
+Y_w \\
+Z_w \\
+1
+\end{bmatrix}.\f]
+
+Combining the projective transformation and the homogeneous transformation, we obtain the projective
+transformation that maps 3D points in world coordinates into 2D points in the image plane and in
+normalized camera coordinates:
+
+\f[Z_c \begin{bmatrix}
+x' \\
+y' \\
+1
+\end{bmatrix} = \begin{bmatrix} R|t \end{bmatrix} \begin{bmatrix}
+X_w \\
+Y_w \\
+Z_w \\
+1
+\end{bmatrix} = \begin{bmatrix}
+r_{11} & r_{12} & r_{13} & t_x \\
+r_{21} & r_{22} & r_{23} & t_y \\
+r_{31} & r_{32} & r_{33} & t_z
+\end{bmatrix}
+\begin{bmatrix}
+X_w \\
+Y_w \\
+Z_w \\
+1
+\end{bmatrix},\f]
+
+with \f$x' = X_c / Z_c\f$ and \f$y' = Y_c / Z_c\f$. Putting the equations for instrincs and extrinsics together, we can write out
+\f$s \; p = A \begin{bmatrix} R|t \end{bmatrix} P_w\f$ as
+
+\f[s \vecthree{u}{v}{1} = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}
+\begin{bmatrix}
+r_{11} & r_{12} & r_{13} & t_x \\
+r_{21} & r_{22} & r_{23} & t_y \\
+r_{31} & r_{32} & r_{33} & t_z
+\end{bmatrix}
+\begin{bmatrix}
+X_w \\
+Y_w \\
+Z_w \\
+1
+\end{bmatrix}.\f]
+
+If \f$Z_c \ne 0\f$, the transformation above is equivalent to the following,
+
+\f[\begin{bmatrix}
+u \\
+v
+\end{bmatrix} = \begin{bmatrix}
+f_x X_c/Z_c + c_x \\
+f_y Y_c/Z_c + c_y
+\end{bmatrix}\f]
+
+with
+
+\f[\vecthree{X_c}{Y_c}{Z_c} = \begin{bmatrix}
+R|t
+\end{bmatrix} \begin{bmatrix}
+X_w \\
+Y_w \\
+Z_w \\
+1
+\end{bmatrix}.\f]
+
+The following figure illustrates the pinhole camera model.
+
+
+
+Real lenses usually have some distortion, mostly radial distortion, and slight tangential distortion.
+So, the above model is extended as:
+
+\f[\begin{bmatrix}
+u \\
+v
+\end{bmatrix} = \begin{bmatrix}
+f_x x'' + c_x \\
+f_y y'' + c_y
+\end{bmatrix}\f]
+
+where
+
+\f[\begin{bmatrix}
+x'' \\
+y''
+\end{bmatrix} = \begin{bmatrix}
+x' \frac{1 + k_1 r^2 + k_2 r^4 + k_3 r^6}{1 + k_4 r^2 + k_5 r^4 + k_6 r^6} + 2 p_1 x' y' + p_2(r^2 + 2 x'^2) + s_1 r^2 + s_2 r^4 \\
+y' \frac{1 + k_1 r^2 + k_2 r^4 + k_3 r^6}{1 + k_4 r^2 + k_5 r^4 + k_6 r^6} + p_1 (r^2 + 2 y'^2) + 2 p_2 x' y' + s_3 r^2 + s_4 r^4 \\
+\end{bmatrix}\f]
+
+with
+
+\f[r^2 = x'^2 + y'^2\f]
+
+and
+
+\f[\begin{bmatrix}
+x'\\
+y'
+\end{bmatrix} = \begin{bmatrix}
+X_c/Z_c \\
+Y_c/Z_c
+\end{bmatrix},\f]
+
+if \f$Z_c \ne 0\f$.
+
+The distortion parameters are the radial coefficients \f$k_1\f$, \f$k_2\f$, \f$k_3\f$, \f$k_4\f$, \f$k_5\f$, and \f$k_6\f$
+,\f$p_1\f$ and \f$p_2\f$ are the tangential distortion coefficients, and \f$s_1\f$, \f$s_2\f$, \f$s_3\f$, and \f$s_4\f$,
+are the thin prism distortion coefficients. Higher-order coefficients are not considered in OpenCV.
+
+The next figures show two common types of radial distortion: barrel distortion
+(\f$ 1 + k_1 r^2 + k_2 r^4 + k_3 r^6 \f$ monotonically decreasing)
+and pincushion distortion (\f$ 1 + k_1 r^2 + k_2 r^4 + k_3 r^6 \f$ monotonically increasing).
+Radial distortion is always monotonic for real lenses,
+and if the estimator produces a non-monotonic result,
+this should be considered a calibration failure.
+More generally, radial distortion must be monotonic and the distortion function must be bijective.
+A failed estimation result may look deceptively good near the image center
+but will work poorly in e.g. AR/SFM applications.
+The optimization method used in OpenCV camera calibration does not include these constraints as
+the framework does not support the required integer programming and polynomial inequalities.
+See [issue #15992](https://github.com/opencv/opencv/issues/15992) for additional information.
+
+
+
+
+In some cases, the image sensor may be tilted in order to focus an oblique plane in front of the
+camera (Scheimpflug principle). This can be useful for particle image velocimetry (PIV) or
+triangulation with a laser fan. The tilt causes a perspective distortion of \f$x''\f$ and
+\f$y''\f$. This distortion can be modeled in the following way, see e.g. @cite Louhichi07.
+
+\f[\begin{bmatrix}
+u \\
+v
+\end{bmatrix} = \begin{bmatrix}
+f_x x''' + c_x \\
+f_y y''' + c_y
+\end{bmatrix},\f]
+
+where
+
+\f[s\vecthree{x'''}{y'''}{1} =
+\vecthreethree{R_{33}(\tau_x, \tau_y)}{0}{-R_{13}(\tau_x, \tau_y)}
+{0}{R_{33}(\tau_x, \tau_y)}{-R_{23}(\tau_x, \tau_y)}
+{0}{0}{1} R(\tau_x, \tau_y) \vecthree{x''}{y''}{1}\f]
+
+and the matrix \f$R(\tau_x, \tau_y)\f$ is defined by two rotations with angular parameter
+\f$\tau_x\f$ and \f$\tau_y\f$, respectively,
+
+\f[
+R(\tau_x, \tau_y) =
+\vecthreethree{\cos(\tau_y)}{0}{-\sin(\tau_y)}{0}{1}{0}{\sin(\tau_y)}{0}{\cos(\tau_y)}
+\vecthreethree{1}{0}{0}{0}{\cos(\tau_x)}{\sin(\tau_x)}{0}{-\sin(\tau_x)}{\cos(\tau_x)} =
+\vecthreethree{\cos(\tau_y)}{\sin(\tau_y)\sin(\tau_x)}{-\sin(\tau_y)\cos(\tau_x)}
+{0}{\cos(\tau_x)}{\sin(\tau_x)}
+{\sin(\tau_y)}{-\cos(\tau_y)\sin(\tau_x)}{\cos(\tau_y)\cos(\tau_x)}.
+\f]
+
+In the functions below the coefficients are passed or returned as
+
+\f[(k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6 [, s_1, s_2, s_3, s_4[, \tau_x, \tau_y]]]])\f]
+
+vector. That is, if the vector contains four elements, it means that \f$k_3=0\f$ . The distortion
+coefficients do not depend on the scene viewed. Thus, they also belong to the intrinsic camera
+parameters. And they remain the same regardless of the captured image resolution. If, for example, a
+camera has been calibrated on images of 320 x 240 resolution, absolutely the same distortion
+coefficients can be used for 640 x 480 images from the same camera while \f$f_x\f$, \f$f_y\f$,
+\f$c_x\f$, and \f$c_y\f$ need to be scaled appropriately.
+
+The functions below use the above model to do the following:
+
+- Project 3D points to the image plane given intrinsic and extrinsic parameters.
+- Compute extrinsic parameters given intrinsic parameters, a few 3D points, and their
+projections.
+- Estimate intrinsic and extrinsic camera parameters from several views of a known calibration
+pattern (every view is described by several 3D-2D point correspondences).
+- Estimate the relative position and orientation of the stereo camera "heads" and compute the
+*rectification* transformation that makes the camera optical axes parallel.
+
+ Homogeneous Coordinates
+Homogeneous Coordinates are a system of coordinates that are used in projective geometry. Their use
+allows to represent points at infinity by finite coordinates and simplifies formulas when compared
+to the cartesian counterparts, e.g. they have the advantage that affine transformations can be
+expressed as linear homogeneous transformation.
+
+One obtains the homogeneous vector \f$P_h\f$ by appending a 1 along an n-dimensional cartesian
+vector \f$P\f$ e.g. for a 3D cartesian vector the mapping \f$P \rightarrow P_h\f$ is:
+
+\f[\begin{bmatrix}
+X \\
+Y \\
+Z
+\end{bmatrix} \rightarrow \begin{bmatrix}
+X \\
+Y \\
+Z \\
+1
+\end{bmatrix}.\f]
+
+For the inverse mapping \f$P_h \rightarrow P\f$, one divides all elements of the homogeneous vector
+by its last element, e.g. for a 3D homogeneous vector one gets its 2D cartesian counterpart by:
+
+\f[\begin{bmatrix}
+X \\
+Y \\
+W
+\end{bmatrix} \rightarrow \begin{bmatrix}
+X / W \\
+Y / W
+\end{bmatrix},\f]
+
+if \f$W \ne 0\f$.
+
+Due to this mapping, all multiples \f$k P_h\f$, for \f$k \ne 0\f$, of a homogeneous point represent
+the same point \f$P_h\f$. An intuitive understanding of this property is that under a projective
+transformation, all multiples of \f$P_h\f$ are mapped to the same point. This is the physical
+observation one does for pinhole cameras, as all points along a ray through the camera's pinhole are
+projected to the same image point, e.g. all points along the red ray in the image of the pinhole
+camera model above would be mapped to the same image coordinate. This property is also the source
+for the scale ambiguity s in the equation of the pinhole camera model.
+
+As mentioned, by using homogeneous coordinates we can express any change of basis parameterized by
+\f$R\f$ and \f$t\f$ as a linear transformation, e.g. for the change of basis from coordinate system
+0 to coordinate system 1 becomes:
+
+\f[P_1 = R P_0 + t \rightarrow P_{h_1} = \begin{bmatrix}
+R & t \\
+0 & 1
+\end{bmatrix} P_{h_0}.\f]
+
+ Homogeneous Transformations, Object frame / Camera frame
+Change of basis or computing the 3D coordinates from one frame to another frame can be achieved easily using
+the following notation:
+
+\f[
+\mathbf{X}_c = \hspace{0.2em}
+{}^{c}\mathbf{T}_o \hspace{0.2em} \mathbf{X}_o
+\f]
+
+\f[
+\begin{bmatrix}
+X_c \\
+Y_c \\
+Z_c \\
+1
+\end{bmatrix} =
+\begin{bmatrix}
+{}^{c}\mathbf{R}_o & {}^{c}\mathbf{t}_o \\
+0_{1 \times 3} & 1
+\end{bmatrix}
+\begin{bmatrix}
+X_o \\
+Y_o \\
+Z_o \\
+1
+\end{bmatrix}
+\f]
+
+For a 3D points (\f$ \mathbf{X}_o \f$) expressed in the object frame, the homogeneous transformation matrix
+\f$ {}^{c}\mathbf{T}_o \f$ allows computing the corresponding coordinate (\f$ \mathbf{X}_c \f$) in the camera frame.
+This transformation matrix is composed of a 3x3 rotation matrix \f$ {}^{c}\mathbf{R}_o \f$ and a 3x1 translation vector
+\f$ {}^{c}\mathbf{t}_o \f$.
+The 3x1 translation vector \f$ {}^{c}\mathbf{t}_o \f$ is the position of the object frame in the camera frame and the
+3x3 rotation matrix \f$ {}^{c}\mathbf{R}_o \f$ the orientation of the object frame in the camera frame.
+
+With this simple notation, it is easy to chain the transformations. For instance, to compute the 3D coordinates of a point
+expressed in the object frame in the world frame can be done with:
+
+\f[
+\mathbf{X}_w = \hspace{0.2em}
+{}^{w}\mathbf{T}_c \hspace{0.2em} {}^{c}\mathbf{T}_o \hspace{0.2em}
+\mathbf{X}_o =
+{}^{w}\mathbf{T}_o \hspace{0.2em} \mathbf{X}_o
+\f]
+
+Similarly, computing the inverse transformation can be done with:
+
+\f[
+\mathbf{X}_o = \hspace{0.2em}
+{}^{o}\mathbf{T}_c \hspace{0.2em} \mathbf{X}_c =
+\left( {}^{c}\mathbf{T}_o \right)^{-1} \hspace{0.2em} \mathbf{X}_c
+\f]
+
+The inverse of an homogeneous transformation matrix is then:
+
+\f[
+{}^{o}\mathbf{T}_c = \left( {}^{c}\mathbf{T}_o \right)^{-1} =
+\begin{bmatrix}
+{}^{c}\mathbf{R}^{\top}_o & - \hspace{0.2em} {}^{c}\mathbf{R}^{\top}_o \hspace{0.2em} {}^{c}\mathbf{t}_o \\
+0_{1 \times 3} & 1
+\end{bmatrix}
+\f]
+
+One can note that the inverse of a 3x3 rotation matrix is directly its matrix transpose.
+
+
+
+This figure summarizes the whole process. The object pose returned for instance by the @ref solvePnP function
+or pose from fiducial marker detection is this \f$ {}^{c}\mathbf{T}_o \f$ transformation.
+
+The camera intrinsic matrix \f$ \mathbf{K} \f$ allows projecting the 3D point expressed in the camera frame onto the image plane
+assuming a perspective projection model (pinhole camera model). Image coordinates extracted from classical image processing functions
+assume a (u,v) top-left coordinates frame.
+
+\note
+- for an online video course on this topic, see for instance:
+ - ["3.3.1. Homogeneous Transformation Matrices", Modern Robotics, Kevin M. Lynch and Frank C. Park](https://modernrobotics.northwestern.edu/nu-gm-book-resource/3-3-1-homogeneous-transformation-matrices/)
+- the 3x3 rotation matrix is composed of 9 values but describes a 3 dof transformation
+- some additional properties of the 3x3 rotation matrix are:
+ - \f$ \mathrm{det} \left( \mathbf{R} \right) = 1 \f$
+ - \f$ \mathbf{R} \mathbf{R}^{\top} = \mathbf{R}^{\top} \mathbf{R} = \mathrm{I}_{3 \times 3} \f$
+ - interpolating rotation can be done using the [Slerp (spherical linear interpolation)](https://en.wikipedia.org/wiki/Slerp) method
+- quick conversions between the different rotation formalisms can be done using this [online tool](https://www.andre-gaschler.com/rotationconverter/)
+
+ Intrinsic parameters from camera lens specifications
+When dealing with industrial cameras, the camera intrinsic matrix or more precisely \f$ \left(f_x, f_y \right) \f$
+can be deduced, approximated from the camera specifications:
+
+\f[
+f_x = \frac{f_{\text{mm}}}{\text{pixel_size_in_mm}} = \frac{f_{\text{mm}}}{\text{sensor_size_in_mm} / \text{nb_pixels}}
+\f]
+
+In a same way, the physical focal length can be deduced from the angular field of view:
+
+\f[
+f_{\text{mm}} = \frac{\text{sensor_size_in_mm}}{2 \times \tan{\frac{\text{fov}}{2}}}
+\f]
+
+This latter conversion can be useful when using a rendering software to mimic a physical camera device.
+
+@note
+ - See also #calibrationMatrixValues
+
+ Additional references, notes
+@note
+ - Many functions in this module take a camera intrinsic matrix as an input parameter. Although all
+ functions assume the same structure of this parameter, they may name it differently. The
+ parameter's description, however, will be clear in that a camera intrinsic matrix with the structure
+ shown above is required.
+ - A calibration sample for 3 cameras in a horizontal position can be found at
+ opencv_source_code/samples/cpp/3calibration.cpp
+ - A calibration sample based on a sequence of images can be found at
+ opencv_source_code/samples/cpp/calibration.cpp
+ - A calibration sample in order to do 3D reconstruction can be found at
+ opencv_source_code/samples/cpp/build3dmodel.cpp
+ - A calibration example on stereo calibration can be found at
+ opencv_source_code/samples/cpp/stereo_calib.cpp
+ - A calibration example on stereo matching can be found at
+ opencv_source_code/samples/cpp/stereo_match.cpp
+ - (Python) A camera calibration sample can be found at
+ opencv_source_code/samples/python/calibrate.py
+
+ @{
+ @defgroup calib3d_fisheye Fisheye camera model
+
+ Definitions: Let P be a point in 3D of coordinates X in the world reference frame (stored in the
+ matrix X) The coordinate vector of P in the camera reference frame is:
+
+ \f[Xc = R X + T\f]
+
+ where R is the rotation matrix corresponding to the rotation vector om: R = rodrigues(om); call x, y
+ and z the 3 coordinates of Xc:
+
+ \f[\begin{array}{l} x = Xc_1 \\ y = Xc_2 \\ z = Xc_3 \end{array} \f]
+
+ The pinhole projection coordinates of P is [a; b] where
+
+ \f[\begin{array}{l} a = x / z \ and \ b = y / z \\ r^2 = a^2 + b^2 \\ \theta = atan(r) \end{array} \f]
+
+ Fisheye distortion:
+
+ \f[\theta_d = \theta (1 + k_1 \theta^2 + k_2 \theta^4 + k_3 \theta^6 + k_4 \theta^8)\f]
+
+ The distorted point coordinates are [x'; y'] where
+
+ \f[\begin{array}{l} x' = (\theta_d / r) a \\ y' = (\theta_d / r) b \end{array} \f]
+
+ Finally, conversion into pixel coordinates: The final pixel coordinates vector [u; v] where:
+
+ \f[\begin{array}{l} u = f_x (x' + \alpha y') + c_x \\
+ v = f_y y' + c_y \end{array} \f]
+
+ Summary:
+ Generic camera model @cite Kannala2006 with perspective projection and without distortion correction
+
+ @}
+ */
+
+namespace cv
+{
+
+//! @addtogroup calib3d
+//! @{
+
+//! type of the robust estimation algorithm
+enum { LMEDS = 4, //!< least-median of squares algorithm
+ RANSAC = 8, //!< RANSAC algorithm
+ RHO = 16, //!< RHO algorithm
+ USAC_DEFAULT = 32, //!< USAC algorithm, default settings
+ USAC_PARALLEL = 33, //!< USAC, parallel version
+ USAC_FM_8PTS = 34, //!< USAC, fundamental matrix 8 points
+ USAC_FAST = 35, //!< USAC, fast settings
+ USAC_ACCURATE = 36, //!< USAC, accurate settings
+ USAC_PROSAC = 37, //!< USAC, sorted points, runs PROSAC
+ USAC_MAGSAC = 38 //!< USAC, runs MAGSAC++
+ };
+
+enum SolvePnPMethod {
+ SOLVEPNP_ITERATIVE = 0, //!< Pose refinement using non-linear Levenberg-Marquardt minimization scheme @cite Madsen04 @cite Eade13 \n
+ //!< Initial solution for non-planar "objectPoints" needs at least 6 points and uses the DLT algorithm. \n
+ //!< Initial solution for planar "objectPoints" needs at least 4 points and uses pose from homography decomposition.
+ SOLVEPNP_EPNP = 1, //!< EPnP: Efficient Perspective-n-Point Camera Pose Estimation @cite lepetit2009epnp
+ SOLVEPNP_P3P = 2, //!< Revisiting the P3P Problem @cite ding2023revisiting
+ SOLVEPNP_DLS = 3, //!< **Broken implementation. Using this flag will fallback to EPnP.** \n
+ //!< A Direct Least-Squares (DLS) Method for PnP @cite hesch2011direct
+ SOLVEPNP_UPNP = 4, //!< **Broken implementation. Using this flag will fallback to EPnP.** \n
+ //!< Exhaustive Linearization for Robust Camera Pose and Focal Length Estimation @cite penate2013exhaustive
+ SOLVEPNP_AP3P = 5, //!< An Efficient Algebraic Solution to the Perspective-Three-Point Problem @cite Ke17
+ SOLVEPNP_IPPE = 6, //!< Infinitesimal Plane-Based Pose Estimation @cite Collins14 \n
+ //!< Object points must be coplanar.
+ SOLVEPNP_IPPE_SQUARE = 7, //!< Infinitesimal Plane-Based Pose Estimation @cite Collins14 \n
+ //!< This is a special case suitable for marker pose estimation.\n
+ //!< 4 coplanar object points must be defined in the following order:
+ //!< - point 0: [-squareLength / 2, squareLength / 2, 0]
+ //!< - point 1: [ squareLength / 2, squareLength / 2, 0]
+ //!< - point 2: [ squareLength / 2, -squareLength / 2, 0]
+ //!< - point 3: [-squareLength / 2, -squareLength / 2, 0]
+ SOLVEPNP_SQPNP = 8, //!< SQPnP: A Consistently Fast and Globally OptimalSolution to the Perspective-n-Point Problem @cite Terzakis2020SQPnP
+#ifndef CV_DOXYGEN
+ SOLVEPNP_MAX_COUNT //!< Used for count
+#endif
+};
+
+enum { CALIB_CB_ADAPTIVE_THRESH = 1,
+ CALIB_CB_NORMALIZE_IMAGE = 2,
+ CALIB_CB_FILTER_QUADS = 4,
+ CALIB_CB_FAST_CHECK = 8,
+ CALIB_CB_EXHAUSTIVE = 16,
+ CALIB_CB_ACCURACY = 32,
+ CALIB_CB_LARGER = 64,
+ CALIB_CB_MARKER = 128,
+ CALIB_CB_PLAIN = 256
+ };
+
+enum { CALIB_CB_SYMMETRIC_GRID = 1,
+ CALIB_CB_ASYMMETRIC_GRID = 2,
+ CALIB_CB_CLUSTERING = 4
+ };
+
+enum { CALIB_NINTRINSIC = 18,
+ CALIB_USE_INTRINSIC_GUESS = 0x00001,
+ CALIB_FIX_ASPECT_RATIO = 0x00002,
+ CALIB_FIX_PRINCIPAL_POINT = 0x00004,
+ CALIB_ZERO_TANGENT_DIST = 0x00008,
+ CALIB_FIX_FOCAL_LENGTH = 0x00010,
+ CALIB_FIX_K1 = 0x00020,
+ CALIB_FIX_K2 = 0x00040,
+ CALIB_FIX_K3 = 0x00080,
+ CALIB_FIX_K4 = 0x00800,
+ CALIB_FIX_K5 = 0x01000,
+ CALIB_FIX_K6 = 0x02000,
+ CALIB_RATIONAL_MODEL = 0x04000,
+ CALIB_THIN_PRISM_MODEL = 0x08000,
+ CALIB_FIX_S1_S2_S3_S4 = 0x10000,
+ CALIB_TILTED_MODEL = 0x40000,
+ CALIB_FIX_TAUX_TAUY = 0x80000,
+ CALIB_USE_QR = 0x100000, //!< use QR instead of SVD decomposition for solving. Faster but potentially less precise
+ CALIB_FIX_TANGENT_DIST = 0x200000,
+ // only for stereo
+ CALIB_FIX_INTRINSIC = 0x00100,
+ CALIB_SAME_FOCAL_LENGTH = 0x00200,
+ // for stereo rectification
+ CALIB_ZERO_DISPARITY = 0x00400,
+ CALIB_USE_LU = (1 << 17), //!< use LU instead of SVD decomposition for solving. much faster but potentially less precise
+ CALIB_USE_EXTRINSIC_GUESS = (1 << 22) //!< for stereoCalibrate
+ };
+
+//! the algorithm for finding fundamental matrix
+enum { FM_7POINT = 1, //!< 7-point algorithm
+ FM_8POINT = 2, //!< 8-point algorithm
+ FM_LMEDS = 4, //!< least-median algorithm. 7-point algorithm is used.
+ FM_RANSAC = 8 //!< RANSAC algorithm. It needs at least 15 points. 7-point algorithm is used.
+ };
+
+enum HandEyeCalibrationMethod
+{
+ CALIB_HAND_EYE_TSAI = 0, //!< A New Technique for Fully Autonomous and Efficient 3D Robotics Hand/Eye Calibration @cite Tsai89
+ CALIB_HAND_EYE_PARK = 1, //!< Robot Sensor Calibration: Solving AX = XB on the Euclidean Group @cite Park94
+ CALIB_HAND_EYE_HORAUD = 2, //!< Hand-eye Calibration @cite Horaud95
+ CALIB_HAND_EYE_ANDREFF = 3, //!< On-line Hand-Eye Calibration @cite Andreff99
+ CALIB_HAND_EYE_DANIILIDIS = 4 //!< Hand-Eye Calibration Using Dual Quaternions @cite Daniilidis98
+};
+
+enum RobotWorldHandEyeCalibrationMethod
+{
+ CALIB_ROBOT_WORLD_HAND_EYE_SHAH = 0, //!< Solving the robot-world/hand-eye calibration problem using the kronecker product @cite Shah2013SolvingTR
+ CALIB_ROBOT_WORLD_HAND_EYE_LI = 1 //!< Simultaneous robot-world and hand-eye calibration using dual-quaternions and kronecker product @cite Li2010SimultaneousRA
+};
+
+enum SamplingMethod { SAMPLING_UNIFORM=0, SAMPLING_PROGRESSIVE_NAPSAC=1, SAMPLING_NAPSAC=2,
+ SAMPLING_PROSAC=3 };
+enum LocalOptimMethod {LOCAL_OPTIM_NULL=0, LOCAL_OPTIM_INNER_LO=1, LOCAL_OPTIM_INNER_AND_ITER_LO=2,
+ LOCAL_OPTIM_GC=3, LOCAL_OPTIM_SIGMA=4};
+enum ScoreMethod {SCORE_METHOD_RANSAC=0, SCORE_METHOD_MSAC=1, SCORE_METHOD_MAGSAC=2, SCORE_METHOD_LMEDS=3};
+enum NeighborSearchMethod { NEIGH_FLANN_KNN=0, NEIGH_GRID=1, NEIGH_FLANN_RADIUS=2 };
+enum PolishingMethod { NONE_POLISHER=0, LSQ_POLISHER=1, MAGSAC=2, COV_POLISHER=3 };
+
+struct CV_EXPORTS_W_SIMPLE UsacParams
+{ // in alphabetical order
+ CV_WRAP UsacParams();
+ CV_PROP_RW double confidence;
+ CV_PROP_RW bool isParallel;
+ CV_PROP_RW int loIterations;
+ CV_PROP_RW LocalOptimMethod loMethod;
+ CV_PROP_RW int loSampleSize;
+ CV_PROP_RW int maxIterations;
+ CV_PROP_RW NeighborSearchMethod neighborsSearch;
+ CV_PROP_RW int randomGeneratorState;
+ CV_PROP_RW SamplingMethod sampler;
+ CV_PROP_RW ScoreMethod score;
+ CV_PROP_RW double threshold;
+ CV_PROP_RW PolishingMethod final_polisher;
+ CV_PROP_RW int final_polisher_iterations;
+};
+
+/** @brief Converts a rotation matrix to a rotation vector or vice versa.
+
+@param src Input rotation vector (3x1 or 1x3) or rotation matrix (3x3).
+@param dst Output rotation matrix (3x3) or rotation vector (3x1 or 1x3), respectively.
+@param jacobian Optional output Jacobian matrix, 3x9 or 9x3, which is a matrix of partial
+derivatives of the output array components with respect to the input array components.
+
+\f[\begin{array}{l} \theta \leftarrow norm(r) \\ r \leftarrow r/ \theta \\ R = \cos(\theta) I + (1- \cos{\theta} ) r r^T + \sin(\theta) \vecthreethree{0}{-r_z}{r_y}{r_z}{0}{-r_x}{-r_y}{r_x}{0} \end{array}\f]
+
+Inverse transformation can be also done easily, since
+
+\f[\sin ( \theta ) \vecthreethree{0}{-r_z}{r_y}{r_z}{0}{-r_x}{-r_y}{r_x}{0} = \frac{R - R^T}{2}\f]
+
+A rotation vector is a convenient and most compact representation of a rotation matrix (since any
+rotation matrix has just 3 degrees of freedom). The representation is used in the global 3D geometry
+optimization procedures like @ref calibrateCamera, @ref stereoCalibrate, or @ref solvePnP .
+
+@note More information about the computation of the derivative of a 3D rotation matrix with respect to its exponential coordinate
+can be found in:
+ - A Compact Formula for the Derivative of a 3-D Rotation in Exponential Coordinates, Guillermo Gallego, Anthony J. Yezzi @cite Gallego2014ACF
+
+@note Useful information on SE(3) and Lie Groups can be found in:
+ - A tutorial on SE(3) transformation parameterizations and on-manifold optimization, Jose-Luis Blanco @cite blanco2010tutorial
+ - Lie Groups for 2D and 3D Transformation, Ethan Eade @cite Eade17
+ - A micro Lie theory for state estimation in robotics, Joan Solà, Jérémie Deray, Dinesh Atchuthan @cite Sol2018AML
+ */
+CV_EXPORTS_W void Rodrigues( InputArray src, OutputArray dst, OutputArray jacobian = noArray() );
+
+
+
+/** Levenberg-Marquardt solver. Starting with the specified vector of parameters it
+ optimizes the target vector criteria "err"
+ (finds local minima of each target vector component absolute value).
+
+ When needed, it calls user-provided callback.
+*/
+class CV_EXPORTS LMSolver : public Algorithm
+{
+public:
+ class CV_EXPORTS Callback
+ {
+ public:
+ virtual ~Callback() {}
+ /**
+ computes error and Jacobian for the specified vector of parameters
+
+ @param param the current vector of parameters
+ @param err output vector of errors: err_i = actual_f_i - ideal_f_i
+ @param J output Jacobian: J_ij = d(ideal_f_i)/d(param_j)
+
+ when J=noArray(), it means that it does not need to be computed.
+ Dimensionality of error vector and param vector can be different.
+ The callback should explicitly allocate (with "create" method) each output array
+ (unless it's noArray()).
+ */
+ virtual bool compute(InputArray param, OutputArray err, OutputArray J) const = 0;
+ };
+
+ /**
+ Runs Levenberg-Marquardt algorithm using the passed vector of parameters as the start point.
+ The final vector of parameters (whether the algorithm converged or not) is stored at the same
+ vector. The method returns the number of iterations used. If it's equal to the previously specified
+ maxIters, there is a big chance the algorithm did not converge.
+
+ @param param initial/final vector of parameters.
+
+ Note that the dimensionality of parameter space is defined by the size of param vector,
+ and the dimensionality of optimized criteria is defined by the size of err vector
+ computed by the callback.
+ */
+ virtual int run(InputOutputArray param) const = 0;
+
+ /**
+ Sets the maximum number of iterations
+ @param maxIters the number of iterations
+ */
+ virtual void setMaxIters(int maxIters) = 0;
+ /**
+ Retrieves the current maximum number of iterations
+ */
+ virtual int getMaxIters() const = 0;
+
+ /**
+ Creates Levenberg-Marquard solver
+
+ @param cb callback
+ @param maxIters maximum number of iterations that can be further
+ modified using setMaxIters() method.
+ */
+ static Ptr create(const Ptr& cb, int maxIters);
+ static Ptr create(const Ptr& cb, int maxIters, double eps);
+};
+
+
+
+/** @example samples/cpp/tutorial_code/features2D/Homography/pose_from_homography.cpp
+An example program about pose estimation from coplanar points
+
+Check @ref tutorial_homography "the corresponding tutorial" for more details
+*/
+
+/** @brief Finds a perspective transformation between two planes.
+
+@param srcPoints Coordinates of the points in the original plane, a matrix of the type CV_32FC2
+or vector\ .
+@param dstPoints Coordinates of the points in the target plane, a matrix of the type CV_32FC2 or
+a vector\ .
+@param method Method used to compute a homography matrix. The following methods are possible:
+- **0** - a regular method using all the points, i.e., the least squares method
+- @ref RANSAC - RANSAC-based robust method
+- @ref LMEDS - Least-Median robust method
+- @ref RHO - PROSAC-based robust method
+@param ransacReprojThreshold Maximum allowed reprojection error to treat a point pair as an inlier
+(used in the RANSAC and RHO methods only). That is, if
+\f[\| \texttt{dstPoints} _i - \texttt{convertPointsHomogeneous} ( \texttt{H} \cdot \texttt{srcPoints} _i) \|_2 > \texttt{ransacReprojThreshold}\f]
+then the point \f$i\f$ is considered as an outlier. If srcPoints and dstPoints are measured in pixels,
+it usually makes sense to set this parameter somewhere in the range of 1 to 10.
+@param mask Optional output mask set by a robust method ( RANSAC or LMeDS ). Note that the input
+mask values are ignored.
+@param maxIters The maximum number of RANSAC iterations.
+@param confidence Confidence level, between 0 and 1.
+
+The function finds and returns the perspective transformation \f$H\f$ between the source and the
+destination planes:
+
+\f[s_i \vecthree{x'_i}{y'_i}{1} \sim H \vecthree{x_i}{y_i}{1}\f]
+
+so that the back-projection error
+
+\f[\sum _i \left ( x'_i- \frac{h_{11} x_i + h_{12} y_i + h_{13}}{h_{31} x_i + h_{32} y_i + h_{33}} \right )^2+ \left ( y'_i- \frac{h_{21} x_i + h_{22} y_i + h_{23}}{h_{31} x_i + h_{32} y_i + h_{33}} \right )^2\f]
+
+is minimized. If the parameter method is set to the default value 0, the function uses all the point
+pairs to compute an initial homography estimate with a simple least-squares scheme.
+
+However, if not all of the point pairs ( \f$srcPoints_i\f$, \f$dstPoints_i\f$ ) fit the rigid perspective
+transformation (that is, there are some outliers), this initial estimate will be poor. In this case,
+you can use one of the three robust methods. The methods RANSAC, LMeDS and RHO try many different
+random subsets of the corresponding point pairs (of four pairs each, collinear pairs are discarded), estimate the homography matrix
+using this subset and a simple least-squares algorithm, and then compute the quality/goodness of the
+computed homography (which is the number of inliers for RANSAC or the least median re-projection error for
+LMeDS). The best subset is then used to produce the initial estimate of the homography matrix and
+the mask of inliers/outliers.
+
+Regardless of the method, robust or not, the computed homography matrix is refined further (using
+inliers only in case of a robust method) with the Levenberg-Marquardt method to reduce the
+re-projection error even more.
+
+The methods RANSAC and RHO can handle practically any ratio of outliers but need a threshold to
+distinguish inliers from outliers. The method LMeDS does not need any threshold but it works
+correctly only when there are more than 50% of inliers. Finally, if there are no outliers and the
+noise is rather small, use the default method (method=0).
+
+The function is used to find initial intrinsic and extrinsic matrices. Homography matrix is
+determined up to a scale. If \f$h_{33}\f$ is non-zero, the matrix is normalized so that \f$h_{33}=1\f$.
+@note Whenever an \f$H\f$ matrix cannot be estimated, an empty one will be returned.
+
+@sa
+getAffineTransform, estimateAffine2D, estimateAffinePartial2D, getPerspectiveTransform, warpPerspective,
+perspectiveTransform
+ */
+CV_EXPORTS_W Mat findHomography( InputArray srcPoints, InputArray dstPoints,
+ int method = 0, double ransacReprojThreshold = 3,
+ OutputArray mask=noArray(), const int maxIters = 2000,
+ const double confidence = 0.995);
+
+/** @overload */
+CV_EXPORTS Mat findHomography( InputArray srcPoints, InputArray dstPoints,
+ OutputArray mask, int method = 0, double ransacReprojThreshold = 3 );
+
+
+CV_EXPORTS_W Mat findHomography(InputArray srcPoints, InputArray dstPoints, OutputArray mask,
+ const UsacParams ¶ms);
+
+/** @brief Computes an RQ decomposition of 3x3 matrices.
+
+@param src 3x3 input matrix.
+@param mtxR Output 3x3 upper-triangular matrix.
+@param mtxQ Output 3x3 orthogonal matrix.
+@param Qx Optional output 3x3 rotation matrix around x-axis.
+@param Qy Optional output 3x3 rotation matrix around y-axis.
+@param Qz Optional output 3x3 rotation matrix around z-axis.
+
+The function computes a RQ decomposition using the given rotations. This function is used in
+#decomposeProjectionMatrix to decompose the left 3x3 submatrix of a projection matrix into a camera
+and a rotation matrix.
+
+It optionally returns three rotation matrices, one for each axis, and the three Euler angles in
+degrees (as the return value) that could be used in OpenGL. Note, there is always more than one
+sequence of rotations about the three principal axes that results in the same orientation of an
+object, e.g. see @cite Slabaugh . Returned three rotation matrices and corresponding three Euler angles
+are only one of the possible solutions.
+ */
+CV_EXPORTS_W Vec3d RQDecomp3x3( InputArray src, OutputArray mtxR, OutputArray mtxQ,
+ OutputArray Qx = noArray(),
+ OutputArray Qy = noArray(),
+ OutputArray Qz = noArray());
+
+/** @brief Decomposes a projection matrix into a rotation matrix and a camera intrinsic matrix.
+
+@param projMatrix 3x4 input projection matrix P.
+@param cameraMatrix Output 3x3 camera intrinsic matrix \f$\cameramatrix{A}\f$.
+@param rotMatrix Output 3x3 external rotation matrix R.
+@param transVect Output 4x1 translation vector T.
+@param rotMatrixX Optional 3x3 rotation matrix around x-axis.
+@param rotMatrixY Optional 3x3 rotation matrix around y-axis.
+@param rotMatrixZ Optional 3x3 rotation matrix around z-axis.
+@param eulerAngles Optional three-element vector containing three Euler angles of rotation in
+degrees.
+
+The function computes a decomposition of a projection matrix into a calibration and a rotation
+matrix and the position of a camera.
+
+It optionally returns three rotation matrices, one for each axis, and three Euler angles that could
+be used in OpenGL. Note, there is always more than one sequence of rotations about the three
+principal axes that results in the same orientation of an object, e.g. see @cite Slabaugh . Returned
+three rotation matrices and corresponding three Euler angles are only one of the possible solutions.
+
+The function is based on #RQDecomp3x3 .
+ */
+CV_EXPORTS_W void decomposeProjectionMatrix( InputArray projMatrix, OutputArray cameraMatrix,
+ OutputArray rotMatrix, OutputArray transVect,
+ OutputArray rotMatrixX = noArray(),
+ OutputArray rotMatrixY = noArray(),
+ OutputArray rotMatrixZ = noArray(),
+ OutputArray eulerAngles =noArray() );
+
+/** @brief Computes partial derivatives of the matrix product for each multiplied matrix.
+
+@param A First multiplied matrix.
+@param B Second multiplied matrix.
+@param dABdA First output derivative matrix d(A\*B)/dA of size
+\f$\texttt{A.rows*B.cols} \times {A.rows*A.cols}\f$ .
+@param dABdB Second output derivative matrix d(A\*B)/dB of size
+\f$\texttt{A.rows*B.cols} \times {B.rows*B.cols}\f$ .
+
+The function computes partial derivatives of the elements of the matrix product \f$A*B\f$ with regard to
+the elements of each of the two input matrices. The function is used to compute the Jacobian
+matrices in #stereoCalibrate but can also be used in any other similar optimization function.
+ */
+CV_EXPORTS_W void matMulDeriv( InputArray A, InputArray B, OutputArray dABdA, OutputArray dABdB );
+
+/** @brief Combines two rotation-and-shift transformations.
+
+@param rvec1 First rotation vector.
+@param tvec1 First translation vector.
+@param rvec2 Second rotation vector.
+@param tvec2 Second translation vector.
+@param rvec3 Output rotation vector of the superposition.
+@param tvec3 Output translation vector of the superposition.
+@param dr3dr1 Optional output derivative of rvec3 with regard to rvec1
+@param dr3dt1 Optional output derivative of rvec3 with regard to tvec1
+@param dr3dr2 Optional output derivative of rvec3 with regard to rvec2
+@param dr3dt2 Optional output derivative of rvec3 with regard to tvec2
+@param dt3dr1 Optional output derivative of tvec3 with regard to rvec1
+@param dt3dt1 Optional output derivative of tvec3 with regard to tvec1
+@param dt3dr2 Optional output derivative of tvec3 with regard to rvec2
+@param dt3dt2 Optional output derivative of tvec3 with regard to tvec2
+
+The functions compute:
+
+\f[\begin{array}{l} \texttt{rvec3} = \mathrm{rodrigues} ^{-1} \left ( \mathrm{rodrigues} ( \texttt{rvec2} ) \cdot \mathrm{rodrigues} ( \texttt{rvec1} ) \right ) \\ \texttt{tvec3} = \mathrm{rodrigues} ( \texttt{rvec2} ) \cdot \texttt{tvec1} + \texttt{tvec2} \end{array} ,\f]
+
+where \f$\mathrm{rodrigues}\f$ denotes a rotation vector to a rotation matrix transformation, and
+\f$\mathrm{rodrigues}^{-1}\f$ denotes the inverse transformation. See #Rodrigues for details.
+
+Also, the functions can compute the derivatives of the output vectors with regards to the input
+vectors (see #matMulDeriv ). The functions are used inside #stereoCalibrate but can also be used in
+your own code where Levenberg-Marquardt or another gradient-based solver is used to optimize a
+function that contains a matrix multiplication.
+ */
+CV_EXPORTS_W void composeRT( InputArray rvec1, InputArray tvec1,
+ InputArray rvec2, InputArray tvec2,
+ OutputArray rvec3, OutputArray tvec3,
+ OutputArray dr3dr1 = noArray(), OutputArray dr3dt1 = noArray(),
+ OutputArray dr3dr2 = noArray(), OutputArray dr3dt2 = noArray(),
+ OutputArray dt3dr1 = noArray(), OutputArray dt3dt1 = noArray(),
+ OutputArray dt3dr2 = noArray(), OutputArray dt3dt2 = noArray() );
+
+/** @brief Projects 3D points to an image plane.
+
+@param objectPoints Array of object points expressed wrt. the world coordinate frame. A 3xN/Nx3
+1-channel or 1xN/Nx1 3-channel (or vector\ ), where N is the number of points in the view.
+@param rvec The rotation vector (@ref Rodrigues) that, together with tvec, performs a change of
+basis from world to camera coordinate system, see @ref calibrateCamera for details.
+@param tvec The translation vector, see parameter description above.
+@param cameraMatrix Camera intrinsic matrix \f$\cameramatrix{A}\f$ .
+@param distCoeffs Input vector of distortion coefficients
+\f$\distcoeffs\f$ . If the vector is empty, the zero distortion coefficients are assumed.
+@param imagePoints Output array of image points, 1xN/Nx1 2-channel, or
+vector\ .
+@param jacobian Optional output 2Nx(10+\) jacobian matrix of derivatives of image
+points with respect to components of the rotation vector, translation vector, focal lengths,
+coordinates of the principal point and the distortion coefficients. In the old interface different
+components of the jacobian are returned via different output parameters.
+@param aspectRatio Optional "fixed aspect ratio" parameter. If the parameter is not 0, the
+function assumes that the aspect ratio (\f$f_x / f_y\f$) is fixed and correspondingly adjusts the
+jacobian matrix.
+
+The function computes the 2D projections of 3D points to the image plane, given intrinsic and
+extrinsic camera parameters. Optionally, the function computes Jacobians -matrices of partial
+derivatives of image points coordinates (as functions of all the input parameters) with respect to
+the particular parameters, intrinsic and/or extrinsic. The Jacobians are used during the global
+optimization in @ref calibrateCamera, @ref solvePnP, and @ref stereoCalibrate. The function itself
+can also be used to compute a re-projection error, given the current intrinsic and extrinsic
+parameters.
+
+@note By setting rvec = tvec = \f$[0, 0, 0]\f$, or by setting cameraMatrix to a 3x3 identity matrix,
+or by passing zero distortion coefficients, one can get various useful partial cases of the
+function. This means, one can compute the distorted coordinates for a sparse set of points or apply
+a perspective transformation (and also compute the derivatives) in the ideal zero-distortion setup.
+ */
+CV_EXPORTS_W void projectPoints( InputArray objectPoints,
+ InputArray rvec, InputArray tvec,
+ InputArray cameraMatrix, InputArray distCoeffs,
+ OutputArray imagePoints,
+ OutputArray jacobian = noArray(),
+ double aspectRatio = 0 );
+
+/** @example samples/cpp/tutorial_code/features2D/Homography/homography_from_camera_displacement.cpp
+An example program about homography from the camera displacement
+
+Check @ref tutorial_homography "the corresponding tutorial" for more details
+*/
+
+/** @brief Finds an object pose \f$ {}^{c}\mathbf{T}_o \f$ from 3D-2D point correspondences:
+
+{ width=50% }
+
+@see @ref calib3d_solvePnP
+
+This function returns the rotation and the translation vectors that transform a 3D point expressed in the object
+coordinate frame to the camera coordinate frame, using different methods:
+- P3P methods (@ref SOLVEPNP_P3P, @ref SOLVEPNP_AP3P): need 4 input points to return a unique solution.
+- @ref SOLVEPNP_IPPE Input points must be >= 4 and object points must be coplanar.
+- @ref SOLVEPNP_IPPE_SQUARE Special case suitable for marker pose estimation.
+Number of input points must be 4. Object points must be defined in the following order:
+ - point 0: [-squareLength / 2, squareLength / 2, 0]
+ - point 1: [ squareLength / 2, squareLength / 2, 0]
+ - point 2: [ squareLength / 2, -squareLength / 2, 0]
+ - point 3: [-squareLength / 2, -squareLength / 2, 0]
+- for all the other flags, number of input points must be >= 4 and object points can be in any configuration.
+
+@param objectPoints Array of object points in the object coordinate space, Nx3 1-channel or
+1xN/Nx1 3-channel, where N is the number of points. vector\ can be also passed here.
+@param imagePoints Array of corresponding image points, Nx2 1-channel or 1xN/Nx1 2-channel,
+where N is the number of points. vector\ can be also passed here.
+@param cameraMatrix Input camera intrinsic matrix \f$\cameramatrix{A}\f$ .
+@param distCoeffs Input vector of distortion coefficients
+\f$\distcoeffs\f$. If the vector is NULL/empty, the zero distortion coefficients are
+assumed.
+@param rvec Output rotation vector (see @ref Rodrigues ) that, together with tvec, brings points from
+the model coordinate system to the camera coordinate system.
+@param tvec Output translation vector.
+@param useExtrinsicGuess Parameter used for #SOLVEPNP_ITERATIVE. If true (1), the function uses
+the provided rvec and tvec values as initial approximations of the rotation and translation
+vectors, respectively, and further optimizes them.
+@param flags Method for solving a PnP problem: see @ref calib3d_solvePnP_flags
+
+More information about Perspective-n-Points is described in @ref calib3d_solvePnP
+
+@note
+ - An example of how to use solvePnP for planar augmented reality can be found at
+ opencv_source_code/samples/python/plane_ar.py
+ - If you are using Python:
+ - Numpy array slices won't work as input because solvePnP requires contiguous
+ arrays (enforced by the assertion using cv::Mat::checkVector() around line 55 of
+ modules/calib3d/src/solvepnp.cpp version 2.4.9)
+ - The P3P algorithm requires image points to be in an array of shape (N,1,2) due
+ to its calling of #undistortPoints (around line 75 of modules/calib3d/src/solvepnp.cpp version 2.4.9)
+ which requires 2-channel information.
+ - Thus, given some data D = np.array(...) where D.shape = (N,M), in order to use a subset of
+ it as, e.g., imagePoints, one must effectively copy it into a new array: imagePoints =
+ np.ascontiguousarray(D[:,:2]).reshape((N,1,2))
+ - The methods @ref SOLVEPNP_DLS and @ref SOLVEPNP_UPNP cannot be used as the current implementations are
+ unstable and sometimes give completely wrong results. If you pass one of these two
+ flags, @ref SOLVEPNP_EPNP method will be used instead.
+ - The minimum number of points is 4 in the general case. In the case of @ref SOLVEPNP_P3P and @ref SOLVEPNP_AP3P
+ methods, it is required to use exactly 4 points (the first 3 points are used to estimate all the solutions
+ of the P3P problem, the last one is used to retain the best solution that minimizes the reprojection error).
+ - With @ref SOLVEPNP_ITERATIVE method and `useExtrinsicGuess=true`, the minimum number of points is 3 (3 points
+ are sufficient to compute a pose but there are up to 4 solutions). The initial solution should be close to the
+ global solution to converge. The function returns true if some solution is found. User code is responsible for
+ solution quality assessment.
+ - With @ref SOLVEPNP_IPPE input points must be >= 4 and object points must be coplanar.
+ - With @ref SOLVEPNP_IPPE_SQUARE this is a special case suitable for marker pose estimation.
+ Number of input points must be 4. Object points must be defined in the following order:
+ - point 0: [-squareLength / 2, squareLength / 2, 0]
+ - point 1: [ squareLength / 2, squareLength / 2, 0]
+ - point 2: [ squareLength / 2, -squareLength / 2, 0]
+ - point 3: [-squareLength / 2, -squareLength / 2, 0]
+ - With @ref SOLVEPNP_SQPNP input points must be >= 3
+ */
+CV_EXPORTS_W bool solvePnP( InputArray objectPoints, InputArray imagePoints,
+ InputArray cameraMatrix, InputArray distCoeffs,
+ OutputArray rvec, OutputArray tvec,
+ bool useExtrinsicGuess = false, int flags = SOLVEPNP_ITERATIVE );
+
+/** @brief Finds an object pose \f$ {}^{c}\mathbf{T}_o \f$ from 3D-2D point correspondences using the RANSAC scheme to deal with bad matches.
+
+{ width=50% }
+
+@see @ref calib3d_solvePnP
+
+@param objectPoints Array of object points in the object coordinate space, Nx3 1-channel or
+1xN/Nx1 3-channel, where N is the number of points. vector\ can be also passed here.
+@param imagePoints Array of corresponding image points, Nx2 1-channel or 1xN/Nx1 2-channel,
+where N is the number of points. vector\ can be also passed here.
+@param cameraMatrix Input camera intrinsic matrix \f$\cameramatrix{A}\f$ .
+@param distCoeffs Input vector of distortion coefficients
+\f$\distcoeffs\f$. If the vector is NULL/empty, the zero distortion coefficients are
+assumed.
+@param rvec Output rotation vector (see @ref Rodrigues ) that, together with tvec, brings points from
+the model coordinate system to the camera coordinate system.
+@param tvec Output translation vector.
+@param useExtrinsicGuess Parameter used for @ref SOLVEPNP_ITERATIVE. If true (1), the function uses
+the provided rvec and tvec values as initial approximations of the rotation and translation
+vectors, respectively, and further optimizes them.
+@param iterationsCount Number of iterations.
+@param reprojectionError Inlier threshold value used by the RANSAC procedure. The parameter value
+is the maximum allowed distance between the observed and computed point projections to consider it
+an inlier.
+@param confidence The probability that the algorithm produces a useful result.
+@param inliers Output vector that contains indices of inliers in objectPoints and imagePoints .
+@param flags Method for solving a PnP problem (see @ref solvePnP ).
+
+The function estimates an object pose given a set of object points, their corresponding image
+projections, as well as the camera intrinsic matrix and the distortion coefficients. This function finds such
+a pose that minimizes reprojection error, that is, the sum of squared distances between the observed
+projections imagePoints and the projected (using @ref projectPoints ) objectPoints. The use of RANSAC
+makes the function resistant to outliers.
+
+@note
+ - An example of how to use solvePnPRansac for object detection can be found at
+ @ref tutorial_real_time_pose
+ - The default method used to estimate the camera pose for the Minimal Sample Sets step
+ is #SOLVEPNP_EPNP. Exceptions are:
+ - if you choose #SOLVEPNP_P3P or #SOLVEPNP_AP3P, these methods will be used.
+ - if the number of input points is equal to 4, #SOLVEPNP_P3P is used.
+ - The method used to estimate the camera pose using all the inliers is defined by the
+ flags parameters unless it is equal to #SOLVEPNP_P3P or #SOLVEPNP_AP3P. In this case,
+ the method #SOLVEPNP_EPNP will be used instead.
+ */
+CV_EXPORTS_W bool solvePnPRansac( InputArray objectPoints, InputArray imagePoints,
+ InputArray cameraMatrix, InputArray distCoeffs,
+ OutputArray rvec, OutputArray tvec,
+ bool useExtrinsicGuess = false, int iterationsCount = 100,
+ float reprojectionError = 8.0, double confidence = 0.99,
+ OutputArray inliers = noArray(), int flags = SOLVEPNP_ITERATIVE );
+
+
+/*
+Finds rotation and translation vector.
+If cameraMatrix is given then run P3P. Otherwise run linear P6P and output cameraMatrix too.
+*/
+CV_EXPORTS_W bool solvePnPRansac( InputArray objectPoints, InputArray imagePoints,
+ InputOutputArray cameraMatrix, InputArray distCoeffs,
+ OutputArray rvec, OutputArray tvec, OutputArray inliers,
+ const UsacParams ¶ms=UsacParams());
+
+/** @brief Finds an object pose \f$ {}^{c}\mathbf{T}_o \f$ from **3** 3D-2D point correspondences.
+
+{ width=50% }
+
+@see @ref calib3d_solvePnP
+
+@param objectPoints Array of object points in the object coordinate space, 3x3 1-channel or
+1x3/3x1 3-channel. vector\ can be also passed here.
+@param imagePoints Array of corresponding image points, 3x2 1-channel or 1x3/3x1 2-channel.
+ vector\ can be also passed here.
+@param cameraMatrix Input camera intrinsic matrix \f$\cameramatrix{A}\f$ .
+@param distCoeffs Input vector of distortion coefficients
+\f$\distcoeffs\f$. If the vector is NULL/empty, the zero distortion coefficients are
+assumed.
+@param rvecs Output rotation vectors (see @ref Rodrigues ) that, together with tvecs, brings points from
+the model coordinate system to the camera coordinate system. A P3P problem has up to 4 solutions.
+@param tvecs Output translation vectors.
+@param flags Method for solving a P3P problem:
+- @ref SOLVEPNP_P3P Method is based on the paper of Ding, Y., Yang, J., Larsson, V., Olsson, C., & Åstrom, K.
+"Revisiting the P3P Problem" (@cite ding2023revisiting).
+- @ref SOLVEPNP_AP3P Method is based on the paper of T. Ke and S. Roumeliotis.
+"An Efficient Algebraic Solution to the Perspective-Three-Point Problem" (@cite Ke17).
+
+The function estimates the object pose given 3 object points, their corresponding image
+projections, as well as the camera intrinsic matrix and the distortion coefficients.
+
+@note
+The solutions are sorted by reprojection errors (lowest to highest).
+ */
+CV_EXPORTS_W int solveP3P( InputArray objectPoints, InputArray imagePoints,
+ InputArray cameraMatrix, InputArray distCoeffs,
+ OutputArrayOfArrays rvecs, OutputArrayOfArrays tvecs,
+ int flags );
+
+/** @brief Refine a pose (the translation and the rotation that transform a 3D point expressed in the object coordinate frame
+to the camera coordinate frame) from a 3D-2D point correspondences and starting from an initial solution.
+
+@see @ref calib3d_solvePnP
+
+@param objectPoints Array of object points in the object coordinate space, Nx3 1-channel or 1xN/Nx1 3-channel,
+where N is the number of points. vector\ can also be passed here.
+@param imagePoints Array of corresponding image points, Nx2 1-channel or 1xN/Nx1 2-channel,
+where N is the number of points. vector\ can also be passed here.
+@param cameraMatrix Input camera intrinsic matrix \f$\cameramatrix{A}\f$ .
+@param distCoeffs Input vector of distortion coefficients
+\f$\distcoeffs\f$. If the vector is NULL/empty, the zero distortion coefficients are
+assumed.
+@param rvec Input/Output rotation vector (see @ref Rodrigues ) that, together with tvec, brings points from
+the model coordinate system to the camera coordinate system. Input values are used as an initial solution.
+@param tvec Input/Output translation vector. Input values are used as an initial solution.
+@param criteria Criteria when to stop the Levenberg-Marquard iterative algorithm.
+
+The function refines the object pose given at least 3 object points, their corresponding image
+projections, an initial solution for the rotation and translation vector,
+as well as the camera intrinsic matrix and the distortion coefficients.
+The function minimizes the projection error with respect to the rotation and the translation vectors, according
+to a Levenberg-Marquardt iterative minimization @cite Madsen04 @cite Eade13 process.
+ */
+CV_EXPORTS_W void solvePnPRefineLM( InputArray objectPoints, InputArray imagePoints,
+ InputArray cameraMatrix, InputArray distCoeffs,
+ InputOutputArray rvec, InputOutputArray tvec,
+ TermCriteria criteria = TermCriteria(TermCriteria::EPS + TermCriteria::COUNT, 20, FLT_EPSILON));
+
+/** @brief Refine a pose (the translation and the rotation that transform a 3D point expressed in the object coordinate frame
+to the camera coordinate frame) from a 3D-2D point correspondences and starting from an initial solution.
+
+@see @ref calib3d_solvePnP
+
+@param objectPoints Array of object points in the object coordinate space, Nx3 1-channel or 1xN/Nx1 3-channel,
+where N is the number of points. vector\ can also be passed here.
+@param imagePoints Array of corresponding image points, Nx2 1-channel or 1xN/Nx1 2-channel,
+where N is the number of points. vector\ can also be passed here.
+@param cameraMatrix Input camera intrinsic matrix \f$\cameramatrix{A}\f$ .
+@param distCoeffs Input vector of distortion coefficients
+\f$\distcoeffs\f$. If the vector is NULL/empty, the zero distortion coefficients are
+assumed.
+@param rvec Input/Output rotation vector (see @ref Rodrigues ) that, together with tvec, brings points from
+the model coordinate system to the camera coordinate system. Input values are used as an initial solution.
+@param tvec Input/Output translation vector. Input values are used as an initial solution.
+@param criteria Criteria when to stop the Levenberg-Marquard iterative algorithm.
+@param VVSlambda Gain for the virtual visual servoing control law, equivalent to the \f$\alpha\f$
+gain in the Damped Gauss-Newton formulation.
+
+The function refines the object pose given at least 3 object points, their corresponding image
+projections, an initial solution for the rotation and translation vector,
+as well as the camera intrinsic matrix and the distortion coefficients.
+The function minimizes the projection error with respect to the rotation and the translation vectors, using a
+virtual visual servoing (VVS) @cite Chaumette06 @cite Marchand16 scheme.
+ */
+CV_EXPORTS_W void solvePnPRefineVVS( InputArray objectPoints, InputArray imagePoints,
+ InputArray cameraMatrix, InputArray distCoeffs,
+ InputOutputArray rvec, InputOutputArray tvec,
+ TermCriteria criteria = TermCriteria(TermCriteria::EPS + TermCriteria::COUNT, 20, FLT_EPSILON),
+ double VVSlambda = 1);
+
+/** @brief Finds an object pose \f$ {}^{c}\mathbf{T}_o \f$ from 3D-2D point correspondences.
+
+{ width=50% }
+
+@see @ref calib3d_solvePnP
+
+This function returns a list of all the possible solutions (a solution is a
+couple), depending on the number of input points and the chosen method:
+- P3P methods (@ref SOLVEPNP_P3P, @ref SOLVEPNP_AP3P): 3 or 4 input points. Number of returned solutions can be between 0 and 4 with 3 input points.
+- @ref SOLVEPNP_IPPE Input points must be >= 4 and object points must be coplanar. Returns 2 solutions.
+- @ref SOLVEPNP_IPPE_SQUARE Special case suitable for marker pose estimation.
+Number of input points must be 4 and 2 solutions are returned. Object points must be defined in the following order:
+ - point 0: [-squareLength / 2, squareLength / 2, 0]
+ - point 1: [ squareLength / 2, squareLength / 2, 0]
+ - point 2: [ squareLength / 2, -squareLength / 2, 0]
+ - point 3: [-squareLength / 2, -squareLength / 2, 0]
+- for all the other flags, number of input points must be >= 4 and object points can be in any configuration.
+Only 1 solution is returned.
+
+@param objectPoints Array of object points in the object coordinate space, Nx3 1-channel or
+1xN/Nx1 3-channel, where N is the number of points. vector\ can be also passed here.
+@param imagePoints Array of corresponding image points, Nx2 1-channel or 1xN/Nx1 2-channel,
+where N is the number of points. vector\ can be also passed here.
+@param cameraMatrix Input camera intrinsic matrix \f$\cameramatrix{A}\f$ .
+@param distCoeffs Input vector of distortion coefficients
+\f$\distcoeffs\f$. If the vector is NULL/empty, the zero distortion coefficients are
+assumed.
+@param rvecs Vector of output rotation vectors (see @ref Rodrigues ) that, together with tvecs, brings points from
+the model coordinate system to the camera coordinate system.
+@param tvecs Vector of output translation vectors.
+@param useExtrinsicGuess Parameter used for #SOLVEPNP_ITERATIVE. If true (1), the function uses
+the provided rvec and tvec values as initial approximations of the rotation and translation
+vectors, respectively, and further optimizes them.
+@param flags Method for solving a PnP problem: see @ref calib3d_solvePnP_flags
+@param rvec Rotation vector used to initialize an iterative PnP refinement algorithm, when flag is @ref SOLVEPNP_ITERATIVE
+and useExtrinsicGuess is set to true.
+@param tvec Translation vector used to initialize an iterative PnP refinement algorithm, when flag is @ref SOLVEPNP_ITERATIVE
+and useExtrinsicGuess is set to true.
+@param reprojectionError Optional vector of reprojection error, that is the RMS error
+(\f$ \text{RMSE} = \sqrt{\frac{\sum_{i}^{N} \left ( \hat{y_i} - y_i \right )^2}{N}} \f$) between the input image points
+and the 3D object points projected with the estimated pose.
+
+More information is described in @ref calib3d_solvePnP
+
+@note
+ - An example of how to use solvePnP for planar augmented reality can be found at
+ opencv_source_code/samples/python/plane_ar.py
+ - If you are using Python:
+ - Numpy array slices won't work as input because solvePnP requires contiguous
+ arrays (enforced by the assertion using cv::Mat::checkVector() around line 55 of
+ modules/calib3d/src/solvepnp.cpp version 2.4.9)
+ - The P3P algorithm requires image points to be in an array of shape (N,1,2) due
+ to its calling of #undistortPoints (around line 75 of modules/calib3d/src/solvepnp.cpp version 2.4.9)
+ which requires 2-channel information.
+ - Thus, given some data D = np.array(...) where D.shape = (N,M), in order to use a subset of
+ it as, e.g., imagePoints, one must effectively copy it into a new array: imagePoints =
+ np.ascontiguousarray(D[:,:2]).reshape((N,1,2))
+ - The methods @ref SOLVEPNP_DLS and @ref SOLVEPNP_UPNP cannot be used as the current implementations are
+ unstable and sometimes give completely wrong results. If you pass one of these two
+ flags, @ref SOLVEPNP_EPNP method will be used instead.
+ - The minimum number of points is 4 in the general case. In the case of @ref SOLVEPNP_P3P and @ref SOLVEPNP_AP3P
+ methods, it is required to use exactly 4 points (the first 3 points are used to estimate all the solutions
+ of the P3P problem, the last one is used to retain the best solution that minimizes the reprojection error).
+ - With @ref SOLVEPNP_ITERATIVE method and `useExtrinsicGuess=true`, the minimum number of points is 3 (3 points
+ are sufficient to compute a pose but there are up to 4 solutions). The initial solution should be close to the
+ global solution to converge.
+ - With @ref SOLVEPNP_IPPE input points must be >= 4 and object points must be coplanar.
+ - With @ref SOLVEPNP_IPPE_SQUARE this is a special case suitable for marker pose estimation.
+ Number of input points must be 4. Object points must be defined in the following order:
+ - point 0: [-squareLength / 2, squareLength / 2, 0]
+ - point 1: [ squareLength / 2, squareLength / 2, 0]
+ - point 2: [ squareLength / 2, -squareLength / 2, 0]
+ - point 3: [-squareLength / 2, -squareLength / 2, 0]
+ - With @ref SOLVEPNP_SQPNP input points must be >= 3
+ */
+CV_EXPORTS_W int solvePnPGeneric( InputArray objectPoints, InputArray imagePoints,
+ InputArray cameraMatrix, InputArray distCoeffs,
+ OutputArrayOfArrays rvecs, OutputArrayOfArrays tvecs,
+ bool useExtrinsicGuess = false, SolvePnPMethod flags = SOLVEPNP_ITERATIVE,
+ InputArray rvec = noArray(), InputArray tvec = noArray(),
+ OutputArray reprojectionError = noArray() );
+
+/** @brief Finds an initial camera intrinsic matrix from 3D-2D point correspondences.
+
+@param objectPoints Vector of vectors of the calibration pattern points in the calibration pattern
+coordinate space. In the old interface all the per-view vectors are concatenated. See
+#calibrateCamera for details.
+@param imagePoints Vector of vectors of the projections of the calibration pattern points. In the
+old interface all the per-view vectors are concatenated.
+@param imageSize Image size in pixels used to initialize the principal point.
+@param aspectRatio If it is zero or negative, both \f$f_x\f$ and \f$f_y\f$ are estimated independently.
+Otherwise, \f$f_x = f_y \cdot \texttt{aspectRatio}\f$ .
+
+The function estimates and returns an initial camera intrinsic matrix for the camera calibration process.
+Currently, the function only supports planar calibration patterns, which are patterns where each
+object point has z-coordinate =0.
+ */
+CV_EXPORTS_W Mat initCameraMatrix2D( InputArrayOfArrays objectPoints,
+ InputArrayOfArrays imagePoints,
+ Size imageSize, double aspectRatio = 1.0 );
+
+/** @brief Finds the positions of internal corners of the chessboard.
+
+@param image Source chessboard view. It must be an 8-bit grayscale or color image.
+@param patternSize Number of inner corners per a chessboard row and column
+( patternSize = cv::Size(points_per_row,points_per_colum) = cv::Size(columns,rows) ).
+@param corners Output array of detected corners.
+@param flags Various operation flags that can be zero or a combination of the following values:
+- @ref CALIB_CB_ADAPTIVE_THRESH Use adaptive thresholding to convert the image to black
+and white, rather than a fixed threshold level (computed from the average image brightness).
+- @ref CALIB_CB_NORMALIZE_IMAGE Normalize the image gamma with #equalizeHist before
+applying fixed or adaptive thresholding.
+- @ref CALIB_CB_FILTER_QUADS Use additional criteria (like contour area, perimeter,
+square-like shape) to filter out false quads extracted at the contour retrieval stage.
+- @ref CALIB_CB_FAST_CHECK Run a fast check on the image that looks for chessboard corners,
+and shortcut the call if none is found. This can drastically speed up the call in the
+degenerate condition when no chessboard is observed.
+- @ref CALIB_CB_PLAIN All other flags are ignored. The input image is taken as is.
+No image processing is done to improve to find the checkerboard. This has the effect of speeding up the
+execution of the function but could lead to not recognizing the checkerboard if the image
+is not previously binarized in the appropriate manner.
+
+The function attempts to determine whether the input image is a view of the chessboard pattern and
+locate the internal chessboard corners. The function returns a non-zero value if all of the corners
+are found and they are placed in a certain order (row by row, left to right in every row).
+Otherwise, if the function fails to find all the corners or reorder them, it returns 0. For example,
+a regular chessboard has 8 x 8 squares and 7 x 7 internal corners, that is, points where the black
+squares touch each other. The detected coordinates are approximate, and to determine their positions
+more accurately, the function calls #cornerSubPix. You also may use the function #cornerSubPix with
+different parameters if returned coordinates are not accurate enough.
+
+Sample usage of detecting and drawing chessboard corners: :
+@code
+ Size patternsize(8,6); //interior number of corners
+ Mat gray = ....; //source image
+ vector corners; //this will be filled by the detected corners
+
+ //CALIB_CB_FAST_CHECK saves a lot of time on images
+ //that do not contain any chessboard corners
+ bool patternfound = findChessboardCorners(gray, patternsize, corners,
+ CALIB_CB_ADAPTIVE_THRESH + CALIB_CB_NORMALIZE_IMAGE
+ + CALIB_CB_FAST_CHECK);
+
+ if(patternfound)
+ cornerSubPix(gray, corners, Size(11, 11), Size(-1, -1),
+ TermCriteria(CV_TERMCRIT_EPS + CV_TERMCRIT_ITER, 30, 0.1));
+
+ drawChessboardCorners(img, patternsize, Mat(corners), patternfound);
+@endcode
+@note The function requires white space (like a square-thick border, the wider the better) around
+the board to make the detection more robust in various environments. Otherwise, if there is no
+border and the background is dark, the outer black squares cannot be segmented properly and so the
+square grouping and ordering algorithm fails.
+
+Use the `generate_pattern.py` Python script (@ref tutorial_camera_calibration_pattern)
+to create the desired checkerboard pattern.
+ */
+CV_EXPORTS_W bool findChessboardCorners( InputArray image, Size patternSize, OutputArray corners,
+ int flags = CALIB_CB_ADAPTIVE_THRESH + CALIB_CB_NORMALIZE_IMAGE );
+
+/*
+ Checks whether the image contains chessboard of the specific size or not.
+ If yes, nonzero value is returned.
+*/
+CV_EXPORTS_W bool checkChessboard(InputArray img, Size size);
+
+/** @brief Finds the positions of internal corners of the chessboard using a sector based approach.
+
+@param image Source chessboard view. It must be an 8-bit grayscale or color image.
+@param patternSize Number of inner corners per a chessboard row and column
+( patternSize = cv::Size(points_per_row,points_per_colum) = cv::Size(columns,rows) ).
+@param corners Output array of detected corners.
+@param flags Various operation flags that can be zero or a combination of the following values:
+- @ref CALIB_CB_NORMALIZE_IMAGE Normalize the image gamma with equalizeHist before detection.
+- @ref CALIB_CB_EXHAUSTIVE Run an exhaustive search to improve detection rate.
+- @ref CALIB_CB_ACCURACY Up sample input image to improve sub-pixel accuracy due to aliasing effects.
+- @ref CALIB_CB_LARGER The detected pattern is allowed to be larger than patternSize (see description).
+- @ref CALIB_CB_MARKER The detected pattern must have a marker (see description).
+This should be used if an accurate camera calibration is required.
+@param meta Optional output array of detected corners (CV_8UC1 and size = cv::Size(columns,rows)).
+Each entry stands for one corner of the pattern and can have one of the following values:
+- 0 = no meta data attached
+- 1 = left-top corner of a black cell
+- 2 = left-top corner of a white cell
+- 3 = left-top corner of a black cell with a white marker dot
+- 4 = left-top corner of a white cell with a black marker dot (pattern origin in case of markers otherwise first corner)
+
+The function is analog to #findChessboardCorners but uses a localized radon
+transformation approximated by box filters being more robust to all sort of
+noise, faster on larger images and is able to directly return the sub-pixel
+position of the internal chessboard corners. The Method is based on the paper
+@cite duda2018 "Accurate Detection and Localization of Checkerboard Corners for
+Calibration" demonstrating that the returned sub-pixel positions are more
+accurate than the one returned by cornerSubPix allowing a precise camera
+calibration for demanding applications.
+
+In the case, the flags @ref CALIB_CB_LARGER or @ref CALIB_CB_MARKER are given,
+the result can be recovered from the optional meta array. Both flags are
+helpful to use calibration patterns exceeding the field of view of the camera.
+These oversized patterns allow more accurate calibrations as corners can be
+utilized, which are as close as possible to the image borders. For a
+consistent coordinate system across all images, the optional marker (see image
+below) can be used to move the origin of the board to the location where the
+black circle is located.
+
+@note The function requires a white boarder with roughly the same width as one
+of the checkerboard fields around the whole board to improve the detection in
+various environments. In addition, because of the localized radon
+transformation it is beneficial to use round corners for the field corners
+which are located on the outside of the board. The following figure illustrates
+a sample checkerboard optimized for the detection. However, any other checkerboard
+can be used as well.
+
+Use the `generate_pattern.py` Python script (@ref tutorial_camera_calibration_pattern)
+to create the corresponding checkerboard pattern:
+\image html pics/checkerboard_radon.png width=60%
+ */
+CV_EXPORTS_AS(findChessboardCornersSBWithMeta)
+bool findChessboardCornersSB(InputArray image,Size patternSize, OutputArray corners,
+ int flags,OutputArray meta);
+/** @overload */
+CV_EXPORTS_W inline
+bool findChessboardCornersSB(InputArray image, Size patternSize, OutputArray corners,
+ int flags = 0)
+{
+ return findChessboardCornersSB(image, patternSize, corners, flags, noArray());
+}
+
+/** @brief Estimates the sharpness of a detected chessboard.
+
+Image sharpness, as well as brightness, are a critical parameter for accuracte
+camera calibration. For accessing these parameters for filtering out
+problematic calibraiton images, this method calculates edge profiles by traveling from
+black to white chessboard cell centers. Based on this, the number of pixels is
+calculated required to transit from black to white. This width of the
+transition area is a good indication of how sharp the chessboard is imaged
+and should be below ~3.0 pixels.
+
+@param image Gray image used to find chessboard corners
+@param patternSize Size of a found chessboard pattern
+@param corners Corners found by #findChessboardCornersSB
+@param rise_distance Rise distance 0.8 means 10% ... 90% of the final signal strength
+@param vertical By default edge responses for horizontal lines are calculated
+@param sharpness Optional output array with a sharpness value for calculated edge responses (see description)
+
+The optional sharpness array is of type CV_32FC1 and has for each calculated
+profile one row with the following five entries:
+* 0 = x coordinate of the underlying edge in the image
+* 1 = y coordinate of the underlying edge in the image
+* 2 = width of the transition area (sharpness)
+* 3 = signal strength in the black cell (min brightness)
+* 4 = signal strength in the white cell (max brightness)
+
+@return Scalar(average sharpness, average min brightness, average max brightness,0)
+*/
+CV_EXPORTS_W Scalar estimateChessboardSharpness(InputArray image, Size patternSize, InputArray corners,
+ float rise_distance=0.8F,bool vertical=false,
+ OutputArray sharpness=noArray());
+
+
+//! finds subpixel-accurate positions of the chessboard corners
+CV_EXPORTS_W bool find4QuadCornerSubpix( InputArray img, InputOutputArray corners, Size region_size );
+
+/** @brief Renders the detected chessboard corners.
+
+@param image Destination image. It must be an 8-bit color image.
+@param patternSize Number of inner corners per a chessboard row and column
+(patternSize = cv::Size(points_per_row,points_per_column)).
+@param corners Array of detected corners, the output of #findChessboardCorners.
+@param patternWasFound Parameter indicating whether the complete board was found or not. The
+return value of #findChessboardCorners should be passed here.
+
+The function draws individual chessboard corners detected either as red circles if the board was not
+found, or as colored corners connected with lines if the board was found.
+ */
+CV_EXPORTS_W void drawChessboardCorners( InputOutputArray image, Size patternSize,
+ InputArray corners, bool patternWasFound );
+
+/** @brief Draw axes of the world/object coordinate system from pose estimation. @sa solvePnP
+
+@param image Input/output image. It must have 1 or 3 channels. The number of channels is not altered.
+@param cameraMatrix Input 3x3 floating-point matrix of camera intrinsic parameters.
+\f$\cameramatrix{A}\f$
+@param distCoeffs Input vector of distortion coefficients
+\f$\distcoeffs\f$. If the vector is empty, the zero distortion coefficients are assumed.
+@param rvec Rotation vector (see @ref Rodrigues ) that, together with tvec, brings points from
+the model coordinate system to the camera coordinate system.
+@param tvec Translation vector.
+@param length Length of the painted axes in the same unit than tvec (usually in meters).
+@param thickness Line thickness of the painted axes.
+
+This function draws the axes of the world/object coordinate system w.r.t. to the camera frame.
+OX is drawn in red, OY in green and OZ in blue.
+ */
+CV_EXPORTS_W void drawFrameAxes(InputOutputArray image, InputArray cameraMatrix, InputArray distCoeffs,
+ InputArray rvec, InputArray tvec, float length, int thickness=3);
+
+struct CV_EXPORTS_W_SIMPLE CirclesGridFinderParameters
+{
+ CV_WRAP CirclesGridFinderParameters();
+ CV_PROP_RW cv::Size2f densityNeighborhoodSize;
+ CV_PROP_RW float minDensity;
+ CV_PROP_RW int kmeansAttempts;
+ CV_PROP_RW int minDistanceToAddKeypoint;
+ CV_PROP_RW int keypointScale;
+ CV_PROP_RW float minGraphConfidence;
+ CV_PROP_RW float vertexGain;
+ CV_PROP_RW float vertexPenalty;
+ CV_PROP_RW float existingVertexGain;
+ CV_PROP_RW float edgeGain;
+ CV_PROP_RW float edgePenalty;
+ CV_PROP_RW float convexHullFactor;
+ CV_PROP_RW float minRNGEdgeSwitchDist;
+
+ enum GridType
+ {
+ SYMMETRIC_GRID, ASYMMETRIC_GRID
+ };
+ CV_PROP_RW GridType gridType;
+
+ CV_PROP_RW float squareSize; //!< Distance between two adjacent points. Used by CALIB_CB_CLUSTERING.
+ CV_PROP_RW float maxRectifiedDistance; //!< Max deviation from prediction. Used by CALIB_CB_CLUSTERING.
+};
+
+#ifndef DISABLE_OPENCV_3_COMPATIBILITY
+typedef CirclesGridFinderParameters CirclesGridFinderParameters2;
+#endif
+
+/** @brief Finds centers in the grid of circles.
+
+@param image grid view of input circles; it must be an 8-bit grayscale or color image.
+@param patternSize number of circles per row and column
+( patternSize = Size(points_per_row, points_per_colum) ).
+@param centers output array of detected centers.
+@param flags various operation flags that can be one of the following values:
+- @ref CALIB_CB_SYMMETRIC_GRID uses symmetric pattern of circles.
+- @ref CALIB_CB_ASYMMETRIC_GRID uses asymmetric pattern of circles.
+- @ref CALIB_CB_CLUSTERING uses a special algorithm for grid detection. It is more robust to
+perspective distortions but much more sensitive to background clutter.
+@param blobDetector feature detector that finds blobs like dark circles on light background.
+ If `blobDetector` is NULL then `image` represents Point2f array of candidates.
+@param parameters struct for finding circles in a grid pattern.
+
+The function attempts to determine whether the input image contains a grid of circles. If it is, the
+function locates centers of the circles. The function returns a non-zero value if all of the centers
+have been found and they have been placed in a certain order (row by row, left to right in every
+row). Otherwise, if the function fails to find all the corners or reorder them, it returns 0.
+
+Sample usage of detecting and drawing the centers of circles: :
+@code
+ Size patternsize(7,7); //number of centers
+ Mat gray = ...; //source image
+ vector centers; //this will be filled by the detected centers
+
+ bool patternfound = findCirclesGrid(gray, patternsize, centers);
+
+ drawChessboardCorners(img, patternsize, Mat(centers), patternfound);
+@endcode
+@note The function requires white space (like a square-thick border, the wider the better) around
+the board to make the detection more robust in various environments.
+ */
+CV_EXPORTS_W bool findCirclesGrid( InputArray image, Size patternSize,
+ OutputArray centers, int flags,
+ const Ptr &blobDetector,
+ const CirclesGridFinderParameters& parameters);
+
+/** @overload */
+CV_EXPORTS_W bool findCirclesGrid( InputArray image, Size patternSize,
+ OutputArray centers, int flags = CALIB_CB_SYMMETRIC_GRID,
+ const Ptr &blobDetector = SimpleBlobDetector::create());
+
+/** @brief Finds the camera intrinsic and extrinsic parameters from several views of a calibration
+pattern.
+
+@param objectPoints In the new interface it is a vector of vectors of calibration pattern points in
+the calibration pattern coordinate space (e.g. std::vector>). The outer
+vector contains as many elements as the number of pattern views. If the same calibration pattern
+is shown in each view and it is fully visible, all the vectors will be the same. Although, it is
+possible to use partially occluded patterns or even different patterns in different views. Then,
+the vectors will be different. Although the points are 3D, they all lie in the calibration pattern's
+XY coordinate plane (thus 0 in the Z-coordinate), if the used calibration pattern is a planar rig.
+In the old interface all the vectors of object points from different views are concatenated
+together.
+@param imagePoints In the new interface it is a vector of vectors of the projections of calibration
+pattern points (e.g. std::vector>). imagePoints.size() and
+objectPoints.size(), and imagePoints[i].size() and objectPoints[i].size() for each i, must be equal,
+respectively. In the old interface all the vectors of object points from different views are
+concatenated together.
+@param imageSize Size of the image used only to initialize the camera intrinsic matrix.
+@param cameraMatrix Input/output 3x3 floating-point camera intrinsic matrix
+\f$\cameramatrix{A}\f$ . If @ref CALIB_USE_INTRINSIC_GUESS
+and/or @ref CALIB_FIX_ASPECT_RATIO, @ref CALIB_FIX_PRINCIPAL_POINT or @ref CALIB_FIX_FOCAL_LENGTH
+are specified, some or all of fx, fy, cx, cy must be initialized before calling the function.
+@param distCoeffs Input/output vector of distortion coefficients
+\f$\distcoeffs\f$.
+@param rvecs Output vector of rotation vectors (@ref Rodrigues ) estimated for each pattern view
+(e.g. std::vector>). That is, each i-th rotation vector together with the corresponding
+i-th translation vector (see the next output parameter description) brings the calibration pattern
+from the object coordinate space (in which object points are specified) to the camera coordinate
+space. In more technical terms, the tuple of the i-th rotation and translation vector performs
+a change of basis from object coordinate space to camera coordinate space. Due to its duality, this
+tuple is equivalent to the position of the calibration pattern with respect to the camera coordinate
+space.
+@param tvecs Output vector of translation vectors estimated for each pattern view, see parameter
+describtion above.
+@param stdDeviationsIntrinsics Output vector of standard deviations estimated for intrinsic
+parameters. Order of deviations values:
+\f$(f_x, f_y, c_x, c_y, k_1, k_2, p_1, p_2, k_3, k_4, k_5, k_6 , s_1, s_2, s_3,
+ s_4, \tau_x, \tau_y)\f$ If one of parameters is not estimated, it's deviation is equals to zero.
+@param stdDeviationsExtrinsics Output vector of standard deviations estimated for extrinsic
+parameters. Order of deviations values: \f$(R_0, T_0, \dotsc , R_{M - 1}, T_{M - 1})\f$ where M is
+the number of pattern views. \f$R_i, T_i\f$ are concatenated 1x3 vectors.
+ @param perViewErrors Output vector of the RMS re-projection error estimated for each pattern view.
+@param flags Different flags that may be zero or a combination of the following values:
+- @ref CALIB_USE_INTRINSIC_GUESS cameraMatrix contains valid initial values of
+fx, fy, cx, cy that are optimized further. Otherwise, (cx, cy) is initially set to the image
+center ( imageSize is used), and focal distances are computed in a least-squares fashion.
+Note, that if intrinsic parameters are known, there is no need to use this function just to
+estimate extrinsic parameters. Use @ref solvePnP instead.
+- @ref CALIB_FIX_PRINCIPAL_POINT The principal point is not changed during the global
+optimization. It stays at the center or at a different location specified when
+ @ref CALIB_USE_INTRINSIC_GUESS is set too.
+- @ref CALIB_FIX_ASPECT_RATIO The functions consider only fy as a free parameter. The
+ratio fx/fy stays the same as in the input cameraMatrix . When
+ @ref CALIB_USE_INTRINSIC_GUESS is not set, the actual input values of fx and fy are
+ignored, only their ratio is computed and used further.
+- @ref CALIB_ZERO_TANGENT_DIST Tangential distortion coefficients \f$(p_1, p_2)\f$ are set
+to zeros and stay zero.
+- @ref CALIB_FIX_FOCAL_LENGTH The focal length is not changed during the global optimization if
+ @ref CALIB_USE_INTRINSIC_GUESS is set.
+- @ref CALIB_FIX_K1,..., @ref CALIB_FIX_K6 The corresponding radial distortion
+coefficient is not changed during the optimization. If @ref CALIB_USE_INTRINSIC_GUESS is
+set, the coefficient from the supplied distCoeffs matrix is used. Otherwise, it is set to 0.
+- @ref CALIB_RATIONAL_MODEL Coefficients k4, k5, and k6 are enabled. To provide the
+backward compatibility, this extra flag should be explicitly specified to make the
+calibration function use the rational model and return 8 coefficients or more.
+- @ref CALIB_THIN_PRISM_MODEL Coefficients s1, s2, s3 and s4 are enabled. To provide the
+backward compatibility, this extra flag should be explicitly specified to make the
+calibration function use the thin prism model and return 12 coefficients or more.
+- @ref CALIB_FIX_S1_S2_S3_S4 The thin prism distortion coefficients are not changed during
+the optimization. If @ref CALIB_USE_INTRINSIC_GUESS is set, the coefficient from the
+supplied distCoeffs matrix is used. Otherwise, it is set to 0.
+- @ref CALIB_TILTED_MODEL Coefficients tauX and tauY are enabled. To provide the
+backward compatibility, this extra flag should be explicitly specified to make the
+calibration function use the tilted sensor model and return 14 coefficients.
+- @ref CALIB_FIX_TAUX_TAUY The coefficients of the tilted sensor model are not changed during
+the optimization. If @ref CALIB_USE_INTRINSIC_GUESS is set, the coefficient from the
+supplied distCoeffs matrix is used. Otherwise, it is set to 0.
+@param criteria Termination criteria for the iterative optimization algorithm.
+
+@return the overall RMS re-projection error.
+
+The function estimates the intrinsic camera parameters and extrinsic parameters for each of the
+views. The algorithm is based on @cite Zhang2000 and @cite BouguetMCT . The coordinates of 3D object
+points and their corresponding 2D projections in each view must be specified. That may be achieved
+by using an object with known geometry and easily detectable feature points. Such an object is
+called a calibration rig or calibration pattern, and OpenCV has built-in support for a chessboard as
+a calibration rig (see @ref findChessboardCorners). Currently, initialization of intrinsic
+parameters (when @ref CALIB_USE_INTRINSIC_GUESS is not set) is only implemented for planar calibration
+patterns (where Z-coordinates of the object points must be all zeros). 3D calibration rigs can also
+be used as long as initial cameraMatrix is provided.
+
+The algorithm performs the following steps:
+
+- Compute the initial intrinsic parameters (the option only available for planar calibration
+ patterns) or read them from the input parameters. The distortion coefficients are all set to
+ zeros initially unless some of CALIB_FIX_K? are specified.
+
+- Estimate the initial camera pose as if the intrinsic parameters have been already known. This is
+ done using @ref solvePnP .
+
+- Run the global Levenberg-Marquardt optimization algorithm to minimize the reprojection error,
+ that is, the total sum of squared distances between the observed feature points imagePoints and
+ the projected (using the current estimates for camera parameters and the poses) object points
+ objectPoints. See @ref projectPoints for details.
+
+@note
+ If you use a non-square (i.e. non-N-by-N) grid and @ref findChessboardCorners for calibration,
+ and @ref calibrateCamera returns bad values (zero distortion coefficients, \f$c_x\f$ and
+ \f$c_y\f$ very far from the image center, and/or large differences between \f$f_x\f$ and
+ \f$f_y\f$ (ratios of 10:1 or more)), then you are probably using patternSize=cvSize(rows,cols)
+ instead of using patternSize=cvSize(cols,rows) in @ref findChessboardCorners.
+
+@note
+ The function may throw exceptions, if unsupported combination of parameters is provided or
+ the system is underconstrained.
+
+@sa
+ calibrateCameraRO, findChessboardCorners, solvePnP, initCameraMatrix2D, stereoCalibrate,
+ undistort
+ */
+CV_EXPORTS_AS(calibrateCameraExtended) double calibrateCamera( InputArrayOfArrays objectPoints,
+ InputArrayOfArrays imagePoints, Size imageSize,
+ InputOutputArray cameraMatrix, InputOutputArray distCoeffs,
+ OutputArrayOfArrays rvecs, OutputArrayOfArrays tvecs,
+ OutputArray stdDeviationsIntrinsics,
+ OutputArray stdDeviationsExtrinsics,
+ OutputArray perViewErrors,
+ int flags = 0, TermCriteria criteria = TermCriteria(
+ TermCriteria::COUNT + TermCriteria::EPS, 30, DBL_EPSILON) );
+
+/** @overload */
+CV_EXPORTS_W double calibrateCamera( InputArrayOfArrays objectPoints,
+ InputArrayOfArrays imagePoints, Size imageSize,
+ InputOutputArray cameraMatrix, InputOutputArray distCoeffs,
+ OutputArrayOfArrays rvecs, OutputArrayOfArrays tvecs,
+ int flags = 0, TermCriteria criteria = TermCriteria(
+ TermCriteria::COUNT + TermCriteria::EPS, 30, DBL_EPSILON) );
+
+/** @brief Finds the camera intrinsic and extrinsic parameters from several views of a calibration pattern.
+
+This function is an extension of #calibrateCamera with the method of releasing object which was
+proposed in @cite strobl2011iccv. In many common cases with inaccurate, unmeasured, roughly planar
+targets (calibration plates), this method can dramatically improve the precision of the estimated
+camera parameters. Both the object-releasing method and standard method are supported by this
+function. Use the parameter **iFixedPoint** for method selection. In the internal implementation,
+#calibrateCamera is a wrapper for this function.
+
+@param objectPoints Vector of vectors of calibration pattern points in the calibration pattern
+coordinate space. See #calibrateCamera for details. If the method of releasing object to be used,
+the identical calibration board must be used in each view and it must be fully visible, and all
+objectPoints[i] must be the same and all points should be roughly close to a plane. **The calibration
+target has to be rigid, or at least static if the camera (rather than the calibration target) is
+shifted for grabbing images.**
+@param imagePoints Vector of vectors of the projections of calibration pattern points. See
+#calibrateCamera for details.
+@param imageSize Size of the image used only to initialize the intrinsic camera matrix.
+@param iFixedPoint The index of the 3D object point in objectPoints[0] to be fixed. It also acts as
+a switch for calibration method selection. If object-releasing method to be used, pass in the
+parameter in the range of [1, objectPoints[0].size()-2], otherwise a value out of this range will
+make standard calibration method selected. Usually the top-right corner point of the calibration
+board grid is recommended to be fixed when object-releasing method being utilized. According to
+\cite strobl2011iccv, two other points are also fixed. In this implementation, objectPoints[0].front
+and objectPoints[0].back.z are used. With object-releasing method, accurate rvecs, tvecs and
+newObjPoints are only possible if coordinates of these three fixed points are accurate enough.
+@param cameraMatrix Output 3x3 floating-point camera matrix. See #calibrateCamera for details.
+@param distCoeffs Output vector of distortion coefficients. See #calibrateCamera for details.
+@param rvecs Output vector of rotation vectors estimated for each pattern view. See #calibrateCamera
+for details.
+@param tvecs Output vector of translation vectors estimated for each pattern view.
+@param newObjPoints The updated output vector of calibration pattern points. The coordinates might
+be scaled based on three fixed points. The returned coordinates are accurate only if the above
+mentioned three fixed points are accurate. If not needed, noArray() can be passed in. This parameter
+is ignored with standard calibration method.
+@param stdDeviationsIntrinsics Output vector of standard deviations estimated for intrinsic parameters.
+See #calibrateCamera for details.
+@param stdDeviationsExtrinsics Output vector of standard deviations estimated for extrinsic parameters.
+See #calibrateCamera for details.
+@param stdDeviationsObjPoints Output vector of standard deviations estimated for refined coordinates
+of calibration pattern points. It has the same size and order as objectPoints[0] vector. This
+parameter is ignored with standard calibration method.
+ @param perViewErrors Output vector of the RMS re-projection error estimated for each pattern view.
+@param flags Different flags that may be zero or a combination of some predefined values. See
+#calibrateCamera for details. If the method of releasing object is used, the calibration time may
+be much longer. CALIB_USE_QR or CALIB_USE_LU could be used for faster calibration with potentially
+less precise and less stable in some rare cases.
+@param criteria Termination criteria for the iterative optimization algorithm.
+
+@return the overall RMS re-projection error.
+
+The function estimates the intrinsic camera parameters and extrinsic parameters for each of the
+views. The algorithm is based on @cite Zhang2000, @cite BouguetMCT and @cite strobl2011iccv. See
+#calibrateCamera for other detailed explanations.
+@sa
+ calibrateCamera, findChessboardCorners, solvePnP, initCameraMatrix2D, stereoCalibrate, undistort
+ */
+CV_EXPORTS_AS(calibrateCameraROExtended) double calibrateCameraRO( InputArrayOfArrays objectPoints,
+ InputArrayOfArrays imagePoints, Size imageSize, int iFixedPoint,
+ InputOutputArray cameraMatrix, InputOutputArray distCoeffs,
+ OutputArrayOfArrays rvecs, OutputArrayOfArrays tvecs,
+ OutputArray newObjPoints,
+ OutputArray stdDeviationsIntrinsics,
+ OutputArray stdDeviationsExtrinsics,
+ OutputArray stdDeviationsObjPoints,
+ OutputArray perViewErrors,
+ int flags = 0, TermCriteria criteria = TermCriteria(
+ TermCriteria::COUNT + TermCriteria::EPS, 30, DBL_EPSILON) );
+
+/** @overload */
+CV_EXPORTS_W double calibrateCameraRO( InputArrayOfArrays objectPoints,
+ InputArrayOfArrays imagePoints, Size imageSize, int iFixedPoint,
+ InputOutputArray cameraMatrix, InputOutputArray distCoeffs,
+ OutputArrayOfArrays rvecs, OutputArrayOfArrays tvecs,
+ OutputArray newObjPoints,
+ int flags = 0, TermCriteria criteria = TermCriteria(
+ TermCriteria::COUNT + TermCriteria::EPS, 30, DBL_EPSILON) );
+
+/** @brief Computes useful camera characteristics from the camera intrinsic matrix.
+
+@param cameraMatrix Input camera intrinsic matrix that can be estimated by #calibrateCamera or
+#stereoCalibrate .
+@param imageSize Input image size in pixels.
+@param apertureWidth Physical width in mm of the sensor.
+@param apertureHeight Physical height in mm of the sensor.
+@param fovx Output field of view in degrees along the horizontal sensor axis.
+@param fovy Output field of view in degrees along the vertical sensor axis.
+@param focalLength Focal length of the lens in mm.
+@param principalPoint Principal point in mm.
+@param aspectRatio \f$f_y/f_x\f$
+
+The function computes various useful camera characteristics from the previously estimated camera
+matrix.
+
+@note
+ Do keep in mind that the unity measure 'mm' stands for whatever unit of measure one chooses for
+ the chessboard pitch (it can thus be any value).
+ */
+CV_EXPORTS_W void calibrationMatrixValues( InputArray cameraMatrix, Size imageSize,
+ double apertureWidth, double apertureHeight,
+ CV_OUT double& fovx, CV_OUT double& fovy,
+ CV_OUT double& focalLength, CV_OUT Point2d& principalPoint,
+ CV_OUT double& aspectRatio );
+
+/** @brief Calibrates a stereo camera set up. This function finds the intrinsic parameters
+for each of the two cameras and the extrinsic parameters between the two cameras.
+
+@param objectPoints Vector of vectors of the calibration pattern points. The same structure as
+in @ref calibrateCamera. For each pattern view, both cameras need to see the same object
+points. Therefore, objectPoints.size(), imagePoints1.size(), and imagePoints2.size() need to be
+equal as well as objectPoints[i].size(), imagePoints1[i].size(), and imagePoints2[i].size() need to
+be equal for each i.
+@param imagePoints1 Vector of vectors of the projections of the calibration pattern points,
+observed by the first camera. The same structure as in @ref calibrateCamera.
+@param imagePoints2 Vector of vectors of the projections of the calibration pattern points,
+observed by the second camera. The same structure as in @ref calibrateCamera.
+@param cameraMatrix1 Input/output camera intrinsic matrix for the first camera, the same as in
+@ref calibrateCamera. Furthermore, for the stereo case, additional flags may be used, see below.
+@param distCoeffs1 Input/output vector of distortion coefficients, the same as in
+@ref calibrateCamera.
+@param cameraMatrix2 Input/output second camera intrinsic matrix for the second camera. See description for
+cameraMatrix1.
+@param distCoeffs2 Input/output lens distortion coefficients for the second camera. See
+description for distCoeffs1.
+@param imageSize Size of the image used only to initialize the camera intrinsic matrices.
+@param R Output rotation matrix. Together with the translation vector T, this matrix brings
+points given in the first camera's coordinate system to points in the second camera's
+coordinate system. In more technical terms, the tuple of R and T performs a change of basis
+from the first camera's coordinate system to the second camera's coordinate system. Due to its
+duality, this tuple is equivalent to the position of the first camera with respect to the
+second camera coordinate system.
+@param T Output translation vector, see description above.
+@param E Output essential matrix.
+@param F Output fundamental matrix.
+@param rvecs Output vector of rotation vectors ( @ref Rodrigues ) estimated for each pattern view in the
+coordinate system of the first camera of the stereo pair (e.g. std::vector). More in detail, each
+i-th rotation vector together with the corresponding i-th translation vector (see the next output parameter
+description) brings the calibration pattern from the object coordinate space (in which object points are
+specified) to the camera coordinate space of the first camera of the stereo pair. In more technical terms,
+the tuple of the i-th rotation and translation vector performs a change of basis from object coordinate space
+to camera coordinate space of the first camera of the stereo pair.
+@param tvecs Output vector of translation vectors estimated for each pattern view, see parameter description
+of previous output parameter ( rvecs ).
+@param perViewErrors Output vector of the RMS re-projection error estimated for each pattern view.
+@param flags Different flags that may be zero or a combination of the following values:
+- @ref CALIB_FIX_INTRINSIC Fix cameraMatrix? and distCoeffs? so that only R, T, E, and F
+matrices are estimated.
+- @ref CALIB_USE_INTRINSIC_GUESS Optimize some or all of the intrinsic parameters
+according to the specified flags. Initial values are provided by the user.
+- @ref CALIB_USE_EXTRINSIC_GUESS R and T contain valid initial values that are optimized further.
+Otherwise R and T are initialized to the median value of the pattern views (each dimension separately).
+- @ref CALIB_FIX_PRINCIPAL_POINT Fix the principal points during the optimization.
+- @ref CALIB_FIX_FOCAL_LENGTH Fix \f$f^{(j)}_x\f$ and \f$f^{(j)}_y\f$ .
+- @ref CALIB_FIX_ASPECT_RATIO Optimize \f$f^{(j)}_y\f$ . Fix the ratio \f$f^{(j)}_x/f^{(j)}_y\f$
+.
+- @ref CALIB_SAME_FOCAL_LENGTH Enforce \f$f^{(0)}_x=f^{(1)}_x\f$ and \f$f^{(0)}_y=f^{(1)}_y\f$ .
+- @ref CALIB_ZERO_TANGENT_DIST Set tangential distortion coefficients for each camera to
+zeros and fix there.
+- @ref CALIB_FIX_K1,..., @ref CALIB_FIX_K6 Do not change the corresponding radial
+distortion coefficient during the optimization. If @ref CALIB_USE_INTRINSIC_GUESS is set,
+the coefficient from the supplied distCoeffs matrix is used. Otherwise, it is set to 0.
+- @ref CALIB_RATIONAL_MODEL Enable coefficients k4, k5, and k6. To provide the backward
+compatibility, this extra flag should be explicitly specified to make the calibration
+function use the rational model and return 8 coefficients. If the flag is not set, the
+function computes and returns only 5 distortion coefficients.
+- @ref CALIB_THIN_PRISM_MODEL Coefficients s1, s2, s3 and s4 are enabled. To provide the
+backward compatibility, this extra flag should be explicitly specified to make the
+calibration function use the thin prism model and return 12 coefficients. If the flag is not
+set, the function computes and returns only 5 distortion coefficients.
+- @ref CALIB_FIX_S1_S2_S3_S4 The thin prism distortion coefficients are not changed during
+the optimization. If @ref CALIB_USE_INTRINSIC_GUESS is set, the coefficient from the
+supplied distCoeffs matrix is used. Otherwise, it is set to 0.
+- @ref CALIB_TILTED_MODEL Coefficients tauX and tauY are enabled. To provide the
+backward compatibility, this extra flag should be explicitly specified to make the
+calibration function use the tilted sensor model and return 14 coefficients. If the flag is not
+set, the function computes and returns only 5 distortion coefficients.
+- @ref CALIB_FIX_TAUX_TAUY The coefficients of the tilted sensor model are not changed during
+the optimization. If @ref CALIB_USE_INTRINSIC_GUESS is set, the coefficient from the
+supplied distCoeffs matrix is used. Otherwise, it is set to 0.
+@param criteria Termination criteria for the iterative optimization algorithm.
+
+The function estimates the transformation between two cameras making a stereo pair. If one computes
+the poses of an object relative to the first camera and to the second camera,
+( \f$R_1\f$,\f$T_1\f$ ) and (\f$R_2\f$,\f$T_2\f$), respectively, for a stereo camera where the
+relative position and orientation between the two cameras are fixed, then those poses definitely
+relate to each other. This means, if the relative position and orientation (\f$R\f$,\f$T\f$) of the
+two cameras is known, it is possible to compute (\f$R_2\f$,\f$T_2\f$) when (\f$R_1\f$,\f$T_1\f$) is
+given. This is what the described function does. It computes (\f$R\f$,\f$T\f$) such that:
+
+\f[R_2=R R_1\f]
+\f[T_2=R T_1 + T.\f]
+
+Therefore, one can compute the coordinate representation of a 3D point for the second camera's
+coordinate system when given the point's coordinate representation in the first camera's coordinate
+system:
+
+\f[\begin{bmatrix}
+X_2 \\
+Y_2 \\
+Z_2 \\
+1
+\end{bmatrix} = \begin{bmatrix}
+R & T \\
+0 & 1
+\end{bmatrix} \begin{bmatrix}
+X_1 \\
+Y_1 \\
+Z_1 \\
+1
+\end{bmatrix}.\f]
+
+
+Optionally, it computes the essential matrix E:
+
+\f[E= \vecthreethree{0}{-T_2}{T_1}{T_2}{0}{-T_0}{-T_1}{T_0}{0} R\f]
+
+where \f$T_i\f$ are components of the translation vector \f$T\f$ : \f$T=[T_0, T_1, T_2]^T\f$ .
+And the function can also compute the fundamental matrix F:
+
+\f[F = cameraMatrix2^{-T}\cdot E \cdot cameraMatrix1^{-1}\f]
+
+Besides the stereo-related information, the function can also perform a full calibration of each of
+the two cameras. However, due to the high dimensionality of the parameter space and noise in the
+input data, the function can diverge from the correct solution. If the intrinsic parameters can be
+estimated with high accuracy for each of the cameras individually (for example, using
+#calibrateCamera ), you are recommended to do so and then pass @ref CALIB_FIX_INTRINSIC flag to the
+function along with the computed intrinsic parameters. Otherwise, if all the parameters are
+estimated at once, it makes sense to restrict some parameters, for example, pass
+ @ref CALIB_SAME_FOCAL_LENGTH and @ref CALIB_ZERO_TANGENT_DIST flags, which is usually a
+reasonable assumption.
+
+Similarly to #calibrateCamera, the function minimizes the total re-projection error for all the
+points in all the available views from both cameras. The function returns the final value of the
+re-projection error.
+ */
+CV_EXPORTS_AS(stereoCalibrateExtended) double stereoCalibrate( InputArrayOfArrays objectPoints,
+ InputArrayOfArrays imagePoints1, InputArrayOfArrays imagePoints2,
+ InputOutputArray cameraMatrix1, InputOutputArray distCoeffs1,
+ InputOutputArray cameraMatrix2, InputOutputArray distCoeffs2,
+ Size imageSize, InputOutputArray R, InputOutputArray T, OutputArray E, OutputArray F,
+ OutputArrayOfArrays rvecs, OutputArrayOfArrays tvecs, OutputArray perViewErrors, int flags = CALIB_FIX_INTRINSIC,
+ TermCriteria criteria = TermCriteria(TermCriteria::COUNT+TermCriteria::EPS, 30, 1e-6) );
+
+/// @overload
+CV_EXPORTS_W double stereoCalibrate( InputArrayOfArrays objectPoints,
+ InputArrayOfArrays imagePoints1, InputArrayOfArrays imagePoints2,
+ InputOutputArray cameraMatrix1, InputOutputArray distCoeffs1,
+ InputOutputArray cameraMatrix2, InputOutputArray distCoeffs2,
+ Size imageSize, OutputArray R,OutputArray T, OutputArray E, OutputArray F,
+ int flags = CALIB_FIX_INTRINSIC,
+ TermCriteria criteria = TermCriteria(TermCriteria::COUNT+TermCriteria::EPS, 30, 1e-6) );
+
+/// @overload
+CV_EXPORTS_W double stereoCalibrate( InputArrayOfArrays objectPoints,
+ InputArrayOfArrays imagePoints1, InputArrayOfArrays imagePoints2,
+ InputOutputArray cameraMatrix1, InputOutputArray distCoeffs1,
+ InputOutputArray cameraMatrix2, InputOutputArray distCoeffs2,
+ Size imageSize, InputOutputArray R, InputOutputArray T, OutputArray E, OutputArray F,
+ OutputArray perViewErrors, int flags = CALIB_FIX_INTRINSIC,
+ TermCriteria criteria = TermCriteria(TermCriteria::COUNT+TermCriteria::EPS, 30, 1e-6) );
+
+/** @brief Computes rectification transforms for each head of a calibrated stereo camera.
+
+@param cameraMatrix1 First camera intrinsic matrix.
+@param distCoeffs1 First camera distortion parameters.
+@param cameraMatrix2 Second camera intrinsic matrix.
+@param distCoeffs2 Second camera distortion parameters.
+@param imageSize Size of the image used for stereo calibration.
+@param R Rotation matrix from the coordinate system of the first camera to the second camera,
+see @ref stereoCalibrate.
+@param T Translation vector from the coordinate system of the first camera to the second camera,
+see @ref stereoCalibrate.
+@param R1 Output 3x3 rectification transform (rotation matrix) for the first camera. This matrix
+brings points given in the unrectified first camera's coordinate system to points in the rectified
+first camera's coordinate system. In more technical terms, it performs a change of basis from the
+unrectified first camera's coordinate system to the rectified first camera's coordinate system.
+@param R2 Output 3x3 rectification transform (rotation matrix) for the second camera. This matrix
+brings points given in the unrectified second camera's coordinate system to points in the rectified
+second camera's coordinate system. In more technical terms, it performs a change of basis from the
+unrectified second camera's coordinate system to the rectified second camera's coordinate system.
+@param P1 Output 3x4 projection matrix in the new (rectified) coordinate systems for the first
+camera, i.e. it projects points given in the rectified first camera coordinate system into the
+rectified first camera's image.
+@param P2 Output 3x4 projection matrix in the new (rectified) coordinate systems for the second
+camera, i.e. it projects points given in the rectified first camera coordinate system into the
+rectified second camera's image.
+@param Q Output \f$4 \times 4\f$ disparity-to-depth mapping matrix (see @ref reprojectImageTo3D).
+@param flags Operation flags that may be zero or @ref CALIB_ZERO_DISPARITY . If the flag is set,
+the function makes the principal points of each camera have the same pixel coordinates in the
+rectified views. And if the flag is not set, the function may still shift the images in the
+horizontal or vertical direction (depending on the orientation of epipolar lines) to maximize the
+useful image area.
+@param alpha Free scaling parameter. If it is -1 or absent, the function performs the default
+scaling. Otherwise, the parameter should be between 0 and 1. alpha=0 means that the rectified
+images are zoomed and shifted so that only valid pixels are visible (no black areas after
+rectification). alpha=1 means that the rectified image is decimated and shifted so that all the
+pixels from the original images from the cameras are retained in the rectified images (no source
+image pixels are lost). Any intermediate value yields an intermediate result between
+those two extreme cases.
+@param newImageSize New image resolution after rectification. The same size should be passed to
+#initUndistortRectifyMap (see the stereo_calib.cpp sample in OpenCV samples directory). When (0,0)
+is passed (default), it is set to the original imageSize . Setting it to a larger value can help you
+preserve details in the original image, especially when there is a big radial distortion.
+@param validPixROI1 Optional output rectangles inside the rectified images where all the pixels
+are valid. If alpha=0 , the ROIs cover the whole images. Otherwise, they are likely to be smaller
+(see the picture below).
+@param validPixROI2 Optional output rectangles inside the rectified images where all the pixels
+are valid. If alpha=0 , the ROIs cover the whole images. Otherwise, they are likely to be smaller
+(see the picture below).
+
+The function computes the rotation matrices for each camera that (virtually) make both camera image
+planes the same plane. Consequently, this makes all the epipolar lines parallel and thus simplifies
+the dense stereo correspondence problem. The function takes the matrices computed by #stereoCalibrate
+as input. As output, it provides two rotation matrices and also two projection matrices in the new
+coordinates. The function distinguishes the following two cases:
+
+- **Horizontal stereo**: the first and the second camera views are shifted relative to each other
+ mainly along the x-axis (with possible small vertical shift). In the rectified images, the
+ corresponding epipolar lines in the left and right cameras are horizontal and have the same
+ y-coordinate. P1 and P2 look like:
+
+ \f[\texttt{P1} = \begin{bmatrix}
+ f & 0 & cx_1 & 0 \\
+ 0 & f & cy & 0 \\
+ 0 & 0 & 1 & 0
+ \end{bmatrix}\f]
+
+ \f[\texttt{P2} = \begin{bmatrix}
+ f & 0 & cx_2 & T_x \cdot f \\
+ 0 & f & cy & 0 \\
+ 0 & 0 & 1 & 0
+ \end{bmatrix} ,\f]
+
+ \f[\texttt{Q} = \begin{bmatrix}
+ 1 & 0 & 0 & -cx_1 \\
+ 0 & 1 & 0 & -cy \\
+ 0 & 0 & 0 & f \\
+ 0 & 0 & -\frac{1}{T_x} & \frac{cx_1 - cx_2}{T_x}
+ \end{bmatrix} \f]
+
+ where \f$T_x\f$ is a horizontal shift between the cameras and \f$cx_1=cx_2\f$ if
+ @ref CALIB_ZERO_DISPARITY is set.
+
+- **Vertical stereo**: the first and the second camera views are shifted relative to each other
+ mainly in the vertical direction (and probably a bit in the horizontal direction too). The epipolar
+ lines in the rectified images are vertical and have the same x-coordinate. P1 and P2 look like:
+
+ \f[\texttt{P1} = \begin{bmatrix}
+ f & 0 & cx & 0 \\
+ 0 & f & cy_1 & 0 \\
+ 0 & 0 & 1 & 0
+ \end{bmatrix}\f]
+
+ \f[\texttt{P2} = \begin{bmatrix}
+ f & 0 & cx & 0 \\
+ 0 & f & cy_2 & T_y \cdot f \\
+ 0 & 0 & 1 & 0
+ \end{bmatrix},\f]
+
+ \f[\texttt{Q} = \begin{bmatrix}
+ 1 & 0 & 0 & -cx \\
+ 0 & 1 & 0 & -cy_1 \\
+ 0 & 0 & 0 & f \\
+ 0 & 0 & -\frac{1}{T_y} & \frac{cy_1 - cy_2}{T_y}
+ \end{bmatrix} \f]
+
+ where \f$T_y\f$ is a vertical shift between the cameras and \f$cy_1=cy_2\f$ if
+ @ref CALIB_ZERO_DISPARITY is set.
+
+As you can see, the first three columns of P1 and P2 will effectively be the new "rectified" camera
+matrices. The matrices, together with R1 and R2 , can then be passed to #initUndistortRectifyMap to
+initialize the rectification map for each camera.
+
+See below the screenshot from the stereo_calib.cpp sample. Some red horizontal lines pass through
+the corresponding image regions. This means that the images are well rectified, which is what most
+stereo correspondence algorithms rely on. The green rectangles are roi1 and roi2 . You see that
+their interiors are all valid pixels.
+
+
+ */
+CV_EXPORTS_W void stereoRectify( InputArray cameraMatrix1, InputArray distCoeffs1,
+ InputArray cameraMatrix2, InputArray distCoeffs2,
+ Size imageSize, InputArray R, InputArray T,
+ OutputArray R1, OutputArray R2,
+ OutputArray P1, OutputArray P2,
+ OutputArray Q, int flags = CALIB_ZERO_DISPARITY,
+ double alpha = -1, Size newImageSize = Size(),
+ CV_OUT Rect* validPixROI1 = 0, CV_OUT Rect* validPixROI2 = 0 );
+
+/** @brief Computes a rectification transform for an uncalibrated stereo camera.
+
+@param points1 Array of feature points in the first image.
+@param points2 The corresponding points in the second image. The same formats as in
+#findFundamentalMat are supported.
+@param F Input fundamental matrix. It can be computed from the same set of point pairs using
+#findFundamentalMat .
+@param imgSize Size of the image.
+@param H1 Output rectification homography matrix for the first image.
+@param H2 Output rectification homography matrix for the second image.
+@param threshold Optional threshold used to filter out the outliers. If the parameter is greater
+than zero, all the point pairs that do not comply with the epipolar geometry (that is, the points
+for which \f$|\texttt{points2[i]}^T \cdot \texttt{F} \cdot \texttt{points1[i]}|>\texttt{threshold}\f$ )
+are rejected prior to computing the homographies. Otherwise, all the points are considered inliers.
+
+The function computes the rectification transformations without knowing intrinsic parameters of the
+cameras and their relative position in the space, which explains the suffix "uncalibrated". Another
+related difference from #stereoRectify is that the function outputs not the rectification
+transformations in the object (3D) space, but the planar perspective transformations encoded by the
+homography matrices H1 and H2 . The function implements the algorithm @cite Hartley99 .
+
+@note
+ While the algorithm does not need to know the intrinsic parameters of the cameras, it heavily
+ depends on the epipolar geometry. Therefore, if the camera lenses have a significant distortion,
+ it would be better to correct it before computing the fundamental matrix and calling this
+ function. For example, distortion coefficients can be estimated for each head of stereo camera
+ separately by using #calibrateCamera . Then, the images can be corrected using #undistort , or
+ just the point coordinates can be corrected with #undistortPoints .
+ */
+CV_EXPORTS_W bool stereoRectifyUncalibrated( InputArray points1, InputArray points2,
+ InputArray F, Size imgSize,
+ OutputArray H1, OutputArray H2,
+ double threshold = 5 );
+
+//! computes the rectification transformations for 3-head camera, where all the heads are on the same line.
+CV_EXPORTS_W float rectify3Collinear( InputArray cameraMatrix1, InputArray distCoeffs1,
+ InputArray cameraMatrix2, InputArray distCoeffs2,
+ InputArray cameraMatrix3, InputArray distCoeffs3,
+ InputArrayOfArrays imgpt1, InputArrayOfArrays imgpt3,
+ Size imageSize, InputArray R12, InputArray T12,
+ InputArray R13, InputArray T13,
+ OutputArray R1, OutputArray R2, OutputArray R3,
+ OutputArray P1, OutputArray P2, OutputArray P3,
+ OutputArray Q, double alpha, Size newImgSize,
+ CV_OUT Rect* roi1, CV_OUT Rect* roi2, int flags );
+
+/** @brief Returns the new camera intrinsic matrix based on the free scaling parameter.
+
+@param cameraMatrix Input camera intrinsic matrix.
+@param distCoeffs Input vector of distortion coefficients
+\f$\distcoeffs\f$. If the vector is NULL/empty, the zero distortion coefficients are
+assumed.
+@param imageSize Original image size.
+@param alpha Free scaling parameter between 0 (when all the pixels in the undistorted image are
+valid) and 1 (when all the source image pixels are retained in the undistorted image). See
+#stereoRectify for details.
+@param newImgSize Image size after rectification. By default, it is set to imageSize .
+@param validPixROI Optional output rectangle that outlines all-good-pixels region in the
+undistorted image. See roi1, roi2 description in #stereoRectify .
+@param centerPrincipalPoint Optional flag that indicates whether in the new camera intrinsic matrix the
+principal point should be at the image center or not. By default, the principal point is chosen to
+best fit a subset of the source image (determined by alpha) to the corrected image.
+@return new_camera_matrix Output new camera intrinsic matrix.
+
+The function computes and returns the optimal new camera intrinsic matrix based on the free scaling parameter.
+By varying this parameter, you may retrieve only sensible pixels alpha=0 , keep all the original
+image pixels if there is valuable information in the corners alpha=1 , or get something in between.
+When alpha\>0 , the undistorted result is likely to have some black pixels corresponding to
+"virtual" pixels outside of the captured distorted image. The original camera intrinsic matrix, distortion
+coefficients, the computed new camera intrinsic matrix, and newImageSize should be passed to
+#initUndistortRectifyMap to produce the maps for #remap .
+ */
+CV_EXPORTS_W Mat getOptimalNewCameraMatrix( InputArray cameraMatrix, InputArray distCoeffs,
+ Size imageSize, double alpha, Size newImgSize = Size(),
+ CV_OUT Rect* validPixROI = 0,
+ bool centerPrincipalPoint = false);
+
+/** @brief Computes Hand-Eye calibration: \f$_{}^{g}\textrm{T}_c\f$
+
+@param[in] R_gripper2base Rotation part extracted from the homogeneous matrix that transforms a point
+expressed in the gripper frame to the robot base frame (\f$_{}^{b}\textrm{T}_g\f$).
+This is a vector (`vector`) that contains the rotation, `(3x3)` rotation matrices or `(3x1)` rotation vectors,
+for all the transformations from gripper frame to robot base frame.
+@param[in] t_gripper2base Translation part extracted from the homogeneous matrix that transforms a point
+expressed in the gripper frame to the robot base frame (\f$_{}^{b}\textrm{T}_g\f$).
+This is a vector (`vector`) that contains the `(3x1)` translation vectors for all the transformations
+from gripper frame to robot base frame.
+@param[in] R_target2cam Rotation part extracted from the homogeneous matrix that transforms a point
+expressed in the target frame to the camera frame (\f$_{}^{c}\textrm{T}_t\f$).
+This is a vector (`vector`) that contains the rotation, `(3x3)` rotation matrices or `(3x1)` rotation vectors,
+for all the transformations from calibration target frame to camera frame.
+@param[in] t_target2cam Rotation part extracted from the homogeneous matrix that transforms a point
+expressed in the target frame to the camera frame (\f$_{}^{c}\textrm{T}_t\f$).
+This is a vector (`vector`) that contains the `(3x1)` translation vectors for all the transformations
+from calibration target frame to camera frame.
+@param[out] R_cam2gripper Estimated `(3x3)` rotation part extracted from the homogeneous matrix that transforms a point
+expressed in the camera frame to the gripper frame (\f$_{}^{g}\textrm{T}_c\f$).
+@param[out] t_cam2gripper Estimated `(3x1)` translation part extracted from the homogeneous matrix that transforms a point
+expressed in the camera frame to the gripper frame (\f$_{}^{g}\textrm{T}_c\f$).
+@param[in] method One of the implemented Hand-Eye calibration method, see cv::HandEyeCalibrationMethod
+
+The function performs the Hand-Eye calibration using various methods. One approach consists in estimating the
+rotation then the translation (separable solutions) and the following methods are implemented:
+ - R. Tsai, R. Lenz A New Technique for Fully Autonomous and Efficient 3D Robotics Hand/EyeCalibration \cite Tsai89
+ - F. Park, B. Martin Robot Sensor Calibration: Solving AX = XB on the Euclidean Group \cite Park94
+ - R. Horaud, F. Dornaika Hand-Eye Calibration \cite Horaud95
+
+Another approach consists in estimating simultaneously the rotation and the translation (simultaneous solutions),
+with the following implemented methods:
+ - N. Andreff, R. Horaud, B. Espiau On-line Hand-Eye Calibration \cite Andreff99
+ - K. Daniilidis Hand-Eye Calibration Using Dual Quaternions \cite Daniilidis98
+
+The following picture describes the Hand-Eye calibration problem where the transformation between a camera ("eye")
+mounted on a robot gripper ("hand") has to be estimated. This configuration is called eye-in-hand.
+
+The eye-to-hand configuration consists in a static camera observing a calibration pattern mounted on the robot
+end-effector. The transformation from the camera to the robot base frame can then be estimated by inputting
+the suitable transformations to the function, see below.
+
+
+
+The calibration procedure is the following:
+ - a static calibration pattern is used to estimate the transformation between the target frame
+ and the camera frame
+ - the robot gripper is moved in order to acquire several poses
+ - for each pose, the homogeneous transformation between the gripper frame and the robot base frame is recorded using for
+ instance the robot kinematics
+\f[
+ \begin{bmatrix}
+ X_b\\
+ Y_b\\
+ Z_b\\
+ 1
+ \end{bmatrix}
+ =
+ \begin{bmatrix}
+ _{}^{b}\textrm{R}_g & _{}^{b}\textrm{t}_g \\
+ 0_{1 \times 3} & 1
+ \end{bmatrix}
+ \begin{bmatrix}
+ X_g\\
+ Y_g\\
+ Z_g\\
+ 1
+ \end{bmatrix}
+\f]
+ - for each pose, the homogeneous transformation between the calibration target frame and the camera frame is recorded using
+ for instance a pose estimation method (PnP) from 2D-3D point correspondences
+\f[
+ \begin{bmatrix}
+ X_c\\
+ Y_c\\
+ Z_c\\
+ 1
+ \end{bmatrix}
+ =
+ \begin{bmatrix}
+ _{}^{c}\textrm{R}_t & _{}^{c}\textrm{t}_t \\
+ 0_{1 \times 3} & 1
+ \end{bmatrix}
+ \begin{bmatrix}
+ X_t\\
+ Y_t\\
+ Z_t\\
+ 1
+ \end{bmatrix}
+\f]
+
+The Hand-Eye calibration procedure returns the following homogeneous transformation
+\f[
+ \begin{bmatrix}
+ X_g\\
+ Y_g\\
+ Z_g\\
+ 1
+ \end{bmatrix}
+ =
+ \begin{bmatrix}
+ _{}^{g}\textrm{R}_c & _{}^{g}\textrm{t}_c \\
+ 0_{1 \times 3} & 1
+ \end{bmatrix}
+ \begin{bmatrix}
+ X_c\\
+ Y_c\\
+ Z_c\\
+ 1
+ \end{bmatrix}
+\f]
+
+This problem is also known as solving the \f$\mathbf{A}\mathbf{X}=\mathbf{X}\mathbf{B}\f$ equation:
+ - for an eye-in-hand configuration
+\f[
+ \begin{align*}
+ ^{b}{\textrm{T}_g}^{(1)} \hspace{0.2em} ^{g}\textrm{T}_c \hspace{0.2em} ^{c}{\textrm{T}_t}^{(1)} &=
+ \hspace{0.1em} ^{b}{\textrm{T}_g}^{(2)} \hspace{0.2em} ^{g}\textrm{T}_c \hspace{0.2em} ^{c}{\textrm{T}_t}^{(2)} \\
+
+ (^{b}{\textrm{T}_g}^{(2)})^{-1} \hspace{0.2em} ^{b}{\textrm{T}_g}^{(1)} \hspace{0.2em} ^{g}\textrm{T}_c &=
+ \hspace{0.1em} ^{g}\textrm{T}_c \hspace{0.2em} ^{c}{\textrm{T}_t}^{(2)} (^{c}{\textrm{T}_t}^{(1)})^{-1} \\
+
+ \textrm{A}_i \textrm{X} &= \textrm{X} \textrm{B}_i \\
+ \end{align*}
+\f]
+
+ - for an eye-to-hand configuration
+\f[
+ \begin{align*}
+ ^{g}{\textrm{T}_b}^{(1)} \hspace{0.2em} ^{b}\textrm{T}_c \hspace{0.2em} ^{c}{\textrm{T}_t}^{(1)} &=
+ \hspace{0.1em} ^{g}{\textrm{T}_b}^{(2)} \hspace{0.2em} ^{b}\textrm{T}_c \hspace{0.2em} ^{c}{\textrm{T}_t}^{(2)} \\
+
+ (^{g}{\textrm{T}_b}^{(2)})^{-1} \hspace{0.2em} ^{g}{\textrm{T}_b}^{(1)} \hspace{0.2em} ^{b}\textrm{T}_c &=
+ \hspace{0.1em} ^{b}\textrm{T}_c \hspace{0.2em} ^{c}{\textrm{T}_t}^{(2)} (^{c}{\textrm{T}_t}^{(1)})^{-1} \\
+
+ \textrm{A}_i \textrm{X} &= \textrm{X} \textrm{B}_i \\
+ \end{align*}
+\f]
+
+\note
+Additional information can be found on this [website](http://campar.in.tum.de/Chair/HandEyeCalibration).
+\note
+A minimum of 2 motions with non parallel rotation axes are necessary to determine the hand-eye transformation.
+So at least 3 different poses are required, but it is strongly recommended to use many more poses.
+
+ */
+CV_EXPORTS_W void calibrateHandEye( InputArrayOfArrays R_gripper2base, InputArrayOfArrays t_gripper2base,
+ InputArrayOfArrays R_target2cam, InputArrayOfArrays t_target2cam,
+ OutputArray R_cam2gripper, OutputArray t_cam2gripper,
+ HandEyeCalibrationMethod method=CALIB_HAND_EYE_TSAI );
+
+/** @brief Computes Robot-World/Hand-Eye calibration: \f$_{}^{w}\textrm{T}_b\f$ and \f$_{}^{c}\textrm{T}_g\f$
+
+@param[in] R_world2cam Rotation part extracted from the homogeneous matrix that transforms a point
+expressed in the world frame to the camera frame (\f$_{}^{c}\textrm{T}_w\f$).
+This is a vector (`vector`) that contains the rotation, `(3x3)` rotation matrices or `(3x1)` rotation vectors,
+for all the transformations from world frame to the camera frame.
+@param[in] t_world2cam Translation part extracted from the homogeneous matrix that transforms a point
+expressed in the world frame to the camera frame (\f$_{}^{c}\textrm{T}_w\f$).
+This is a vector (`vector`) that contains the `(3x1)` translation vectors for all the transformations
+from world frame to the camera frame.
+@param[in] R_base2gripper Rotation part extracted from the homogeneous matrix that transforms a point
+expressed in the robot base frame to the gripper frame (\f$_{}^{g}\textrm{T}_b\f$).
+This is a vector (`vector`) that contains the rotation, `(3x3)` rotation matrices or `(3x1)` rotation vectors,
+for all the transformations from robot base frame to the gripper frame.
+@param[in] t_base2gripper Rotation part extracted from the homogeneous matrix that transforms a point
+expressed in the robot base frame to the gripper frame (\f$_{}^{g}\textrm{T}_b\f$).
+This is a vector (`vector`) that contains the `(3x1)` translation vectors for all the transformations
+from robot base frame to the gripper frame.
+@param[out] R_base2world Estimated `(3x3)` rotation part extracted from the homogeneous matrix that transforms a point
+expressed in the robot base frame to the world frame (\f$_{}^{w}\textrm{T}_b\f$).
+@param[out] t_base2world Estimated `(3x1)` translation part extracted from the homogeneous matrix that transforms a point
+expressed in the robot base frame to the world frame (\f$_{}^{w}\textrm{T}_b\f$).
+@param[out] R_gripper2cam Estimated `(3x3)` rotation part extracted from the homogeneous matrix that transforms a point
+expressed in the gripper frame to the camera frame (\f$_{}^{c}\textrm{T}_g\f$).
+@param[out] t_gripper2cam Estimated `(3x1)` translation part extracted from the homogeneous matrix that transforms a point
+expressed in the gripper frame to the camera frame (\f$_{}^{c}\textrm{T}_g\f$).
+@param[in] method One of the implemented Robot-World/Hand-Eye calibration method, see cv::RobotWorldHandEyeCalibrationMethod
+
+The function performs the Robot-World/Hand-Eye calibration using various methods. One approach consists in estimating the
+rotation then the translation (separable solutions):
+ - M. Shah, Solving the robot-world/hand-eye calibration problem using the kronecker product \cite Shah2013SolvingTR
+
+Another approach consists in estimating simultaneously the rotation and the translation (simultaneous solutions),
+with the following implemented method:
+ - A. Li, L. Wang, and D. Wu, Simultaneous robot-world and hand-eye calibration using dual-quaternions and kronecker product \cite Li2010SimultaneousRA
+
+The following picture describes the Robot-World/Hand-Eye calibration problem where the transformations between a robot and a world frame
+and between a robot gripper ("hand") and a camera ("eye") mounted at the robot end-effector have to be estimated.
+
+
+
+The calibration procedure is the following:
+ - a static calibration pattern is used to estimate the transformation between the target frame
+ and the camera frame
+ - the robot gripper is moved in order to acquire several poses
+ - for each pose, the homogeneous transformation between the gripper frame and the robot base frame is recorded using for
+ instance the robot kinematics
+\f[
+ \begin{bmatrix}
+ X_g\\
+ Y_g\\
+ Z_g\\
+ 1
+ \end{bmatrix}
+ =
+ \begin{bmatrix}
+ _{}^{g}\textrm{R}_b & _{}^{g}\textrm{t}_b \\
+ 0_{1 \times 3} & 1
+ \end{bmatrix}
+ \begin{bmatrix}
+ X_b\\
+ Y_b\\
+ Z_b\\
+ 1
+ \end{bmatrix}
+\f]
+ - for each pose, the homogeneous transformation between the calibration target frame (the world frame) and the camera frame is recorded using
+ for instance a pose estimation method (PnP) from 2D-3D point correspondences
+\f[
+ \begin{bmatrix}
+ X_c\\
+ Y_c\\
+ Z_c\\
+ 1
+ \end{bmatrix}
+ =
+ \begin{bmatrix}
+ _{}^{c}\textrm{R}_w & _{}^{c}\textrm{t}_w \\
+ 0_{1 \times 3} & 1
+ \end{bmatrix}
+ \begin{bmatrix}
+ X_w\\
+ Y_w\\
+ Z_w\\
+ 1
+ \end{bmatrix}
+\f]
+
+The Robot-World/Hand-Eye calibration procedure returns the following homogeneous transformations
+\f[
+ \begin{bmatrix}
+ X_w\\
+ Y_w\\
+ Z_w\\
+ 1
+ \end{bmatrix}
+ =
+ \begin{bmatrix}
+ _{}^{w}\textrm{R}_b & _{}^{w}\textrm{t}_b \\
+ 0_{1 \times 3} & 1
+ \end{bmatrix}
+ \begin{bmatrix}
+ X_b\\
+ Y_b\\
+ Z_b\\
+ 1
+ \end{bmatrix}
+\f]
+\f[
+ \begin{bmatrix}
+ X_c\\
+ Y_c\\
+ Z_c\\
+ 1
+ \end{bmatrix}
+ =
+ \begin{bmatrix}
+ _{}^{c}\textrm{R}_g & _{}^{c}\textrm{t}_g \\
+ 0_{1 \times 3} & 1
+ \end{bmatrix}
+ \begin{bmatrix}
+ X_g\\
+ Y_g\\
+ Z_g\\
+ 1
+ \end{bmatrix}
+\f]
+
+This problem is also known as solving the \f$\mathbf{A}\mathbf{X}=\mathbf{Z}\mathbf{B}\f$ equation, with:
+ - \f$\mathbf{A} \Leftrightarrow \hspace{0.1em} _{}^{c}\textrm{T}_w\f$
+ - \f$\mathbf{X} \Leftrightarrow \hspace{0.1em} _{}^{w}\textrm{T}_b\f$
+ - \f$\mathbf{Z} \Leftrightarrow \hspace{0.1em} _{}^{c}\textrm{T}_g\f$
+ - \f$\mathbf{B} \Leftrightarrow \hspace{0.1em} _{}^{g}\textrm{T}_b\f$
+
+\note
+At least 3 measurements are required (input vectors size must be greater or equal to 3).
+
+ */
+CV_EXPORTS_W void calibrateRobotWorldHandEye( InputArrayOfArrays R_world2cam, InputArrayOfArrays t_world2cam,
+ InputArrayOfArrays R_base2gripper, InputArrayOfArrays t_base2gripper,
+ OutputArray R_base2world, OutputArray t_base2world,
+ OutputArray R_gripper2cam, OutputArray t_gripper2cam,
+ RobotWorldHandEyeCalibrationMethod method=CALIB_ROBOT_WORLD_HAND_EYE_SHAH );
+
+/** @brief Converts points from Euclidean to homogeneous space.
+
+@param src Input vector of N-dimensional points.
+@param dst Output vector of N+1-dimensional points.
+
+The function converts points from Euclidean to homogeneous space by appending 1's to the tuple of
+point coordinates. That is, each point (x1, x2, ..., xn) is converted to (x1, x2, ..., xn, 1).
+ */
+CV_EXPORTS_W void convertPointsToHomogeneous( InputArray src, OutputArray dst );
+
+/** @brief Converts points from homogeneous to Euclidean space.
+
+@param src Input vector of N-dimensional points.
+@param dst Output vector of N-1-dimensional points.
+
+The function converts points homogeneous to Euclidean space using perspective projection. That is,
+each point (x1, x2, ... x(n-1), xn) is converted to (x1/xn, x2/xn, ..., x(n-1)/xn). When xn=0, the
+output point coordinates will be (0,0,0,...).
+ */
+CV_EXPORTS_W void convertPointsFromHomogeneous( InputArray src, OutputArray dst );
+
+/** @brief Converts points to/from homogeneous coordinates.
+
+@param src Input array or vector of 2D, 3D, or 4D points.
+@param dst Output vector of 2D, 3D, or 4D points.
+
+The function converts 2D or 3D points from/to homogeneous coordinates by calling either
+#convertPointsToHomogeneous or #convertPointsFromHomogeneous.
+
+@note The function is obsolete. Use one of the previous two functions instead.
+ */
+CV_EXPORTS void convertPointsHomogeneous( InputArray src, OutputArray dst );
+
+/** @brief Calculates a fundamental matrix from the corresponding points in two images.
+
+@param points1 Array of N points from the first image. The point coordinates should be
+floating-point (single or double precision).
+@param points2 Array of the second image points of the same size and format as points1 .
+@param method Method for computing a fundamental matrix.
+- @ref FM_7POINT for a 7-point algorithm. \f$N = 7\f$
+- @ref FM_8POINT for an 8-point algorithm. \f$N \ge 8\f$
+- @ref FM_RANSAC for the RANSAC algorithm. \f$N \ge 8\f$
+- @ref FM_LMEDS for the LMedS algorithm. \f$N \ge 8\f$
+@param ransacReprojThreshold Parameter used only for RANSAC. It is the maximum distance from a point to an epipolar
+line in pixels, beyond which the point is considered an outlier and is not used for computing the
+final fundamental matrix. It can be set to something like 1-3, depending on the accuracy of the
+point localization, image resolution, and the image noise.
+@param confidence Parameter used for the RANSAC and LMedS methods only. It specifies a desirable level
+of confidence (probability) that the estimated matrix is correct.
+@param[out] mask optional output mask
+@param maxIters The maximum number of robust method iterations.
+
+The epipolar geometry is described by the following equation:
+
+\f[[p_2; 1]^T F [p_1; 1] = 0\f]
+
+where \f$F\f$ is a fundamental matrix, \f$p_1\f$ and \f$p_2\f$ are corresponding points in the first and the
+second images, respectively.
+
+The function calculates the fundamental matrix using one of four methods listed above and returns
+the found fundamental matrix. Normally just one matrix is found. But in case of the 7-point
+algorithm, the function may return up to 3 solutions ( \f$9 \times 3\f$ matrix that stores all 3
+matrices sequentially).
+
+The calculated fundamental matrix may be passed further to #computeCorrespondEpilines that finds the
+epipolar lines corresponding to the specified points. It can also be passed to
+#stereoRectifyUncalibrated to compute the rectification transformation. :
+@code
+ // Example. Estimation of fundamental matrix using the RANSAC algorithm
+ int point_count = 100;
+ vector points1(point_count);
+ vector points2(point_count);
+
+ // initialize the points here ...
+ for( int i = 0; i < point_count; i++ )
+ {
+ points1[i] = ...;
+ points2[i] = ...;
+ }
+
+ Mat fundamental_matrix =
+ findFundamentalMat(points1, points2, FM_RANSAC, 3, 0.99);
+@endcode
+ */
+CV_EXPORTS_W Mat findFundamentalMat( InputArray points1, InputArray points2,
+ int method, double ransacReprojThreshold, double confidence,
+ int maxIters, OutputArray mask = noArray() );
+
+/** @overload */
+CV_EXPORTS_W Mat findFundamentalMat( InputArray points1, InputArray points2,
+ int method = FM_RANSAC,
+ double ransacReprojThreshold = 3., double confidence = 0.99,
+ OutputArray mask = noArray() );
+
+/** @overload */
+CV_EXPORTS Mat findFundamentalMat( InputArray points1, InputArray points2,
+ OutputArray mask, int method = FM_RANSAC,
+ double ransacReprojThreshold = 3., double confidence = 0.99 );
+
+
+CV_EXPORTS_W Mat findFundamentalMat( InputArray points1, InputArray points2,
+ OutputArray mask, const UsacParams ¶ms);
+
+/** @brief Calculates an essential matrix from the corresponding points in two images.
+
+@param points1 Array of N (N \>= 5) 2D points from the first image. The point coordinates should
+be floating-point (single or double precision).
+@param points2 Array of the second image points of the same size and format as points1.
+@param cameraMatrix Camera intrinsic matrix \f$\cameramatrix{A}\f$ .
+Note that this function assumes that points1 and points2 are feature points from cameras with the
+same camera intrinsic matrix. If this assumption does not hold for your use case, use another
+function overload or #undistortPoints with `P = cv::NoArray()` for both cameras to transform image
+points to normalized image coordinates, which are valid for the identity camera intrinsic matrix.
+When passing these coordinates, pass the identity matrix for this parameter.
+@param method Method for computing an essential matrix.
+- @ref RANSAC for the RANSAC algorithm.
+- @ref LMEDS for the LMedS algorithm.
+@param prob Parameter used for the RANSAC or LMedS methods only. It specifies a desirable level of
+confidence (probability) that the estimated matrix is correct.
+@param threshold Parameter used for RANSAC. It is the maximum distance from a point to an epipolar
+line in pixels, beyond which the point is considered an outlier and is not used for computing the
+final fundamental matrix. It can be set to something like 1-3, depending on the accuracy of the
+point localization, image resolution, and the image noise.
+@param mask Output array of N elements, every element of which is set to 0 for outliers and to 1
+for the other points. The array is computed only in the RANSAC and LMedS methods.
+@param maxIters The maximum number of robust method iterations.
+
+This function estimates essential matrix based on the five-point algorithm solver in @cite Nister03 .
+@cite SteweniusCFS is also a related. The epipolar geometry is described by the following equation:
+
+\f[[p_2; 1]^T K^{-T} E K^{-1} [p_1; 1] = 0\f]
+
+where \f$E\f$ is an essential matrix, \f$p_1\f$ and \f$p_2\f$ are corresponding points in the first and the
+second images, respectively. The result of this function may be passed further to
+#decomposeEssentialMat or #recoverPose to recover the relative pose between cameras.
+ */
+CV_EXPORTS_W
+Mat findEssentialMat(
+ InputArray points1, InputArray points2,
+ InputArray cameraMatrix, int method = RANSAC,
+ double prob = 0.999, double threshold = 1.0,
+ int maxIters = 1000, OutputArray mask = noArray()
+);
+
+/** @overload */
+CV_EXPORTS
+Mat findEssentialMat(
+ InputArray points1, InputArray points2,
+ InputArray cameraMatrix, int method,
+ double prob, double threshold,
+ OutputArray mask
+); // TODO remove from OpenCV 5.0
+
+/** @overload
+@param points1 Array of N (N \>= 5) 2D points from the first image. The point coordinates should
+be floating-point (single or double precision).
+@param points2 Array of the second image points of the same size and format as points1 .
+@param focal focal length of the camera. Note that this function assumes that points1 and points2
+are feature points from cameras with same focal length and principal point.
+@param pp principal point of the camera.
+@param method Method for computing a fundamental matrix.
+- @ref RANSAC for the RANSAC algorithm.
+- @ref LMEDS for the LMedS algorithm.
+@param threshold Parameter used for RANSAC. It is the maximum distance from a point to an epipolar
+line in pixels, beyond which the point is considered an outlier and is not used for computing the
+final fundamental matrix. It can be set to something like 1-3, depending on the accuracy of the
+point localization, image resolution, and the image noise.
+@param prob Parameter used for the RANSAC or LMedS methods only. It specifies a desirable level of
+confidence (probability) that the estimated matrix is correct.
+@param mask Output array of N elements, every element of which is set to 0 for outliers and to 1
+for the other points. The array is computed only in the RANSAC and LMedS methods.
+@param maxIters The maximum number of robust method iterations.
+
+This function differs from the one above that it computes camera intrinsic matrix from focal length and
+principal point:
+
+\f[A =
+\begin{bmatrix}
+f & 0 & x_{pp} \\
+0 & f & y_{pp} \\
+0 & 0 & 1
+\end{bmatrix}\f]
+ */
+CV_EXPORTS_W
+Mat findEssentialMat(
+ InputArray points1, InputArray points2,
+ double focal = 1.0, Point2d pp = Point2d(0, 0),
+ int method = RANSAC, double prob = 0.999,
+ double threshold = 1.0, int maxIters = 1000,
+ OutputArray mask = noArray()
+);
+
+/** @overload */
+CV_EXPORTS
+Mat findEssentialMat(
+ InputArray points1, InputArray points2,
+ double focal, Point2d pp,
+ int method, double prob,
+ double threshold, OutputArray mask
+); // TODO remove from OpenCV 5.0
+
+/** @brief Calculates an essential matrix from the corresponding points in two images from potentially two different cameras.
+
+@param points1 Array of N (N \>= 5) 2D points from the first image. The point coordinates should
+be floating-point (single or double precision).
+@param points2 Array of the second image points of the same size and format as points1.
+@param cameraMatrix1 Camera matrix for the first camera \f$K = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}\f$ .
+@param cameraMatrix2 Camera matrix for the second camera \f$K = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}\f$ .
+@param distCoeffs1 Input vector of distortion coefficients for the first camera
+\f$(k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6[, s_1, s_2, s_3, s_4[, \tau_x, \tau_y]]]])\f$
+of 4, 5, 8, 12 or 14 elements. If the vector is NULL/empty, the zero distortion coefficients are assumed.
+@param distCoeffs2 Input vector of distortion coefficients for the second camera
+\f$(k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6[, s_1, s_2, s_3, s_4[, \tau_x, \tau_y]]]])\f$
+of 4, 5, 8, 12 or 14 elements. If the vector is NULL/empty, the zero distortion coefficients are assumed.
+@param method Method for computing an essential matrix.
+- @ref RANSAC for the RANSAC algorithm.
+- @ref LMEDS for the LMedS algorithm.
+@param prob Parameter used for the RANSAC or LMedS methods only. It specifies a desirable level of
+confidence (probability) that the estimated matrix is correct.
+@param threshold Parameter used for RANSAC. It is the maximum distance from a point to an epipolar
+line in pixels, beyond which the point is considered an outlier and is not used for computing the
+final fundamental matrix. It can be set to something like 1-3, depending on the accuracy of the
+point localization, image resolution, and the image noise.
+@param mask Output array of N elements, every element of which is set to 0 for outliers and to 1
+for the other points. The array is computed only in the RANSAC and LMedS methods.
+
+This function estimates essential matrix based on the five-point algorithm solver in @cite Nister03 .
+@cite SteweniusCFS is also a related. The epipolar geometry is described by the following equation:
+
+\f[[p_2; 1]^T K^{-T} E K^{-1} [p_1; 1] = 0\f]
+
+where \f$E\f$ is an essential matrix, \f$p_1\f$ and \f$p_2\f$ are corresponding points in the first and the
+second images, respectively. The result of this function may be passed further to
+#decomposeEssentialMat or #recoverPose to recover the relative pose between cameras.
+ */
+CV_EXPORTS_W Mat findEssentialMat( InputArray points1, InputArray points2,
+ InputArray cameraMatrix1, InputArray distCoeffs1,
+ InputArray cameraMatrix2, InputArray distCoeffs2,
+ int method = RANSAC,
+ double prob = 0.999, double threshold = 1.0,
+ OutputArray mask = noArray() );
+
+
+CV_EXPORTS_W Mat findEssentialMat( InputArray points1, InputArray points2,
+ InputArray cameraMatrix1, InputArray cameraMatrix2,
+ InputArray dist_coeff1, InputArray dist_coeff2, OutputArray mask,
+ const UsacParams ¶ms);
+
+/** @brief Decompose an essential matrix to possible rotations and translation.
+
+@param E The input essential matrix.
+@param R1 One possible rotation matrix.
+@param R2 Another possible rotation matrix.
+@param t One possible translation.
+
+This function decomposes the essential matrix E using svd decomposition @cite HartleyZ00. In
+general, four possible poses exist for the decomposition of E. They are \f$[R_1, t]\f$,
+\f$[R_1, -t]\f$, \f$[R_2, t]\f$, \f$[R_2, -t]\f$.
+
+If E gives the epipolar constraint \f$[p_2; 1]^T A^{-T} E A^{-1} [p_1; 1] = 0\f$ between the image
+points \f$p_1\f$ in the first image and \f$p_2\f$ in second image, then any of the tuples
+\f$[R_1, t]\f$, \f$[R_1, -t]\f$, \f$[R_2, t]\f$, \f$[R_2, -t]\f$ is a change of basis from the first
+camera's coordinate system to the second camera's coordinate system. However, by decomposing E, one
+can only get the direction of the translation. For this reason, the translation t is returned with
+unit length.
+ */
+CV_EXPORTS_W void decomposeEssentialMat( InputArray E, OutputArray R1, OutputArray R2, OutputArray t );
+
+/** @brief Recovers the relative camera rotation and the translation from corresponding points in two images from two different cameras, using cheirality check. Returns the number of
+inliers that pass the check.
+
+@param points1 Array of N 2D points from the first image. The point coordinates should be
+floating-point (single or double precision).
+@param points2 Array of the second image points of the same size and format as points1 .
+@param cameraMatrix1 Input/output camera matrix for the first camera, the same as in
+@ref calibrateCamera. Furthermore, for the stereo case, additional flags may be used, see below.
+@param distCoeffs1 Input/output vector of distortion coefficients, the same as in
+@ref calibrateCamera.
+@param cameraMatrix2 Input/output camera matrix for the first camera, the same as in
+@ref calibrateCamera. Furthermore, for the stereo case, additional flags may be used, see below.
+@param distCoeffs2 Input/output vector of distortion coefficients, the same as in
+@ref calibrateCamera.
+@param E The output essential matrix.
+@param R Output rotation matrix. Together with the translation vector, this matrix makes up a tuple
+that performs a change of basis from the first camera's coordinate system to the second camera's
+coordinate system. Note that, in general, t can not be used for this tuple, see the parameter
+described below.
+@param t Output translation vector. This vector is obtained by @ref decomposeEssentialMat and
+therefore is only known up to scale, i.e. t is the direction of the translation vector and has unit
+length.
+@param method Method for computing an essential matrix.
+- @ref RANSAC for the RANSAC algorithm.
+- @ref LMEDS for the LMedS algorithm.
+@param prob Parameter used for the RANSAC or LMedS methods only. It specifies a desirable level of
+confidence (probability) that the estimated matrix is correct.
+@param threshold Parameter used for RANSAC. It is the maximum distance from a point to an epipolar
+line in pixels, beyond which the point is considered an outlier and is not used for computing the
+final fundamental matrix. It can be set to something like 1-3, depending on the accuracy of the
+point localization, image resolution, and the image noise.
+@param mask Input/output mask for inliers in points1 and points2. If it is not empty, then it marks
+inliers in points1 and points2 for then given essential matrix E. Only these inliers will be used to
+recover pose. In the output mask only inliers which pass the cheirality check.
+
+This function decomposes an essential matrix using @ref decomposeEssentialMat and then verifies
+possible pose hypotheses by doing cheirality check. The cheirality check means that the
+triangulated 3D points should have positive depth. Some details can be found in @cite Nister03.
+
+This function can be used to process the output E and mask from @ref findEssentialMat. In this
+scenario, points1 and points2 are the same input for findEssentialMat.:
+@code
+ // Example. Estimation of fundamental matrix using the RANSAC algorithm
+ int point_count = 100;
+ vector points1(point_count);
+ vector points2(point_count);
+
+ // initialize the points here ...
+ for( int i = 0; i < point_count; i++ )
+ {
+ points1[i] = ...;
+ points2[i] = ...;
+ }
+
+ // Input: camera calibration of both cameras, for example using intrinsic chessboard calibration.
+ Mat cameraMatrix1, distCoeffs1, cameraMatrix2, distCoeffs2;
+
+ // Output: Essential matrix, relative rotation and relative translation.
+ Mat E, R, t, mask;
+
+ recoverPose(points1, points2, cameraMatrix1, distCoeffs1, cameraMatrix2, distCoeffs2, E, R, t, mask);
+@endcode
+ */
+CV_EXPORTS_W int recoverPose( InputArray points1, InputArray points2,
+ InputArray cameraMatrix1, InputArray distCoeffs1,
+ InputArray cameraMatrix2, InputArray distCoeffs2,
+ OutputArray E, OutputArray R, OutputArray t,
+ int method = cv::RANSAC, double prob = 0.999, double threshold = 1.0,
+ InputOutputArray mask = noArray());
+
+/** @brief Recovers the relative camera rotation and the translation from an estimated essential
+matrix and the corresponding points in two images, using chirality check. Returns the number of
+inliers that pass the check.
+
+@param E The input essential matrix.
+@param points1 Array of N 2D points from the first image. The point coordinates should be
+floating-point (single or double precision).
+@param points2 Array of the second image points of the same size and format as points1 .
+@param cameraMatrix Camera intrinsic matrix \f$\cameramatrix{A}\f$ .
+Note that this function assumes that points1 and points2 are feature points from cameras with the
+same camera intrinsic matrix.
+@param R Output rotation matrix. Together with the translation vector, this matrix makes up a tuple
+that performs a change of basis from the first camera's coordinate system to the second camera's
+coordinate system. Note that, in general, t can not be used for this tuple, see the parameter
+described below.
+@param t Output translation vector. This vector is obtained by @ref decomposeEssentialMat and
+therefore is only known up to scale, i.e. t is the direction of the translation vector and has unit
+length.
+@param mask Input/output mask for inliers in points1 and points2. If it is not empty, then it marks
+inliers in points1 and points2 for the given essential matrix E. Only these inliers will be used to
+recover pose. In the output mask only inliers which pass the chirality check.
+
+This function decomposes an essential matrix using @ref decomposeEssentialMat and then verifies
+possible pose hypotheses by doing chirality check. The chirality check means that the
+triangulated 3D points should have positive depth. Some details can be found in @cite Nister03.
+
+This function can be used to process the output E and mask from @ref findEssentialMat. In this
+scenario, points1 and points2 are the same input for #findEssentialMat :
+@code
+ // Example. Estimation of fundamental matrix using the RANSAC algorithm
+ int point_count = 100;
+ vector points1(point_count);
+ vector points2(point_count);
+
+ // initialize the points here ...
+ for( int i = 0; i < point_count; i++ )
+ {
+ points1[i] = ...;
+ points2[i] = ...;
+ }
+
+ // cametra matrix with both focal lengths = 1, and principal point = (0, 0)
+ Mat cameraMatrix = Mat::eye(3, 3, CV_64F);
+
+ Mat E, R, t, mask;
+
+ E = findEssentialMat(points1, points2, cameraMatrix, RANSAC, 0.999, 1.0, mask);
+ recoverPose(E, points1, points2, cameraMatrix, R, t, mask);
+@endcode
+ */
+CV_EXPORTS_W int recoverPose( InputArray E, InputArray points1, InputArray points2,
+ InputArray cameraMatrix, OutputArray R, OutputArray t,
+ InputOutputArray mask = noArray() );
+
+/** @overload
+@param E The input essential matrix.
+@param points1 Array of N 2D points from the first image. The point coordinates should be
+floating-point (single or double precision).
+@param points2 Array of the second image points of the same size and format as points1 .
+@param R Output rotation matrix. Together with the translation vector, this matrix makes up a tuple
+that performs a change of basis from the first camera's coordinate system to the second camera's
+coordinate system. Note that, in general, t can not be used for this tuple, see the parameter
+description below.
+@param t Output translation vector. This vector is obtained by @ref decomposeEssentialMat and
+therefore is only known up to scale, i.e. t is the direction of the translation vector and has unit
+length.
+@param focal Focal length of the camera. Note that this function assumes that points1 and points2
+are feature points from cameras with same focal length and principal point.
+@param pp principal point of the camera.
+@param mask Input/output mask for inliers in points1 and points2. If it is not empty, then it marks
+inliers in points1 and points2 for the given essential matrix E. Only these inliers will be used to
+recover pose. In the output mask only inliers which pass the chirality check.
+
+This function differs from the one above that it computes camera intrinsic matrix from focal length and
+principal point:
+
+\f[A =
+\begin{bmatrix}
+f & 0 & x_{pp} \\
+0 & f & y_{pp} \\
+0 & 0 & 1
+\end{bmatrix}\f]
+ */
+CV_EXPORTS_W int recoverPose( InputArray E, InputArray points1, InputArray points2,
+ OutputArray R, OutputArray t,
+ double focal = 1.0, Point2d pp = Point2d(0, 0),
+ InputOutputArray mask = noArray() );
+
+/** @overload
+@param E The input essential matrix.
+@param points1 Array of N 2D points from the first image. The point coordinates should be
+floating-point (single or double precision).
+@param points2 Array of the second image points of the same size and format as points1.
+@param cameraMatrix Camera intrinsic matrix \f$\cameramatrix{A}\f$ .
+Note that this function assumes that points1 and points2 are feature points from cameras with the
+same camera intrinsic matrix.
+@param R Output rotation matrix. Together with the translation vector, this matrix makes up a tuple
+that performs a change of basis from the first camera's coordinate system to the second camera's
+coordinate system. Note that, in general, t can not be used for this tuple, see the parameter
+description below.
+@param t Output translation vector. This vector is obtained by @ref decomposeEssentialMat and
+therefore is only known up to scale, i.e. t is the direction of the translation vector and has unit
+length.
+@param distanceThresh threshold distance which is used to filter out far away points (i.e. infinite
+points).
+@param mask Input/output mask for inliers in points1 and points2. If it is not empty, then it marks
+inliers in points1 and points2 for the given essential matrix E. Only these inliers will be used to
+recover pose. In the output mask only inliers which pass the chirality check.
+@param triangulatedPoints 3D points which were reconstructed by triangulation.
+
+This function differs from the one above that it outputs the triangulated 3D point that are used for
+the chirality check.
+ */
+CV_EXPORTS_W int recoverPose( InputArray E, InputArray points1, InputArray points2,
+ InputArray cameraMatrix, OutputArray R, OutputArray t, double distanceThresh, InputOutputArray mask = noArray(),
+ OutputArray triangulatedPoints = noArray());
+
+/** @brief For points in an image of a stereo pair, computes the corresponding epilines in the other image.
+
+@param points Input points. \f$N \times 1\f$ or \f$1 \times N\f$ matrix of type CV_32FC2 or
+vector\ .
+@param whichImage Index of the image (1 or 2) that contains the points .
+@param F Fundamental matrix that can be estimated using #findFundamentalMat or #stereoRectify .
+@param lines Output vector of the epipolar lines corresponding to the points in the other image.
+Each line \f$ax + by + c=0\f$ is encoded by 3 numbers \f$(a, b, c)\f$ .
+
+For every point in one of the two images of a stereo pair, the function finds the equation of the
+corresponding epipolar line in the other image.
+
+From the fundamental matrix definition (see #findFundamentalMat ), line \f$l^{(2)}_i\f$ in the second
+image for the point \f$p^{(1)}_i\f$ in the first image (when whichImage=1 ) is computed as:
+
+\f[l^{(2)}_i = F p^{(1)}_i\f]
+
+And vice versa, when whichImage=2, \f$l^{(1)}_i\f$ is computed from \f$p^{(2)}_i\f$ as:
+
+\f[l^{(1)}_i = F^T p^{(2)}_i\f]
+
+Line coefficients are defined up to a scale. They are normalized so that \f$a_i^2+b_i^2=1\f$ .
+ */
+CV_EXPORTS_W void computeCorrespondEpilines( InputArray points, int whichImage,
+ InputArray F, OutputArray lines );
+
+/** @brief This function reconstructs 3-dimensional points (in homogeneous coordinates) by using
+their observations with a stereo camera.
+
+@param projMatr1 3x4 projection matrix of the first camera, i.e. this matrix projects 3D points
+given in the world's coordinate system into the first image.
+@param projMatr2 3x4 projection matrix of the second camera, i.e. this matrix projects 3D points
+given in the world's coordinate system into the second image.
+@param projPoints1 2xN array of feature points in the first image. In the case of the c++ version,
+it can be also a vector of feature points or two-channel matrix of size 1xN or Nx1.
+@param projPoints2 2xN array of corresponding points in the second image. In the case of the c++
+version, it can be also a vector of feature points or two-channel matrix of size 1xN or Nx1.
+@param points4D 4xN array of reconstructed points in homogeneous coordinates. These points are
+returned in the world's coordinate system.
+
+@note
+ Keep in mind that all input data should be of float type in order for this function to work.
+
+@note
+ If the projection matrices from @ref stereoRectify are used, then the returned points are
+ represented in the first camera's rectified coordinate system.
+
+@sa
+ reprojectImageTo3D
+ */
+CV_EXPORTS_W void triangulatePoints( InputArray projMatr1, InputArray projMatr2,
+ InputArray projPoints1, InputArray projPoints2,
+ OutputArray points4D );
+
+/** @brief Refines coordinates of corresponding points.
+
+@param F 3x3 fundamental matrix.
+@param points1 1xN array containing the first set of points.
+@param points2 1xN array containing the second set of points.
+@param newPoints1 The optimized points1.
+@param newPoints2 The optimized points2.
+
+The function implements the Optimal Triangulation Method (see Multiple View Geometry @cite HartleyZ00 for details).
+For each given point correspondence points1[i] \<-\> points2[i], and a fundamental matrix F, it
+computes the corrected correspondences newPoints1[i] \<-\> newPoints2[i] that minimize the geometric
+error \f$d(points1[i], newPoints1[i])^2 + d(points2[i],newPoints2[i])^2\f$ (where \f$d(a,b)\f$ is the
+geometric distance between points \f$a\f$ and \f$b\f$ ) subject to the epipolar constraint
+\f$newPoints2^T \cdot F \cdot newPoints1 = 0\f$ .
+ */
+CV_EXPORTS_W void correctMatches( InputArray F, InputArray points1, InputArray points2,
+ OutputArray newPoints1, OutputArray newPoints2 );
+
+/** @brief Filters off small noise blobs (speckles) in the disparity map
+
+@param img The input 16-bit signed disparity image
+@param newVal The disparity value used to paint-off the speckles
+@param maxSpeckleSize The maximum speckle size to consider it a speckle. Larger blobs are not
+affected by the algorithm
+@param maxDiff Maximum difference between neighbor disparity pixels to put them into the same
+blob. Note that since StereoBM, StereoSGBM and may be other algorithms return a fixed-point
+disparity map, where disparity values are multiplied by 16, this scale factor should be taken into
+account when specifying this parameter value.
+@param buf The optional temporary buffer to avoid memory allocation within the function.
+ */
+CV_EXPORTS_W void filterSpeckles( InputOutputArray img, double newVal,
+ int maxSpeckleSize, double maxDiff,
+ InputOutputArray buf = noArray() );
+
+//! computes valid disparity ROI from the valid ROIs of the rectified images (that are returned by #stereoRectify)
+CV_EXPORTS_W Rect getValidDisparityROI( Rect roi1, Rect roi2,
+ int minDisparity, int numberOfDisparities,
+ int blockSize );
+
+//! validates disparity using the left-right check. The matrix "cost" should be computed by the stereo correspondence algorithm
+CV_EXPORTS_W void validateDisparity( InputOutputArray disparity, InputArray cost,
+ int minDisparity, int numberOfDisparities,
+ int disp12MaxDisp = 1 );
+
+/** @brief Reprojects a disparity image to 3D space.
+
+@param disparity Input single-channel 8-bit unsigned, 16-bit signed, 32-bit signed or 32-bit
+floating-point disparity image. The values of 8-bit / 16-bit signed formats are assumed to have no
+fractional bits. If the disparity is 16-bit signed format, as computed by @ref StereoBM or
+@ref StereoSGBM and maybe other algorithms, it should be divided by 16 (and scaled to float) before
+being used here.
+@param _3dImage Output 3-channel floating-point image of the same size as disparity. Each element of
+_3dImage(x,y) contains 3D coordinates of the point (x,y) computed from the disparity map. If one
+uses Q obtained by @ref stereoRectify, then the returned points are represented in the first
+camera's rectified coordinate system.
+@param Q \f$4 \times 4\f$ perspective transformation matrix that can be obtained with
+@ref stereoRectify.
+@param handleMissingValues Indicates, whether the function should handle missing values (i.e.
+points where the disparity was not computed). If handleMissingValues=true, then pixels with the
+minimal disparity that corresponds to the outliers (see StereoMatcher::compute ) are transformed
+to 3D points with a very large Z value (currently set to 10000).
+@param ddepth The optional output array depth. If it is -1, the output image will have CV_32F
+depth. ddepth can also be set to CV_16S, CV_32S or CV_32F.
+
+The function transforms a single-channel disparity map to a 3-channel image representing a 3D
+surface. That is, for each pixel (x,y) and the corresponding disparity d=disparity(x,y) , it
+computes:
+
+\f[\begin{bmatrix}
+X \\
+Y \\
+Z \\
+W
+\end{bmatrix} = Q \begin{bmatrix}
+x \\
+y \\
+\texttt{disparity} (x,y) \\
+1
+\end{bmatrix}.\f]
+
+@sa
+ To reproject a sparse set of points {(x,y,d),...} to 3D space, use perspectiveTransform.
+ */
+CV_EXPORTS_W void reprojectImageTo3D( InputArray disparity,
+ OutputArray _3dImage, InputArray Q,
+ bool handleMissingValues = false,
+ int ddepth = -1 );
+
+/** @brief Calculates the Sampson Distance between two points.
+
+The function cv::sampsonDistance calculates and returns the first order approximation of the geometric error as:
+\f[
+sd( \texttt{pt1} , \texttt{pt2} )=
+\frac{(\texttt{pt2}^t \cdot \texttt{F} \cdot \texttt{pt1})^2}
+{((\texttt{F} \cdot \texttt{pt1})(0))^2 +
+((\texttt{F} \cdot \texttt{pt1})(1))^2 +
+((\texttt{F}^t \cdot \texttt{pt2})(0))^2 +
+((\texttt{F}^t \cdot \texttt{pt2})(1))^2}
+\f]
+The fundamental matrix may be calculated using the #findFundamentalMat function. See @cite HartleyZ00 11.4.3 for details.
+@param pt1 first homogeneous 2d point
+@param pt2 second homogeneous 2d point
+@param F fundamental matrix
+@return The computed Sampson distance.
+*/
+CV_EXPORTS_W double sampsonDistance(InputArray pt1, InputArray pt2, InputArray F);
+
+/** @brief Computes an optimal affine transformation between two 3D point sets.
+
+It computes
+\f[
+\begin{bmatrix}
+x\\
+y\\
+z\\
+\end{bmatrix}
+=
+\begin{bmatrix}
+a_{11} & a_{12} & a_{13}\\
+a_{21} & a_{22} & a_{23}\\
+a_{31} & a_{32} & a_{33}\\
+\end{bmatrix}
+\begin{bmatrix}
+X\\
+Y\\
+Z\\
+\end{bmatrix}
++
+\begin{bmatrix}
+b_1\\
+b_2\\
+b_3\\
+\end{bmatrix}
+\f]
+
+@param src First input 3D point set containing \f$(X,Y,Z)\f$.
+@param dst Second input 3D point set containing \f$(x,y,z)\f$.
+@param out Output 3D affine transformation matrix \f$3 \times 4\f$ of the form
+\f[
+\begin{bmatrix}
+a_{11} & a_{12} & a_{13} & b_1\\
+a_{21} & a_{22} & a_{23} & b_2\\
+a_{31} & a_{32} & a_{33} & b_3\\
+\end{bmatrix}
+\f]
+@param inliers Output vector indicating which points are inliers (1-inlier, 0-outlier).
+@param ransacThreshold Maximum reprojection error in the RANSAC algorithm to consider a point as
+an inlier.
+@param confidence Confidence level, between 0 and 1, for the estimated transformation. Anything
+between 0.95 and 0.99 is usually good enough. Values too close to 1 can slow down the estimation
+significantly. Values lower than 0.8-0.9 can result in an incorrectly estimated transformation.
+
+The function estimates an optimal 3D affine transformation between two 3D point sets using the
+RANSAC algorithm.
+ */
+CV_EXPORTS_W int estimateAffine3D(InputArray src, InputArray dst,
+ OutputArray out, OutputArray inliers,
+ double ransacThreshold = 3, double confidence = 0.99);
+
+/** @brief Computes an optimal affine transformation between two 3D point sets.
+
+It computes \f$R,s,t\f$ minimizing \f$\sum{i} dst_i - c \cdot R \cdot src_i \f$
+where \f$R\f$ is a 3x3 rotation matrix, \f$t\f$ is a 3x1 translation vector and \f$s\f$ is a
+scalar size value. This is an implementation of the algorithm by Umeyama \cite umeyama1991least .
+The estimated affine transform has a homogeneous scale which is a subclass of affine
+transformations with 7 degrees of freedom. The paired point sets need to comprise at least 3
+points each.
+
+@param src First input 3D point set.
+@param dst Second input 3D point set.
+@param scale If null is passed, the scale parameter c will be assumed to be 1.0.
+Else the pointed-to variable will be set to the optimal scale.
+@param force_rotation If true, the returned rotation will never be a reflection.
+This might be unwanted, e.g. when optimizing a transform between a right- and a
+left-handed coordinate system.
+@return 3D affine transformation matrix \f$3 \times 4\f$ of the form
+\f[T =
+\begin{bmatrix}
+R & t\\
+\end{bmatrix}
+\f]
+
+ */
+CV_EXPORTS_W cv::Mat estimateAffine3D(InputArray src, InputArray dst,
+ CV_OUT double* scale = nullptr, bool force_rotation = true);
+
+/** @brief Computes an optimal translation between two 3D point sets.
+ *
+ * It computes
+ * \f[
+ * \begin{bmatrix}
+ * x\\
+ * y\\
+ * z\\
+ * \end{bmatrix}
+ * =
+ * \begin{bmatrix}
+ * X\\
+ * Y\\
+ * Z\\
+ * \end{bmatrix}
+ * +
+ * \begin{bmatrix}
+ * b_1\\
+ * b_2\\
+ * b_3\\
+ * \end{bmatrix}
+ * \f]
+ *
+ * @param src First input 3D point set containing \f$(X,Y,Z)\f$.
+ * @param dst Second input 3D point set containing \f$(x,y,z)\f$.
+ * @param out Output 3D translation vector \f$3 \times 1\f$ of the form
+ * \f[
+ * \begin{bmatrix}
+ * b_1 \\
+ * b_2 \\
+ * b_3 \\
+ * \end{bmatrix}
+ * \f]
+ * @param inliers Output vector indicating which points are inliers (1-inlier, 0-outlier).
+ * @param ransacThreshold Maximum reprojection error in the RANSAC algorithm to consider a point as
+ * an inlier.
+ * @param confidence Confidence level, between 0 and 1, for the estimated transformation. Anything
+ * between 0.95 and 0.99 is usually good enough. Values too close to 1 can slow down the estimation
+ * significantly. Values lower than 0.8-0.9 can result in an incorrectly estimated transformation.
+ *
+ * The function estimates an optimal 3D translation between two 3D point sets using the
+ * RANSAC algorithm.
+ * */
+CV_EXPORTS_W int estimateTranslation3D(InputArray src, InputArray dst,
+ OutputArray out, OutputArray inliers,
+ double ransacThreshold = 3, double confidence = 0.99);
+
+/** @brief Computes an optimal affine transformation between two 2D point sets.
+
+It computes
+\f[
+\begin{bmatrix}
+x\\
+y\\
+\end{bmatrix}
+=
+\begin{bmatrix}
+a_{11} & a_{12}\\
+a_{21} & a_{22}\\
+\end{bmatrix}
+\begin{bmatrix}
+X\\
+Y\\
+\end{bmatrix}
++
+\begin{bmatrix}
+b_1\\
+b_2\\
+\end{bmatrix}
+\f]
+
+@param from First input 2D point set containing \f$(X,Y)\f$.
+@param to Second input 2D point set containing \f$(x,y)\f$.
+@param inliers Output vector indicating which points are inliers (1-inlier, 0-outlier).
+@param method Robust method used to compute transformation. The following methods are possible:
+- @ref RANSAC - RANSAC-based robust method
+- @ref LMEDS - Least-Median robust method
+RANSAC is the default method.
+@param ransacReprojThreshold Maximum reprojection error in the RANSAC algorithm to consider
+a point as an inlier. Applies only to RANSAC.
+@param maxIters The maximum number of robust method iterations.
+@param confidence Confidence level, between 0 and 1, for the estimated transformation. Anything
+between 0.95 and 0.99 is usually good enough. Values too close to 1 can slow down the estimation
+significantly. Values lower than 0.8-0.9 can result in an incorrectly estimated transformation.
+@param refineIters Maximum number of iterations of refining algorithm (Levenberg-Marquardt).
+Passing 0 will disable refining, so the output matrix will be output of robust method.
+
+@return Output 2D affine transformation matrix \f$2 \times 3\f$ or empty matrix if transformation
+could not be estimated. The returned matrix has the following form:
+\f[
+\begin{bmatrix}
+a_{11} & a_{12} & b_1\\
+a_{21} & a_{22} & b_2\\
+\end{bmatrix}
+\f]
+
+The function estimates an optimal 2D affine transformation between two 2D point sets using the
+selected robust algorithm.
+
+The computed transformation is then refined further (using only inliers) with the
+Levenberg-Marquardt method to reduce the re-projection error even more.
+
+@note
+The RANSAC method can handle practically any ratio of outliers but needs a threshold to
+distinguish inliers from outliers. The method LMeDS does not need any threshold but it works
+correctly only when there are more than 50% of inliers.
+
+@sa estimateAffinePartial2D, getAffineTransform
+*/
+CV_EXPORTS_W cv::Mat estimateAffine2D(InputArray from, InputArray to, OutputArray inliers = noArray(),
+ int method = RANSAC, double ransacReprojThreshold = 3,
+ size_t maxIters = 2000, double confidence = 0.99,
+ size_t refineIters = 10);
+
+
+CV_EXPORTS_W cv::Mat estimateAffine2D(InputArray pts1, InputArray pts2, OutputArray inliers,
+ const UsacParams ¶ms);
+
+/** @brief Computes an optimal limited affine transformation with 4 degrees of freedom between
+two 2D point sets.
+
+@param from First input 2D point set.
+@param to Second input 2D point set.
+@param inliers Output vector indicating which points are inliers.
+@param method Robust method used to compute transformation. The following methods are possible:
+- @ref RANSAC - RANSAC-based robust method
+- @ref LMEDS - Least-Median robust method
+RANSAC is the default method.
+@param ransacReprojThreshold Maximum reprojection error in the RANSAC algorithm to consider
+a point as an inlier. Applies only to RANSAC.
+@param maxIters The maximum number of robust method iterations.
+@param confidence Confidence level, between 0 and 1, for the estimated transformation. Anything
+between 0.95 and 0.99 is usually good enough. Values too close to 1 can slow down the estimation
+significantly. Values lower than 0.8-0.9 can result in an incorrectly estimated transformation.
+@param refineIters Maximum number of iterations of refining algorithm (Levenberg-Marquardt).
+Passing 0 will disable refining, so the output matrix will be output of robust method.
+
+@return Output 2D affine transformation (4 degrees of freedom) matrix \f$2 \times 3\f$ or
+empty matrix if transformation could not be estimated.
+
+The function estimates an optimal 2D affine transformation with 4 degrees of freedom limited to
+combinations of translation, rotation, and uniform scaling. Uses the selected algorithm for robust
+estimation.
+
+The computed transformation is then refined further (using only inliers) with the
+Levenberg-Marquardt method to reduce the re-projection error even more.
+
+Estimated transformation matrix is:
+\f[ \begin{bmatrix} \cos(\theta) \cdot s & -\sin(\theta) \cdot s & t_x \\
+ \sin(\theta) \cdot s & \cos(\theta) \cdot s & t_y
+\end{bmatrix} \f]
+Where \f$ \theta \f$ is the rotation angle, \f$ s \f$ the scaling factor and \f$ t_x, t_y \f$ are
+translations in \f$ x, y \f$ axes respectively.
+
+@note
+The RANSAC method can handle practically any ratio of outliers but need a threshold to
+distinguish inliers from outliers. The method LMeDS does not need any threshold but it works
+correctly only when there are more than 50% of inliers.
+
+@sa estimateAffine2D, getAffineTransform
+*/
+CV_EXPORTS_W cv::Mat estimateAffinePartial2D(InputArray from, InputArray to, OutputArray inliers = noArray(),
+ int method = RANSAC, double ransacReprojThreshold = 3,
+ size_t maxIters = 2000, double confidence = 0.99,
+ size_t refineIters = 10);
+
+/** @brief Computes a pure 2D translation between two 2D point sets.
+
+It computes
+\f[
+\begin{bmatrix}
+x\\
+y
+\end{bmatrix}
+=
+\begin{bmatrix}
+1 & 0\\
+0 & 1
+\end{bmatrix}
+\begin{bmatrix}
+X\\
+Y
+\end{bmatrix}
++
+\begin{bmatrix}
+t_x\\
+t_y
+\end{bmatrix}.
+\f]
+
+@param from First input 2D point set containing \f$(X,Y)\f$.
+@param to Second input 2D point set containing \f$(x,y)\f$.
+@param inliers Output vector indicating which points are inliers (1-inlier, 0-outlier).
+@param method Robust method used to compute the transformation. The following methods are possible:
+- @ref RANSAC - RANSAC-based robust method
+- @ref LMEDS - Least-Median robust method
+RANSAC is the default method.
+@param ransacReprojThreshold Maximum reprojection error in the RANSAC algorithm to consider
+a point as an inlier. Applies only to RANSAC.
+@param maxIters The maximum number of robust method iterations.
+@param confidence Confidence level, between 0 and 1, for the estimated transformation. Anything
+between 0.95 and 0.99 is usually good enough. Values too close to 1 can slow down the estimation
+significantly. Values lower than 0.8–0.9 can result in an incorrectly estimated transformation.
+@param refineIters Maximum number of iterations of the refining algorithm. For pure translation
+the least-squares solution on inliers is closed-form, so passing 0 is recommended (no additional refine).
+
+@return A 2D translation vector \f$[t_x, t_y]^T\f$ as `cv::Vec2d`. If the translation could not be
+estimated, both components are set to NaN and, if @p inliers is provided, the mask is filled with zeros.
+
+\par Converting to a 2x3 transformation matrix:
+\f[
+\begin{bmatrix}
+1 & 0 & t_x\\
+0 & 1 & t_y
+\end{bmatrix}
+\f]
+
+@code{.cpp}
+cv::Vec2d t = cv::estimateTranslation2D(from, to, inliers);
+cv::Mat T = (cv::Mat_(2,3) << 1,0,t[0], 0,1,t[1]);
+@endcode
+
+The function estimates a pure 2D translation between two 2D point sets using the selected robust
+algorithm. Inliers are determined by the reprojection error threshold.
+
+@note
+The RANSAC method can handle practically any ratio of outliers but needs a threshold to
+distinguish inliers from outliers. The method LMeDS does not need any threshold but works
+correctly only when there are more than 50% inliers.
+
+@sa estimateAffine2D, estimateAffinePartial2D, getAffineTransform
+*/
+CV_EXPORTS_W cv::Vec2d estimateTranslation2D(InputArray from, InputArray to, OutputArray inliers = noArray(),
+ int method = RANSAC,
+ double ransacReprojThreshold = 3,
+ size_t maxIters = 2000, double confidence = 0.99,
+ size_t refineIters = 0);
+
+/** @example samples/cpp/tutorial_code/features2D/Homography/decompose_homography.cpp
+An example program with homography decomposition.
+
+Check @ref tutorial_homography "the corresponding tutorial" for more details.
+*/
+
+/** @brief Decompose a homography matrix to rotation(s), translation(s) and plane normal(s).
+
+@param H The input homography matrix between two images.
+@param K The input camera intrinsic matrix.
+@param rotations Array of rotation matrices.
+@param translations Array of translation matrices.
+@param normals Array of plane normal matrices.
+
+This function extracts relative camera motion between two views of a planar object and returns up to
+four mathematical solution tuples of rotation, translation, and plane normal. The decomposition of
+the homography matrix H is described in detail in @cite Malis2007.
+
+If the homography H, induced by the plane, gives the constraint
+\f[s_i \vecthree{x'_i}{y'_i}{1} \sim H \vecthree{x_i}{y_i}{1}\f] on the source image points
+\f$p_i\f$ and the destination image points \f$p'_i\f$, then the tuple of rotations[k] and
+translations[k] is a change of basis from the source camera's coordinate system to the destination
+camera's coordinate system. However, by decomposing H, one can only get the translation normalized
+by the (typically unknown) depth of the scene, i.e. its direction but with normalized length.
+
+If point correspondences are available, at least two solutions may further be invalidated, by
+applying positive depth constraint, i.e. all points must be in front of the camera.
+ */
+CV_EXPORTS_W int decomposeHomographyMat(InputArray H,
+ InputArray K,
+ OutputArrayOfArrays rotations,
+ OutputArrayOfArrays translations,
+ OutputArrayOfArrays normals);
+
+/** @brief Filters homography decompositions based on additional information.
+
+@param rotations Vector of rotation matrices.
+@param normals Vector of plane normal matrices.
+@param beforePoints Vector of (rectified) visible reference points before the homography is applied
+@param afterPoints Vector of (rectified) visible reference points after the homography is applied
+@param possibleSolutions Vector of int indices representing the viable solution set after filtering
+@param pointsMask optional Mat/Vector of 8u type representing the mask for the inliers as given by the #findHomography function
+
+This function is intended to filter the output of the #decomposeHomographyMat based on additional
+information as described in @cite Malis2007 . The summary of the method: the #decomposeHomographyMat function
+returns 2 unique solutions and their "opposites" for a total of 4 solutions. If we have access to the
+sets of points visible in the camera frame before and after the homography transformation is applied,
+we can determine which are the true potential solutions and which are the opposites by verifying which
+homographies are consistent with all visible reference points being in front of the camera. The inputs
+are left unchanged; the filtered solution set is returned as indices into the existing one.
+
+*/
+CV_EXPORTS_W void filterHomographyDecompByVisibleRefpoints(InputArrayOfArrays rotations,
+ InputArrayOfArrays normals,
+ InputArray beforePoints,
+ InputArray afterPoints,
+ OutputArray possibleSolutions,
+ InputArray pointsMask = noArray());
+
+/** @brief The base class for stereo correspondence algorithms.
+ */
+class CV_EXPORTS_W StereoMatcher : public Algorithm
+{
+public:
+ enum { DISP_SHIFT = 4,
+ DISP_SCALE = (1 << DISP_SHIFT)
+ };
+
+ /** @brief Computes disparity map for the specified stereo pair
+
+ @param left Left 8-bit single-channel image.
+ @param right Right image of the same size and the same type as the left one.
+ @param disparity Output disparity map. It has the same size as the input images. Some algorithms,
+ like StereoBM or StereoSGBM compute 16-bit fixed-point disparity map (where each disparity value
+ has 4 fractional bits), whereas other algorithms output 32-bit floating-point disparity map.
+ */
+ CV_WRAP virtual void compute( InputArray left, InputArray right,
+ OutputArray disparity ) = 0;
+
+ CV_WRAP virtual int getMinDisparity() const = 0;
+ CV_WRAP virtual void setMinDisparity(int minDisparity) = 0;
+
+ CV_WRAP virtual int getNumDisparities() const = 0;
+ CV_WRAP virtual void setNumDisparities(int numDisparities) = 0;
+
+ CV_WRAP virtual int getBlockSize() const = 0;
+ CV_WRAP virtual void setBlockSize(int blockSize) = 0;
+
+ CV_WRAP virtual int getSpeckleWindowSize() const = 0;
+ CV_WRAP virtual void setSpeckleWindowSize(int speckleWindowSize) = 0;
+
+ CV_WRAP virtual int getSpeckleRange() const = 0;
+ CV_WRAP virtual void setSpeckleRange(int speckleRange) = 0;
+
+ CV_WRAP virtual int getDisp12MaxDiff() const = 0;
+ CV_WRAP virtual void setDisp12MaxDiff(int disp12MaxDiff) = 0;
+};
+
+
+/**
+ * @brief Class for computing stereo correspondence using the block matching algorithm, introduced and contributed to OpenCV by K. Konolige.
+ * @details This class implements a block matching algorithm for stereo correspondence, which is used to compute disparity maps from stereo image pairs. It provides methods to fine-tune parameters such as pre-filtering, texture thresholds, uniqueness ratios, and regions of interest (ROIs) to optimize performance and accuracy.
+ */
+class CV_EXPORTS_W StereoBM : public StereoMatcher
+{
+public:
+ /**
+ * @brief Pre-filter types for the stereo matching algorithm.
+ * @details These constants define the type of pre-filtering applied to the images before computing the disparity map.
+ * - PREFILTER_NORMALIZED_RESPONSE: Uses normalized response for pre-filtering.
+ * - PREFILTER_XSOBEL: Uses the X-Sobel operator for pre-filtering.
+ */
+ enum {
+ PREFILTER_NORMALIZED_RESPONSE = 0, ///< Normalized response pre-filter
+ PREFILTER_XSOBEL = 1 ///< X-Sobel pre-filter
+ };
+
+ /**
+ * @brief Gets the type of pre-filtering currently used in the algorithm.
+ * @return The current pre-filter type: 0 for PREFILTER_NORMALIZED_RESPONSE or 1 for PREFILTER_XSOBEL.
+ */
+ CV_WRAP virtual int getPreFilterType() const = 0;
+
+ /**
+ * @brief Sets the type of pre-filtering used in the algorithm.
+ * @param preFilterType The type of pre-filter to use. Possible values are:
+ * - PREFILTER_NORMALIZED_RESPONSE (0): Uses normalized response for pre-filtering.
+ * - PREFILTER_XSOBEL (1): Uses the X-Sobel operator for pre-filtering.
+ * @details The pre-filter type affects how the images are prepared before computing the disparity map. Different pre-filtering methods can enhance specific image features or reduce noise, influencing the quality of the disparity map.
+ */
+ CV_WRAP virtual void setPreFilterType(int preFilterType) = 0;
+
+ /**
+ * @brief Gets the current size of the pre-filter kernel.
+ * @return The current pre-filter size.
+ */
+ CV_WRAP virtual int getPreFilterSize() const = 0;
+
+ /**
+ * @brief Sets the size of the pre-filter kernel.
+ * @param preFilterSize The size of the pre-filter kernel. Must be an odd integer, typically between 5 and 255.
+ * @details The pre-filter size determines the spatial extent of the pre-filtering operation, which prepares the images for disparity computation by normalizing brightness and enhancing texture. Larger sizes reduce noise but may blur details, while smaller sizes preserve details but are more susceptible to noise.
+ */
+ CV_WRAP virtual void setPreFilterSize(int preFilterSize) = 0;
+
+ /**
+ * @brief Gets the current truncation value for prefiltered pixels.
+ * @return The current pre-filter cap value.
+ */
+ CV_WRAP virtual int getPreFilterCap() const = 0;
+
+ /**
+ * @brief Sets the truncation value for prefiltered pixels.
+ * @param preFilterCap The truncation value. Typically in the range [1, 63].
+ * @details This value caps the output of the pre-filter to [-preFilterCap, preFilterCap], helping to reduce the impact of noise and outliers in the pre-filtered image.
+ */
+ CV_WRAP virtual void setPreFilterCap(int preFilterCap) = 0;
+
+ /**
+ * @brief Gets the current texture threshold value.
+ * @return The current texture threshold.
+ */
+ CV_WRAP virtual int getTextureThreshold() const = 0;
+
+ /**
+ * @brief Sets the threshold for filtering low-texture regions.
+ * @param textureThreshold The threshold value. Must be non-negative.
+ * @details This parameter filters out regions with low texture, where establishing correspondences is difficult, thus reducing noise in the disparity map. Higher values filter more aggressively but may discard valid information.
+ */
+ CV_WRAP virtual void setTextureThreshold(int textureThreshold) = 0;
+
+ /**
+ * @brief Gets the current uniqueness ratio value.
+ * @return The current uniqueness ratio.
+ */
+ CV_WRAP virtual int getUniquenessRatio() const = 0;
+
+ /**
+ * @brief Sets the uniqueness ratio for filtering ambiguous matches.
+ * @param uniquenessRatio The uniqueness ratio value. Typically in the range [5, 15], but can be from 0 to 100.
+ * @details This parameter ensures that the best match is sufficiently better than the next best match, reducing false positives. Higher values are stricter but may filter out valid matches in difficult regions.
+ */
+ CV_WRAP virtual void setUniquenessRatio(int uniquenessRatio) = 0;
+
+ /**
+ * @brief Gets the current size of the smaller block used for texture check.
+ * @return The current smaller block size.
+ */
+ CV_WRAP virtual int getSmallerBlockSize() const = 0;
+
+ /**
+ * @brief Sets the size of the smaller block used for texture check.
+ * @param blockSize The size of the smaller block. Must be an odd integer between 5 and 255.
+ * @details This parameter determines the size of the block used to compute texture variance. Smaller blocks capture finer details but are more sensitive to noise, while larger blocks are more robust but may miss fine details.
+ */
+ CV_WRAP virtual void setSmallerBlockSize(int blockSize) = 0;
+
+ /**
+ * @brief Gets the current Region of Interest (ROI) for the left image.
+ * @return The current ROI for the left image.
+ */
+ CV_WRAP virtual Rect getROI1() const = 0;
+
+ /**
+ * @brief Sets the Region of Interest (ROI) for the left image.
+ * @param roi1 The ROI rectangle for the left image.
+ * @details By setting the ROI, the stereo matching computation is limited to the specified region, improving performance and potentially accuracy by focusing on relevant parts of the image.
+ */
+ CV_WRAP virtual void setROI1(Rect roi1) = 0;
+
+ /**
+ * @brief Gets the current Region of Interest (ROI) for the right image.
+ * @return The current ROI for the right image.
+ */
+ CV_WRAP virtual Rect getROI2() const = 0;
+
+ /**
+ * @brief Sets the Region of Interest (ROI) for the right image.
+ * @param roi2 The ROI rectangle for the right image.
+ * @details Similar to setROI1, this limits the computation to the specified region in the right image.
+ */
+ CV_WRAP virtual void setROI2(Rect roi2) = 0;
+
+ /**
+ * @brief Creates StereoBM object
+ * @param numDisparities The disparity search range. For each pixel, the algorithm will find the best disparity from 0 (default minimum disparity) to numDisparities. The search range can be shifted by changing the minimum disparity.
+ * @param blockSize The linear size of the blocks compared by the algorithm. The size should be odd (as the block is centered at the current pixel). Larger block size implies smoother, though less accurate disparity map. Smaller block size gives more detailed disparity map, but there is a higher chance for the algorithm to find a wrong correspondence.
+ * @return A pointer to the created StereoBM object.
+ * @details The function creates a StereoBM object. You can then call StereoBM::compute() to compute disparity for a specific stereo pair.
+ */
+ CV_WRAP static Ptr create(int numDisparities = 0, int blockSize = 21);
+};
+
+/** @brief The class implements the modified H. Hirschmuller algorithm @cite HH08 that differs from the original
+one as follows:
+
+- By default, the algorithm is single-pass, which means that you consider only 5 directions
+instead of 8. Set mode=StereoSGBM::MODE_HH in createStereoSGBM to run the full variant of the
+algorithm but beware that it may consume a lot of memory.
+- The algorithm matches blocks, not individual pixels. Though, setting blockSize=1 reduces the
+blocks to single pixels.
+- Mutual information cost function is not implemented. Instead, a simpler Birchfield-Tomasi
+sub-pixel metric from @cite BT98 is used. Though, the color images are supported as well.
+- Some pre- and post- processing steps from K. Konolige algorithm StereoBM are included, for
+example: pre-filtering (StereoBM::PREFILTER_XSOBEL type) and post-filtering (uniqueness
+check, quadratic interpolation and speckle filtering).
+
+@note
+ - (Python) An example illustrating the use of the StereoSGBM matching algorithm can be found
+ at opencv_source_code/samples/python/stereo_match.py
+ */
+class CV_EXPORTS_W StereoSGBM : public StereoMatcher
+{
+public:
+ enum
+ {
+ MODE_SGBM = 0,
+ MODE_HH = 1,
+ MODE_SGBM_3WAY = 2,
+ MODE_HH4 = 3
+ };
+
+ CV_WRAP virtual int getPreFilterCap() const = 0;
+ CV_WRAP virtual void setPreFilterCap(int preFilterCap) = 0;
+
+ CV_WRAP virtual int getUniquenessRatio() const = 0;
+ CV_WRAP virtual void setUniquenessRatio(int uniquenessRatio) = 0;
+
+ CV_WRAP virtual int getP1() const = 0;
+ CV_WRAP virtual void setP1(int P1) = 0;
+
+ CV_WRAP virtual int getP2() const = 0;
+ CV_WRAP virtual void setP2(int P2) = 0;
+
+ CV_WRAP virtual int getMode() const = 0;
+ CV_WRAP virtual void setMode(int mode) = 0;
+
+ /** @brief Creates StereoSGBM object
+
+ @param minDisparity Minimum possible disparity value. Normally, it is zero but sometimes
+ rectification algorithms can shift images, so this parameter needs to be adjusted accordingly.
+ @param numDisparities Maximum disparity minus minimum disparity. The value is always greater than
+ zero. In the current implementation, this parameter must be divisible by 16.
+ @param blockSize Matched block size. It must be an odd number \>=1 . Normally, it should be
+ somewhere in the 3..11 range.
+ @param P1 The first parameter controlling the disparity smoothness. See below.
+ @param P2 The second parameter controlling the disparity smoothness. The larger the values are,
+ the smoother the disparity is. P1 is the penalty on the disparity change by plus or minus 1
+ between neighbor pixels. P2 is the penalty on the disparity change by more than 1 between neighbor
+ pixels. The algorithm requires P2 \> P1 . See stereo_match.cpp sample where some reasonably good
+ P1 and P2 values are shown (like 8\*number_of_image_channels\*blockSize\*blockSize and
+ 32\*number_of_image_channels\*blockSize\*blockSize , respectively).
+ @param disp12MaxDiff Maximum allowed difference (in integer pixel units) in the left-right
+ disparity check. Set it to a non-positive value to disable the check.
+ @param preFilterCap Truncation value for the prefiltered image pixels. The algorithm first
+ computes x-derivative at each pixel and clips its value by [-preFilterCap, preFilterCap] interval.
+ The result values are passed to the Birchfield-Tomasi pixel cost function.
+ @param uniquenessRatio Margin in percentage by which the best (minimum) computed cost function
+ value should "win" the second best value to consider the found match correct. Normally, a value
+ within the 5-15 range is good enough.
+ @param speckleWindowSize Maximum size of smooth disparity regions to consider their noise speckles
+ and invalidate. Set it to 0 to disable speckle filtering. Otherwise, set it somewhere in the
+ 50-200 range.
+ @param speckleRange Maximum disparity variation within each connected component. If you do speckle
+ filtering, set the parameter to a positive value, it will be implicitly multiplied by 16.
+ Normally, 1 or 2 is good enough.
+ @param mode Set it to StereoSGBM::MODE_HH to run the full-scale two-pass dynamic programming
+ algorithm. It will consume O(W\*H\*numDisparities) bytes, which is large for 640x480 stereo and
+ huge for HD-size pictures. By default, it is set to false .
+
+ The first constructor initializes StereoSGBM with all the default parameters. So, you only have to
+ set StereoSGBM::numDisparities at minimum. The second constructor enables you to set each parameter
+ to a custom value.
+ */
+ CV_WRAP static Ptr create(int minDisparity = 0, int numDisparities = 16, int blockSize = 3,
+ int P1 = 0, int P2 = 0, int disp12MaxDiff = 0,
+ int preFilterCap = 0, int uniquenessRatio = 0,
+ int speckleWindowSize = 0, int speckleRange = 0,
+ int mode = StereoSGBM::MODE_SGBM);
+};
+
+
+//! cv::undistort mode
+enum UndistortTypes
+{
+ PROJ_SPHERICAL_ORTHO = 0,
+ PROJ_SPHERICAL_EQRECT = 1
+};
+
+/** @brief Transforms an image to compensate for lens distortion.
+
+The function transforms an image to compensate radial and tangential lens distortion.
+
+The function is simply a combination of #initUndistortRectifyMap (with unity R ) and #remap
+(with bilinear interpolation). See the former function for details of the transformation being
+performed.
+
+Those pixels in the destination image, for which there is no correspondent pixels in the source
+image, are filled with zeros (black color).
+
+A particular subset of the source image that will be visible in the corrected image can be regulated
+by newCameraMatrix. You can use #getOptimalNewCameraMatrix to compute the appropriate
+newCameraMatrix depending on your requirements.
+
+The camera matrix and the distortion parameters can be determined using #calibrateCamera. If
+the resolution of images is different from the resolution used at the calibration stage, \f$f_x,
+f_y, c_x\f$ and \f$c_y\f$ need to be scaled accordingly, while the distortion coefficients remain
+the same.
+
+@param src Input (distorted) image.
+@param dst Output (corrected) image that has the same size and type as src .
+@param cameraMatrix Input camera matrix \f$A = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}\f$ .
+@param distCoeffs Input vector of distortion coefficients
+\f$(k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6[, s_1, s_2, s_3, s_4[, \tau_x, \tau_y]]]])\f$
+of 4, 5, 8, 12 or 14 elements. If the vector is NULL/empty, the zero distortion coefficients are assumed.
+@param newCameraMatrix Camera matrix of the distorted image. By default, it is the same as
+cameraMatrix but you may additionally scale and shift the result by using a different matrix.
+ */
+CV_EXPORTS_W void undistort( InputArray src, OutputArray dst,
+ InputArray cameraMatrix,
+ InputArray distCoeffs,
+ InputArray newCameraMatrix = noArray() );
+
+/** @brief Computes the undistortion and rectification transformation map.
+
+The function computes the joint undistortion and rectification transformation and represents the
+result in the form of maps for #remap. The undistorted image looks like original, as if it is
+captured with a camera using the camera matrix =newCameraMatrix and zero distortion. In case of a
+monocular camera, newCameraMatrix is usually equal to cameraMatrix, or it can be computed by
+#getOptimalNewCameraMatrix for a better control over scaling. In case of a stereo camera,
+newCameraMatrix is normally set to P1 or P2 computed by #stereoRectify .
+
+Also, this new camera is oriented differently in the coordinate space, according to R. That, for
+example, helps to align two heads of a stereo camera so that the epipolar lines on both images
+become horizontal and have the same y- coordinate (in case of a horizontally aligned stereo camera).
+
+The function actually builds the maps for the inverse mapping algorithm that is used by #remap. That
+is, for each pixel \f$(u, v)\f$ in the destination (corrected and rectified) image, the function
+computes the corresponding coordinates in the source image (that is, in the original image from
+camera). The following process is applied:
+\f[
+\begin{array}{l}
+x \leftarrow (u - {c'}_x)/{f'}_x \\
+y \leftarrow (v - {c'}_y)/{f'}_y \\
+{[X\,Y\,W]} ^T \leftarrow R^{-1}*[x \, y \, 1]^T \\
+x' \leftarrow X/W \\
+y' \leftarrow Y/W \\
+r^2 \leftarrow x'^2 + y'^2 \\
+x'' \leftarrow x' \frac{1 + k_1 r^2 + k_2 r^4 + k_3 r^6}{1 + k_4 r^2 + k_5 r^4 + k_6 r^6}
++ 2p_1 x' y' + p_2(r^2 + 2 x'^2) + s_1 r^2 + s_2 r^4\\
+y'' \leftarrow y' \frac{1 + k_1 r^2 + k_2 r^4 + k_3 r^6}{1 + k_4 r^2 + k_5 r^4 + k_6 r^6}
++ p_1 (r^2 + 2 y'^2) + 2 p_2 x' y' + s_3 r^2 + s_4 r^4 \\
+s\vecthree{x'''}{y'''}{1} =
+\vecthreethree{R_{33}(\tau_x, \tau_y)}{0}{-R_{13}((\tau_x, \tau_y)}
+{0}{R_{33}(\tau_x, \tau_y)}{-R_{23}(\tau_x, \tau_y)}
+{0}{0}{1} R(\tau_x, \tau_y) \vecthree{x''}{y''}{1}\\
+map_x(u,v) \leftarrow x''' f_x + c_x \\
+map_y(u,v) \leftarrow y''' f_y + c_y
+\end{array}
+\f]
+where \f$(k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6[, s_1, s_2, s_3, s_4[, \tau_x, \tau_y]]]])\f$
+are the distortion coefficients.
+
+In case of a stereo camera, this function is called twice: once for each camera head, after
+#stereoRectify, which in its turn is called after #stereoCalibrate. But if the stereo camera
+was not calibrated, it is still possible to compute the rectification transformations directly from
+the fundamental matrix using #stereoRectifyUncalibrated. For each camera, the function computes
+homography H as the rectification transformation in a pixel domain, not a rotation matrix R in 3D
+space. R can be computed from H as
+\f[\texttt{R} = \texttt{cameraMatrix} ^{-1} \cdot \texttt{H} \cdot \texttt{cameraMatrix}\f]
+where cameraMatrix can be chosen arbitrarily.
+
+@param cameraMatrix Input camera matrix \f$A=\vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}\f$ .
+@param distCoeffs Input vector of distortion coefficients
+\f$(k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6[, s_1, s_2, s_3, s_4[, \tau_x, \tau_y]]]])\f$
+of 4, 5, 8, 12 or 14 elements. If the vector is NULL/empty, the zero distortion coefficients are assumed.
+@param R Optional rectification transformation in the object space (3x3 matrix). R1 or R2 ,
+computed by #stereoRectify can be passed here. If the matrix is empty, the identity transformation
+is assumed. In #initUndistortRectifyMap R assumed to be an identity matrix.
+@param newCameraMatrix New camera matrix \f$A'=\vecthreethree{f_x'}{0}{c_x'}{0}{f_y'}{c_y'}{0}{0}{1}\f$.
+@param size Undistorted image size.
+@param m1type Type of the first output map that can be CV_32FC1, CV_32FC2 or CV_16SC2, see #convertMaps
+@param map1 The first output map.
+@param map2 The second output map.
+ */
+CV_EXPORTS_W
+void initUndistortRectifyMap(InputArray cameraMatrix, InputArray distCoeffs,
+ InputArray R, InputArray newCameraMatrix,
+ Size size, int m1type, OutputArray map1, OutputArray map2);
+
+/** @brief Computes the projection and inverse-rectification transformation map. In essense, this is the inverse of
+#initUndistortRectifyMap to accomodate stereo-rectification of projectors ('inverse-cameras') in projector-camera pairs.
+
+The function computes the joint projection and inverse rectification transformation and represents the
+result in the form of maps for #remap. The projected image looks like a distorted version of the original which,
+once projected by a projector, should visually match the original. In case of a monocular camera, newCameraMatrix
+is usually equal to cameraMatrix, or it can be computed by
+#getOptimalNewCameraMatrix for a better control over scaling. In case of a projector-camera pair,
+newCameraMatrix is normally set to P1 or P2 computed by #stereoRectify .
+
+The projector is oriented differently in the coordinate space, according to R. In case of projector-camera pairs,
+this helps align the projector (in the same manner as #initUndistortRectifyMap for the camera) to create a stereo-rectified pair. This
+allows epipolar lines on both images to become horizontal and have the same y-coordinate (in case of a horizontally aligned projector-camera pair).
+
+The function builds the maps for the inverse mapping algorithm that is used by #remap. That
+is, for each pixel \f$(u, v)\f$ in the destination (projected and inverse-rectified) image, the function
+computes the corresponding coordinates in the source image (that is, in the original digital image). The following process is applied:
+
+\f[
+\begin{array}{l}
+\text{newCameraMatrix}\\
+x \leftarrow (u - {c'}_x)/{f'}_x \\
+y \leftarrow (v - {c'}_y)/{f'}_y \\
+
+\\\text{Undistortion}
+\\\scriptsize{\textit{though equation shown is for radial undistortion, function implements cv::undistortPoints()}}\\
+r^2 \leftarrow x^2 + y^2 \\
+\theta \leftarrow \frac{1 + k_1 r^2 + k_2 r^4 + k_3 r^6}{1 + k_4 r^2 + k_5 r^4 + k_6 r^6}\\
+x' \leftarrow \frac{x}{\theta} \\
+y' \leftarrow \frac{y}{\theta} \\
+
+\\\text{Rectification}\\
+{[X\,Y\,W]} ^T \leftarrow R*[x' \, y' \, 1]^T \\
+x'' \leftarrow X/W \\
+y'' \leftarrow Y/W \\
+
+\\\text{cameraMatrix}\\
+map_x(u,v) \leftarrow x'' f_x + c_x \\
+map_y(u,v) \leftarrow y'' f_y + c_y
+\end{array}
+\f]
+where \f$(k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6[, s_1, s_2, s_3, s_4[, \tau_x, \tau_y]]]])\f$
+are the distortion coefficients vector distCoeffs.
+
+In case of a stereo-rectified projector-camera pair, this function is called for the projector while #initUndistortRectifyMap is called for the camera head.
+This is done after #stereoRectify, which in turn is called after #stereoCalibrate. If the projector-camera pair
+is not calibrated, it is still possible to compute the rectification transformations directly from
+the fundamental matrix using #stereoRectifyUncalibrated. For the projector and camera, the function computes
+homography H as the rectification transformation in a pixel domain, not a rotation matrix R in 3D
+space. R can be computed from H as
+\f[\texttt{R} = \texttt{cameraMatrix} ^{-1} \cdot \texttt{H} \cdot \texttt{cameraMatrix}\f]
+where cameraMatrix can be chosen arbitrarily.
+
+@param cameraMatrix Input camera matrix \f$A=\vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}\f$ .
+@param distCoeffs Input vector of distortion coefficients
+\f$(k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6[, s_1, s_2, s_3, s_4[, \tau_x, \tau_y]]]])\f$
+of 4, 5, 8, 12 or 14 elements. If the vector is NULL/empty, the zero distortion coefficients are assumed.
+@param R Optional rectification transformation in the object space (3x3 matrix). R1 or R2,
+computed by #stereoRectify can be passed here. If the matrix is empty, the identity transformation
+is assumed.
+@param newCameraMatrix New camera matrix \f$A'=\vecthreethree{f_x'}{0}{c_x'}{0}{f_y'}{c_y'}{0}{0}{1}\f$.
+@param size Distorted image size.
+@param m1type Type of the first output map. Can be CV_32FC1, CV_32FC2 or CV_16SC2, see #convertMaps
+@param map1 The first output map for #remap.
+@param map2 The second output map for #remap.
+ */
+CV_EXPORTS_W
+void initInverseRectificationMap( InputArray cameraMatrix, InputArray distCoeffs,
+ InputArray R, InputArray newCameraMatrix,
+ const Size& size, int m1type, OutputArray map1, OutputArray map2 );
+
+//! initializes maps for #remap for wide-angle
+CV_EXPORTS
+float initWideAngleProjMap(InputArray cameraMatrix, InputArray distCoeffs,
+ Size imageSize, int destImageWidth,
+ int m1type, OutputArray map1, OutputArray map2,
+ enum UndistortTypes projType = PROJ_SPHERICAL_EQRECT, double alpha = 0);
+static inline
+float initWideAngleProjMap(InputArray cameraMatrix, InputArray distCoeffs,
+ Size imageSize, int destImageWidth,
+ int m1type, OutputArray map1, OutputArray map2,
+ int projType, double alpha = 0)
+{
+ return initWideAngleProjMap(cameraMatrix, distCoeffs, imageSize, destImageWidth,
+ m1type, map1, map2, (UndistortTypes)projType, alpha);
+}
+
+/** @brief Returns the default new camera matrix.
+
+The function returns the camera matrix that is either an exact copy of the input cameraMatrix (when
+centerPrinicipalPoint=false ), or the modified one (when centerPrincipalPoint=true).
+
+In the latter case, the new camera matrix will be:
+
+\f[\begin{bmatrix} f_x && 0 && ( \texttt{imgSize.width} -1)*0.5 \\ 0 && f_y && ( \texttt{imgSize.height} -1)*0.5 \\ 0 && 0 && 1 \end{bmatrix} ,\f]
+
+where \f$f_x\f$ and \f$f_y\f$ are \f$(0,0)\f$ and \f$(1,1)\f$ elements of cameraMatrix, respectively.
+
+By default, the undistortion functions in OpenCV (see #initUndistortRectifyMap, #undistort) do not
+move the principal point. However, when you work with stereo, it is important to move the principal
+points in both views to the same y-coordinate (which is required by most of stereo correspondence
+algorithms), and may be to the same x-coordinate too. So, you can form the new camera matrix for
+each view where the principal points are located at the center.
+
+@param cameraMatrix Input camera matrix.
+@param imgsize Camera view image size in pixels.
+@param centerPrincipalPoint Location of the principal point in the new camera matrix. The
+parameter indicates whether this location should be at the image center or not.
+ */
+CV_EXPORTS_W
+Mat getDefaultNewCameraMatrix(InputArray cameraMatrix, Size imgsize = Size(),
+ bool centerPrincipalPoint = false);
+
+/** @brief Computes the ideal point coordinates from the observed point coordinates.
+
+The function is similar to #undistort and #initUndistortRectifyMap but it operates on a
+sparse set of points instead of a raster image. Also the function performs a reverse transformation
+to #projectPoints. In case of a 3D object, it does not reconstruct its 3D coordinates, but for a
+planar object, it does, up to a translation vector, if the proper R is specified.
+
+For each observed point coordinate \f$(u, v)\f$ the function computes:
+\f[
+\begin{array}{l}
+x^{"} \leftarrow (u - c_x)/f_x \\
+y^{"} \leftarrow (v - c_y)/f_y \\
+(x',y') = undistort(x^{"},y^{"}, \texttt{distCoeffs}) \\
+{[X\,Y\,W]} ^T \leftarrow R*[x' \, y' \, 1]^T \\
+x \leftarrow X/W \\
+y \leftarrow Y/W \\
+\text{only performed if P is specified:} \\
+u' \leftarrow x {f'}_x + {c'}_x \\
+v' \leftarrow y {f'}_y + {c'}_y
+\end{array}
+\f]
+
+where *undistort* is an approximate iterative algorithm that estimates the normalized original
+point coordinates out of the normalized distorted point coordinates ("normalized" means that the
+coordinates do not depend on the camera matrix).
+
+The function can be used for both a stereo camera head or a monocular camera (when R is empty).
+@param src Observed point coordinates, 2xN/Nx2 1-channel or 1xN/Nx1 2-channel (CV_32FC2 or CV_64FC2) (or
+vector\ ).
+@param dst Output ideal point coordinates (1xN/Nx1 2-channel or vector\ ) after undistortion and reverse perspective
+transformation. If matrix P is identity or omitted, dst will contain normalized point coordinates.
+@param cameraMatrix Camera matrix \f$\vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}\f$ .
+@param distCoeffs Input vector of distortion coefficients
+\f$(k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6[, s_1, s_2, s_3, s_4[, \tau_x, \tau_y]]]])\f$
+of 4, 5, 8, 12 or 14 elements. If the vector is NULL/empty, the zero distortion coefficients are assumed.
+@param R Rectification transformation in the object space (3x3 matrix). R1 or R2 computed by
+#stereoRectify can be passed here. If the matrix is empty, the identity transformation is used.
+@param P New camera matrix (3x3) or new projection matrix (3x4) \f$\begin{bmatrix} {f'}_x & 0 & {c'}_x & t_x \\ 0 & {f'}_y & {c'}_y & t_y \\ 0 & 0 & 1 & t_z \end{bmatrix}\f$. P1 or P2 computed by
+#stereoRectify can be passed here. If the matrix is empty, the identity new camera matrix is used.
+ */
+CV_EXPORTS_W
+void undistortPoints(InputArray src, OutputArray dst,
+ InputArray cameraMatrix, InputArray distCoeffs,
+ InputArray R = noArray(), InputArray P = noArray());
+/** @overload
+ @note Default version of #undistortPoints does 5 iterations to compute undistorted points.
+ */
+CV_EXPORTS_AS(undistortPointsIter)
+void undistortPoints(InputArray src, OutputArray dst,
+ InputArray cameraMatrix, InputArray distCoeffs,
+ InputArray R, InputArray P, TermCriteria criteria);
+
+/**
+ * @brief Compute undistorted image points position
+ *
+ * @param src Observed points position, 2xN/Nx2 1-channel or 1xN/Nx1 2-channel (CV_32FC2 or
+CV_64FC2) (or vector\ ).
+ * @param dst Output undistorted points position (1xN/Nx1 2-channel or vector\ ).
+ * @param cameraMatrix Camera matrix \f$\vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}\f$ .
+ * @param distCoeffs Distortion coefficients
+ */
+CV_EXPORTS_W
+void undistortImagePoints(InputArray src, OutputArray dst, InputArray cameraMatrix,
+ InputArray distCoeffs,
+ TermCriteria = TermCriteria(TermCriteria::MAX_ITER, 5, 0.01));
+
+//! @} calib3d
+
+/** @brief The methods in this namespace use a so-called fisheye camera model.
+ @ingroup calib3d_fisheye
+*/
+namespace fisheye
+{
+//! @addtogroup calib3d_fisheye
+//! @{
+
+ enum{
+ CALIB_USE_INTRINSIC_GUESS = 1 << 0,
+ CALIB_RECOMPUTE_EXTRINSIC = 1 << 1,
+ CALIB_CHECK_COND = 1 << 2,
+ CALIB_FIX_SKEW = 1 << 3,
+ CALIB_FIX_K1 = 1 << 4,
+ CALIB_FIX_K2 = 1 << 5,
+ CALIB_FIX_K3 = 1 << 6,
+ CALIB_FIX_K4 = 1 << 7,
+ CALIB_FIX_INTRINSIC = 1 << 8,
+ CALIB_FIX_PRINCIPAL_POINT = 1 << 9,
+ CALIB_ZERO_DISPARITY = 1 << 10,
+ CALIB_FIX_FOCAL_LENGTH = 1 << 11
+ };
+
+ /** @brief Projects points using fisheye model
+
+ @param objectPoints Array of object points, 1xN/Nx1 3-channel (or vector\ ), where N is
+ the number of points in the view.
+ @param imagePoints Output array of image points, 2xN/Nx2 1-channel or 1xN/Nx1 2-channel, or
+ vector\.
+ @param affine
+ @param K Camera intrinsic matrix \f$\cameramatrix{K}\f$.
+ @param D Input vector of distortion coefficients \f$\distcoeffsfisheye\f$.
+ @param alpha The skew coefficient.
+ @param jacobian Optional output 2Nx15 jacobian matrix of derivatives of image points with respect
+ to components of the focal lengths, coordinates of the principal point, distortion coefficients,
+ rotation vector, translation vector, and the skew. In the old interface different components of
+ the jacobian are returned via different output parameters.
+
+ The function computes projections of 3D points to the image plane given intrinsic and extrinsic
+ camera parameters. Optionally, the function computes Jacobians - matrices of partial derivatives of
+ image points coordinates (as functions of all the input parameters) with respect to the particular
+ parameters, intrinsic and/or extrinsic.
+ */
+ CV_EXPORTS void projectPoints(InputArray objectPoints, OutputArray imagePoints, const Affine3d& affine,
+ InputArray K, InputArray D, double alpha = 0, OutputArray jacobian = noArray());
+
+ /** @overload */
+ CV_EXPORTS_W void projectPoints(InputArray objectPoints, OutputArray imagePoints, InputArray rvec, InputArray tvec,
+ InputArray K, InputArray D, double alpha = 0, OutputArray jacobian = noArray());
+
+ /** @brief Distorts 2D points using fisheye model.
+
+ @param undistorted Array of object points, 1xN/Nx1 2-channel (or vector\ ), where N is
+ the number of points in the view.
+ @param K Camera intrinsic matrix \f$\cameramatrix{K}\f$.
+ @param D Input vector of distortion coefficients \f$\distcoeffsfisheye\f$.
+ @param alpha The skew coefficient.
+ @param distorted Output array of image points, 1xN/Nx1 2-channel, or vector\ .
+
+ Note that the function assumes the camera intrinsic matrix of the undistorted points to be identity.
+ This means if you want to distort image points you have to multiply them with \f$K^{-1}\f$ or
+ use another function overload.
+ */
+ CV_EXPORTS_W void distortPoints(InputArray undistorted, OutputArray distorted, InputArray K, InputArray D, double alpha = 0);
+
+ /** @overload
+ Overload of distortPoints function to handle cases when undistorted points are obtained with non-identity
+ camera matrix, e.g. output of #estimateNewCameraMatrixForUndistortRectify.
+ @param undistorted Array of object points, 1xN/Nx1 2-channel (or vector\ ), where N is
+ the number of points in the view.
+ @param Kundistorted Camera intrinsic matrix used as new camera matrix for undistortion.
+ @param K Camera intrinsic matrix \f$\cameramatrix{K}\f$.
+ @param D Input vector of distortion coefficients \f$\distcoeffsfisheye\f$.
+ @param alpha The skew coefficient.
+ @param distorted Output array of image points, 1xN/Nx1 2-channel, or vector\ .
+ @sa estimateNewCameraMatrixForUndistortRectify
+ */
+ CV_EXPORTS_W void distortPoints(InputArray undistorted, OutputArray distorted, InputArray Kundistorted, InputArray K, InputArray D, double alpha = 0);
+
+ /** @brief Undistorts 2D points using fisheye model
+
+ @param distorted Array of object points, 1xN/Nx1 2-channel (or vector\ ), where N is the
+ number of points in the view.
+ @param K Camera intrinsic matrix \f$\cameramatrix{K}\f$.
+ @param D Input vector of distortion coefficients \f$\distcoeffsfisheye\f$.
+ @param R Rectification transformation in the object space: 3x3 1-channel, or vector: 3x1/1x3
+ 1-channel or 1x1 3-channel
+ @param P New camera intrinsic matrix (3x3) or new projection matrix (3x4)
+ @param criteria Termination criteria
+ @param undistorted Output array of image points, 1xN/Nx1 2-channel, or vector\ .
+ */
+ CV_EXPORTS_W void undistortPoints(InputArray distorted, OutputArray undistorted,
+ InputArray K, InputArray D, InputArray R = noArray(), InputArray P = noArray(),
+ TermCriteria criteria = TermCriteria(TermCriteria::MAX_ITER + TermCriteria::EPS, 10, 1e-8));
+
+ /** @brief Computes undistortion and rectification maps for image transform by #remap. If D is empty zero
+ distortion is used, if R or P is empty identity matrixes are used.
+
+ @param K Camera intrinsic matrix \f$\cameramatrix{K}\f$.
+ @param D Input vector of distortion coefficients \f$\distcoeffsfisheye\f$.
+ @param R Rectification transformation in the object space: 3x3 1-channel, or vector: 3x1/1x3
+ 1-channel or 1x1 3-channel
+ @param P New camera intrinsic matrix (3x3) or new projection matrix (3x4)
+ @param size Undistorted image size.
+ @param m1type Type of the first output map that can be CV_32FC1 or CV_16SC2 . See #convertMaps
+ for details.
+ @param map1 The first output map.
+ @param map2 The second output map.
+ */
+ CV_EXPORTS_W void initUndistortRectifyMap(InputArray K, InputArray D, InputArray R, InputArray P,
+ const cv::Size& size, int m1type, OutputArray map1, OutputArray map2);
+
+ /** @brief Transforms an image to compensate for fisheye lens distortion.
+
+ @param distorted image with fisheye lens distortion.
+ @param undistorted Output image with compensated fisheye lens distortion.
+ @param K Camera intrinsic matrix \f$\cameramatrix{K}\f$.
+ @param D Input vector of distortion coefficients \f$\distcoeffsfisheye\f$.
+ @param Knew Camera intrinsic matrix of the distorted image. By default, it is the identity matrix but you
+ may additionally scale and shift the result by using a different matrix.
+ @param new_size the new size
+
+ The function transforms an image to compensate radial lens distortion.
+
+ The function is simply a combination of #fisheye::initUndistortRectifyMap (with unity R ) and #remap
+ (with bilinear interpolation). See the former function for details of the transformation being
+ performed.
+
+ See below the results of undistortImage.
+ - a\) result of undistort of perspective camera model (all possible coefficients (k_1, k_2, k_3,
+ k_4, k_5, k_6) of distortion were optimized under calibration)
+ - b\) result of #fisheye::undistortImage of fisheye camera model (all possible coefficients (k_1, k_2,
+ k_3, k_4) of fisheye distortion were optimized under calibration)
+ - c\) original image was captured with fisheye lens
+
+ Pictures a) and b) almost the same. But if we consider points of image located far from the center
+ of image, we can notice that on image a) these points are distorted.
+
+ 
+ */
+ CV_EXPORTS_W void undistortImage(InputArray distorted, OutputArray undistorted,
+ InputArray K, InputArray D, InputArray Knew = cv::noArray(), const Size& new_size = Size());
+
+ /** @brief Estimates new camera intrinsic matrix for undistortion or rectification.
+
+ @param K Camera intrinsic matrix \f$\cameramatrix{K}\f$.
+ @param image_size Size of the image
+ @param D Input vector of distortion coefficients \f$\distcoeffsfisheye\f$.
+ @param R Rectification transformation in the object space: 3x3 1-channel, or vector: 3x1/1x3
+ 1-channel or 1x1 3-channel
+ @param P New camera intrinsic matrix (3x3) or new projection matrix (3x4)
+ @param balance Sets the new focal length in range between the min focal length and the max focal
+ length. Balance is in range of [0, 1].
+ @param new_size the new size
+ @param fov_scale Divisor for new focal length.
+ */
+ CV_EXPORTS_W void estimateNewCameraMatrixForUndistortRectify(InputArray K, InputArray D, const Size &image_size, InputArray R,
+ OutputArray P, double balance = 0.0, const Size& new_size = Size(), double fov_scale = 1.0);
+
+ /** @brief Performs camera calibration
+
+ @param objectPoints vector of vectors of calibration pattern points in the calibration pattern
+ coordinate space.
+ @param imagePoints vector of vectors of the projections of calibration pattern points.
+ imagePoints.size() and objectPoints.size() and imagePoints[i].size() must be equal to
+ objectPoints[i].size() for each i.
+ @param image_size Size of the image used only to initialize the camera intrinsic matrix.
+ @param K Output 3x3 floating-point camera intrinsic matrix
+ \f$\cameramatrix{A}\f$ . If
+ @ref fisheye::CALIB_USE_INTRINSIC_GUESS is specified, some or all of fx, fy, cx, cy must be
+ initialized before calling the function.
+ @param D Output vector of distortion coefficients \f$\distcoeffsfisheye\f$.
+ @param rvecs Output vector of rotation vectors (see @ref Rodrigues ) estimated for each pattern view.
+ That is, each k-th rotation vector together with the corresponding k-th translation vector (see
+ the next output parameter description) brings the calibration pattern from the model coordinate
+ space (in which object points are specified) to the world coordinate space, that is, a real
+ position of the calibration pattern in the k-th pattern view (k=0.. *M* -1).
+ @param tvecs Output vector of translation vectors estimated for each pattern view.
+ @param flags Different flags that may be zero or a combination of the following values:
+ - @ref fisheye::CALIB_USE_INTRINSIC_GUESS cameraMatrix contains valid initial values of
+ fx, fy, cx, cy that are optimized further. Otherwise, (cx, cy) is initially set to the image
+ center ( imageSize is used), and focal distances are computed in a least-squares fashion.
+ - @ref fisheye::CALIB_RECOMPUTE_EXTRINSIC Extrinsic will be recomputed after each iteration
+ of intrinsic optimization.
+ - @ref fisheye::CALIB_CHECK_COND The functions will check validity of condition number.
+ - @ref fisheye::CALIB_FIX_SKEW Skew coefficient (alpha) is set to zero and stay zero.
+ - @ref fisheye::CALIB_FIX_K1,..., @ref fisheye::CALIB_FIX_K4 Selected distortion coefficients
+ are set to zeros and stay zero.
+ - @ref fisheye::CALIB_FIX_PRINCIPAL_POINT The principal point is not changed during the global
+optimization. It stays at the center or at a different location specified when @ref fisheye::CALIB_USE_INTRINSIC_GUESS is set too.
+ - @ref fisheye::CALIB_FIX_FOCAL_LENGTH The focal length is not changed during the global
+optimization. It is the \f$max(width,height)/\pi\f$ or the provided \f$f_x\f$, \f$f_y\f$ when @ref fisheye::CALIB_USE_INTRINSIC_GUESS is set too.
+ @param criteria Termination criteria for the iterative optimization algorithm.
+ */
+ CV_EXPORTS_W double calibrate(InputArrayOfArrays objectPoints, InputArrayOfArrays imagePoints, const Size& image_size,
+ InputOutputArray K, InputOutputArray D, OutputArrayOfArrays rvecs, OutputArrayOfArrays tvecs, int flags = 0,
+ TermCriteria criteria = TermCriteria(TermCriteria::COUNT + TermCriteria::EPS, 100, DBL_EPSILON));
+
+ /** @brief Stereo rectification for fisheye camera model
+
+ @param K1 First camera intrinsic matrix.
+ @param D1 First camera distortion parameters.
+ @param K2 Second camera intrinsic matrix.
+ @param D2 Second camera distortion parameters.
+ @param imageSize Size of the image used for stereo calibration.
+ @param R Rotation matrix between the coordinate systems of the first and the second
+ cameras.
+ @param tvec Translation vector between coordinate systems of the cameras.
+ @param R1 Output 3x3 rectification transform (rotation matrix) for the first camera.
+ @param R2 Output 3x3 rectification transform (rotation matrix) for the second camera.
+ @param P1 Output 3x4 projection matrix in the new (rectified) coordinate systems for the first
+ camera.
+ @param P2 Output 3x4 projection matrix in the new (rectified) coordinate systems for the second
+ camera.
+ @param Q Output \f$4 \times 4\f$ disparity-to-depth mapping matrix (see #reprojectImageTo3D ).
+ @param flags Operation flags that may be zero or @ref fisheye::CALIB_ZERO_DISPARITY . If the flag is set,
+ the function makes the principal points of each camera have the same pixel coordinates in the
+ rectified views. And if the flag is not set, the function may still shift the images in the
+ horizontal or vertical direction (depending on the orientation of epipolar lines) to maximize the
+ useful image area.
+ @param newImageSize New image resolution after rectification. The same size should be passed to
+ #initUndistortRectifyMap (see the stereo_calib.cpp sample in OpenCV samples directory). When (0,0)
+ is passed (default), it is set to the original imageSize . Setting it to larger value can help you
+ preserve details in the original image, especially when there is a big radial distortion.
+ @param balance Sets the new focal length in range between the min focal length and the max focal
+ length. Balance is in range of [0, 1].
+ @param fov_scale Divisor for new focal length.
+ */
+ CV_EXPORTS_W void stereoRectify(InputArray K1, InputArray D1, InputArray K2, InputArray D2, const Size &imageSize, InputArray R, InputArray tvec,
+ OutputArray R1, OutputArray R2, OutputArray P1, OutputArray P2, OutputArray Q, int flags, const Size &newImageSize = Size(),
+ double balance = 0.0, double fov_scale = 1.0);
+
+ /** @brief Performs stereo calibration
+
+ @param objectPoints Vector of vectors of the calibration pattern points.
+ @param imagePoints1 Vector of vectors of the projections of the calibration pattern points,
+ observed by the first camera.
+ @param imagePoints2 Vector of vectors of the projections of the calibration pattern points,
+ observed by the second camera.
+ @param K1 Input/output first camera intrinsic matrix:
+ \f$\vecthreethree{f_x^{(j)}}{0}{c_x^{(j)}}{0}{f_y^{(j)}}{c_y^{(j)}}{0}{0}{1}\f$ , \f$j = 0,\, 1\f$ . If
+ any of @ref fisheye::CALIB_USE_INTRINSIC_GUESS , @ref fisheye::CALIB_FIX_INTRINSIC are specified,
+ some or all of the matrix components must be initialized.
+ @param D1 Input/output vector of distortion coefficients \f$\distcoeffsfisheye\f$ of 4 elements.
+ @param K2 Input/output second camera intrinsic matrix. The parameter is similar to K1 .
+ @param D2 Input/output lens distortion coefficients for the second camera. The parameter is
+ similar to D1 .
+ @param imageSize Size of the image used only to initialize camera intrinsic matrix.
+ @param R Output rotation matrix between the 1st and the 2nd camera coordinate systems.
+ @param T Output translation vector between the coordinate systems of the cameras.
+ @param rvecs Output vector of rotation vectors ( @ref Rodrigues ) estimated for each pattern view in the
+ coordinate system of the first camera of the stereo pair (e.g. std::vector). More in detail, each
+ i-th rotation vector together with the corresponding i-th translation vector (see the next output parameter
+ description) brings the calibration pattern from the object coordinate space (in which object points are
+ specified) to the camera coordinate space of the first camera of the stereo pair. In more technical terms,
+ the tuple of the i-th rotation and translation vector performs a change of basis from object coordinate space
+ to camera coordinate space of the first camera of the stereo pair.
+ @param tvecs Output vector of translation vectors estimated for each pattern view, see parameter description
+ of previous output parameter ( rvecs ).
+ @param flags Different flags that may be zero or a combination of the following values:
+ - @ref fisheye::CALIB_FIX_INTRINSIC Fix K1, K2? and D1, D2? so that only R, T matrices
+ are estimated.
+ - @ref fisheye::CALIB_USE_INTRINSIC_GUESS K1, K2 contains valid initial values of
+ fx, fy, cx, cy that are optimized further. Otherwise, (cx, cy) is initially set to the image
+ center (imageSize is used), and focal distances are computed in a least-squares fashion.
+ - @ref fisheye::CALIB_RECOMPUTE_EXTRINSIC Extrinsic will be recomputed after each iteration
+ of intrinsic optimization.
+ - @ref fisheye::CALIB_CHECK_COND The functions will check validity of condition number.
+ - @ref fisheye::CALIB_FIX_SKEW Skew coefficient (alpha) is set to zero and stay zero.
+ - @ref fisheye::CALIB_FIX_K1,..., @ref fisheye::CALIB_FIX_K4 Selected distortion coefficients are set to zeros and stay
+ zero.
+ @param criteria Termination criteria for the iterative optimization algorithm.
+ */
+ CV_EXPORTS_W double stereoCalibrate(InputArrayOfArrays objectPoints, InputArrayOfArrays imagePoints1, InputArrayOfArrays imagePoints2,
+ InputOutputArray K1, InputOutputArray D1, InputOutputArray K2, InputOutputArray D2, Size imageSize,
+ OutputArray R, OutputArray T, OutputArrayOfArrays rvecs, OutputArrayOfArrays tvecs, int flags = fisheye::CALIB_FIX_INTRINSIC,
+ TermCriteria criteria = TermCriteria(TermCriteria::COUNT + TermCriteria::EPS, 100, DBL_EPSILON));
+
+ /// @overload
+ CV_EXPORTS_W double stereoCalibrate(InputArrayOfArrays objectPoints, InputArrayOfArrays imagePoints1, InputArrayOfArrays imagePoints2,
+ InputOutputArray K1, InputOutputArray D1, InputOutputArray K2, InputOutputArray D2, Size imageSize,
+ OutputArray R, OutputArray T, int flags = fisheye::CALIB_FIX_INTRINSIC,
+ TermCriteria criteria = TermCriteria(TermCriteria::COUNT + TermCriteria::EPS, 100, DBL_EPSILON));
+
+ /**
+ @brief Finds an object pose from 3D-2D point correspondences for fisheye camera model.
+
+ @param objectPoints Array of object points in the object coordinate space, Nx3 1-channel or
+ 1xN/Nx1 3-channel, where N is the number of points. vector\ can also be passed here.
+ @param imagePoints Array of corresponding image points, Nx2 1-channel or 1xN/Nx1 2-channel,
+ where N is the number of points. vector\ can also be passed here.
+ @param cameraMatrix Input camera intrinsic matrix \f$\cameramatrix{A}\f$ .
+ @param distCoeffs Input vector of distortion coefficients (4x1/1x4).
+ @param rvec Output rotation vector (see @ref Rodrigues ) that, together with tvec, brings points from
+ the model coordinate system to the camera coordinate system.
+ @param tvec Output translation vector.
+ @param useExtrinsicGuess Parameter used for #SOLVEPNP_ITERATIVE. If true (1), the function uses
+ the provided rvec and tvec values as initial approximations of the rotation and translation
+ vectors, respectively, and further optimizes them.
+ @param flags Method for solving a PnP problem: see @ref calib3d_solvePnP_flags
+ @param criteria Termination criteria for internal undistortPoints call.
+ The function internally undistorts points with @ref undistortPoints and call @ref cv::solvePnP,
+ thus the input are very similar. More information about Perspective-n-Points is described in @ref calib3d_solvePnP
+ for more information.
+ */
+ CV_EXPORTS_W bool solvePnP( InputArray objectPoints, InputArray imagePoints,
+ InputArray cameraMatrix, InputArray distCoeffs,
+ OutputArray rvec, OutputArray tvec,
+ bool useExtrinsicGuess = false, int flags = SOLVEPNP_ITERATIVE,
+ TermCriteria criteria = TermCriteria(TermCriteria::MAX_ITER + TermCriteria::EPS, 10, 1e-8)
+ );
+
+ /**
+ @brief Finds an object pose from 3D-2D point correspondences using the RANSAC scheme for fisheye camera moodel.
+
+ @param objectPoints Array of object points in the object coordinate space, Nx3 1-channel or
+ 1xN/Nx1 3-channel, where N is the number of points. vector\ can be also passed here.
+ @param imagePoints Array of corresponding image points, Nx2 1-channel or 1xN/Nx1 2-channel,
+ where N is the number of points. vector\ can be also passed here.
+ @param cameraMatrix Input camera intrinsic matrix \f$\cameramatrix{A}\f$ .
+ @param distCoeffs Input vector of distortion coefficients (4x1/1x4).
+ @param rvec Output rotation vector (see @ref Rodrigues ) that, together with tvec, brings points from
+ the model coordinate system to the camera coordinate system.
+ @param tvec Output translation vector.
+ @param useExtrinsicGuess Parameter used for #SOLVEPNP_ITERATIVE. If true (1), the function uses
+ the provided rvec and tvec values as initial approximations of the rotation and translation
+ vectors, respectively, and further optimizes them.
+ @param iterationsCount Number of iterations.
+ @param reprojectionError Inlier threshold value used by the RANSAC procedure. The parameter value
+ is the maximum allowed distance between the observed and computed point projections to consider it
+ an inlier.
+ @param confidence The probability that the algorithm produces a useful result.
+ @param inliers Output vector that contains indices of inliers in objectPoints and imagePoints .
+ @param flags Method for solving a PnP problem: see @ref calib3d_solvePnP_flags
+ This function returns the rotation and the translation vectors that transform a 3D point expressed in the object
+ coordinate frame to the camera coordinate frame, using different methods:
+ - P3P methods (@ref SOLVEPNP_P3P, @ref SOLVEPNP_AP3P): need 4 input points to return a unique solution.
+ - @ref SOLVEPNP_IPPE Input points must be >= 4 and object points must be coplanar.
+ - @ref SOLVEPNP_IPPE_SQUARE Special case suitable for marker pose estimation.
+ Number of input points must be 4. Object points must be defined in the following order:
+ - point 0: [-squareLength / 2, squareLength / 2, 0]
+ - point 1: [ squareLength / 2, squareLength / 2, 0]
+ - point 2: [ squareLength / 2, -squareLength / 2, 0]
+ - point 3: [-squareLength / 2, -squareLength / 2, 0]
+ - for all the other flags, number of input points must be >= 4 and object points can be in any configuration.
+ @param criteria Termination criteria for internal undistortPoints call.
+ The function interally undistorts points with @ref undistortPoints and call @ref cv::solvePnP,
+ thus the input are very similar. More information about Perspective-n-Points is described in @ref calib3d_solvePnP
+ for more information.
+ */
+ CV_EXPORTS_W bool solvePnPRansac( InputArray objectPoints, InputArray imagePoints,
+ InputArray cameraMatrix, InputArray distCoeffs,
+ OutputArray rvec, OutputArray tvec,
+ bool useExtrinsicGuess = false, int iterationsCount = 100,
+ float reprojectionError = 8.0, double confidence = 0.99,
+ OutputArray inliers = noArray(), int flags = SOLVEPNP_ITERATIVE,
+ TermCriteria criteria = TermCriteria(TermCriteria::MAX_ITER + TermCriteria::EPS, 10, 1e-8)
+ );
+
+//! @} calib3d_fisheye
+} // end namespace fisheye
+
+} //end namespace cv
+
+#if 0 //def __cplusplus
+//////////////////////////////////////////////////////////////////////////////////////////
+class CV_EXPORTS CvLevMarq
+{
+public:
+ CvLevMarq();
+ CvLevMarq( int nparams, int nerrs, CvTermCriteria criteria=
+ cvTermCriteria(CV_TERMCRIT_EPS+CV_TERMCRIT_ITER,30,DBL_EPSILON),
+ bool completeSymmFlag=false );
+ ~CvLevMarq();
+ void init( int nparams, int nerrs, CvTermCriteria criteria=
+ cvTermCriteria(CV_TERMCRIT_EPS+CV_TERMCRIT_ITER,30,DBL_EPSILON),
+ bool completeSymmFlag=false );
+ bool update( const CvMat*& param, CvMat*& J, CvMat*& err );
+ bool updateAlt( const CvMat*& param, CvMat*& JtJ, CvMat*& JtErr, double*& errNorm );
+
+ void clear();
+ void step();
+ enum { DONE=0, STARTED=1, CALC_J=2, CHECK_ERR=3 };
+
+ cv::Ptr mask;
+ cv::Ptr prevParam;
+ cv::Ptr param;
+ cv::Ptr J;
+ cv::Ptr err;
+ cv::Ptr JtJ;
+ cv::Ptr JtJN;
+ cv::Ptr JtErr;
+ cv::Ptr JtJV;
+ cv::Ptr JtJW;
+ double prevErrNorm, errNorm;
+ int lambdaLg10;
+ CvTermCriteria criteria;
+ int state;
+ int iters;
+ bool completeSymmFlag;
+ int solveMethod;
+};
+#endif
+
+#endif
diff --git a/3rdpart/OpenCV/include/opencv2/calib3d/calib3d.hpp b/3rdpart/OpenCV/include/opencv2/calib3d/calib3d.hpp
new file mode 100644
index 0000000..b3da45e
--- /dev/null
+++ b/3rdpart/OpenCV/include/opencv2/calib3d/calib3d.hpp
@@ -0,0 +1,48 @@
+/*M///////////////////////////////////////////////////////////////////////////////////////
+//
+// IMPORTANT: READ BEFORE DOWNLOADING, COPYING, INSTALLING OR USING.
+//
+// By downloading, copying, installing or using the software you agree to this license.
+// If you do not agree to this license, do not download, install,
+// copy or use the software.
+//
+//
+// License Agreement
+// For Open Source Computer Vision Library
+//
+// Copyright (C) 2000-2008, Intel Corporation, all rights reserved.
+// Copyright (C) 2009, Willow Garage Inc., all rights reserved.
+// Copyright (C) 2013, OpenCV Foundation, all rights reserved.
+// Third party copyrights are property of their respective owners.
+//
+// Redistribution and use in source and binary forms, with or without modification,
+// are permitted provided that the following conditions are met:
+//
+// * Redistribution's of source code must retain the above copyright notice,
+// this list of conditions and the following disclaimer.
+//
+// * Redistribution's in binary form must reproduce the above copyright notice,
+// this list of conditions and the following disclaimer in the documentation
+// and/or other materials provided with the distribution.
+//
+// * The name of the copyright holders may not be used to endorse or promote products
+// derived from this software without specific prior written permission.
+//
+// This software is provided by the copyright holders and contributors "as is" and
+// any express or implied warranties, including, but not limited to, the implied
+// warranties of merchantability and fitness for a particular purpose are disclaimed.
+// In no event shall the Intel Corporation or contributors be liable for any direct,
+// indirect, incidental, special, exemplary, or consequential damages
+// (including, but not limited to, procurement of substitute goods or services;
+// loss of use, data, or profits; or business interruption) however caused
+// and on any theory of liability, whether in contract, strict liability,
+// or tort (including negligence or otherwise) arising in any way out of
+// the use of this software, even if advised of the possibility of such damage.
+//
+//M*/
+
+#ifdef __OPENCV_BUILD
+#error this is a compatibility header which should not be used inside the OpenCV library
+#endif
+
+#include "opencv2/calib3d.hpp"
diff --git a/3rdpart/OpenCV/include/opencv2/calib3d/calib3d_c.h b/3rdpart/OpenCV/include/opencv2/calib3d/calib3d_c.h
new file mode 100644
index 0000000..e2af07b
--- /dev/null
+++ b/3rdpart/OpenCV/include/opencv2/calib3d/calib3d_c.h
@@ -0,0 +1,150 @@
+/*M///////////////////////////////////////////////////////////////////////////////////////
+//
+// IMPORTANT: READ BEFORE DOWNLOADING, COPYING, INSTALLING OR USING.
+//
+// By downloading, copying, installing or using the software you agree to this license.
+// If you do not agree to this license, do not download, install,
+// copy or use the software.
+//
+//
+// License Agreement
+// For Open Source Computer Vision Library
+//
+// Copyright (C) 2000-2008, Intel Corporation, all rights reserved.
+// Copyright (C) 2009, Willow Garage Inc., all rights reserved.
+// Copyright (C) 2013, OpenCV Foundation, all rights reserved.
+// Third party copyrights are property of their respective owners.
+//
+// Redistribution and use in source and binary forms, with or without modification,
+// are permitted provided that the following conditions are met:
+//
+// * Redistribution's of source code must retain the above copyright notice,
+// this list of conditions and the following disclaimer.
+//
+// * Redistribution's in binary form must reproduce the above copyright notice,
+// this list of conditions and the following disclaimer in the documentation
+// and/or other materials provided with the distribution.
+//
+// * The name of the copyright holders may not be used to endorse or promote products
+// derived from this software without specific prior written permission.
+//
+// This software is provided by the copyright holders and contributors "as is" and
+// any express or implied warranties, including, but not limited to, the implied
+// warranties of merchantability and fitness for a particular purpose are disclaimed.
+// In no event shall the Intel Corporation or contributors be liable for any direct,
+// indirect, incidental, special, exemplary, or consequential damages
+// (including, but not limited to, procurement of substitute goods or services;
+// loss of use, data, or profits; or business interruption) however caused
+// and on any theory of liability, whether in contract, strict liability,
+// or tort (including negligence or otherwise) arising in any way out of
+// the use of this software, even if advised of the possibility of such damage.
+//
+//M*/
+
+#ifndef OPENCV_CALIB3D_C_H
+#define OPENCV_CALIB3D_C_H
+
+#include "opencv2/core/types_c.h"
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+/* Calculates fundamental matrix given a set of corresponding points */
+#define CV_FM_7POINT 1
+#define CV_FM_8POINT 2
+
+#define CV_LMEDS 4
+#define CV_RANSAC 8
+
+#define CV_FM_LMEDS_ONLY CV_LMEDS
+#define CV_FM_RANSAC_ONLY CV_RANSAC
+#define CV_FM_LMEDS CV_LMEDS
+#define CV_FM_RANSAC CV_RANSAC
+
+enum
+{
+ CV_ITERATIVE = 0,
+ CV_EPNP = 1, // F.Moreno-Noguer, V.Lepetit and P.Fua "EPnP: Efficient Perspective-n-Point Camera Pose Estimation"
+ CV_P3P = 2, // X.S. Gao, X.-R. Hou, J. Tang, H.-F. Chang; "Complete Solution Classification for the Perspective-Three-Point Problem"
+ CV_DLS = 3 // Joel A. Hesch and Stergios I. Roumeliotis. "A Direct Least-Squares (DLS) Method for PnP"
+};
+
+#define CV_CALIB_CB_ADAPTIVE_THRESH 1
+#define CV_CALIB_CB_NORMALIZE_IMAGE 2
+#define CV_CALIB_CB_FILTER_QUADS 4
+#define CV_CALIB_CB_FAST_CHECK 8
+
+#define CV_CALIB_USE_INTRINSIC_GUESS 1
+#define CV_CALIB_FIX_ASPECT_RATIO 2
+#define CV_CALIB_FIX_PRINCIPAL_POINT 4
+#define CV_CALIB_ZERO_TANGENT_DIST 8
+#define CV_CALIB_FIX_FOCAL_LENGTH 16
+#define CV_CALIB_FIX_K1 32
+#define CV_CALIB_FIX_K2 64
+#define CV_CALIB_FIX_K3 128
+#define CV_CALIB_FIX_K4 2048
+#define CV_CALIB_FIX_K5 4096
+#define CV_CALIB_FIX_K6 8192
+#define CV_CALIB_RATIONAL_MODEL 16384
+#define CV_CALIB_THIN_PRISM_MODEL 32768
+#define CV_CALIB_FIX_S1_S2_S3_S4 65536
+#define CV_CALIB_TILTED_MODEL 262144
+#define CV_CALIB_FIX_TAUX_TAUY 524288
+#define CV_CALIB_FIX_TANGENT_DIST 2097152
+
+#define CV_CALIB_NINTRINSIC 18
+
+#define CV_CALIB_FIX_INTRINSIC 256
+#define CV_CALIB_SAME_FOCAL_LENGTH 512
+
+#define CV_CALIB_ZERO_DISPARITY 1024
+
+/* stereo correspondence parameters and functions */
+#define CV_STEREO_BM_NORMALIZED_RESPONSE 0
+#define CV_STEREO_BM_XSOBEL 1
+
+#ifdef __cplusplus
+} // extern "C"
+
+//////////////////////////////////////////////////////////////////////////////////////////
+class CV_EXPORTS CvLevMarq
+{
+public:
+ CvLevMarq();
+ CvLevMarq( int nparams, int nerrs, CvTermCriteria criteria=
+ cvTermCriteria(CV_TERMCRIT_EPS+CV_TERMCRIT_ITER,30,DBL_EPSILON),
+ bool completeSymmFlag=false );
+ ~CvLevMarq();
+ void init( int nparams, int nerrs, CvTermCriteria criteria=
+ cvTermCriteria(CV_TERMCRIT_EPS+CV_TERMCRIT_ITER,30,DBL_EPSILON),
+ bool completeSymmFlag=false );
+ bool update( const CvMat*& param, CvMat*& J, CvMat*& err );
+ bool updateAlt( const CvMat*& param, CvMat*& JtJ, CvMat*& JtErr, double*& errNorm );
+
+ void clear();
+ void step();
+ enum { DONE=0, STARTED=1, CALC_J=2, CHECK_ERR=3 };
+
+ cv::Ptr mask;
+ cv::Ptr prevParam;
+ cv::Ptr param;
+ cv::Ptr J;
+ cv::Ptr err;
+ cv::Ptr JtJ;
+ cv::Ptr JtJN;
+ cv::Ptr JtErr;
+ cv::Ptr JtJV;
+ cv::Ptr JtJW;
+ double prevErrNorm, errNorm;
+ int lambdaLg10;
+ CvTermCriteria criteria;
+ int state;
+ int iters;
+ bool completeSymmFlag;
+ int solveMethod;
+};
+
+#endif
+
+#endif /* OPENCV_CALIB3D_C_H */
diff --git a/3rdpart/OpenCV/include/opencv2/core.hpp b/3rdpart/OpenCV/include/opencv2/core.hpp
new file mode 100644
index 0000000..e383652
--- /dev/null
+++ b/3rdpart/OpenCV/include/opencv2/core.hpp
@@ -0,0 +1,3427 @@
+/*M///////////////////////////////////////////////////////////////////////////////////////
+//
+// IMPORTANT: READ BEFORE DOWNLOADING, COPYING, INSTALLING OR USING.
+//
+// By downloading, copying, installing or using the software you agree to this license.
+// If you do not agree to this license, do not download, install,
+// copy or use the software.
+//
+//
+// License Agreement
+// For Open Source Computer Vision Library
+//
+// Copyright (C) 2000-2015, Intel Corporation, all rights reserved.
+// Copyright (C) 2009-2011, Willow Garage Inc., all rights reserved.
+// Copyright (C) 2015, OpenCV Foundation, all rights reserved.
+// Copyright (C) 2015, Itseez Inc., all rights reserved.
+// Third party copyrights are property of their respective owners.
+//
+// Redistribution and use in source and binary forms, with or without modification,
+// are permitted provided that the following conditions are met:
+//
+// * Redistribution's of source code must retain the above copyright notice,
+// this list of conditions and the following disclaimer.
+//
+// * Redistribution's in binary form must reproduce the above copyright notice,
+// this list of conditions and the following disclaimer in the documentation
+// and/or other materials provided with the distribution.
+//
+// * The name of the copyright holders may not be used to endorse or promote products
+// derived from this software without specific prior written permission.
+//
+// This software is provided by the copyright holders and contributors "as is" and
+// any express or implied warranties, including, but not limited to, the implied
+// warranties of merchantability and fitness for a particular purpose are disclaimed.
+// In no event shall the Intel Corporation or contributors be liable for any direct,
+// indirect, incidental, special, exemplary, or consequential damages
+// (including, but not limited to, procurement of substitute goods or services;
+// loss of use, data, or profits; or business interruption) however caused
+// and on any theory of liability, whether in contract, strict liability,
+// or tort (including negligence or otherwise) arising in any way out of
+// the use of this software, even if advised of the possibility of such damage.
+//
+//M*/
+
+#ifndef OPENCV_CORE_HPP
+#define OPENCV_CORE_HPP
+
+#ifndef __cplusplus
+# error core.hpp header must be compiled as C++
+#endif
+
+#include "opencv2/core/cvdef.h"
+#include "opencv2/core/base.hpp"
+#include "opencv2/core/cvstd.hpp"
+#include "opencv2/core/traits.hpp"
+#include "opencv2/core/matx.hpp"
+#include "opencv2/core/types.hpp"
+#include "opencv2/core/mat.hpp"
+#include "opencv2/core/persistence.hpp"
+
+/**
+@defgroup core Core functionality
+
+The Core module is the backbone of OpenCV, offering fundamental data structures, matrix operations,
+and utility functions that other modules depend on. It’s essential for handling image data,
+performing mathematical computations, and managing memory efficiently within the OpenCV ecosystem.
+
+@{
+ @defgroup core_basic Basic structures
+ @defgroup core_array Operations on arrays
+ @defgroup core_async Asynchronous API
+ @defgroup core_xml XML/YAML/JSON Persistence
+ @defgroup core_cluster Clustering
+ @defgroup core_utils Utility and system functions and macros
+ @{
+ @defgroup core_logging Logging facilities
+ @defgroup core_utils_sse SSE utilities
+ @defgroup core_utils_neon NEON utilities
+ @defgroup core_utils_vsx VSX utilities
+ @defgroup core_utils_softfloat Softfloat support
+ @defgroup core_utils_samples Utility functions for OpenCV samples
+ @}
+ @defgroup core_opengl OpenGL interoperability
+ @defgroup core_optim Optimization Algorithms
+ @defgroup core_directx DirectX interoperability
+ @defgroup core_eigen Eigen support
+ @defgroup core_opencl OpenCL support
+ @defgroup core_va_intel Intel VA-API/OpenCL (CL-VA) interoperability
+ @defgroup core_hal Hardware Acceleration Layer
+ @{
+ @defgroup core_hal_functions Functions
+ @defgroup core_hal_interface Interface
+ @defgroup core_hal_intrin Universal intrinsics
+ @{
+ @defgroup core_hal_intrin_impl Private implementation helpers
+ @}
+ @defgroup core_lowlevel_api Low-level API for external libraries / plugins
+ @}
+ @defgroup core_parallel Parallel Processing
+ @{
+ @defgroup core_parallel_backend Parallel backends API
+ @}
+ @defgroup core_quaternion Quaternion
+@}
+ */
+
+namespace cv {
+
+//! @addtogroup core_utils
+//! @{
+
+/*! @brief Class passed to an error.
+
+This class encapsulates all or almost all necessary
+information about the error happened in the program. The exception is
+usually constructed and thrown implicitly via CV_Error and CV_Error_ macros.
+@see error
+ */
+class CV_EXPORTS Exception : public std::exception
+{
+public:
+ /*!
+ Default constructor
+ */
+ Exception();
+ /*!
+ Full constructor. Normally the constructor is not called explicitly.
+ Instead, the macros CV_Error(), CV_Error_() and CV_Assert() are used.
+ */
+ Exception(int _code, const String& _err, const String& _func, const String& _file, int _line);
+ virtual ~Exception() CV_NOEXCEPT;
+
+ /*!
+ \return the error description and the context as a text string.
+ */
+ virtual const char *what() const CV_NOEXCEPT CV_OVERRIDE;
+ void formatMessage();
+
+ String msg; ///< the formatted error message
+
+ int code; ///< error code @see CVStatus
+ String err; ///< error description
+ String func; ///< function name. Available only when the compiler supports getting it
+ String file; ///< source file name where the error has occurred
+ int line; ///< line number in the source file where the error has occurred
+};
+
+/*! @brief Signals an error and raises the exception.
+
+By default the function prints information about the error to stderr,
+then it either stops if cv::setBreakOnError() had been called before or raises the exception.
+It is possible to alternate error processing by using #redirectError().
+@param exc the exception raisen.
+@deprecated drop this version
+ */
+CV_EXPORTS CV_NORETURN void error(const Exception& exc);
+
+enum SortFlags { SORT_EVERY_ROW = 0, //!< each matrix row is sorted independently
+ SORT_EVERY_COLUMN = 1, //!< each matrix column is sorted
+ //!< independently; this flag and the previous one are
+ //!< mutually exclusive.
+ SORT_ASCENDING = 0, //!< each matrix row is sorted in the ascending
+ //!< order.
+ SORT_DESCENDING = 16 //!< each matrix row is sorted in the
+ //!< descending order; this flag and the previous one are also
+ //!< mutually exclusive.
+ };
+
+//! @} core_utils
+
+//! @addtogroup core_array
+//! @{
+
+//! Covariation flags
+enum CovarFlags {
+ /** The output covariance matrix is calculated as:
+ \f[\texttt{scale} \cdot [ \texttt{vects} [0]- \texttt{mean} , \texttt{vects} [1]- \texttt{mean} ,...]^T \cdot [ \texttt{vects} [0]- \texttt{mean} , \texttt{vects} [1]- \texttt{mean} ,...],\f]
+ The covariance matrix will be nsamples x nsamples. Such an unusual covariance matrix is used
+ for fast PCA of a set of very large vectors (see, for example, the EigenFaces technique for
+ face recognition). Eigenvalues of this "scrambled" matrix match the eigenvalues of the true
+ covariance matrix. The "true" eigenvectors can be easily calculated from the eigenvectors of
+ the "scrambled" covariance matrix. */
+ COVAR_SCRAMBLED = 0,
+ /**The output covariance matrix is calculated as:
+ \f[\texttt{scale} \cdot [ \texttt{vects} [0]- \texttt{mean} , \texttt{vects} [1]- \texttt{mean} ,...] \cdot [ \texttt{vects} [0]- \texttt{mean} , \texttt{vects} [1]- \texttt{mean} ,...]^T,\f]
+ covar will be a square matrix of the same size as the total number of elements in each input
+ vector. One and only one of #COVAR_SCRAMBLED and #COVAR_NORMAL must be specified.*/
+ COVAR_NORMAL = 1,
+ /** If the flag is specified, the function does not calculate mean from
+ the input vectors but, instead, uses the passed mean vector. This is useful if mean has been
+ pre-calculated or known in advance, or if the covariance matrix is calculated by parts. In
+ this case, mean is not a mean vector of the input sub-set of vectors but rather the mean
+ vector of the whole set.*/
+ COVAR_USE_AVG = 2,
+ /** If the flag is specified, the covariance matrix is scaled. In the
+ "normal" mode, scale is 1./nsamples . In the "scrambled" mode, scale is the reciprocal of the
+ total number of elements in each input vector. By default (if the flag is not specified), the
+ covariance matrix is not scaled ( scale=1 ).*/
+ COVAR_SCALE = 4,
+ /** If the flag is
+ specified, all the input vectors are stored as rows of the samples matrix. mean should be a
+ single-row vector in this case.*/
+ COVAR_ROWS = 8,
+ /** If the flag is
+ specified, all the input vectors are stored as columns of the samples matrix. mean should be a
+ single-column vector in this case.*/
+ COVAR_COLS = 16
+};
+
+enum ReduceTypes { REDUCE_SUM = 0, //!< the output is the sum of all rows/columns of the matrix.
+ REDUCE_AVG = 1, //!< the output is the mean vector of all rows/columns of the matrix.
+ REDUCE_MAX = 2, //!< the output is the maximum (column/row-wise) of all rows/columns of the matrix.
+ REDUCE_MIN = 3, //!< the output is the minimum (column/row-wise) of all rows/columns of the matrix.
+ REDUCE_SUM2 = 4 //!< the output is the sum of all squared rows/columns of the matrix.
+ };
+
+/** @brief Swaps two matrices
+*/
+CV_EXPORTS void swap(Mat& a, Mat& b);
+/** @overload */
+CV_EXPORTS void swap( UMat& a, UMat& b );
+
+/** @brief Computes the source location of an extrapolated pixel.
+
+The function computes and returns the coordinate of a donor pixel corresponding to the specified
+extrapolated pixel when using the specified extrapolation border mode. For example, if you use
+cv::BORDER_WRAP mode in the horizontal direction, cv::BORDER_REFLECT_101 in the vertical direction and
+want to compute value of the "virtual" pixel Point(-5, 100) in a floating-point image img, it
+looks like:
+@code{.cpp}
+ float val = img.at(borderInterpolate(100, img.rows, cv::BORDER_REFLECT_101),
+ borderInterpolate(-5, img.cols, cv::BORDER_WRAP));
+@endcode
+Normally, the function is not called directly. It is used inside filtering functions and also in
+copyMakeBorder.
+@param p 0-based coordinate of the extrapolated pixel along one of the axes, likely \<0 or \>= len
+@param len Length of the array along the corresponding axis.
+@param borderType Border type, one of the #BorderTypes, except for #BORDER_TRANSPARENT and
+#BORDER_ISOLATED. When borderType==#BORDER_CONSTANT, the function always returns -1, regardless
+of p and len.
+
+@sa copyMakeBorder
+*/
+CV_EXPORTS_W int borderInterpolate(int p, int len, int borderType);
+
+/** @example samples/cpp/tutorial_code/ImgTrans/copyMakeBorder_demo.cpp
+An example using copyMakeBorder function.
+Check @ref tutorial_copyMakeBorder "the corresponding tutorial" for more details
+*/
+
+/** @brief Forms a border around an image.
+
+The function copies the source image into the middle of the destination image. The areas to the
+left, to the right, above and below the copied source image will be filled with extrapolated
+pixels. This is not what filtering functions based on it do (they extrapolate pixels on-fly), but
+what other more complex functions, including your own, may do to simplify image boundary handling.
+
+The function supports the mode when src is already in the middle of dst . In this case, the
+function does not copy src itself but simply constructs the border, for example:
+
+@code{.cpp}
+ // let border be the same in all directions
+ int border=2;
+ // constructs a larger image to fit both the image and the border
+ Mat gray_buf(rgb.rows + border*2, rgb.cols + border*2, rgb.depth());
+ // select the middle part of it w/o copying data
+ Mat gray(gray_canvas, Rect(border, border, rgb.cols, rgb.rows));
+ // convert image from RGB to grayscale
+ cvtColor(rgb, gray, COLOR_RGB2GRAY);
+ // form a border in-place
+ copyMakeBorder(gray, gray_buf, border, border,
+ border, border, BORDER_REPLICATE);
+ // now do some custom filtering ...
+ ...
+@endcode
+@note When the source image is a part (ROI) of a bigger image, the function will try to use the
+pixels outside of the ROI to form a border. To disable this feature and always do extrapolation, as
+if src was not a ROI, use borderType | #BORDER_ISOLATED.
+
+@param src Source image.
+@param dst Destination image of the same type as src and the size Size(src.cols+left+right,
+src.rows+top+bottom) .
+@param top the top pixels
+@param bottom the bottom pixels
+@param left the left pixels
+@param right Parameter specifying how many pixels in each direction from the source image rectangle
+to extrapolate. For example, top=1, bottom=1, left=1, right=1 mean that 1 pixel-wide border needs
+to be built.
+@param borderType Border type. See borderInterpolate for details.
+@param value Border value if borderType==BORDER_CONSTANT .
+
+@sa borderInterpolate
+*/
+CV_EXPORTS_W void copyMakeBorder(InputArray src, OutputArray dst,
+ int top, int bottom, int left, int right,
+ int borderType, const Scalar& value = Scalar() );
+
+/** @brief Calculates the per-element sum of two arrays or an array and a scalar.
+
+The function add calculates:
+- Sum of two arrays when both input arrays have the same size and the same number of channels:
+\f[\texttt{dst}(I) = \texttt{saturate} ( \texttt{src1}(I) + \texttt{src2}(I)) \quad \texttt{if mask}(I) \ne0\f]
+- Sum of an array and a scalar when src2 is constructed from Scalar or has the same number of
+elements as `src1.channels()`:
+\f[\texttt{dst}(I) = \texttt{saturate} ( \texttt{src1}(I) + \texttt{src2} ) \quad \texttt{if mask}(I) \ne0\f]
+- Sum of a scalar and an array when src1 is constructed from Scalar or has the same number of
+elements as `src2.channels()`:
+\f[\texttt{dst}(I) = \texttt{saturate} ( \texttt{src1} + \texttt{src2}(I) ) \quad \texttt{if mask}(I) \ne0\f]
+where `I` is a multi-dimensional index of array elements. In case of multi-channel arrays, each
+channel is processed independently.
+
+The first function in the list above can be replaced with matrix expressions:
+@code{.cpp}
+ dst = src1 + src2;
+ dst += src1; // equivalent to add(dst, src1, dst);
+@endcode
+The input arrays and the output array can all have the same or different depths. For example, you
+can add a 16-bit unsigned array to a 8-bit signed array and store the sum as a 32-bit
+floating-point array. Depth of the output array is determined by the dtype parameter. In the second
+and third cases above, as well as in the first case, when src1.depth() == src2.depth(), dtype can
+be set to the default -1. In this case, the output array will have the same depth as the input
+array, be it src1, src2 or both.
+@note Saturation is not applied when the output array has the depth CV_32S. You may even get
+result of an incorrect sign in the case of overflow.
+@note (Python) Be careful to difference behaviour between src1/src2 are single number and they are tuple/array.
+`add(src,X)` means `add(src,(X,X,X,X))`.
+`add(src,(X,))` means `add(src,(X,0,0,0))`.
+@param src1 first input array or a scalar.
+@param src2 second input array or a scalar.
+@param dst output array that has the same size and number of channels as the input array(s); the
+depth is defined by dtype or src1/src2.
+@param mask optional operation mask - 8-bit single channel array, that specifies elements of the
+output array to be changed.
+@param dtype optional depth of the output array (see the discussion below).
+@sa subtract, addWeighted, scaleAdd, Mat::convertTo
+*/
+CV_EXPORTS_W void add(InputArray src1, InputArray src2, OutputArray dst,
+ InputArray mask = noArray(), int dtype = -1);
+
+/** @brief Calculates the per-element difference between two arrays or array and a scalar.
+
+The function subtract calculates:
+- Difference between two arrays, when both input arrays have the same size and the same number of
+channels:
+ \f[\texttt{dst}(I) = \texttt{saturate} ( \texttt{src1}(I) - \texttt{src2}(I)) \quad \texttt{if mask}(I) \ne0\f]
+- Difference between an array and a scalar, when src2 is constructed from Scalar or has the same
+number of elements as `src1.channels()`:
+ \f[\texttt{dst}(I) = \texttt{saturate} ( \texttt{src1}(I) - \texttt{src2} ) \quad \texttt{if mask}(I) \ne0\f]
+- Difference between a scalar and an array, when src1 is constructed from Scalar or has the same
+number of elements as `src2.channels()`:
+ \f[\texttt{dst}(I) = \texttt{saturate} ( \texttt{src1} - \texttt{src2}(I) ) \quad \texttt{if mask}(I) \ne0\f]
+- The reverse difference between a scalar and an array in the case of `SubRS`:
+ \f[\texttt{dst}(I) = \texttt{saturate} ( \texttt{src2} - \texttt{src1}(I) ) \quad \texttt{if mask}(I) \ne0\f]
+where I is a multi-dimensional index of array elements. In case of multi-channel arrays, each
+channel is processed independently.
+
+The first function in the list above can be replaced with matrix expressions:
+@code{.cpp}
+ dst = src1 - src2;
+ dst -= src1; // equivalent to subtract(dst, src1, dst);
+@endcode
+The input arrays and the output array can all have the same or different depths. For example, you
+can subtract to 8-bit unsigned arrays and store the difference in a 16-bit signed array. Depth of
+the output array is determined by dtype parameter. In the second and third cases above, as well as
+in the first case, when src1.depth() == src2.depth(), dtype can be set to the default -1. In this
+case the output array will have the same depth as the input array, be it src1, src2 or both.
+@note Saturation is not applied when the output array has the depth CV_32S. You may even get
+result of an incorrect sign in the case of overflow.
+@note (Python) Be careful to difference behaviour between src1/src2 are single number and they are tuple/array.
+`subtract(src,X)` means `subtract(src,(X,X,X,X))`.
+`subtract(src,(X,))` means `subtract(src,(X,0,0,0))`.
+@param src1 first input array or a scalar.
+@param src2 second input array or a scalar.
+@param dst output array of the same size and the same number of channels as the input array.
+@param mask optional operation mask; this is an 8-bit single channel array that specifies elements
+of the output array to be changed.
+@param dtype optional depth of the output array
+@sa add, addWeighted, scaleAdd, Mat::convertTo
+ */
+CV_EXPORTS_W void subtract(InputArray src1, InputArray src2, OutputArray dst,
+ InputArray mask = noArray(), int dtype = -1);
+
+
+/** @brief Calculates the per-element scaled product of two arrays.
+
+The function multiply calculates the per-element product of two arrays:
+
+\f[\texttt{dst} (I)= \texttt{saturate} ( \texttt{scale} \cdot \texttt{src1} (I) \cdot \texttt{src2} (I))\f]
+
+There is also a @ref MatrixExpressions -friendly variant of the first function. See Mat::mul .
+
+For a not-per-element matrix product, see gemm .
+
+@note Saturation is not applied when the output array has the depth
+CV_32S. You may even get result of an incorrect sign in the case of
+overflow.
+@note (Python) Be careful to difference behaviour between src1/src2 are single number and they are tuple/array.
+`multiply(src,X)` means `multiply(src,(X,X,X,X))`.
+`multiply(src,(X,))` means `multiply(src,(X,0,0,0))`.
+@param src1 first input array.
+@param src2 second input array of the same size and the same type as src1.
+@param dst output array of the same size and type as src1.
+@param scale optional scale factor.
+@param dtype optional depth of the output array
+@sa add, subtract, divide, scaleAdd, addWeighted, accumulate, accumulateProduct, accumulateSquare,
+Mat::convertTo
+*/
+CV_EXPORTS_W void multiply(InputArray src1, InputArray src2,
+ OutputArray dst, double scale = 1, int dtype = -1);
+
+/** @brief Performs per-element division of two arrays or a scalar by an array.
+
+The function cv::divide divides one array by another:
+\f[\texttt{dst(I) = saturate(src1(I)*scale/src2(I))}\f]
+or a scalar by an array when there is no src1 :
+\f[\texttt{dst(I) = saturate(scale/src2(I))}\f]
+
+Different channels of multi-channel arrays are processed independently.
+
+For integer types when src2(I) is zero, dst(I) will also be zero.
+
+@note In case of floating point data there is no special defined behavior for zero src2(I) values.
+Regular floating-point division is used.
+Expect correct IEEE-754 behaviour for floating-point data (with NaN, Inf result values).
+
+@note Saturation is not applied when the output array has the depth CV_32S. You may even get
+result of an incorrect sign in the case of overflow.
+@note (Python) Be careful to difference behaviour between src1/src2 are single number and they are tuple/array.
+`divide(src,X)` means `divide(src,(X,X,X,X))`.
+`divide(src,(X,))` means `divide(src,(X,0,0,0))`.
+@param src1 first input array.
+@param src2 second input array of the same size and type as src1.
+@param scale scalar factor.
+@param dst output array of the same size and type as src2.
+@param dtype optional depth of the output array; if -1, dst will have depth src2.depth(), but in
+case of an array-by-array division, you can only pass -1 when src1.depth()==src2.depth().
+@sa multiply, add, subtract
+*/
+CV_EXPORTS_W void divide(InputArray src1, InputArray src2, OutputArray dst,
+ double scale = 1, int dtype = -1);
+
+/** @overload */
+CV_EXPORTS_W void divide(double scale, InputArray src2,
+ OutputArray dst, int dtype = -1);
+
+/** @brief Calculates the sum of a scaled array and another array.
+
+The function scaleAdd is one of the classical primitive linear algebra operations, known as DAXPY
+or SAXPY in [BLAS](http://en.wikipedia.org/wiki/Basic_Linear_Algebra_Subprograms). It calculates
+the sum of a scaled array and another array:
+\f[\texttt{dst} (I)= \texttt{scale} \cdot \texttt{src1} (I) + \texttt{src2} (I)\f]
+The function can also be emulated with a matrix expression, for example:
+@code{.cpp}
+ Mat A(3, 3, CV_64F);
+ ...
+ A.row(0) = A.row(1)*2 + A.row(2);
+@endcode
+@param src1 first input array.
+@param alpha scale factor for the first array.
+@param src2 second input array of the same size and type as src1.
+@param dst output array of the same size and type as src1.
+@sa add, addWeighted, subtract, Mat::dot, Mat::convertTo
+*/
+CV_EXPORTS_W void scaleAdd(InputArray src1, double alpha, InputArray src2, OutputArray dst);
+
+/** @brief Calculates the weighted sum of two arrays.
+
+The function addWeighted calculates the weighted sum of two arrays as follows:
+\f[\texttt{dst} (I)= \texttt{saturate} ( \texttt{src1} (I)* \texttt{alpha} + \texttt{src2} (I)* \texttt{beta} + \texttt{gamma} )\f]
+where I is a multi-dimensional index of array elements. In case of multi-channel arrays, each
+channel is processed independently.
+The function can be replaced with a matrix expression:
+@code{.cpp}
+ dst = src1*alpha + src2*beta + gamma;
+@endcode
+@note Saturation is not applied when the output array has the depth CV_32S. You may even get
+result of an incorrect sign in the case of overflow.
+@param src1 first input array.
+@param alpha weight of the first array elements.
+@param src2 second input array of the same size and channel number as src1.
+@param beta weight of the second array elements.
+@param gamma scalar added to each sum.
+@param dst output array that has the same size and number of channels as the input arrays.
+@param dtype optional depth of the output array; when both input arrays have the same depth, dtype
+can be set to -1, which will be equivalent to src1.depth().
+@sa add, subtract, scaleAdd, Mat::convertTo
+*/
+CV_EXPORTS_W void addWeighted(InputArray src1, double alpha, InputArray src2,
+ double beta, double gamma, OutputArray dst, int dtype = -1);
+
+/** @brief Scales, calculates absolute values, and converts the result to 8-bit.
+
+On each element of the input array, the function convertScaleAbs
+performs three operations sequentially: scaling, taking an absolute
+value, conversion to an unsigned 8-bit type:
+\f[\texttt{dst} (I)= \texttt{saturate\_cast} (| \texttt{src} (I)* \texttt{alpha} + \texttt{beta} |)\f]
+In case of multi-channel arrays, the function processes each channel
+independently. When the output is not 8-bit, the operation can be
+emulated by calling the Mat::convertTo method (or by using matrix
+expressions) and then by calculating an absolute value of the result.
+For example:
+@code{.cpp}
+ Mat_ A(30,30);
+ randu(A, Scalar(-100), Scalar(100));
+ Mat_ B = A*5 + 3;
+ B = abs(B);
+ // Mat_ B = abs(A*5+3) will also do the job,
+ // but it will allocate a temporary matrix
+@endcode
+@param src input array.
+@param dst output array.
+@param alpha optional scale factor.
+@param beta optional delta added to the scaled values.
+@sa Mat::convertTo, cv::abs(const Mat&)
+*/
+CV_EXPORTS_W void convertScaleAbs(InputArray src, OutputArray dst,
+ double alpha = 1, double beta = 0);
+
+/** @brief Converts an array to half precision floating number.
+
+This function converts FP32 (single precision floating point) from/to FP16 (half precision floating point). CV_16S format is used to represent FP16 data.
+There are two use modes (src -> dst): CV_32F -> CV_16S and CV_16S -> CV_32F. The input array has to have type of CV_32F or
+CV_16S to represent the bit depth. If the input array is neither of them, the function will raise an error.
+The format of half precision floating point is defined in IEEE 754-2008.
+
+@param src input array.
+@param dst output array.
+
+@deprecated Use Mat::convertTo with CV_16F instead.
+*/
+CV_EXPORTS_W void convertFp16(InputArray src, OutputArray dst);
+
+/** @example samples/cpp/tutorial_code/core/how_to_scan_images/how_to_scan_images.cpp
+Check @ref tutorial_how_to_scan_images "the corresponding tutorial" for more details
+*/
+
+/** @brief Performs a look-up table transform of an array.
+
+The function LUT fills the output array with values from the look-up table. Indices of the entries
+are taken from the input array. That is, the function processes each element of src as follows:
+\f[\texttt{dst} (I) \leftarrow \texttt{lut(src(I) + d)}\f]
+where
+\f[d = \forkthree{0}{if \(\texttt{src}\) has depth \(\texttt{CV_8U}\) or \(\texttt{CV_16U}\)}{128}{if \(\texttt{src}\) has depth \(\texttt{CV_8S}\)}{32768}{if \(\texttt{src}\) has depth \(\texttt{CV_16S}\)}\f]
+@param src input array of 8-bit or 16-bit integer elements.
+@param lut look-up table of 256 elements (if src has depth CV_8U or CV_8S) or 65536 elements(if src has depth CV_16U or CV_16S); in case of multi-channel input array, the table should
+either have a single channel (in this case the same table is used for all channels) or the same
+number of channels as in the input array.
+@param dst output array of the same size and number of channels as src, and the same depth as lut.
+@sa convertScaleAbs, Mat::convertTo
+*/
+CV_EXPORTS_W void LUT(InputArray src, InputArray lut, OutputArray dst);
+
+/** @brief Calculates the sum of array elements.
+
+The function cv::sum calculates and returns the sum of array elements,
+independently for each channel.
+@param src input array that must have from 1 to 4 channels.
+@sa countNonZero, mean, meanStdDev, norm, minMaxLoc, reduce
+*/
+CV_EXPORTS_AS(sumElems) Scalar sum(InputArray src);
+
+/** @brief Checks for the presence of at least one non-zero array element.
+
+The function returns whether there are non-zero elements in src
+
+The function do not work with multi-channel arrays. If you need to check non-zero array
+elements across all the channels, use Mat::reshape first to reinterpret the array as
+single-channel. Or you may extract the particular channel using either extractImageCOI, or
+mixChannels, or split.
+
+@note
+- If the location of non-zero array elements is important, @ref findNonZero is helpful.
+- If the count of non-zero array elements is important, @ref countNonZero is helpful.
+@param src single-channel array.
+@sa mean, meanStdDev, norm, minMaxLoc, calcCovarMatrix
+@sa findNonZero, countNonZero
+*/
+CV_EXPORTS_W bool hasNonZero( InputArray src );
+
+/** @brief Counts non-zero array elements.
+
+The function returns the number of non-zero elements in src :
+\f[\sum _{I: \; \texttt{src} (I) \ne0 } 1\f]
+
+The function do not work with multi-channel arrays. If you need to count non-zero array
+elements across all the channels, use Mat::reshape first to reinterpret the array as
+single-channel. Or you may extract the particular channel using either extractImageCOI, or
+mixChannels, or split.
+
+@note
+- If only whether there are non-zero elements is important, @ref hasNonZero is helpful.
+- If the location of non-zero array elements is important, @ref findNonZero is helpful.
+@param src single-channel array.
+@sa mean, meanStdDev, norm, minMaxLoc, calcCovarMatrix
+@sa findNonZero, hasNonZero
+*/
+CV_EXPORTS_W int countNonZero( InputArray src );
+
+/** @brief Returns the list of locations of non-zero pixels
+
+Given a binary matrix (likely returned from an operation such
+as threshold(), compare(), >, ==, etc, return all of
+the non-zero indices as a cv::Mat or std::vector (x,y)
+For example:
+@code{.cpp}
+ cv::Mat binaryImage; // input, binary image
+ cv::Mat locations; // output, locations of non-zero pixels
+ cv::findNonZero(binaryImage, locations);
+
+ // access pixel coordinates
+ Point pnt = locations.at(i);
+@endcode
+or
+@code{.cpp}
+ cv::Mat binaryImage; // input, binary image
+ vector locations; // output, locations of non-zero pixels
+ cv::findNonZero(binaryImage, locations);
+
+ // access pixel coordinates
+ Point pnt = locations[i];
+@endcode
+
+The function do not work with multi-channel arrays. If you need to find non-zero
+elements across all the channels, use Mat::reshape first to reinterpret the array as
+single-channel. Or you may extract the particular channel using either extractImageCOI, or
+mixChannels, or split.
+
+@note
+- If only count of non-zero array elements is important, @ref countNonZero is helpful.
+- If only whether there are non-zero elements is important, @ref hasNonZero is helpful.
+@param src single-channel array
+@param idx the output array, type of cv::Mat or std::vector, corresponding to non-zero indices in the input
+@sa countNonZero, hasNonZero
+*/
+CV_EXPORTS_W void findNonZero( InputArray src, OutputArray idx );
+
+/** @brief Calculates an average (mean) of array elements.
+
+The function cv::mean calculates the mean value M of array elements,
+independently for each channel, and return it:
+\f[\begin{array}{l} N = \sum _{I: \; \texttt{mask} (I) \ne 0} 1 \\ M_c = \left ( \sum _{I: \; \texttt{mask} (I) \ne 0}{ \texttt{mtx} (I)_c} \right )/N \end{array}\f]
+When all the mask elements are 0's, the function returns Scalar::all(0)
+@param src input array that should have from 1 to 4 channels so that the result can be stored in
+Scalar_ .
+@param mask optional operation mask.
+@sa countNonZero, meanStdDev, norm, minMaxLoc
+*/
+CV_EXPORTS_W Scalar mean(InputArray src, InputArray mask = noArray());
+
+/** Calculates a mean and standard deviation of array elements.
+
+The function cv::meanStdDev calculates the mean and the standard deviation M
+of array elements independently for each channel and returns it via the
+output parameters:
+\f[\begin{array}{l} N = \sum _{I, \texttt{mask} (I) \ne 0} 1 \\ \texttt{mean} _c = \frac{\sum_{ I: \; \texttt{mask}(I) \ne 0} \texttt{src} (I)_c}{N} \\ \texttt{stddev} _c = \sqrt{\frac{\sum_{ I: \; \texttt{mask}(I) \ne 0} \left ( \texttt{src} (I)_c - \texttt{mean} _c \right )^2}{N}} \end{array}\f]
+When all the mask elements are 0's, the function returns
+mean=stddev=Scalar::all(0).
+@note The calculated standard deviation is only the diagonal of the
+complete normalized covariance matrix. If the full matrix is needed, you
+can reshape the multi-channel array M x N to the single-channel array
+M\*N x mtx.channels() (only possible when the matrix is continuous) and
+then pass the matrix to calcCovarMatrix .
+@param src input array that should have from 1 to 4 channels so that the results can be stored in
+Scalar_ 's.
+@param mean output parameter: calculated mean value.
+@param stddev output parameter: calculated standard deviation.
+@param mask optional operation mask.
+@sa countNonZero, mean, norm, minMaxLoc, calcCovarMatrix
+*/
+CV_EXPORTS_W void meanStdDev(InputArray src, OutputArray mean, OutputArray stddev,
+ InputArray mask=noArray());
+
+/** @brief Calculates the absolute norm of an array.
+
+This version of #norm calculates the absolute norm of src1. The type of norm to calculate is specified using #NormTypes.
+
+As example for one array consider the function \f$r(x)= \begin{pmatrix} x \\ 1-x \end{pmatrix}, x \in [-1;1]\f$.
+The \f$ L_{1}, L_{2} \f$ and \f$ L_{\infty} \f$ norm for the sample value \f$r(-1) = \begin{pmatrix} -1 \\ 2 \end{pmatrix}\f$
+is calculated as follows
+\f{align*}
+ \| r(-1) \|_{L_1} &= |-1| + |2| = 3 \\
+ \| r(-1) \|_{L_2} &= \sqrt{(-1)^{2} + (2)^{2}} = \sqrt{5} \\
+ \| r(-1) \|_{L_\infty} &= \max(|-1|,|2|) = 2
+\f}
+and for \f$r(0.5) = \begin{pmatrix} 0.5 \\ 0.5 \end{pmatrix}\f$ the calculation is
+\f{align*}
+ \| r(0.5) \|_{L_1} &= |0.5| + |0.5| = 1 \\
+ \| r(0.5) \|_{L_2} &= \sqrt{(0.5)^{2} + (0.5)^{2}} = \sqrt{0.5} \\
+ \| r(0.5) \|_{L_\infty} &= \max(|0.5|,|0.5|) = 0.5.
+\f}
+The following graphic shows all values for the three norm functions \f$\| r(x) \|_{L_1}, \| r(x) \|_{L_2}\f$ and \f$\| r(x) \|_{L_\infty}\f$.
+It is notable that the \f$ L_{1} \f$ norm forms the upper and the \f$ L_{\infty} \f$ norm forms the lower border for the example function \f$ r(x) \f$.
+
+
+When the mask parameter is specified and it is not empty, the norm is
+
+If normType is not specified, #NORM_L2 is used.
+calculated only over the region specified by the mask.
+
+Multi-channel input arrays are treated as single-channel arrays, that is,
+the results for all channels are combined.
+
+Hamming norms can only be calculated with CV_8U depth arrays.
+
+@param src1 first input array.
+@param normType type of the norm (see #NormTypes).
+@param mask optional operation mask; it must have the same size as src1 and CV_8UC1 type.
+*/
+CV_EXPORTS_W double norm(InputArray src1, int normType = NORM_L2, InputArray mask = noArray());
+
+/** @brief Calculates an absolute difference norm or a relative difference norm.
+
+This version of cv::norm calculates the absolute difference norm
+or the relative difference norm of arrays src1 and src2.
+The type of norm to calculate is specified using #NormTypes.
+
+@param src1 first input array.
+@param src2 second input array of the same size and the same type as src1.
+@param normType type of the norm (see #NormTypes).
+@param mask optional operation mask; it must have the same size as src1 and CV_8UC1 type.
+*/
+CV_EXPORTS_W double norm(InputArray src1, InputArray src2,
+ int normType = NORM_L2, InputArray mask = noArray());
+/** @overload
+@param src first input array.
+@param normType type of the norm (see #NormTypes).
+*/
+CV_EXPORTS double norm( const SparseMat& src, int normType );
+
+/** @brief Computes the Peak Signal-to-Noise Ratio (PSNR) image quality metric.
+
+This function calculates the Peak Signal-to-Noise Ratio (PSNR) image quality metric in decibels (dB),
+between two input arrays src1 and src2. The arrays must have the same type.
+
+The PSNR is calculated as follows:
+
+\f[
+\texttt{PSNR} = 10 \cdot \log_{10}{\left( \frac{R^2}{MSE} \right) }
+\f]
+
+where R is the maximum integer value of depth (e.g. 255 in the case of CV_8U data)
+and MSE is the mean squared error between the two arrays.
+
+@param src1 first input array.
+@param src2 second input array of the same size as src1.
+@param R the maximum pixel value (255 by default)
+
+ */
+CV_EXPORTS_W double PSNR(InputArray src1, InputArray src2, double R=255.);
+
+/** @brief naive nearest neighbor finder
+
+see http://en.wikipedia.org/wiki/Nearest_neighbor_search
+@todo document
+ */
+CV_EXPORTS_W void batchDistance(InputArray src1, InputArray src2,
+ OutputArray dist, int dtype, OutputArray nidx,
+ int normType = NORM_L2, int K = 0,
+ InputArray mask = noArray(), int update = 0,
+ bool crosscheck = false);
+
+/** @brief Normalizes the norm or value range of an array.
+
+The function cv::normalize normalizes scale and shift the input array elements so that
+\f[\| \texttt{dst} \| _{L_p}= \texttt{alpha}\f]
+(where p=Inf, 1 or 2) when normType=NORM_INF, NORM_L1, or NORM_L2, respectively; or so that
+\f[\min _I \texttt{dst} (I)= \texttt{alpha} , \, \, \max _I \texttt{dst} (I)= \texttt{beta}\f]
+
+when normType=NORM_MINMAX (for dense arrays only). The optional mask specifies a sub-array to be
+normalized. This means that the norm or min-n-max are calculated over the sub-array, and then this
+sub-array is modified to be normalized. If you want to only use the mask to calculate the norm or
+min-max but modify the whole array, you can use norm and Mat::convertTo.
+
+In case of sparse matrices, only the non-zero values are analyzed and transformed. Because of this,
+the range transformation for sparse matrices is not allowed since it can shift the zero level.
+
+Possible usage with some positive example data:
+@code{.cpp}
+ vector positiveData = { 2.0, 8.0, 10.0 };
+ vector normalizedData_l1, normalizedData_l2, normalizedData_inf, normalizedData_minmax;
+
+ // Norm to probability (total count)
+ // sum(numbers) = 20.0
+ // 2.0 0.1 (2.0/20.0)
+ // 8.0 0.4 (8.0/20.0)
+ // 10.0 0.5 (10.0/20.0)
+ normalize(positiveData, normalizedData_l1, 1.0, 0.0, NORM_L1);
+
+ // Norm to unit vector: ||positiveData|| = 1.0
+ // 2.0 0.15
+ // 8.0 0.62
+ // 10.0 0.77
+ normalize(positiveData, normalizedData_l2, 1.0, 0.0, NORM_L2);
+
+ // Norm to max element
+ // 2.0 0.2 (2.0/10.0)
+ // 8.0 0.8 (8.0/10.0)
+ // 10.0 1.0 (10.0/10.0)
+ normalize(positiveData, normalizedData_inf, 1.0, 0.0, NORM_INF);
+
+ // Norm to range [0.0;1.0]
+ // 2.0 0.0 (shift to left border)
+ // 8.0 0.75 (6.0/8.0)
+ // 10.0 1.0 (shift to right border)
+ normalize(positiveData, normalizedData_minmax, 1.0, 0.0, NORM_MINMAX);
+@endcode
+
+@note Due to rounding issues, min-max normalization can result in values outside provided boundaries.
+If exact range conformity is needed, following workarounds can be used:
+- use double floating point precision (dtype = CV_64F)
+- manually clip values (`cv::max(res, left_bound, res)`, `cv::min(res, right_bound, res)` or `np.clip`)
+
+@param src input array.
+@param dst output array of the same size as src .
+@param alpha norm value to normalize to or the lower range boundary in case of the range
+normalization.
+@param beta upper range boundary in case of the range normalization; it is not used for the norm
+normalization.
+@param norm_type normalization type (see cv::NormTypes).
+@param dtype when negative, the output array has the same type as src; otherwise, it has the same
+number of channels as src and the depth =CV_MAT_DEPTH(dtype).
+@param mask optional operation mask.
+@sa norm, Mat::convertTo, SparseMat::convertTo
+*/
+CV_EXPORTS_W void normalize( InputArray src, InputOutputArray dst, double alpha = 1, double beta = 0,
+ int norm_type = NORM_L2, int dtype = -1, InputArray mask = noArray());
+
+/** @overload
+@param src input array.
+@param dst output array of the same size as src .
+@param alpha norm value to normalize to or the lower range boundary in case of the range
+normalization.
+@param normType normalization type (see cv::NormTypes).
+*/
+CV_EXPORTS void normalize( const SparseMat& src, SparseMat& dst, double alpha, int normType );
+
+/** @brief Finds the global minimum and maximum in an array.
+
+The function cv::minMaxLoc finds the minimum and maximum element values and their positions. The
+extrema are searched across the whole array or, if mask is not an empty array, in the specified
+array region.
+
+In C++, if the input is multi-channel, you should omit the minLoc, maxLoc, and mask arguments
+(i.e. leave them as NULL, NULL, and noArray() respectively). These arguments are not
+supported for multi-channel input arrays. If working with multi-channel input and you
+need the minLoc, maxLoc, or mask arguments, then use Mat::reshape first to reinterpret
+the array as single-channel. Alternatively, you can extract the particular channel using either
+extractImageCOI, mixChannels, or split.
+
+In Python, multi-channel input is not supported at all due to a limitation in the
+binding generation process (there is no way to set minLoc and maxLoc to NULL). A
+workaround is to operate on each channel individually or to use NumPy to achieve the same
+functionality.
+
+@param src input single-channel array.
+@param minVal pointer to the returned minimum value; NULL is used if not required.
+@param maxVal pointer to the returned maximum value; NULL is used if not required.
+@param minLoc pointer to the returned minimum location (in 2D case); NULL is used if not required.
+@param maxLoc pointer to the returned maximum location (in 2D case); NULL is used if not required.
+@param mask optional mask used to select a sub-array.
+@sa max, min, reduceArgMin, reduceArgMax, compare, inRange, extractImageCOI, mixChannels, split, Mat::reshape
+*/
+CV_EXPORTS_W void minMaxLoc(InputArray src, CV_OUT double* minVal,
+ CV_OUT double* maxVal = 0, CV_OUT Point* minLoc = 0,
+ CV_OUT Point* maxLoc = 0, InputArray mask = noArray());
+
+/**
+ * @brief Finds indices of min elements along provided axis
+ *
+ * @note
+ * - If input or output array is not continuous, this function will create an internal copy.
+ * - NaN handling is left unspecified, see patchNaNs().
+ * - The returned index is always in bounds of input matrix.
+ *
+ * @param src input single-channel array.
+ * @param dst output array of type CV_32SC1 with the same dimensionality as src,
+ * except for axis being reduced - it should be set to 1.
+ * @param lastIndex whether to get the index of first or last occurrence of min.
+ * @param axis axis to reduce along.
+ * @sa reduceArgMax, minMaxLoc, min, max, compare, reduce
+ */
+CV_EXPORTS_W void reduceArgMin(InputArray src, OutputArray dst, int axis, bool lastIndex = false);
+
+/**
+ * @brief Finds indices of max elements along provided axis
+ *
+ * @note
+ * - If input or output array is not continuous, this function will create an internal copy.
+ * - NaN handling is left unspecified, see patchNaNs().
+ * - The returned index is always in bounds of input matrix.
+ *
+ * @param src input single-channel array.
+ * @param dst output array of type CV_32SC1 with the same dimensionality as src,
+ * except for axis being reduced - it should be set to 1.
+ * @param lastIndex whether to get the index of first or last occurrence of max.
+ * @param axis axis to reduce along.
+ * @sa reduceArgMin, minMaxLoc, min, max, compare, reduce
+ */
+CV_EXPORTS_W void reduceArgMax(InputArray src, OutputArray dst, int axis, bool lastIndex = false);
+
+/** @brief Finds the global minimum and maximum in an array
+
+The function cv::minMaxIdx finds the minimum and maximum element values and their positions. The
+extremums are searched across the whole array or, if mask is not an empty array, in the specified
+array region. In case of a sparse matrix, the minimum is found among non-zero elements
+only. Multi-channel input is supported without mask and extremums indexes (should be nullptr).
+@note When minIdx is not NULL, it must have at least 2 elements (as well as maxIdx), even if src is
+a single-row or single-column matrix. In OpenCV (following MATLAB) each array has at least 2
+dimensions, i.e. single-column matrix is Mx1 matrix (and therefore minIdx/maxIdx will be
+(i1,0)/(i2,0)) and single-row matrix is 1xN matrix (and therefore minIdx/maxIdx will be
+(0,j1)/(0,j2)).
+@param src input single-channel array.
+@param minVal pointer to the returned minimum value; NULL is used if not required.
+@param maxVal pointer to the returned maximum value; NULL is used if not required.
+@param minIdx pointer to the returned minimum location (in nD case); NULL is used if not required;
+Otherwise, it must point to an array of src.dims elements, the coordinates of the minimum element
+in each dimension are stored there sequentially.
+@param maxIdx pointer to the returned maximum location (in nD case). NULL is used if not required.
+@param mask specified array region
+*/
+CV_EXPORTS void minMaxIdx(InputArray src, double* minVal, double* maxVal = 0,
+ int* minIdx = 0, int* maxIdx = 0, InputArray mask = noArray());
+
+/** @overload
+@param a input single-channel array.
+@param minVal pointer to the returned minimum value; NULL is used if not required.
+@param maxVal pointer to the returned maximum value; NULL is used if not required.
+@param minIdx pointer to the returned minimum location (in nD case); NULL is used if not required;
+Otherwise, it must point to an array of src.dims elements, the coordinates of the minimum element
+in each dimension are stored there sequentially.
+@param maxIdx pointer to the returned maximum location (in nD case). NULL is used if not required.
+*/
+CV_EXPORTS void minMaxLoc(const SparseMat& a, double* minVal,
+ double* maxVal, int* minIdx = 0, int* maxIdx = 0);
+
+/** @brief Reduces a matrix to a vector.
+
+The function #reduce reduces the matrix to a vector by treating the matrix rows/columns as a set of
+1D vectors and performing the specified operation on the vectors until a single row/column is
+obtained. For example, the function can be used to compute horizontal and vertical projections of a
+raster image. In case of #REDUCE_MAX and #REDUCE_MIN, the output image should have the same type as the source one.
+In case of #REDUCE_SUM, #REDUCE_SUM2 and #REDUCE_AVG, the output may have a larger element bit-depth to preserve accuracy.
+And multi-channel arrays are also supported in these two reduction modes.
+
+The following code demonstrates its usage for a single channel matrix.
+@snippet snippets/core_reduce.cpp example
+
+And the following code demonstrates its usage for a two-channel matrix.
+@snippet snippets/core_reduce.cpp example2
+
+@param src input 2D matrix.
+@param dst output vector. Its size and type is defined by dim and dtype parameters.
+@param dim dimension index along which the matrix is reduced. 0 means that the matrix is reduced to
+a single row. 1 means that the matrix is reduced to a single column.
+@param rtype reduction operation that could be one of #ReduceTypes
+@param dtype when negative, the output vector will have the same type as the input matrix,
+otherwise, its type will be CV_MAKE_TYPE(CV_MAT_DEPTH(dtype), src.channels()).
+@sa repeat, reduceArgMin, reduceArgMax
+*/
+CV_EXPORTS_W void reduce(InputArray src, OutputArray dst, int dim, int rtype, int dtype = -1);
+
+/** @brief Creates one multi-channel array out of several single-channel ones.
+
+The function cv::merge merges several arrays to make a single multi-channel array. That is, each
+element of the output array will be a concatenation of the elements of the input arrays, where
+elements of i-th input array are treated as mv[i].channels()-element vectors.
+
+The function cv::split does the reverse operation. If you need to shuffle channels in some other
+advanced way, use cv::mixChannels.
+
+The following example shows how to merge 3 single channel matrices into a single 3-channel matrix.
+@snippet snippets/core_merge.cpp example
+
+@param mv input array of matrices to be merged; all the matrices in mv must have the same
+size and the same depth.
+@param count number of input matrices when mv is a plain C array; it must be greater than zero.
+@param dst output array of the same size and the same depth as mv[0]; The number of channels will
+be equal to the parameter count.
+@sa mixChannels, split, Mat::reshape
+*/
+CV_EXPORTS void merge(const Mat* mv, size_t count, OutputArray dst);
+
+/** @overload
+@param mv input vector of matrices to be merged; all the matrices in mv must have the same
+size and the same depth.
+@param dst output array of the same size and the same depth as mv[0]; The number of channels will
+be the total number of channels in the matrix array.
+ */
+CV_EXPORTS_W void merge(InputArrayOfArrays mv, OutputArray dst);
+
+/** @brief Divides a multi-channel array into several single-channel arrays.
+
+The function cv::split splits a multi-channel array into separate single-channel arrays:
+\f[\texttt{mv} [c](I) = \texttt{src} (I)_c\f]
+If you need to extract a single channel or do some other sophisticated channel permutation, use
+mixChannels.
+
+The following example demonstrates how to split a 3-channel matrix into 3 single channel matrices.
+@snippet snippets/core_split.cpp example
+
+@param src input multi-channel array.
+@param mvbegin output array; the number of arrays must match src.channels(); the arrays themselves are
+reallocated, if needed.
+@sa merge, mixChannels, cvtColor
+*/
+CV_EXPORTS void split(const Mat& src, Mat* mvbegin);
+
+/** @overload
+@param m input multi-channel array.
+@param mv output vector of arrays; the arrays themselves are reallocated, if needed.
+*/
+CV_EXPORTS_W void split(InputArray m, OutputArrayOfArrays mv);
+
+/** @brief Copies specified channels from input arrays to the specified channels of
+output arrays.
+
+The function cv::mixChannels provides an advanced mechanism for shuffling image channels.
+
+cv::split,cv::merge,cv::extractChannel,cv::insertChannel and some forms of cv::cvtColor are partial cases of cv::mixChannels.
+
+In the example below, the code splits a 4-channel BGRA image into a 3-channel BGR (with B and R
+channels swapped) and a separate alpha-channel image:
+@code{.cpp}
+ Mat bgra( 100, 100, CV_8UC4, Scalar(255,0,0,255) );
+ Mat bgr( bgra.rows, bgra.cols, CV_8UC3 );
+ Mat alpha( bgra.rows, bgra.cols, CV_8UC1 );
+
+ // forming an array of matrices is a quite efficient operation,
+ // because the matrix data is not copied, only the headers
+ Mat out[] = { bgr, alpha };
+ // bgra[0] -> bgr[2], bgra[1] -> bgr[1],
+ // bgra[2] -> bgr[0], bgra[3] -> alpha[0]
+ int from_to[] = { 0,2, 1,1, 2,0, 3,3 };
+ mixChannels( &bgra, 1, out, 2, from_to, 4 );
+@endcode
+@note Unlike many other new-style C++ functions in OpenCV (see the introduction section and
+Mat::create ), cv::mixChannels requires the output arrays to be pre-allocated before calling the
+function.
+@param src input array or vector of matrices; all of the matrices must have the same size and the
+same depth.
+@param nsrcs number of matrices in `src`.
+@param dst output array or vector of matrices; all the matrices **must be allocated**; their size and
+depth must be the same as in `src[0]`.
+@param ndsts number of matrices in `dst`.
+@param fromTo array of index pairs specifying which channels are copied and where; fromTo[k\*2] is
+a 0-based index of the input channel in src, fromTo[k\*2+1] is an index of the output channel in
+dst; the continuous channel numbering is used: the first input image channels are indexed from 0 to
+src[0].channels()-1, the second input image channels are indexed from src[0].channels() to
+src[0].channels() + src[1].channels()-1, and so on, the same scheme is used for the output image
+channels; as a special case, when fromTo[k\*2] is negative, the corresponding output channel is
+filled with zero .
+@param npairs number of index pairs in `fromTo`.
+@sa split, merge, extractChannel, insertChannel, cvtColor
+*/
+CV_EXPORTS void mixChannels(const Mat* src, size_t nsrcs, Mat* dst, size_t ndsts,
+ const int* fromTo, size_t npairs);
+
+/** @overload
+@param src input array or vector of matrices; all of the matrices must have the same size and the
+same depth.
+@param dst output array or vector of matrices; all the matrices **must be allocated**; their size and
+depth must be the same as in src[0].
+@param fromTo array of index pairs specifying which channels are copied and where; fromTo[k\*2] is
+a 0-based index of the input channel in src, fromTo[k\*2+1] is an index of the output channel in
+dst; the continuous channel numbering is used: the first input image channels are indexed from 0 to
+src[0].channels()-1, the second input image channels are indexed from src[0].channels() to
+src[0].channels() + src[1].channels()-1, and so on, the same scheme is used for the output image
+channels; as a special case, when fromTo[k\*2] is negative, the corresponding output channel is
+filled with zero .
+@param npairs number of index pairs in fromTo.
+*/
+CV_EXPORTS void mixChannels(InputArrayOfArrays src, InputOutputArrayOfArrays dst,
+ const int* fromTo, size_t npairs);
+
+/** @overload
+@param src input array or vector of matrices; all of the matrices must have the same size and the
+same depth.
+@param dst output array or vector of matrices; all the matrices **must be allocated**; their size and
+depth must be the same as in src[0].
+@param fromTo array of index pairs specifying which channels are copied and where; fromTo[k\*2] is
+a 0-based index of the input channel in src, fromTo[k\*2+1] is an index of the output channel in
+dst; the continuous channel numbering is used: the first input image channels are indexed from 0 to
+src[0].channels()-1, the second input image channels are indexed from src[0].channels() to
+src[0].channels() + src[1].channels()-1, and so on, the same scheme is used for the output image
+channels; as a special case, when fromTo[k\*2] is negative, the corresponding output channel is
+filled with zero .
+*/
+CV_EXPORTS_W void mixChannels(InputArrayOfArrays src, InputOutputArrayOfArrays dst,
+ const std::vector& fromTo);
+
+/** @brief Extracts a single channel from src (coi is 0-based index)
+@param src input array
+@param dst output array
+@param coi index of channel to extract
+@sa mixChannels, split
+*/
+CV_EXPORTS_W void extractChannel(InputArray src, OutputArray dst, int coi);
+
+/** @brief Inserts a single channel to dst (coi is 0-based index)
+@param src input array
+@param dst output array
+@param coi index of channel for insertion
+@sa mixChannels, merge
+*/
+CV_EXPORTS_W void insertChannel(InputArray src, InputOutputArray dst, int coi);
+
+/** @brief Flips a 2D array around vertical, horizontal, or both axes.
+
+The function cv::flip flips the array in one of three different ways (row
+and column indices are 0-based):
+\f[\texttt{dst} _{ij} =
+\left\{
+\begin{array}{l l}
+\texttt{src} _{\texttt{src.rows}-i-1,j} & if\; \texttt{flipCode} = 0 \\
+\texttt{src} _{i, \texttt{src.cols} -j-1} & if\; \texttt{flipCode} > 0 \\
+\texttt{src} _{ \texttt{src.rows} -i-1, \texttt{src.cols} -j-1} & if\; \texttt{flipCode} < 0 \\
+\end{array}
+\right.\f]
+The example scenarios of using the function are the following:
+* Vertical flipping of the image (flipCode == 0) to switch between
+ top-left and bottom-left image origin. This is a typical operation
+ in video processing on Microsoft Windows\* OS.
+* Horizontal flipping of the image with the subsequent horizontal
+ shift and absolute difference calculation to check for a
+ vertical-axis symmetry (flipCode \> 0).
+* Simultaneous horizontal and vertical flipping of the image with
+ the subsequent shift and absolute difference calculation to check
+ for a central symmetry (flipCode \< 0).
+* Reversing the order of point arrays (flipCode \> 0 or
+ flipCode == 0).
+@param src input array.
+@param dst output array of the same size and type as src.
+@param flipCode a flag to specify how to flip the array; 0 means
+flipping around the x-axis and positive value (for example, 1) means
+flipping around y-axis. Negative value (for example, -1) means flipping
+around both axes.
+@sa transpose, repeat, completeSymm
+*/
+CV_EXPORTS_W void flip(InputArray src, OutputArray dst, int flipCode);
+
+/** @brief Flips a n-dimensional at given axis
+ * @param src input array
+ * @param dst output array that has the same shape of src
+ * @param axis axis that performs a flip on. 0 <= axis < src.dims.
+ */
+CV_EXPORTS_W void flipND(InputArray src, OutputArray dst, int axis);
+
+/** @brief Broadcast the given Mat to the given shape.
+ * @param src input array
+ * @param shape target shape. Should be a list of CV_32S numbers. Note that negative values are not supported.
+ * @param dst output array that has the given shape
+ */
+CV_EXPORTS_W void broadcast(InputArray src, InputArray shape, OutputArray dst);
+
+enum RotateFlags {
+ ROTATE_90_CLOCKWISE = 0, //! A = (cv::Mat_(3, 2) << 1, 4,
+ 2, 5,
+ 3, 6);
+ cv::Mat_ B = (cv::Mat_(3, 2) << 7, 10,
+ 8, 11,
+ 9, 12);
+
+ cv::Mat C;
+ cv::hconcat(A, B, C);
+ //C:
+ //[1, 4, 7, 10;
+ // 2, 5, 8, 11;
+ // 3, 6, 9, 12]
+ @endcode
+ @param src1 first input array to be considered for horizontal concatenation.
+ @param src2 second input array to be considered for horizontal concatenation.
+ @param dst output array. It has the same number of rows and depth as the src1 and src2, and the sum of cols of the src1 and src2.
+ */
+CV_EXPORTS void hconcat(InputArray src1, InputArray src2, OutputArray dst);
+/** @overload
+ @code{.cpp}
+ std::vector matrices = { cv::Mat(4, 1, CV_8UC1, cv::Scalar(1)),
+ cv::Mat(4, 1, CV_8UC1, cv::Scalar(2)),
+ cv::Mat(4, 1, CV_8UC1, cv::Scalar(3)),};
+
+ cv::Mat out;
+ cv::hconcat( matrices, out );
+ //out:
+ //[1, 2, 3;
+ // 1, 2, 3;
+ // 1, 2, 3;
+ // 1, 2, 3]
+ @endcode
+ @param src input array or vector of matrices. all of the matrices must have the same number of rows and the same depth.
+ @param dst output array. It has the same number of rows and depth as the src, and the sum of cols of the src.
+same depth.
+ */
+CV_EXPORTS_W void hconcat(InputArrayOfArrays src, OutputArray dst);
+
+/** @brief Applies vertical concatenation to given matrices.
+
+The function vertically concatenates two or more cv::Mat matrices (with the same number of cols).
+@code{.cpp}
+ cv::Mat matArray[] = { cv::Mat(1, 4, CV_8UC1, cv::Scalar(1)),
+ cv::Mat(1, 4, CV_8UC1, cv::Scalar(2)),
+ cv::Mat(1, 4, CV_8UC1, cv::Scalar(3)),};
+
+ cv::Mat out;
+ cv::vconcat( matArray, 3, out );
+ //out:
+ //[1, 1, 1, 1;
+ // 2, 2, 2, 2;
+ // 3, 3, 3, 3]
+@endcode
+@param src input array or vector of matrices. all of the matrices must have the same number of cols and the same depth.
+@param nsrc number of matrices in src.
+@param dst output array. It has the same number of cols and depth as the src, and the sum of rows of the src.
+@sa cv::hconcat(const Mat*, size_t, OutputArray), @sa cv::hconcat(InputArrayOfArrays, OutputArray) and @sa cv::hconcat(InputArray, InputArray, OutputArray)
+*/
+CV_EXPORTS void vconcat(const Mat* src, size_t nsrc, OutputArray dst);
+/** @overload
+ @code{.cpp}
+ cv::Mat_ A = (cv::Mat_(3, 2) << 1, 7,
+ 2, 8,
+ 3, 9);
+ cv::Mat_ B = (cv::Mat_(3, 2) << 4, 10,
+ 5, 11,
+ 6, 12);
+
+ cv::Mat C;
+ cv::vconcat(A, B, C);
+ //C:
+ //[1, 7;
+ // 2, 8;
+ // 3, 9;
+ // 4, 10;
+ // 5, 11;
+ // 6, 12]
+ @endcode
+ @param src1 first input array to be considered for vertical concatenation.
+ @param src2 second input array to be considered for vertical concatenation.
+ @param dst output array. It has the same number of cols and depth as the src1 and src2, and the sum of rows of the src1 and src2.
+ */
+CV_EXPORTS void vconcat(InputArray src1, InputArray src2, OutputArray dst);
+/** @overload
+ @code{.cpp}
+ std::vector matrices = { cv::Mat(1, 4, CV_8UC1, cv::Scalar(1)),
+ cv::Mat(1, 4, CV_8UC1, cv::Scalar(2)),
+ cv::Mat(1, 4, CV_8UC1, cv::Scalar(3)),};
+
+ cv::Mat out;
+ cv::vconcat( matrices, out );
+ //out:
+ //[1, 1, 1, 1;
+ // 2, 2, 2, 2;
+ // 3, 3, 3, 3]
+ @endcode
+ @param src input array or vector of matrices. all of the matrices must have the same number of cols and the same depth
+ @param dst output array. It has the same number of cols and depth as the src, and the sum of rows of the src.
+same depth.
+ */
+CV_EXPORTS_W void vconcat(InputArrayOfArrays src, OutputArray dst);
+
+/** @brief computes bitwise conjunction of the two arrays (dst = src1 & src2)
+Calculates the per-element bit-wise conjunction of two arrays or an
+array and a scalar.
+
+The function cv::bitwise_and calculates the per-element bit-wise logical conjunction for:
+* Two arrays when src1 and src2 have the same size:
+ \f[\texttt{dst} (I) = \texttt{src1} (I) \wedge \texttt{src2} (I) \quad \texttt{if mask} (I) \ne0\f]
+* An array and a scalar when src2 is constructed from Scalar or has
+ the same number of elements as `src1.channels()`:
+ \f[\texttt{dst} (I) = \texttt{src1} (I) \wedge \texttt{src2} \quad \texttt{if mask} (I) \ne0\f]
+* A scalar and an array when src1 is constructed from Scalar or has
+ the same number of elements as `src2.channels()`:
+ \f[\texttt{dst} (I) = \texttt{src1} \wedge \texttt{src2} (I) \quad \texttt{if mask} (I) \ne0\f]
+In case of floating-point arrays, their machine-specific bit
+representations (usually IEEE754-compliant) are used for the operation.
+In case of multi-channel arrays, each channel is processed
+independently. In the second and third cases above, the scalar is first
+converted to the array type.
+@param src1 first input array or a scalar.
+@param src2 second input array or a scalar.
+@param dst output array that has the same size and type as the input
+arrays.
+@param mask optional operation mask, 8-bit single channel array, that
+specifies elements of the output array to be changed.
+*/
+CV_EXPORTS_W void bitwise_and(InputArray src1, InputArray src2,
+ OutputArray dst, InputArray mask = noArray());
+
+/** @brief Calculates the per-element bit-wise disjunction of two arrays or an
+array and a scalar.
+
+The function cv::bitwise_or calculates the per-element bit-wise logical disjunction for:
+* Two arrays when src1 and src2 have the same size:
+ \f[\texttt{dst} (I) = \texttt{src1} (I) \vee \texttt{src2} (I) \quad \texttt{if mask} (I) \ne0\f]
+* An array and a scalar when src2 is constructed from Scalar or has
+ the same number of elements as `src1.channels()`:
+ \f[\texttt{dst} (I) = \texttt{src1} (I) \vee \texttt{src2} \quad \texttt{if mask} (I) \ne0\f]
+* A scalar and an array when src1 is constructed from Scalar or has
+ the same number of elements as `src2.channels()`:
+ \f[\texttt{dst} (I) = \texttt{src1} \vee \texttt{src2} (I) \quad \texttt{if mask} (I) \ne0\f]
+In case of floating-point arrays, their machine-specific bit
+representations (usually IEEE754-compliant) are used for the operation.
+In case of multi-channel arrays, each channel is processed
+independently. In the second and third cases above, the scalar is first
+converted to the array type.
+@param src1 first input array or a scalar.
+@param src2 second input array or a scalar.
+@param dst output array that has the same size and type as the input
+arrays.
+@param mask optional operation mask, 8-bit single channel array, that
+specifies elements of the output array to be changed.
+*/
+CV_EXPORTS_W void bitwise_or(InputArray src1, InputArray src2,
+ OutputArray dst, InputArray mask = noArray());
+
+/** @brief Calculates the per-element bit-wise "exclusive or" operation on two
+arrays or an array and a scalar.
+
+The function cv::bitwise_xor calculates the per-element bit-wise logical "exclusive-or"
+operation for:
+* Two arrays when src1 and src2 have the same size:
+ \f[\texttt{dst} (I) = \texttt{src1} (I) \oplus \texttt{src2} (I) \quad \texttt{if mask} (I) \ne0\f]
+* An array and a scalar when src2 is constructed from Scalar or has
+ the same number of elements as `src1.channels()`:
+ \f[\texttt{dst} (I) = \texttt{src1} (I) \oplus \texttt{src2} \quad \texttt{if mask} (I) \ne0\f]
+* A scalar and an array when src1 is constructed from Scalar or has
+ the same number of elements as `src2.channels()`:
+ \f[\texttt{dst} (I) = \texttt{src1} \oplus \texttt{src2} (I) \quad \texttt{if mask} (I) \ne0\f]
+In case of floating-point arrays, their machine-specific bit
+representations (usually IEEE754-compliant) are used for the operation.
+In case of multi-channel arrays, each channel is processed
+independently. In the 2nd and 3rd cases above, the scalar is first
+converted to the array type.
+@param src1 first input array or a scalar.
+@param src2 second input array or a scalar.
+@param dst output array that has the same size and type as the input
+arrays.
+@param mask optional operation mask, 8-bit single channel array, that
+specifies elements of the output array to be changed.
+*/
+CV_EXPORTS_W void bitwise_xor(InputArray src1, InputArray src2,
+ OutputArray dst, InputArray mask = noArray());
+
+/** @brief Inverts every bit of an array.
+
+The function cv::bitwise_not calculates per-element bit-wise inversion of the input
+array:
+\f[\texttt{dst} (I) = \neg \texttt{src} (I)\f]
+In case of a floating-point input array, its machine-specific bit
+representation (usually IEEE754-compliant) is used for the operation. In
+case of multi-channel arrays, each channel is processed independently.
+@param src input array.
+@param dst output array that has the same size and type as the input
+array.
+@param mask optional operation mask, 8-bit single channel array, that
+specifies elements of the output array to be changed.
+*/
+CV_EXPORTS_W void bitwise_not(InputArray src, OutputArray dst,
+ InputArray mask = noArray());
+
+/** @brief Calculates the per-element absolute difference between two arrays or between an array and a scalar.
+
+The function cv::absdiff calculates:
+* Absolute difference between two arrays when they have the same
+ size and type:
+ \f[\texttt{dst}(I) = \texttt{saturate} (| \texttt{src1}(I) - \texttt{src2}(I)|)\f]
+* Absolute difference between an array and a scalar when the second
+ array is constructed from Scalar or has as many elements as the
+ number of channels in `src1`:
+ \f[\texttt{dst}(I) = \texttt{saturate} (| \texttt{src1}(I) - \texttt{src2} |)\f]
+* Absolute difference between a scalar and an array when the first
+ array is constructed from Scalar or has as many elements as the
+ number of channels in `src2`:
+ \f[\texttt{dst}(I) = \texttt{saturate} (| \texttt{src1} - \texttt{src2}(I) |)\f]
+ where I is a multi-dimensional index of array elements. In case of
+ multi-channel arrays, each channel is processed independently.
+@note Saturation is not applied when the arrays have the depth CV_32S.
+You may even get a negative value in the case of overflow.
+@note (Python) Be careful to difference behaviour between src1/src2 are single number and they are tuple/array.
+`absdiff(src,X)` means `absdiff(src,(X,X,X,X))`.
+`absdiff(src,(X,))` means `absdiff(src,(X,0,0,0))`.
+@param src1 first input array or a scalar.
+@param src2 second input array or a scalar.
+@param dst output array that has the same size and type as input arrays.
+@sa cv::abs(const Mat&)
+*/
+CV_EXPORTS_W void absdiff(InputArray src1, InputArray src2, OutputArray dst);
+
+/** @brief This is an overloaded member function, provided for convenience (python)
+Copies the matrix to another one.
+When the operation mask is specified, if the Mat::create call shown above reallocates the matrix, the newly allocated matrix is initialized with all zeros before copying the data.
+@param src source matrix.
+@param dst Destination matrix. If it does not have a proper size or type before the operation, it is
+reallocated.
+@param mask Operation mask of the same size as \*this. Its non-zero elements indicate which matrix
+elements need to be copied. The mask has to be of type CV_8U and can have 1 or multiple channels.
+*/
+
+void CV_EXPORTS_W copyTo(InputArray src, OutputArray dst, InputArray mask);
+/** @brief Checks if array elements lie between the elements of two other arrays.
+
+The function checks the range as follows:
+- For every element of a single-channel input array:
+ \f[\texttt{dst} (I)= \texttt{lowerb} (I)_0 \leq \texttt{src} (I)_0 \leq \texttt{upperb} (I)_0\f]
+- For two-channel arrays:
+ \f[\texttt{dst} (I)= \texttt{lowerb} (I)_0 \leq \texttt{src} (I)_0 \leq \texttt{upperb} (I)_0 \land \texttt{lowerb} (I)_1 \leq \texttt{src} (I)_1 \leq \texttt{upperb} (I)_1\f]
+- and so forth.
+
+That is, dst (I) is set to 255 (all 1 -bits) if src (I) is within the
+specified 1D, 2D, 3D, ... box and 0 otherwise.
+
+When the lower and/or upper boundary parameters are scalars, the indexes
+(I) at lowerb and upperb in the above formulas should be omitted.
+@param src first input array.
+@param lowerb inclusive lower boundary array or a scalar.
+@param upperb inclusive upper boundary array or a scalar.
+@param dst output array of the same size as src and CV_8U type.
+*/
+CV_EXPORTS_W void inRange(InputArray src, InputArray lowerb,
+ InputArray upperb, OutputArray dst);
+
+/** @brief Performs the per-element comparison of two arrays or an array and scalar value.
+
+The function compares:
+* Elements of two arrays when src1 and src2 have the same size:
+ \f[\texttt{dst} (I) = \texttt{src1} (I) \,\texttt{cmpop}\, \texttt{src2} (I)\f]
+* Elements of src1 with a scalar src2 when src2 is constructed from
+ Scalar or has a single element:
+ \f[\texttt{dst} (I) = \texttt{src1}(I) \,\texttt{cmpop}\, \texttt{src2}\f]
+* src1 with elements of src2 when src1 is constructed from Scalar or
+ has a single element:
+ \f[\texttt{dst} (I) = \texttt{src1} \,\texttt{cmpop}\, \texttt{src2} (I)\f]
+When the comparison result is true, the corresponding element of output
+array is set to 255. The comparison operations can be replaced with the
+equivalent matrix expressions:
+@code{.cpp}
+ Mat dst1 = src1 >= src2;
+ Mat dst2 = src1 < 8;
+ ...
+@endcode
+@param src1 first input array or a scalar; when it is an array, it must have a single channel.
+@param src2 second input array or a scalar; when it is an array, it must have a single channel.
+@param dst output array of type ref CV_8U that has the same size and the same number of channels as
+ the input arrays.
+@param cmpop a flag, that specifies correspondence between the arrays (cv::CmpTypes)
+@sa checkRange, min, max, threshold
+*/
+CV_EXPORTS_W void compare(InputArray src1, InputArray src2, OutputArray dst, int cmpop);
+
+/** @brief Calculates per-element minimum of two arrays or an array and a scalar.
+
+The function cv::min calculates the per-element minimum of two arrays:
+\f[\texttt{dst} (I)= \min ( \texttt{src1} (I), \texttt{src2} (I))\f]
+or array and a scalar:
+\f[\texttt{dst} (I)= \min ( \texttt{src1} (I), \texttt{value} )\f]
+@param src1 first input array.
+@param src2 second input array of the same size and type as src1.
+@param dst output array of the same size and type as src1.
+@sa max, compare, inRange, minMaxLoc
+*/
+CV_EXPORTS_W void min(InputArray src1, InputArray src2, OutputArray dst);
+/** @overload
+needed to avoid conflicts with const _Tp& std::min(const _Tp&, const _Tp&, _Compare)
+*/
+CV_EXPORTS void min(const Mat& src1, const Mat& src2, Mat& dst);
+/** @overload
+needed to avoid conflicts with const _Tp& std::min(const _Tp&, const _Tp&, _Compare)
+*/
+CV_EXPORTS void min(const UMat& src1, const UMat& src2, UMat& dst);
+
+/** @brief Calculates per-element maximum of two arrays or an array and a scalar.
+
+The function cv::max calculates the per-element maximum of two arrays:
+\f[\texttt{dst} (I)= \max ( \texttt{src1} (I), \texttt{src2} (I))\f]
+or array and a scalar:
+\f[\texttt{dst} (I)= \max ( \texttt{src1} (I), \texttt{value} )\f]
+@param src1 first input array.
+@param src2 second input array of the same size and type as src1 .
+@param dst output array of the same size and type as src1.
+@sa min, compare, inRange, minMaxLoc, @ref MatrixExpressions
+*/
+CV_EXPORTS_W void max(InputArray src1, InputArray src2, OutputArray dst);
+/** @overload
+needed to avoid conflicts with const _Tp& std::min(const _Tp&, const _Tp&, _Compare)
+*/
+CV_EXPORTS void max(const Mat& src1, const Mat& src2, Mat& dst);
+/** @overload
+needed to avoid conflicts with const _Tp& std::min(const _Tp&, const _Tp&, _Compare)
+*/
+CV_EXPORTS void max(const UMat& src1, const UMat& src2, UMat& dst);
+
+/** @brief Calculates a square root of array elements.
+
+The function cv::sqrt calculates a square root of each input array element.
+In case of multi-channel arrays, each channel is processed
+independently. The accuracy is approximately the same as of the built-in
+std::sqrt .
+@param src input floating-point array.
+@param dst output array of the same size and type as src.
+*/
+CV_EXPORTS_W void sqrt(InputArray src, OutputArray dst);
+
+/** @brief Raises every array element to a power.
+
+The function cv::pow raises every element of the input array to power :
+\f[\texttt{dst} (I) = \fork{\texttt{src}(I)^{power}}{if \(\texttt{power}\) is integer}{|\texttt{src}(I)|^{power}}{otherwise}\f]
+
+So, for a non-integer power exponent, the absolute values of input array
+elements are used. However, it is possible to get true values for
+negative values using some extra operations. In the example below,
+computing the 5th root of array src shows:
+@code{.cpp}
+ Mat mask = src < 0;
+ pow(src, 1./5, dst);
+ subtract(Scalar::all(0), dst, dst, mask);
+@endcode
+For some values of power, such as integer values, 0.5 and -0.5,
+specialized faster algorithms are used.
+
+Special values (NaN, Inf) are not handled.
+@param src input array.
+@param power exponent of power.
+@param dst output array of the same size and type as src.
+@sa sqrt, exp, log, cartToPolar, polarToCart
+*/
+CV_EXPORTS_W void pow(InputArray src, double power, OutputArray dst);
+
+/** @brief Calculates the exponent of every array element.
+
+The function cv::exp calculates the exponent of every element of the input
+array:
+\f[\texttt{dst} [I] = e^{ src(I) }\f]
+
+The maximum relative error is about 7e-6 for single-precision input and
+less than 1e-10 for double-precision input. Currently, the function
+converts denormalized values to zeros on output. Special values (NaN,
+Inf) are not handled.
+@param src input array.
+@param dst output array of the same size and type as src.
+@sa log, cartToPolar, polarToCart, phase, pow, sqrt, magnitude
+*/
+CV_EXPORTS_W void exp(InputArray src, OutputArray dst);
+
+/** @brief Calculates the natural logarithm of every array element.
+
+The function cv::log calculates the natural logarithm of every element of the input array:
+\f[\texttt{dst} (I) = \log (\texttt{src}(I)) \f]
+
+Output on zero, negative and special (NaN, Inf) values is undefined.
+
+@param src input array.
+@param dst output array of the same size and type as src .
+@sa exp, cartToPolar, polarToCart, phase, pow, sqrt, magnitude
+*/
+CV_EXPORTS_W void log(InputArray src, OutputArray dst);
+
+/** @brief Calculates x and y coordinates of 2D vectors from their magnitude and angle.
+
+The function cv::polarToCart calculates the Cartesian coordinates of each 2D
+vector represented by the corresponding elements of magnitude and angle:
+\f[\begin{array}{l} \texttt{x} (I) = \texttt{magnitude} (I) \cos ( \texttt{angle} (I)) \\ \texttt{y} (I) = \texttt{magnitude} (I) \sin ( \texttt{angle} (I)) \\ \end{array}\f]
+
+The relative accuracy of the estimated coordinates is about 1e-6.
+@param magnitude input floating-point array of magnitudes of 2D vectors;
+it can be an empty matrix (=Mat()), in this case, the function assumes
+that all the magnitudes are =1; if it is not empty, it must have the
+same size and type as angle.
+@param angle input floating-point array of angles of 2D vectors.
+@param x output array of x-coordinates of 2D vectors; it has the same
+size and type as angle.
+@param y output array of y-coordinates of 2D vectors; it has the same
+size and type as angle.
+@param angleInDegrees when true, the input angles are measured in
+degrees, otherwise, they are measured in radians.
+@sa cartToPolar, magnitude, phase, exp, log, pow, sqrt
+*/
+CV_EXPORTS_W void polarToCart(InputArray magnitude, InputArray angle,
+ OutputArray x, OutputArray y, bool angleInDegrees = false);
+
+/** @brief Calculates the magnitude and angle of 2D vectors.
+
+The function cv::cartToPolar calculates either the magnitude, angle, or both
+for every 2D vector (x(I),y(I)):
+\f[\begin{array}{l} \texttt{magnitude} (I)= \sqrt{\texttt{x}(I)^2+\texttt{y}(I)^2} , \\ \texttt{angle} (I)= \texttt{atan2} ( \texttt{y} (I), \texttt{x} (I))[ \cdot180 / \pi ] \end{array}\f]
+
+The angles are calculated with accuracy about 0.3 degrees. For the point
+(0,0), the angle is set to 0.
+@param x array of x-coordinates; this must be a single-precision or
+double-precision floating-point array.
+@param y array of y-coordinates, that must have the same size and same type as x.
+@param magnitude output array of magnitudes of the same size and type as x.
+@param angle output array of angles that has the same size and type as
+x; the angles are measured in radians (from 0 to 2\*Pi) or in degrees (0 to 360 degrees).
+@param angleInDegrees a flag, indicating whether the angles are measured
+in radians (which is by default), or in degrees.
+@sa Sobel, Scharr
+*/
+CV_EXPORTS_W void cartToPolar(InputArray x, InputArray y,
+ OutputArray magnitude, OutputArray angle,
+ bool angleInDegrees = false);
+
+/** @brief Calculates the rotation angle of 2D vectors.
+
+The function cv::phase calculates the rotation angle of each 2D vector that
+is formed from the corresponding elements of x and y :
+\f[\texttt{angle} (I) = \texttt{atan2} ( \texttt{y} (I), \texttt{x} (I))\f]
+
+The angle estimation accuracy is about 0.3 degrees. When x(I)=y(I)=0 ,
+the corresponding angle(I) is set to 0.
+@param x input floating-point array of x-coordinates of 2D vectors.
+@param y input array of y-coordinates of 2D vectors; it must have the
+same size and the same type as x.
+@param angle output array of vector angles; it has the same size and
+same type as x .
+@param angleInDegrees when true, the function calculates the angle in
+degrees, otherwise, they are measured in radians.
+*/
+CV_EXPORTS_W void phase(InputArray x, InputArray y, OutputArray angle,
+ bool angleInDegrees = false);
+
+/** @brief Calculates the magnitude of 2D vectors.
+
+The function cv::magnitude calculates the magnitude of 2D vectors formed
+from the corresponding elements of x and y arrays:
+\f[\texttt{dst} (I) = \sqrt{\texttt{x}(I)^2 + \texttt{y}(I)^2}\f]
+@param x floating-point array of x-coordinates of the vectors.
+@param y floating-point array of y-coordinates of the vectors; it must
+have the same size as x.
+@param magnitude output array of the same size and type as x.
+@sa cartToPolar, polarToCart, phase, sqrt
+*/
+CV_EXPORTS_W void magnitude(InputArray x, InputArray y, OutputArray magnitude);
+
+/** @brief Checks every element of an input array for invalid values.
+
+The function cv::checkRange checks that every array element is neither NaN nor infinite. When minVal \>
+-DBL_MAX and maxVal \< DBL_MAX, the function also checks that each value is between minVal and
+maxVal. In case of multi-channel arrays, each channel is processed independently. If some values
+are out of range, position of the first outlier is stored in pos (when pos != NULL). Then, the
+function either returns false (when quiet=true) or throws an exception.
+@param a input array.
+@param quiet a flag, indicating whether the functions quietly return false when the array elements
+are out of range or they throw an exception.
+@param pos optional output parameter, when not NULL, must be a pointer to array of src.dims
+elements.
+@param minVal inclusive lower boundary of valid values range.
+@param maxVal exclusive upper boundary of valid values range.
+*/
+CV_EXPORTS_W bool checkRange(InputArray a, bool quiet = true, CV_OUT Point* pos = 0,
+ double minVal = -DBL_MAX, double maxVal = DBL_MAX);
+/** @brief Replaces NaNs (Not-a-Number values) in a matrix with the specified value.
+
+This function modifies the input matrix in-place.
+The input matrix must be of type `CV_32F` or `CV_64F`; other types are not supported.
+
+@param a Input/output matrix (CV_32F or CV_64F type).
+@param val Value used to replace NaNs (defaults to 0).
+*/
+CV_EXPORTS_W void patchNaNs(InputOutputArray a, double val = 0);
+
+/** @brief Performs generalized matrix multiplication.
+
+The function cv::gemm performs generalized matrix multiplication similar to the
+gemm functions in BLAS level 3. For example,
+`gemm(src1, src2, alpha, src3, beta, dst, GEMM_1_T + GEMM_3_T)`
+corresponds to
+\f[\texttt{dst} = \texttt{alpha} \cdot \texttt{src1} ^T \cdot \texttt{src2} + \texttt{beta} \cdot \texttt{src3} ^T\f]
+
+In case of complex (two-channel) data, performed a complex matrix
+multiplication.
+
+The function can be replaced with a matrix expression. For example, the
+above call can be replaced with:
+@code{.cpp}
+ dst = alpha*src1.t()*src2 + beta*src3.t();
+@endcode
+@param src1 first multiplied input matrix that could be real(CV_32FC1,
+CV_64FC1) or complex(CV_32FC2, CV_64FC2).
+@param src2 second multiplied input matrix of the same type as src1.
+@param alpha weight of the matrix product.
+@param src3 third optional delta matrix added to the matrix product; it
+should have the same type as src1 and src2.
+@param beta weight of src3.
+@param dst output matrix; it has the proper size and the same type as
+input matrices.
+@param flags operation flags (cv::GemmFlags)
+@sa mulTransposed, transform
+*/
+CV_EXPORTS_W void gemm(InputArray src1, InputArray src2, double alpha,
+ InputArray src3, double beta, OutputArray dst, int flags = 0);
+
+/** @brief Calculates the product of a matrix and its transposition.
+
+The function cv::mulTransposed calculates the product of src and its
+transposition:
+\f[\texttt{dst} = \texttt{scale} ( \texttt{src} - \texttt{delta} )^T ( \texttt{src} - \texttt{delta} )\f]
+if aTa=true, and
+\f[\texttt{dst} = \texttt{scale} ( \texttt{src} - \texttt{delta} ) ( \texttt{src} - \texttt{delta} )^T\f]
+otherwise. The function is used to calculate the covariance matrix. With
+zero delta, it can be used as a faster substitute for general matrix
+product A\*B when B=A'
+@param src input single-channel matrix. Note that unlike gemm, the
+function can multiply not only floating-point matrices.
+@param dst output square matrix.
+@param aTa Flag specifying the multiplication ordering. See the
+description below.
+@param delta Optional delta matrix subtracted from src before the
+multiplication. When the matrix is empty ( delta=noArray() ), it is
+assumed to be zero, that is, nothing is subtracted. If it has the same
+size as src, it is simply subtracted. Otherwise, it is "repeated" (see
+repeat ) to cover the full src and then subtracted. Type of the delta
+matrix, when it is not empty, must be the same as the type of created
+output matrix. See the dtype parameter description below.
+@param scale Optional scale factor for the matrix product.
+@param dtype Optional type of the output matrix. When it is negative,
+the output matrix will have the same type as src . Otherwise, it will be
+type=CV_MAT_DEPTH(dtype) that should be either CV_32F or CV_64F .
+@sa calcCovarMatrix, gemm, repeat, reduce
+*/
+CV_EXPORTS_W void mulTransposed( InputArray src, OutputArray dst, bool aTa,
+ InputArray delta = noArray(),
+ double scale = 1, int dtype = -1 );
+
+/** @brief Transposes a matrix.
+
+The function cv::transpose transposes the matrix src :
+\f[\texttt{dst} (i,j) = \texttt{src} (j,i)\f]
+@note No complex conjugation is done in case of a complex matrix. It
+should be done separately if needed.
+@param src input array.
+@param dst output array of the same type as src.
+*/
+CV_EXPORTS_W void transpose(InputArray src, OutputArray dst);
+
+/** @brief Transpose for n-dimensional matrices.
+ *
+ * @note Input should be continuous single-channel matrix.
+ * @param src input array.
+ * @param order a permutation of [0,1,..,N-1] where N is the number of axes of src.
+ * The i'th axis of dst will correspond to the axis numbered order[i] of the input.
+ * @param dst output array of the same type as src.
+ */
+CV_EXPORTS_W void transposeND(InputArray src, const std::vector& order, OutputArray dst);
+
+/** @brief Performs the matrix transformation of every array element.
+
+The function cv::transform performs the matrix transformation of every
+element of the array src and stores the results in dst :
+\f[\texttt{dst} (I) = \texttt{m} \cdot \texttt{src} (I)\f]
+(when m.cols=src.channels() ), or
+\f[\texttt{dst} (I) = \texttt{m} \cdot [ \texttt{src} (I); 1]\f]
+(when m.cols=src.channels()+1 )
+
+Every element of the N -channel array src is interpreted as N -element
+vector that is transformed using the M x N or M x (N+1) matrix m to
+M-element vector - the corresponding element of the output array dst .
+
+The function may be used for geometrical transformation of
+N -dimensional points, arbitrary linear color space transformation (such
+as various kinds of RGB to YUV transforms), shuffling the image
+channels, and so forth.
+@param src input array that must have as many channels (1 to 4) as
+m.cols or m.cols-1.
+@param dst output array of the same size and depth as src; it has as
+many channels as m.rows.
+@param m transformation 2x2 or 2x3 floating-point matrix.
+@sa perspectiveTransform, getAffineTransform, estimateAffine2D, warpAffine, warpPerspective
+*/
+CV_EXPORTS_W void transform(InputArray src, OutputArray dst, InputArray m );
+
+/** @brief Performs the perspective matrix transformation of vectors.
+
+The function cv::perspectiveTransform transforms every element of src by
+treating it as a 2D or 3D vector, in the following way:
+\f[(x, y, z) \rightarrow (x'/w, y'/w, z'/w)\f]
+where
+\f[(x', y', z', w') = \texttt{mat} \cdot \begin{bmatrix} x & y & z & 1 \end{bmatrix}\f]
+and
+\f[w = \fork{w'}{if \(w' \ne 0\)}{\infty}{otherwise}\f]
+
+Here a 3D vector transformation is shown. In case of a 2D vector
+transformation, the z component is omitted.
+
+@note The function transforms a sparse set of 2D or 3D vectors. If you
+want to transform an image using perspective transformation, use
+warpPerspective . If you have an inverse problem, that is, you want to
+compute the most probable perspective transformation out of several
+pairs of corresponding points, you can use getPerspectiveTransform or
+findHomography .
+@param src input two-channel or three-channel floating-point array; each
+element is a 2D/3D vector to be transformed.
+@param dst output array of the same size and type as src.
+@param m 3x3 or 4x4 floating-point transformation matrix.
+@sa transform, warpPerspective, getPerspectiveTransform, findHomography
+*/
+CV_EXPORTS_W void perspectiveTransform(InputArray src, OutputArray dst, InputArray m );
+
+/** @brief Copies the lower or the upper half of a square matrix to its another half.
+
+The function cv::completeSymm copies the lower or the upper half of a square matrix to
+its another half. The matrix diagonal remains unchanged:
+ - \f$\texttt{m}_{ij}=\texttt{m}_{ji}\f$ for \f$i > j\f$ if
+ lowerToUpper=false
+ - \f$\texttt{m}_{ij}=\texttt{m}_{ji}\f$ for \f$i < j\f$ if
+ lowerToUpper=true
+
+@param m input-output floating-point square matrix.
+@param lowerToUpper operation flag; if true, the lower half is copied to
+the upper half. Otherwise, the upper half is copied to the lower half.
+@sa flip, transpose
+*/
+CV_EXPORTS_W void completeSymm(InputOutputArray m, bool lowerToUpper = false);
+
+/** @brief Initializes a scaled identity matrix.
+
+The function cv::setIdentity initializes a scaled identity matrix:
+\f[\texttt{mtx} (i,j)= \fork{\texttt{value}}{ if \(i=j\)}{0}{otherwise}\f]
+
+The function can also be emulated using the matrix initializers and the
+matrix expressions:
+@code
+ Mat A = Mat::eye(4, 3, CV_32F)*5;
+ // A will be set to [[5, 0, 0], [0, 5, 0], [0, 0, 5], [0, 0, 0]]
+@endcode
+@param mtx matrix to initialize (not necessarily square).
+@param s value to assign to diagonal elements.
+@sa Mat::zeros, Mat::ones, Mat::setTo, Mat::operator=
+*/
+CV_EXPORTS_W void setIdentity(InputOutputArray mtx, const Scalar& s = Scalar(1));
+
+/** @brief Returns the determinant of a square floating-point matrix.
+
+The function cv::determinant calculates and returns the determinant of the
+specified matrix. For small matrices ( mtx.cols=mtx.rows\<=3 ), the
+direct method is used. For larger matrices, the function uses LU
+factorization with partial pivoting.
+
+For symmetric positively-determined matrices, it is also possible to use
+eigen decomposition to calculate the determinant.
+@param mtx input matrix that must have CV_32FC1 or CV_64FC1 type and
+square size.
+@sa trace, invert, solve, eigen, @ref MatrixExpressions
+*/
+CV_EXPORTS_W double determinant(InputArray mtx);
+
+/** @brief Returns the trace of a matrix.
+
+The function cv::trace returns the sum of the diagonal elements of the
+matrix mtx .
+\f[\mathrm{tr} ( \texttt{mtx} ) = \sum _i \texttt{mtx} (i,i)\f]
+@param mtx input matrix.
+*/
+CV_EXPORTS_W Scalar trace(InputArray mtx);
+
+/** @brief Finds the inverse or pseudo-inverse of a matrix.
+
+The function cv::invert inverts the matrix src and stores the result in dst
+. When the matrix src is singular or non-square, the function calculates
+the pseudo-inverse matrix (the dst matrix) so that norm(src\*dst - I) is
+minimal, where I is an identity matrix.
+
+In case of the #DECOMP_LU method, the function returns non-zero value if
+the inverse has been successfully calculated and 0 if src is singular.
+
+In case of the #DECOMP_SVD method, the function returns the inverse
+condition number of src (the ratio of the smallest singular value to the
+largest singular value) and 0 if src is singular. The SVD method
+calculates a pseudo-inverse matrix if src is singular.
+
+Similarly to #DECOMP_LU, the method #DECOMP_CHOLESKY works only with
+non-singular square matrices that should also be symmetrical and
+positively defined. In this case, the function stores the inverted
+matrix in dst and returns non-zero. Otherwise, it returns 0.
+
+@param src input floating-point M x N matrix.
+@param dst output matrix of N x M size and the same type as src.
+@param flags inversion method (cv::DecompTypes)
+@sa solve, SVD
+*/
+CV_EXPORTS_W double invert(InputArray src, OutputArray dst, int flags = DECOMP_LU);
+
+/** @brief Solves one or more linear systems or least-squares problems.
+
+The function cv::solve solves a linear system or least-squares problem (the
+latter is possible with SVD or QR methods, or by specifying the flag
+#DECOMP_NORMAL ):
+\f[\texttt{dst} = \arg \min _X \| \texttt{src1} \cdot \texttt{X} - \texttt{src2} \|\f]
+
+If #DECOMP_LU or #DECOMP_CHOLESKY method is used, the function returns 1
+if src1 (or \f$\texttt{src1}^T\texttt{src1}\f$ ) is non-singular. Otherwise,
+it returns 0. In the latter case, dst is not valid. Other methods find a
+pseudo-solution in case of a singular left-hand side part.
+
+@note If you want to find a unity-norm solution of an under-defined
+singular system \f$\texttt{src1}\cdot\texttt{dst}=0\f$ , the function solve
+will not do the work. Use SVD::solveZ instead.
+
+@param src1 input matrix on the left-hand side of the system.
+@param src2 input matrix on the right-hand side of the system.
+@param dst output solution.
+@param flags solution (matrix inversion) method (#DecompTypes)
+@sa invert, SVD, eigen
+*/
+CV_EXPORTS_W bool solve(InputArray src1, InputArray src2,
+ OutputArray dst, int flags = DECOMP_LU);
+
+/** @brief Sorts each row or each column of a matrix.
+
+The function cv::sort sorts each matrix row or each matrix column in
+ascending or descending order. So you should pass two operation flags to
+get desired behaviour. If you want to sort matrix rows or columns
+lexicographically, you can use STL std::sort generic function with the
+proper comparison predicate.
+
+@param src input single-channel array.
+@param dst output array of the same size and type as src.
+@param flags operation flags, a combination of #SortFlags
+@sa sortIdx, randShuffle
+*/
+CV_EXPORTS_W void sort(InputArray src, OutputArray dst, int flags);
+
+/** @brief Sorts each row or each column of a matrix.
+
+The function cv::sortIdx sorts each matrix row or each matrix column in the
+ascending or descending order. So you should pass two operation flags to
+get desired behaviour. Instead of reordering the elements themselves, it
+stores the indices of sorted elements in the output array. For example:
+@code
+ Mat A = Mat::eye(3,3,CV_32F), B;
+ sortIdx(A, B, SORT_EVERY_ROW + SORT_ASCENDING);
+ // B will probably contain
+ // (because of equal elements in A some permutations are possible):
+ // [[1, 2, 0], [0, 2, 1], [0, 1, 2]]
+@endcode
+@param src input single-channel array.
+@param dst output integer array of the same size as src.
+@param flags operation flags that could be a combination of cv::SortFlags
+@sa sort, randShuffle
+*/
+CV_EXPORTS_W void sortIdx(InputArray src, OutputArray dst, int flags);
+
+/** @brief Finds the real roots of a cubic equation.
+
+The function solveCubic finds the real roots of a cubic equation:
+- if coeffs is a 4-element vector:
+\f[\texttt{coeffs} [0] x^3 + \texttt{coeffs} [1] x^2 + \texttt{coeffs} [2] x + \texttt{coeffs} [3] = 0\f]
+- if coeffs is a 3-element vector:
+\f[x^3 + \texttt{coeffs} [0] x^2 + \texttt{coeffs} [1] x + \texttt{coeffs} [2] = 0\f]
+
+The roots are stored in the roots array.
+@param coeffs equation coefficients, an array of 3 or 4 elements.
+@param roots output array of real roots that has 0, 1, 2 or 3 elements.
+@return number of real roots. It can be -1 (all real numbers), 0, 1, 2 or 3.
+*/
+CV_EXPORTS_W int solveCubic(InputArray coeffs, OutputArray roots);
+
+/** @brief Finds the real or complex roots of a polynomial equation.
+
+The function cv::solvePoly finds real and complex roots of a polynomial equation:
+\f[\texttt{coeffs} [n] x^{n} + \texttt{coeffs} [n-1] x^{n-1} + ... + \texttt{coeffs} [1] x + \texttt{coeffs} [0] = 0\f]
+@param coeffs array of polynomial coefficients.
+@param roots output (complex) array of roots.
+@param maxIters maximum number of iterations the algorithm does.
+*/
+CV_EXPORTS_W double solvePoly(InputArray coeffs, OutputArray roots, int maxIters = 300);
+
+/** @brief Calculates eigenvalues and eigenvectors of a symmetric matrix.
+
+The function cv::eigen calculates just eigenvalues, or eigenvalues and eigenvectors of the symmetric
+matrix src:
+@code
+ src*eigenvectors.row(i).t() = eigenvalues.at(i)*eigenvectors.row(i).t()
+@endcode
+
+@note Use cv::eigenNonSymmetric for calculation of real eigenvalues and eigenvectors of non-symmetric matrix.
+
+@param src input matrix that must have CV_32FC1 or CV_64FC1 type, square size and be symmetrical
+(src ^T^ == src).
+@param eigenvalues output vector of eigenvalues of the same type as src; the eigenvalues are stored
+in the descending order.
+@param eigenvectors output matrix of eigenvectors; it has the same size and type as src; the
+eigenvectors are stored as subsequent matrix rows, in the same order as the corresponding
+eigenvalues.
+@sa eigenNonSymmetric, completeSymm, PCA
+*/
+CV_EXPORTS_W bool eigen(InputArray src, OutputArray eigenvalues,
+ OutputArray eigenvectors = noArray());
+
+/** @brief Calculates eigenvalues and eigenvectors of a non-symmetric matrix (real eigenvalues only).
+
+@note Assumes real eigenvalues.
+
+The function calculates eigenvalues and eigenvectors (optional) of the square matrix src:
+@code
+ src*eigenvectors.row(i).t() = eigenvalues.at(i)*eigenvectors.row(i).t()
+@endcode
+
+@param src input matrix (CV_32FC1 or CV_64FC1 type).
+@param eigenvalues output vector of eigenvalues (type is the same type as src).
+@param eigenvectors output matrix of eigenvectors (type is the same type as src). The eigenvectors are stored as subsequent matrix rows, in the same order as the corresponding eigenvalues.
+@sa eigen
+*/
+CV_EXPORTS_W void eigenNonSymmetric(InputArray src, OutputArray eigenvalues,
+ OutputArray eigenvectors);
+
+/** @brief Calculates the covariance matrix of a set of vectors.
+
+The function cv::calcCovarMatrix calculates the covariance matrix and, optionally, the mean vector of
+the set of input vectors.
+@param samples samples stored as separate matrices
+@param nsamples number of samples
+@param covar output covariance matrix of the type ctype and square size.
+@param mean input or output (depending on the flags) array as the average value of the input vectors.
+@param flags operation flags as a combination of #CovarFlags
+@param ctype type of the matrixl; it equals 'CV_64F' by default.
+@sa PCA, mulTransposed, Mahalanobis
+@todo InputArrayOfArrays
+*/
+CV_EXPORTS void calcCovarMatrix( const Mat* samples, int nsamples, Mat& covar, Mat& mean,
+ int flags, int ctype = CV_64F);
+
+/** @overload
+@note use #COVAR_ROWS or #COVAR_COLS flag
+@param samples samples stored as rows/columns of a single matrix.
+@param covar output covariance matrix of the type ctype and square size.
+@param mean input or output (depending on the flags) array as the average value of the input vectors.
+@param flags operation flags as a combination of #CovarFlags
+@param ctype type of the matrixl; it equals 'CV_64F' by default.
+*/
+CV_EXPORTS_W void calcCovarMatrix( InputArray samples, OutputArray covar,
+ InputOutputArray mean, int flags, int ctype = CV_64F);
+
+/** wrap PCA::operator() */
+CV_EXPORTS_W void PCACompute(InputArray data, InputOutputArray mean,
+ OutputArray eigenvectors, int maxComponents = 0);
+
+/** wrap PCA::operator() and add eigenvalues output parameter */
+CV_EXPORTS_AS(PCACompute2) void PCACompute(InputArray data, InputOutputArray mean,
+ OutputArray eigenvectors, OutputArray eigenvalues,
+ int maxComponents = 0);
+
+/** wrap PCA::operator() */
+CV_EXPORTS_W void PCACompute(InputArray data, InputOutputArray mean,
+ OutputArray eigenvectors, double retainedVariance);
+
+/** wrap PCA::operator() and add eigenvalues output parameter */
+CV_EXPORTS_AS(PCACompute2) void PCACompute(InputArray data, InputOutputArray mean,
+ OutputArray eigenvectors, OutputArray eigenvalues,
+ double retainedVariance);
+
+/** wrap PCA::project */
+CV_EXPORTS_W void PCAProject(InputArray data, InputArray mean,
+ InputArray eigenvectors, OutputArray result);
+
+/** wrap PCA::backProject */
+CV_EXPORTS_W void PCABackProject(InputArray data, InputArray mean,
+ InputArray eigenvectors, OutputArray result);
+
+/** wrap SVD::compute */
+CV_EXPORTS_W void SVDecomp( InputArray src, OutputArray w, OutputArray u, OutputArray vt, int flags = 0 );
+
+/** wrap SVD::backSubst */
+CV_EXPORTS_W void SVBackSubst( InputArray w, InputArray u, InputArray vt,
+ InputArray rhs, OutputArray dst );
+
+/** @brief Calculates the Mahalanobis distance between two vectors.
+
+The function cv::Mahalanobis calculates and returns the weighted distance between two vectors:
+\f[d( \texttt{vec1} , \texttt{vec2} )= \sqrt{\sum_{i,j}{\texttt{icovar(i,j)}\cdot(\texttt{vec1}(I)-\texttt{vec2}(I))\cdot(\texttt{vec1(j)}-\texttt{vec2(j)})} }\f]
+The covariance matrix may be calculated using the #calcCovarMatrix function and then inverted using
+the invert function (preferably using the #DECOMP_SVD method, as the most accurate).
+@param v1 first 1D input vector.
+@param v2 second 1D input vector.
+@param icovar inverse covariance matrix.
+*/
+CV_EXPORTS_W double Mahalanobis(InputArray v1, InputArray v2, InputArray icovar);
+
+/** @brief Performs a forward or inverse Discrete Fourier transform of a 1D or 2D floating-point array.
+
+The function cv::dft performs one of the following:
+- Forward the Fourier transform of a 1D vector of N elements:
+ \f[Y = F^{(N)} \cdot X,\f]
+ where \f$F^{(N)}_{jk}=\exp(-2\pi i j k/N)\f$ and \f$i=\sqrt{-1}\f$
+- Inverse the Fourier transform of a 1D vector of N elements:
+ \f[\begin{array}{l} X'= \left (F^{(N)} \right )^{-1} \cdot Y = \left (F^{(N)} \right )^* \cdot y \\ X = (1/N) \cdot X, \end{array}\f]
+ where \f$F^*=\left(\textrm{Re}(F^{(N)})-\textrm{Im}(F^{(N)})\right)^T\f$
+- Forward the 2D Fourier transform of a M x N matrix:
+ \f[Y = F^{(M)} \cdot X \cdot F^{(N)}\f]
+- Inverse the 2D Fourier transform of a M x N matrix:
+ \f[\begin{array}{l} X'= \left (F^{(M)} \right )^* \cdot Y \cdot \left (F^{(N)} \right )^* \\ X = \frac{1}{M \cdot N} \cdot X' \end{array}\f]
+
+In case of real (single-channel) data, the output spectrum of the forward Fourier transform or input
+spectrum of the inverse Fourier transform can be represented in a packed format called *CCS*
+(complex-conjugate-symmetrical). It was borrowed from IPL (Intel\* Image Processing Library). Here
+is how 2D *CCS* spectrum looks:
+\f[\begin{bmatrix} Re Y_{0,0} & Re Y_{0,1} & Im Y_{0,1} & Re Y_{0,2} & Im Y_{0,2} & \cdots & Re Y_{0,N/2-1} & Im Y_{0,N/2-1} & Re Y_{0,N/2} \\ Re Y_{1,0} & Re Y_{1,1} & Im Y_{1,1} & Re Y_{1,2} & Im Y_{1,2} & \cdots & Re Y_{1,N/2-1} & Im Y_{1,N/2-1} & Re Y_{1,N/2} \\ Im Y_{1,0} & Re Y_{2,1} & Im Y_{2,1} & Re Y_{2,2} & Im Y_{2,2} & \cdots & Re Y_{2,N/2-1} & Im Y_{2,N/2-1} & Im Y_{1,N/2} \\ \hdotsfor{9} \\ Re Y_{M/2-1,0} & Re Y_{M-3,1} & Im Y_{M-3,1} & \hdotsfor{3} & Re Y_{M-3,N/2-1} & Im Y_{M-3,N/2-1}& Re Y_{M/2-1,N/2} \\ Im Y_{M/2-1,0} & Re Y_{M-2,1} & Im Y_{M-2,1} & \hdotsfor{3} & Re Y_{M-2,N/2-1} & Im Y_{M-2,N/2-1}& Im Y_{M/2-1,N/2} \\ Re Y_{M/2,0} & Re Y_{M-1,1} & Im Y_{M-1,1} & \hdotsfor{3} & Re Y_{M-1,N/2-1} & Im Y_{M-1,N/2-1}& Re Y_{M/2,N/2} \end{bmatrix}\f]
+
+In case of 1D transform of a real vector, the output looks like the first row of the matrix above.
+
+So, the function chooses an operation mode depending on the flags and size of the input array:
+- If #DFT_ROWS is set or the input array has a single row or single column, the function
+ performs a 1D forward or inverse transform of each row of a matrix when #DFT_ROWS is set.
+ Otherwise, it performs a 2D transform.
+- If the input array is real and #DFT_INVERSE is not set, the function performs a forward 1D or
+ 2D transform:
+ - When #DFT_COMPLEX_OUTPUT is set, the output is a complex matrix of the same size as
+ input.
+ - When #DFT_COMPLEX_OUTPUT is not set, the output is a real matrix of the same size as
+ input. In case of 2D transform, it uses the packed format as shown above. In case of a
+ single 1D transform, it looks like the first row of the matrix above. In case of
+ multiple 1D transforms (when using the #DFT_ROWS flag), each row of the output matrix
+ looks like the first row of the matrix above.
+- If the input array is complex and either #DFT_INVERSE or #DFT_REAL_OUTPUT are not set, the
+ output is a complex array of the same size as input. The function performs a forward or
+ inverse 1D or 2D transform of the whole input array or each row of the input array
+ independently, depending on the flags DFT_INVERSE and DFT_ROWS.
+- When #DFT_INVERSE is set and the input array is real, or it is complex but #DFT_REAL_OUTPUT
+ is set, the output is a real array of the same size as input. The function performs a 1D or 2D
+ inverse transformation of the whole input array or each individual row, depending on the flags
+ #DFT_INVERSE and #DFT_ROWS.
+
+If #DFT_SCALE is set, the scaling is done after the transformation.
+
+Unlike dct, the function supports arrays of arbitrary size. But only those arrays are processed
+efficiently, whose sizes can be factorized in a product of small prime numbers (2, 3, and 5 in the
+current implementation). Such an efficient DFT size can be calculated using the getOptimalDFTSize
+method.
+
+The sample below illustrates how to calculate a DFT-based convolution of two 2D real arrays:
+@code
+ void convolveDFT(InputArray A, InputArray B, OutputArray C)
+ {
+ // reallocate the output array if needed
+ C.create(abs(A.rows - B.rows)+1, abs(A.cols - B.cols)+1, A.type());
+ Size dftSize;
+ // calculate the size of DFT transform
+ dftSize.width = getOptimalDFTSize(A.cols + B.cols - 1);
+ dftSize.height = getOptimalDFTSize(A.rows + B.rows - 1);
+
+ // allocate temporary buffers and initialize them with 0's
+ Mat tempA(dftSize, A.type(), Scalar::all(0));
+ Mat tempB(dftSize, B.type(), Scalar::all(0));
+
+ // copy A and B to the top-left corners of tempA and tempB, respectively
+ Mat roiA(tempA, Rect(0,0,A.cols,A.rows));
+ A.copyTo(roiA);
+ Mat roiB(tempB, Rect(0,0,B.cols,B.rows));
+ B.copyTo(roiB);
+
+ // now transform the padded A & B in-place;
+ // use "nonzeroRows" hint for faster processing
+ dft(tempA, tempA, 0, A.rows);
+ dft(tempB, tempB, 0, B.rows);
+
+ // multiply the spectrums;
+ // the function handles packed spectrum representations well
+ mulSpectrums(tempA, tempB, tempA);
+
+ // transform the product back from the frequency domain.
+ // Even though all the result rows will be non-zero,
+ // you need only the first C.rows of them, and thus you
+ // pass nonzeroRows == C.rows
+ dft(tempA, tempA, DFT_INVERSE + DFT_SCALE, C.rows);
+
+ // now copy the result back to C.
+ tempA(Rect(0, 0, C.cols, C.rows)).copyTo(C);
+
+ // all the temporary buffers will be deallocated automatically
+ }
+@endcode
+To optimize this sample, consider the following approaches:
+- Since nonzeroRows != 0 is passed to the forward transform calls and since A and B are copied to
+ the top-left corners of tempA and tempB, respectively, it is not necessary to clear the whole
+ tempA and tempB. It is only necessary to clear the tempA.cols - A.cols ( tempB.cols - B.cols)
+ rightmost columns of the matrices.
+- This DFT-based convolution does not have to be applied to the whole big arrays, especially if B
+ is significantly smaller than A or vice versa. Instead, you can calculate convolution by parts.
+ To do this, you need to split the output array C into multiple tiles. For each tile, estimate
+ which parts of A and B are required to calculate convolution in this tile. If the tiles in C are
+ too small, the speed will decrease a lot because of repeated work. In the ultimate case, when
+ each tile in C is a single pixel, the algorithm becomes equivalent to the naive convolution
+ algorithm. If the tiles are too big, the temporary arrays tempA and tempB become too big and
+ there is also a slowdown because of bad cache locality. So, there is an optimal tile size
+ somewhere in the middle.
+- If different tiles in C can be calculated in parallel and, thus, the convolution is done by
+ parts, the loop can be threaded.
+
+All of the above improvements have been implemented in #matchTemplate and #filter2D . Therefore, by
+using them, you can get the performance even better than with the above theoretically optimal
+implementation. Though, those two functions actually calculate cross-correlation, not convolution,
+so you need to "flip" the second convolution operand B vertically and horizontally using flip .
+@note
+- An example using the discrete fourier transform can be found at
+ opencv_source_code/samples/cpp/dft.cpp
+- (Python) An example using the dft functionality to perform Wiener deconvolution can be found
+ at opencv_source/samples/python/deconvolution.py
+- (Python) An example rearranging the quadrants of a Fourier image can be found at
+ opencv_source/samples/python/dft.py
+@param src input array that could be real or complex.
+@param dst output array whose size and type depends on the flags .
+@param flags transformation flags, representing a combination of the #DftFlags
+@param nonzeroRows when the parameter is not zero, the function assumes that only the first
+nonzeroRows rows of the input array (#DFT_INVERSE is not set) or only the first nonzeroRows of the
+output array (#DFT_INVERSE is set) contain non-zeros, thus, the function can handle the rest of the
+rows more efficiently and save some time; this technique is very useful for calculating array
+cross-correlation or convolution using DFT.
+@sa dct, getOptimalDFTSize, mulSpectrums, filter2D, matchTemplate, flip, cartToPolar,
+magnitude, phase
+*/
+CV_EXPORTS_W void dft(InputArray src, OutputArray dst, int flags = 0, int nonzeroRows = 0);
+
+/** @brief Calculates the inverse Discrete Fourier Transform of a 1D or 2D array.
+
+idft(src, dst, flags) is equivalent to dft(src, dst, flags | #DFT_INVERSE) .
+@note None of dft and idft scales the result by default. So, you should pass #DFT_SCALE to one of
+dft or idft explicitly to make these transforms mutually inverse.
+@sa dft, dct, idct, mulSpectrums, getOptimalDFTSize
+@param src input floating-point real or complex array.
+@param dst output array whose size and type depend on the flags.
+@param flags operation flags (see dft and #DftFlags).
+@param nonzeroRows number of dst rows to process; the rest of the rows have undefined content (see
+the convolution sample in dft description.
+*/
+CV_EXPORTS_W void idft(InputArray src, OutputArray dst, int flags = 0, int nonzeroRows = 0);
+
+/** @brief Performs a forward or inverse discrete Cosine transform of 1D or 2D array.
+
+The function cv::dct performs a forward or inverse discrete Cosine transform (DCT) of a 1D or 2D
+floating-point array:
+- Forward Cosine transform of a 1D vector of N elements:
+ \f[Y = C^{(N)} \cdot X\f]
+ where
+ \f[C^{(N)}_{jk}= \sqrt{\alpha_j/N} \cos \left ( \frac{\pi(2k+1)j}{2N} \right )\f]
+ and
+ \f$\alpha_0=1\f$, \f$\alpha_j=2\f$ for *j \> 0*.
+- Inverse Cosine transform of a 1D vector of N elements:
+ \f[X = \left (C^{(N)} \right )^{-1} \cdot Y = \left (C^{(N)} \right )^T \cdot Y\f]
+ (since \f$C^{(N)}\f$ is an orthogonal matrix, \f$C^{(N)} \cdot \left(C^{(N)}\right)^T = I\f$ )
+- Forward 2D Cosine transform of M x N matrix:
+ \f[Y = C^{(N)} \cdot X \cdot \left (C^{(N)} \right )^T\f]
+- Inverse 2D Cosine transform of M x N matrix:
+ \f[X = \left (C^{(N)} \right )^T \cdot X \cdot C^{(N)}\f]
+
+The function chooses the mode of operation by looking at the flags and size of the input array:
+- If (flags & #DCT_INVERSE) == 0, the function does a forward 1D or 2D transform. Otherwise, it
+ is an inverse 1D or 2D transform.
+- If (flags & #DCT_ROWS) != 0, the function performs a 1D transform of each row.
+- If the array is a single column or a single row, the function performs a 1D transform.
+- If none of the above is true, the function performs a 2D transform.
+
+@note Currently dct supports even-size arrays (2, 4, 6 ...). For data analysis and approximation, you
+can pad the array when necessary.
+Also, the function performance depends very much, and not monotonically, on the array size (see
+getOptimalDFTSize ). In the current implementation DCT of a vector of size N is calculated via DFT
+of a vector of size N/2 . Thus, the optimal DCT size N1 \>= N can be calculated as:
+@code
+ size_t getOptimalDCTSize(size_t N) { return 2*getOptimalDFTSize((N+1)/2); }
+ N1 = getOptimalDCTSize(N);
+@endcode
+@param src input floating-point array.
+@param dst output array of the same size and type as src .
+@param flags transformation flags as a combination of cv::DftFlags (DCT_*)
+@sa dft, getOptimalDFTSize, idct
+*/
+CV_EXPORTS_W void dct(InputArray src, OutputArray dst, int flags = 0);
+
+/** @brief Calculates the inverse Discrete Cosine Transform of a 1D or 2D array.
+
+idct(src, dst, flags) is equivalent to dct(src, dst, flags | DCT_INVERSE).
+@param src input floating-point single-channel array.
+@param dst output array of the same size and type as src.
+@param flags operation flags.
+@sa dct, dft, idft, getOptimalDFTSize
+*/
+CV_EXPORTS_W void idct(InputArray src, OutputArray dst, int flags = 0);
+
+/** @brief Performs the per-element multiplication of two Fourier spectrums.
+
+The function cv::mulSpectrums performs the per-element multiplication of the two CCS-packed or complex
+matrices that are results of a real or complex Fourier transform.
+
+The function, together with dft and idft, may be used to calculate convolution (pass conjB=false )
+or correlation (pass conjB=true ) of two arrays rapidly. When the arrays are complex, they are
+simply multiplied (per element) with an optional conjugation of the second-array elements. When the
+arrays are real, they are assumed to be CCS-packed (see dft for details).
+@param a first input array.
+@param b second input array of the same size and type as src1 .
+@param c output array of the same size and type as src1 .
+@param flags operation flags; currently, the only supported flag is cv::DFT_ROWS, which indicates that
+each row of src1 and src2 is an independent 1D Fourier spectrum. If you do not want to use this flag, then simply add a `0` as value.
+@param conjB optional flag that conjugates the second input array before the multiplication (true)
+or not (false).
+*/
+CV_EXPORTS_W void mulSpectrums(InputArray a, InputArray b, OutputArray c,
+ int flags, bool conjB = false);
+
+/** @brief Returns the optimal DFT size for a given vector size.
+
+DFT performance is not a monotonic function of a vector size. Therefore, when you calculate
+convolution of two arrays or perform the spectral analysis of an array, it usually makes sense to
+pad the input data with zeros to get a bit larger array that can be transformed much faster than the
+original one. Arrays whose size is a power-of-two (2, 4, 8, 16, 32, ...) are the fastest to process.
+Though, the arrays whose size is a product of 2's, 3's, and 5's (for example, 300 = 5\*5\*3\*2\*2)
+are also processed quite efficiently.
+
+The function cv::getOptimalDFTSize returns the minimum number N that is greater than or equal to vecsize
+so that the DFT of a vector of size N can be processed efficiently. In the current implementation N
+= 2 ^p^ \* 3 ^q^ \* 5 ^r^ for some integer p, q, r.
+
+The function returns a negative number if vecsize is too large (very close to INT_MAX ).
+
+While the function cannot be used directly to estimate the optimal vector size for DCT transform
+(since the current DCT implementation supports only even-size vectors), it can be easily processed
+as getOptimalDFTSize((vecsize+1)/2)\*2.
+@param vecsize vector size.
+@sa dft, dct, idft, idct, mulSpectrums
+*/
+CV_EXPORTS_W int getOptimalDFTSize(int vecsize);
+
+/** @brief Returns the default random number generator.
+
+The function cv::theRNG returns the default random number generator. For each thread, there is a
+separate random number generator, so you can use the function safely in multi-thread environments.
+If you just need to get a single random number using this generator or initialize an array, you can
+use randu or randn instead. But if you are going to generate many random numbers inside a loop, it
+is much faster to use this function to retrieve the generator and then use RNG::operator _Tp() .
+@sa RNG, randu, randn
+*/
+CV_EXPORTS RNG& theRNG();
+
+/** @brief Sets state of default random number generator.
+
+The function cv::setRNGSeed sets state of default random number generator to custom value.
+@param seed new state for default random number generator
+@sa RNG, randu, randn
+*/
+CV_EXPORTS_W void setRNGSeed(int seed);
+
+/** @brief Generates a single uniformly-distributed random number or an array of random numbers.
+
+Non-template variant of the function fills the matrix dst with uniformly-distributed
+random numbers from the specified range:
+\f[\texttt{low} _c \leq \texttt{dst} (I)_c < \texttt{high} _c\f]
+@param dst output array of random numbers; the array must be pre-allocated.
+@param low inclusive lower boundary of the generated random numbers.
+@param high exclusive upper boundary of the generated random numbers.
+@sa RNG, randn, theRNG
+*/
+CV_EXPORTS_W void randu(InputOutputArray dst, InputArray low, InputArray high);
+
+/** @brief Fills the array with normally distributed random numbers.
+
+The function cv::randn fills the matrix dst with normally distributed random numbers with the specified
+mean vector and the standard deviation matrix. The generated random numbers are clipped to fit the
+value range of the output array data type.
+@param dst output array of random numbers; the array must be pre-allocated and have 1 to 4 channels.
+@param mean mean value (expectation) of the generated random numbers.
+@param stddev standard deviation of the generated random numbers; it can be either a vector (in
+which case a diagonal standard deviation matrix is assumed) or a square matrix.
+@sa RNG, randu
+*/
+CV_EXPORTS_W void randn(InputOutputArray dst, InputArray mean, InputArray stddev);
+
+/** @brief Shuffles the array elements randomly.
+
+The function cv::randShuffle shuffles the specified 1D array by randomly choosing pairs of elements and
+swapping them. The number of such swap operations will be dst.rows\*dst.cols\*iterFactor .
+@param dst input/output numerical 1D array.
+@param iterFactor scale factor that determines the number of random swap operations (see the details
+below).
+@param rng optional random number generator used for shuffling; if it is zero, theRNG () is used
+instead.
+@sa RNG, sort
+*/
+CV_EXPORTS_W void randShuffle(InputOutputArray dst, double iterFactor = 1., RNG* rng = 0);
+
+/** @brief Principal Component Analysis
+
+The class is used to calculate a special basis for a set of vectors. The
+basis will consist of eigenvectors of the covariance matrix calculated
+from the input set of vectors. The class %PCA can also transform
+vectors to/from the new coordinate space defined by the basis. Usually,
+in this new coordinate system, each vector from the original set (and
+any linear combination of such vectors) can be quite accurately
+approximated by taking its first few components, corresponding to the
+eigenvectors of the largest eigenvalues of the covariance matrix.
+Geometrically it means that you calculate a projection of the vector to
+a subspace formed by a few eigenvectors corresponding to the dominant
+eigenvalues of the covariance matrix. And usually such a projection is
+very close to the original vector. So, you can represent the original
+vector from a high-dimensional space with a much shorter vector
+consisting of the projected vector's coordinates in the subspace. Such a
+transformation is also known as Karhunen-Loeve Transform, or KLT.
+See http://en.wikipedia.org/wiki/Principal_component_analysis
+
+The sample below is the function that takes two matrices. The first
+function stores a set of vectors (a row per vector) that is used to
+calculate PCA. The second function stores another "test" set of vectors
+(a row per vector). First, these vectors are compressed with PCA, then
+reconstructed back, and then the reconstruction error norm is computed
+and printed for each vector. :
+
+@code{.cpp}
+using namespace cv;
+
+PCA compressPCA(const Mat& pcaset, int maxComponents,
+ const Mat& testset, Mat& compressed)
+{
+ PCA pca(pcaset, // pass the data
+ Mat(), // we do not have a pre-computed mean vector,
+ // so let the PCA engine to compute it
+ PCA::DATA_AS_ROW, // indicate that the vectors
+ // are stored as matrix rows
+ // (use PCA::DATA_AS_COL if the vectors are
+ // the matrix columns)
+ maxComponents // specify, how many principal components to retain
+ );
+ // if there is no test data, just return the computed basis, ready-to-use
+ if( !testset.data )
+ return pca;
+ CV_Assert( testset.cols == pcaset.cols );
+
+ compressed.create(testset.rows, maxComponents, testset.type());
+
+ Mat reconstructed;
+ for( int i = 0; i < testset.rows; i++ )
+ {
+ Mat vec = testset.row(i), coeffs = compressed.row(i), reconstructed;
+ // compress the vector, the result will be stored
+ // in the i-th row of the output matrix
+ pca.project(vec, coeffs);
+ // and then reconstruct it
+ pca.backProject(coeffs, reconstructed);
+ // and measure the error
+ printf("%d. diff = %g\n", i, norm(vec, reconstructed, NORM_L2));
+ }
+ return pca;
+}
+@endcode
+@sa calcCovarMatrix, mulTransposed, SVD, dft, dct
+*/
+class CV_EXPORTS PCA
+{
+public:
+ enum Flags { DATA_AS_ROW = 0, //!< indicates that the input samples are stored as matrix rows
+ DATA_AS_COL = 1, //!< indicates that the input samples are stored as matrix columns
+ USE_AVG = 2 //!
+ };
+
+ /** @brief default constructor
+
+ The default constructor initializes an empty %PCA structure. The other
+ constructors initialize the structure and call PCA::operator()().
+ */
+ PCA();
+
+ /** @overload
+ @param data input samples stored as matrix rows or matrix columns.
+ @param mean optional mean value; if the matrix is empty (@c noArray()),
+ the mean is computed from the data.
+ @param flags operation flags; currently the parameter is only used to
+ specify the data layout (PCA::Flags)
+ @param maxComponents maximum number of components that %PCA should
+ retain; by default, all the components are retained.
+ */
+ PCA(InputArray data, InputArray mean, int flags, int maxComponents = 0);
+
+ /** @overload
+ @param data input samples stored as matrix rows or matrix columns.
+ @param mean optional mean value; if the matrix is empty (noArray()),
+ the mean is computed from the data.
+ @param flags operation flags; currently the parameter is only used to
+ specify the data layout (PCA::Flags)
+ @param retainedVariance Percentage of variance that PCA should retain.
+ Using this parameter will let the PCA decided how many components to
+ retain but it will always keep at least 2.
+ */
+ PCA(InputArray data, InputArray mean, int flags, double retainedVariance);
+
+ /** @brief performs %PCA
+
+ The operator performs %PCA of the supplied dataset. It is safe to reuse
+ the same PCA structure for multiple datasets. That is, if the structure
+ has been previously used with another dataset, the existing internal
+ data is reclaimed and the new @ref eigenvalues, @ref eigenvectors and @ref
+ mean are allocated and computed.
+
+ The computed @ref eigenvalues are sorted from the largest to the smallest and
+ the corresponding @ref eigenvectors are stored as eigenvectors rows.
+
+ @param data input samples stored as the matrix rows or as the matrix
+ columns.
+ @param mean optional mean value; if the matrix is empty (noArray()),
+ the mean is computed from the data.
+ @param flags operation flags; currently the parameter is only used to
+ specify the data layout. (Flags)
+ @param maxComponents maximum number of components that PCA should
+ retain; by default, all the components are retained.
+ */
+ PCA& operator()(InputArray data, InputArray mean, int flags, int maxComponents = 0);
+
+ /** @overload
+ @param data input samples stored as the matrix rows or as the matrix
+ columns.
+ @param mean optional mean value; if the matrix is empty (noArray()),
+ the mean is computed from the data.
+ @param flags operation flags; currently the parameter is only used to
+ specify the data layout. (PCA::Flags)
+ @param retainedVariance Percentage of variance that %PCA should retain.
+ Using this parameter will let the %PCA decided how many components to
+ retain but it will always keep at least 2.
+ */
+ PCA& operator()(InputArray data, InputArray mean, int flags, double retainedVariance);
+
+ /** @brief Projects vector(s) to the principal component subspace.
+
+ The methods project one or more vectors to the principal component
+ subspace, where each vector projection is represented by coefficients in
+ the principal component basis. The first form of the method returns the
+ matrix that the second form writes to the result. So the first form can
+ be used as a part of expression while the second form can be more
+ efficient in a processing loop.
+ @param vec input vector(s); must have the same dimensionality and the
+ same layout as the input data used at %PCA phase, that is, if
+ DATA_AS_ROW are specified, then `vec.cols==data.cols`
+ (vector dimensionality) and `vec.rows` is the number of vectors to
+ project, and the same is true for the PCA::DATA_AS_COL case.
+ */
+ Mat project(InputArray vec) const;
+
+ /** @overload
+ @param vec input vector(s); must have the same dimensionality and the
+ same layout as the input data used at PCA phase, that is, if
+ DATA_AS_ROW are specified, then `vec.cols==data.cols`
+ (vector dimensionality) and `vec.rows` is the number of vectors to
+ project, and the same is true for the PCA::DATA_AS_COL case.
+ @param result output vectors; in case of PCA::DATA_AS_COL, the
+ output matrix has as many columns as the number of input vectors, this
+ means that `result.cols==vec.cols` and the number of rows match the
+ number of principal components (for example, `maxComponents` parameter
+ passed to the constructor).
+ */
+ void project(InputArray vec, OutputArray result) const;
+
+ /** @brief Reconstructs vectors from their PC projections.
+
+ The methods are inverse operations to PCA::project. They take PC
+ coordinates of projected vectors and reconstruct the original vectors.
+ Unless all the principal components have been retained, the
+ reconstructed vectors are different from the originals. But typically,
+ the difference is small if the number of components is large enough (but
+ still much smaller than the original vector dimensionality). As a
+ result, PCA is used.
+ @param vec coordinates of the vectors in the principal component
+ subspace, the layout and size are the same as of PCA::project output
+ vectors.
+ */
+ Mat backProject(InputArray vec) const;
+
+ /** @overload
+ @param vec coordinates of the vectors in the principal component
+ subspace, the layout and size are the same as of PCA::project output
+ vectors.
+ @param result reconstructed vectors; the layout and size are the same as
+ of PCA::project input vectors.
+ */
+ void backProject(InputArray vec, OutputArray result) const;
+
+ /** @brief write PCA objects
+
+ Writes @ref eigenvalues @ref eigenvectors and @ref mean to specified FileStorage
+ */
+ void write(FileStorage& fs) const;
+
+ /** @brief load PCA objects
+
+ Loads @ref eigenvalues @ref eigenvectors and @ref mean from specified FileNode
+ */
+ void read(const FileNode& fn);
+
+ Mat eigenvectors; //!< eigenvectors of the covariation matrix
+ Mat eigenvalues; //!< eigenvalues of the covariation matrix
+ Mat mean; //!< mean value subtracted before the projection and added after the back projection
+};
+
+/** @example samples/cpp/pca.cpp
+An example using %PCA for dimensionality reduction while maintaining an amount of variance
+*/
+
+/** @example samples/cpp/tutorial_code/ml/introduction_to_pca/introduction_to_pca.cpp
+Check @ref tutorial_introduction_to_pca "the corresponding tutorial" for more details
+*/
+
+/**
+@brief Linear Discriminant Analysis
+@todo document this class
+*/
+class CV_EXPORTS LDA
+{
+public:
+ /** @brief constructor
+ Initializes a LDA with num_components (default 0).
+ */
+ explicit LDA(int num_components = 0);
+
+ /** Initializes and performs a Discriminant Analysis with Fisher's
+ Optimization Criterion on given data in src and corresponding labels
+ in labels. If 0 (or less) number of components are given, they are
+ automatically determined for given data in computation.
+ */
+ LDA(InputArrayOfArrays src, InputArray labels, int num_components = 0);
+
+ /** Serializes this object to a given filename.
+ */
+ void save(const String& filename) const;
+
+ /** Deserializes this object from a given filename.
+ */
+ void load(const String& filename);
+
+ /** Serializes this object to a given cv::FileStorage.
+ */
+ void save(FileStorage& fs) const;
+
+ /** Deserializes this object from a given cv::FileStorage.
+ */
+ void load(const FileStorage& node);
+
+ /** destructor
+ */
+ ~LDA();
+
+ /** Compute the discriminants for data in src (row aligned) and labels.
+ */
+ void compute(InputArrayOfArrays src, InputArray labels);
+
+ /** Projects samples into the LDA subspace.
+ src may be one or more row aligned samples.
+ */
+ Mat project(InputArray src);
+
+ /** Reconstructs projections from the LDA subspace.
+ src may be one or more row aligned projections.
+ */
+ Mat reconstruct(InputArray src);
+
+ /** Returns the eigenvectors of this LDA.
+ */
+ Mat eigenvectors() const { return _eigenvectors; }
+
+ /** Returns the eigenvalues of this LDA.
+ */
+ Mat eigenvalues() const { return _eigenvalues; }
+
+ static Mat subspaceProject(InputArray W, InputArray mean, InputArray src);
+ static Mat subspaceReconstruct(InputArray W, InputArray mean, InputArray src);
+
+protected:
+ int _num_components;
+ Mat _eigenvectors;
+ Mat _eigenvalues;
+ void lda(InputArrayOfArrays src, InputArray labels);
+};
+
+/** @brief Singular Value Decomposition
+
+Class for computing Singular Value Decomposition of a floating-point
+matrix. The Singular Value Decomposition is used to solve least-square
+problems, under-determined linear systems, invert matrices, compute
+condition numbers, and so on.
+
+If you want to compute a condition number of a matrix or an absolute value of
+its determinant, you do not need `u` and `vt`. You can pass
+flags=SVD::NO_UV|... . Another flag SVD::FULL_UV indicates that full-size u
+and vt must be computed, which is not necessary most of the time.
+
+@sa invert, solve, eigen, determinant
+*/
+class CV_EXPORTS SVD
+{
+public:
+ enum Flags {
+ /** allow the algorithm to modify the decomposed matrix; it can save space and speed up
+ processing. currently ignored. */
+ MODIFY_A = 1,
+ /** indicates that only a vector of singular values `w` is to be processed, while u and vt
+ will be set to empty matrices */
+ NO_UV = 2,
+ /** when the matrix is not square, by default the algorithm produces u and vt matrices of
+ sufficiently large size for the further A reconstruction; if, however, FULL_UV flag is
+ specified, u and vt will be full-size square orthogonal matrices.*/
+ FULL_UV = 4
+ };
+
+ /** @brief the default constructor
+
+ initializes an empty SVD structure
+ */
+ SVD();
+
+ /** @overload
+ initializes an empty SVD structure and then calls SVD::operator()
+ @param src decomposed matrix. The depth has to be CV_32F or CV_64F.
+ @param flags operation flags (SVD::Flags)
+ */
+ SVD( InputArray src, int flags = 0 );
+
+ /** @brief the operator that performs SVD. The previously allocated u, w and vt are released.
+
+ The operator performs the singular value decomposition of the supplied
+ matrix. The u,`vt` , and the vector of singular values w are stored in
+ the structure. The same SVD structure can be reused many times with
+ different matrices. Each time, if needed, the previous u,`vt` , and w
+ are reclaimed and the new matrices are created, which is all handled by
+ Mat::create.
+ @param src decomposed matrix. The depth has to be CV_32F or CV_64F.
+ @param flags operation flags (SVD::Flags)
+ */
+ SVD& operator ()( InputArray src, int flags = 0 );
+
+ /** @brief decomposes matrix and stores the results to user-provided matrices
+
+ The methods/functions perform SVD of matrix. Unlike SVD::SVD constructor
+ and SVD::operator(), they store the results to the user-provided
+ matrices:
+
+ @code{.cpp}
+ Mat A, w, u, vt;
+ SVD::compute(A, w, u, vt);
+ @endcode
+
+ @param src decomposed matrix. The depth has to be CV_32F or CV_64F.
+ @param w calculated singular values
+ @param u calculated left singular vectors
+ @param vt transposed matrix of right singular vectors
+ @param flags operation flags - see SVD::Flags.
+ */
+ static void compute( InputArray src, OutputArray w,
+ OutputArray u, OutputArray vt, int flags = 0 );
+
+ /** @overload
+ computes singular values of a matrix
+ @param src decomposed matrix. The depth has to be CV_32F or CV_64F.
+ @param w calculated singular values
+ @param flags operation flags - see SVD::Flags.
+ */
+ static void compute( InputArray src, OutputArray w, int flags = 0 );
+
+ /** @brief performs back substitution
+ */
+ static void backSubst( InputArray w, InputArray u,
+ InputArray vt, InputArray rhs,
+ OutputArray dst );
+
+ /** @brief solves an under-determined singular linear system
+
+ The method finds a unit-length solution x of a singular linear system
+ A\*x = 0. Depending on the rank of A, there can be no solutions, a
+ single solution or an infinite number of solutions. In general, the
+ algorithm solves the following problem:
+ \f[dst = \arg \min _{x: \| x \| =1} \| src \cdot x \|\f]
+ @param src left-hand-side matrix.
+ @param dst found solution.
+ */
+ static void solveZ( InputArray src, OutputArray dst );
+
+ /** @brief performs a singular value back substitution.
+
+ The method calculates a back substitution for the specified right-hand
+ side:
+
+ \f[\texttt{x} = \texttt{vt} ^T \cdot diag( \texttt{w} )^{-1} \cdot \texttt{u} ^T \cdot \texttt{rhs} \sim \texttt{A} ^{-1} \cdot \texttt{rhs}\f]
+
+ Using this technique you can either get a very accurate solution of the
+ convenient linear system, or the best (in the least-squares terms)
+ pseudo-solution of an overdetermined linear system.
+
+ @param rhs right-hand side of a linear system (u\*w\*v')\*dst = rhs to
+ be solved, where A has been previously decomposed.
+
+ @param dst found solution of the system.
+
+ @note Explicit SVD with the further back substitution only makes sense
+ if you need to solve many linear systems with the same left-hand side
+ (for example, src ). If all you need is to solve a single system
+ (possibly with multiple rhs immediately available), simply call solve
+ add pass #DECOMP_SVD there. It does absolutely the same thing.
+ */
+ void backSubst( InputArray rhs, OutputArray dst ) const;
+
+ /** @todo document */
+ template static
+ void compute( const Matx<_Tp, m, n>& a, Matx<_Tp, nm, 1>& w, Matx<_Tp, m, nm>& u, Matx<_Tp, n, nm>& vt );
+
+ /** @todo document */
+ template static
+ void compute( const Matx<_Tp, m, n>& a, Matx<_Tp, nm, 1>& w );
+
+ /** @todo document */
+ template static
+ void backSubst( const Matx<_Tp, nm, 1>& w, const Matx<_Tp, m, nm>& u, const Matx<_Tp, n, nm>& vt, const Matx<_Tp, m, nb>& rhs, Matx<_Tp, n, nb>& dst );
+
+ Mat u, w, vt;
+};
+
+/** @brief Random Number Generator
+
+Random number generator. It encapsulates the state (currently, a 64-bit
+integer) and has methods to return scalar random values and to fill
+arrays with random values. Currently it supports uniform and Gaussian
+(normal) distributions. The generator uses Multiply-With-Carry
+algorithm, introduced by G. Marsaglia (
+ ).
+Gaussian-distribution random numbers are generated using the Ziggurat
+algorithm ( ),
+introduced by G. Marsaglia and W. W. Tsang.
+*/
+class CV_EXPORTS RNG
+{
+public:
+ enum { UNIFORM = 0,
+ NORMAL = 1
+ };
+
+ /** @brief constructor
+
+ These are the RNG constructors. The first form sets the state to some
+ pre-defined value, equal to 2\*\*32-1 in the current implementation. The
+ second form sets the state to the specified value. If you passed state=0
+ , the constructor uses the above default value instead to avoid the
+ singular random number sequence, consisting of all zeros.
+ */
+ RNG();
+ /** @overload
+ @param state 64-bit value used to initialize the RNG.
+ */
+ RNG(uint64 state);
+ /**The method updates the state using the MWC algorithm and returns the
+ next 32-bit random number.*/
+ unsigned next();
+
+ /**Each of the methods updates the state using the MWC algorithm and
+ returns the next random number of the specified type. In case of integer
+ types, the returned number is from the available value range for the
+ specified type. In case of floating-point types, the returned value is
+ from [0,1) range.
+ */
+ operator uchar();
+ /** @overload */
+ operator schar();
+ /** @overload */
+ operator ushort();
+ /** @overload */
+ operator short();
+ /** @overload */
+ operator unsigned();
+ /** @overload */
+ operator int();
+ /** @overload */
+ operator float();
+ /** @overload */
+ operator double();
+
+ /** @brief returns a random integer sampled uniformly from [0, N).
+
+ The methods transform the state using the MWC algorithm and return the
+ next random number. The first form is equivalent to RNG::next . The
+ second form returns the random number modulo N, which means that the
+ result is in the range [0, N) .
+ */
+ unsigned operator ()();
+ /** @overload
+ @param N upper non-inclusive boundary of the returned random number.
+ */
+ unsigned operator ()(unsigned N);
+
+ /** @brief returns uniformly distributed integer random number from [a,b) range
+
+ The methods transform the state using the MWC algorithm and return the
+ next uniformly-distributed random number of the specified type, deduced
+ from the input parameter type, from the range [a, b) . There is a nuance
+ illustrated by the following sample:
+
+ @code{.cpp}
+ RNG rng;
+
+ // always produces 0
+ double a = rng.uniform(0, 1);
+
+ // produces double from [0, 1)
+ double a1 = rng.uniform((double)0, (double)1);
+
+ // produces float from [0, 1)
+ float b = rng.uniform(0.f, 1.f);
+
+ // produces double from [0, 1)
+ double c = rng.uniform(0., 1.);
+
+ // may cause compiler error because of ambiguity:
+ // RNG::uniform(0, (int)0.999999)? or RNG::uniform((double)0, 0.99999)?
+ double d = rng.uniform(0, 0.999999);
+ @endcode
+
+ The compiler does not take into account the type of the variable to
+ which you assign the result of RNG::uniform . The only thing that
+ matters to the compiler is the type of a and b parameters. So, if you
+ want a floating-point random number, but the range boundaries are
+ integer numbers, either put dots in the end, if they are constants, or
+ use explicit type cast operators, as in the a1 initialization above.
+ @param a lower inclusive boundary of the returned random number.
+ @param b upper non-inclusive boundary of the returned random number.
+ */
+ int uniform(int a, int b);
+ /** @overload */
+ float uniform(float a, float b);
+ /** @overload */
+ double uniform(double a, double b);
+
+ /** @brief Fills arrays with random numbers.
+
+ @param mat 2D or N-dimensional matrix; currently matrices with more than
+ 4 channels are not supported by the methods, use Mat::reshape as a
+ possible workaround.
+ @param distType distribution type, RNG::UNIFORM or RNG::NORMAL.
+ @param a first distribution parameter; in case of the uniform
+ distribution, this is an inclusive lower boundary, in case of the normal
+ distribution, this is a mean value.
+ @param b second distribution parameter; in case of the uniform
+ distribution, this is a non-inclusive upper boundary, in case of the
+ normal distribution, this is a standard deviation (diagonal of the
+ standard deviation matrix or the full standard deviation matrix).
+ @param saturateRange pre-saturation flag; for uniform distribution only;
+ if true, the method will first convert a and b to the acceptable value
+ range (according to the mat datatype) and then will generate uniformly
+ distributed random numbers within the range [saturate(a), saturate(b)),
+ if saturateRange=false, the method will generate uniformly distributed
+ random numbers in the original range [a, b) and then will saturate them,
+ it means, for example, that
+ theRNG().fill(mat_8u, RNG::UNIFORM, -DBL_MAX, DBL_MAX) will likely
+ produce array mostly filled with 0's and 255's, since the range (0, 255)
+ is significantly smaller than [-DBL_MAX, DBL_MAX).
+
+ Each of the methods fills the matrix with the random values from the
+ specified distribution. As the new numbers are generated, the RNG state
+ is updated accordingly. In case of multiple-channel images, every
+ channel is filled independently, which means that RNG cannot generate
+ samples from the multi-dimensional Gaussian distribution with
+ non-diagonal covariance matrix directly. To do that, the method
+ generates samples from multi-dimensional standard Gaussian distribution
+ with zero mean and identity covariation matrix, and then transforms them
+ using transform to get samples from the specified Gaussian distribution.
+ */
+ void fill( InputOutputArray mat, int distType, InputArray a, InputArray b, bool saturateRange = false );
+
+ /** @brief Returns the next random number sampled from the Gaussian distribution
+ @param sigma standard deviation of the distribution.
+
+ The method transforms the state using the MWC algorithm and returns the
+ next random number from the Gaussian distribution N(0,sigma) . That is,
+ the mean value of the returned random numbers is zero and the standard
+ deviation is the specified sigma .
+ */
+ double gaussian(double sigma);
+
+ uint64 state;
+
+ bool operator ==(const RNG& other) const;
+};
+
+/** @brief Mersenne Twister random number generator
+
+Inspired by http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/MT2002/CODES/mt19937ar.c
+@todo document
+*/
+class CV_EXPORTS RNG_MT19937
+{
+public:
+ RNG_MT19937();
+ RNG_MT19937(unsigned s);
+ void seed(unsigned s);
+
+ unsigned next();
+
+ operator int();
+ operator unsigned();
+ operator float();
+ operator double();
+
+ unsigned operator ()(unsigned N);
+ unsigned operator ()();
+
+ /** @brief returns uniformly distributed integer random number from [a,b) range*/
+ int uniform(int a, int b);
+ /** @brief returns uniformly distributed floating-point random number from [a,b) range*/
+ float uniform(float a, float b);
+ /** @brief returns uniformly distributed double-precision floating-point random number from [a,b) range*/
+ double uniform(double a, double b);
+
+private:
+ enum PeriodParameters {N = 624, M = 397};
+ unsigned state[N];
+ int mti;
+};
+
+//! @} core_array
+
+//! @addtogroup core_cluster
+//! @{
+
+//! k-means flags
+enum KmeansFlags {
+ /** Select random initial centers in each attempt.*/
+ KMEANS_RANDOM_CENTERS = 0,
+ /** Use kmeans++ center initialization by Arthur and Vassilvitskii [Arthur2007].*/
+ KMEANS_PP_CENTERS = 2,
+ /** During the first (and possibly the only) attempt, use the
+ user-supplied labels instead of computing them from the initial centers. For the second and
+ further attempts, use the random or semi-random centers. Use one of KMEANS_\*_CENTERS flag
+ to specify the exact method.*/
+ KMEANS_USE_INITIAL_LABELS = 1
+};
+
+/** @example samples/cpp/kmeans.cpp
+An example on k-means clustering
+*/
+
+/** @brief Finds centers of clusters and groups input samples around the clusters.
+
+The function kmeans implements a k-means algorithm that finds the centers of cluster_count clusters
+and groups the input samples around the clusters. As an output, \f$\texttt{bestLabels}_i\f$ contains a
+0-based cluster index for the sample stored in the \f$i^{th}\f$ row of the samples matrix.
+
+@note
+- (Python) An example on k-means clustering can be found at
+ opencv_source_code/samples/python/kmeans.py
+@param data Data for clustering. An array of N-Dimensional points with float coordinates is needed.
+Examples of this array can be:
+- Mat points(count, 2, CV_32F);
+- Mat points(count, 1, CV_32FC2);
+- Mat points(1, count, CV_32FC2);
+- std::vector\ points(sampleCount);
+@param K Number of clusters to split the set by.
+@param bestLabels Input/output integer array that stores the cluster indices for every sample.
+@param criteria The algorithm termination criteria, that is, the maximum number of iterations and/or
+the desired accuracy. The accuracy is specified as criteria.epsilon. As soon as each of the cluster
+centers moves by less than criteria.epsilon on some iteration, the algorithm stops.
+@param attempts Flag to specify the number of times the algorithm is executed using different
+initial labellings. The algorithm returns the labels that yield the best compactness (see the last
+function parameter).
+@param flags Flag that can take values of cv::KmeansFlags
+@param centers Output matrix of the cluster centers, one row per each cluster center.
+@return The function returns the compactness measure that is computed as
+\f[\sum _i \| \texttt{samples} _i - \texttt{centers} _{ \texttt{labels} _i} \| ^2\f]
+after every attempt. The best (minimum) value is chosen and the corresponding labels and the
+compactness value are returned by the function. Basically, you can use only the core of the
+function, set the number of attempts to 1, initialize labels each time using a custom algorithm,
+pass them with the ( flags = #KMEANS_USE_INITIAL_LABELS ) flag, and then choose the best
+(most-compact) clustering.
+*/
+CV_EXPORTS_W double kmeans( InputArray data, int K, InputOutputArray bestLabels,
+ TermCriteria criteria, int attempts,
+ int flags, OutputArray centers = noArray() );
+
+//! @} core_cluster
+
+//! @addtogroup core_basic
+//! @{
+
+/////////////////////////////// Formatted output of cv::Mat ///////////////////////////
+
+/** @todo document */
+class CV_EXPORTS Formatted
+{
+public:
+ virtual const char* next() = 0;
+ virtual void reset() = 0;
+ virtual ~Formatted();
+};
+
+/** @todo document */
+class CV_EXPORTS Formatter
+{
+public:
+ enum FormatType {
+ FMT_DEFAULT = 0,
+ FMT_MATLAB = 1,
+ FMT_CSV = 2,
+ FMT_PYTHON = 3,
+ FMT_NUMPY = 4,
+ FMT_C = 5
+ };
+
+ virtual ~Formatter();
+
+ virtual Ptr format(const Mat& mtx) const = 0;
+
+ virtual void set16fPrecision(int p = 4) = 0;
+ virtual void set32fPrecision(int p = 8) = 0;
+ virtual void set64fPrecision(int p = 16) = 0;
+ virtual void setMultiline(bool ml = true) = 0;
+
+ static Ptr get(Formatter::FormatType fmt = FMT_DEFAULT);
+
+};
+
+static inline
+String& operator << (String& out, Ptr fmtd)
+{
+ fmtd->reset();
+ for(const char* str = fmtd->next(); str; str = fmtd->next())
+ out += cv::String(str);
+ return out;
+}
+
+static inline
+String& operator << (String& out, const Mat& mtx)
+{
+ return out << Formatter::get()->format(mtx);
+}
+
+//////////////////////////////////////// Algorithm ////////////////////////////////////
+
+class CV_EXPORTS Algorithm;
+
+template struct ParamType {};
+
+
+/** @brief This is a base class for all more or less complex algorithms in OpenCV
+
+especially for classes of algorithms, for which there can be multiple implementations. The examples
+are stereo correspondence (for which there are algorithms like block matching, semi-global block
+matching, graph-cut etc.), background subtraction (which can be done using mixture-of-gaussians
+models, codebook-based algorithm etc.), optical flow (block matching, Lucas-Kanade, Horn-Schunck
+etc.).
+
+Here is example of SimpleBlobDetector use in your application via Algorithm interface:
+@snippet snippets/core_various.cpp Algorithm
+*/
+class CV_EXPORTS_W Algorithm
+{
+public:
+ Algorithm();
+ virtual ~Algorithm();
+
+ /** @brief Clears the algorithm state
+ */
+ CV_WRAP virtual void clear() {}
+
+ /** @brief Stores algorithm parameters in a file storage
+ */
+ CV_WRAP virtual void write(FileStorage& fs) const { CV_UNUSED(fs); }
+
+ /**
+ * @overload
+ */
+ CV_WRAP void write(FileStorage& fs, const String& name) const;
+#if CV_VERSION_MAJOR < 5
+ /** @deprecated */
+ void write(const Ptr& fs, const String& name = String()) const;
+#endif
+
+ /** @brief Reads algorithm parameters from a file storage
+ */
+ CV_WRAP virtual void read(const FileNode& fn) { CV_UNUSED(fn); }
+
+ /** @brief Returns true if the Algorithm is empty (e.g. in the very beginning or after unsuccessful read
+ */
+ CV_WRAP virtual bool empty() const { return false; }
+
+ /** @brief Reads algorithm from the file node
+
+ This is static template method of Algorithm. It's usage is following (in the case of SVM):
+ @code
+ cv::FileStorage fsRead("example.xml", FileStorage::READ);
+ Ptr svm = Algorithm::read(fsRead.root());
+ @endcode
+ In order to make this method work, the derived class must overwrite Algorithm::read(const
+ FileNode& fn) and also have static create() method without parameters
+ (or with all the optional parameters)
+ */
+ template static Ptr<_Tp> read(const FileNode& fn)
+ {
+ Ptr<_Tp> obj = _Tp::create();
+ obj->read(fn);
+ return !obj->empty() ? obj : Ptr<_Tp>();
+ }
+
+ /** @brief Loads algorithm from the file
+
+ @param filename Name of the file to read.
+ @param objname The optional name of the node to read (if empty, the first top-level node will be used)
+
+ This is static template method of Algorithm. It's usage is following (in the case of SVM):
+ @code
+ Ptr svm = Algorithm::load("my_svm_model.xml");
+ @endcode
+ In order to make this method work, the derived class must overwrite Algorithm::read(const
+ FileNode& fn).
+ */
+ template static Ptr<_Tp> load(const String& filename, const String& objname=String())
+ {
+ FileStorage fs(filename, FileStorage::READ);
+ CV_Assert(fs.isOpened());
+ FileNode fn = objname.empty() ? fs.getFirstTopLevelNode() : fs[objname];
+ if (fn.empty()) return Ptr<_Tp>();
+ Ptr<_Tp> obj = _Tp::create();
+ obj->read(fn);
+ return !obj->empty() ? obj : Ptr<_Tp>();
+ }
+
+ /** @brief Loads algorithm from a String
+
+ @param strModel The string variable containing the model you want to load.
+ @param objname The optional name of the node to read (if empty, the first top-level node will be used)
+
+ This is static template method of Algorithm. It's usage is following (in the case of SVM):
+ @code
+ Ptr svm = Algorithm::loadFromString(myStringModel);
+ @endcode
+ */
+ template static Ptr<_Tp> loadFromString(const String& strModel, const String& objname=String())
+ {
+ FileStorage fs(strModel, FileStorage::READ + FileStorage::MEMORY);
+ FileNode fn = objname.empty() ? fs.getFirstTopLevelNode() : fs[objname];
+ Ptr<_Tp> obj = _Tp::create();
+ obj->read(fn);
+ return !obj->empty() ? obj : Ptr<_Tp>();
+ }
+
+ /** Saves the algorithm to a file.
+ In order to make this method work, the derived class must implement Algorithm::write(FileStorage& fs). */
+ CV_WRAP virtual void save(const String& filename) const;
+
+ /** Returns the algorithm string identifier.
+ This string is used as top level xml/yml node tag when the object is saved to a file or string. */
+ CV_WRAP virtual String getDefaultName() const;
+
+protected:
+ void writeFormat(FileStorage& fs) const;
+};
+
+enum struct Param {
+ INT=0, BOOLEAN=1, REAL=2, STRING=3, MAT=4, MAT_VECTOR=5, ALGORITHM=6, FLOAT=7,
+ UNSIGNED_INT=8, UINT64=9, UCHAR=11, SCALAR=12
+};
+
+
+
+template<> struct ParamType
+{
+ typedef bool const_param_type;
+ typedef bool member_type;
+
+ static const Param type = Param::BOOLEAN;
+};
+
+template<> struct ParamType
+{
+ typedef int const_param_type;
+ typedef int member_type;
+
+ static const Param type = Param::INT;
+};
+
+template<> struct ParamType
+{
+ typedef double const_param_type;
+ typedef double member_type;
+
+ static const Param type = Param::REAL;
+};
+
+template<> struct ParamType
+{
+ typedef const String& const_param_type;
+ typedef String member_type;
+
+ static const Param type = Param::STRING;
+};
+
+template<> struct ParamType
+{
+ typedef const Mat& const_param_type;
+ typedef Mat member_type;
+
+ static const Param type = Param::MAT;
+};
+
+template<> struct ParamType >
+{
+ typedef const std::vector& const_param_type;
+ typedef std::vector member_type;
+
+ static const Param type = Param::MAT_VECTOR;
+};
+
+template<> struct ParamType
+{
+ typedef const Ptr& const_param_type;
+ typedef Ptr member_type;
+
+ static const Param type = Param::ALGORITHM;
+};
+
+template<> struct ParamType
+{
+ typedef float const_param_type;
+ typedef float member_type;
+
+ static const Param type = Param::FLOAT;
+};
+
+template<> struct ParamType
+{
+ typedef unsigned const_param_type;
+ typedef unsigned member_type;
+
+ static const Param type = Param::UNSIGNED_INT;
+};
+
+template<> struct ParamType
+{
+ typedef uint64 const_param_type;
+ typedef uint64 member_type;
+
+ static const Param type = Param::UINT64;
+};
+
+template<> struct ParamType
+{
+ typedef uchar const_param_type;
+ typedef uchar member_type;
+
+ static const Param type = Param::UCHAR;
+};
+
+template<> struct ParamType
+{
+ typedef const Scalar& const_param_type;
+ typedef Scalar member_type;
+
+ static const Param type = Param::SCALAR;
+};
+
+template
+struct ParamType<_Tp, typename std::enable_if< std::is_enum<_Tp>::value >::type>
+{
+ typedef typename std::underlying_type<_Tp>::type const_param_type;
+ typedef typename std::underlying_type<_Tp>::type member_type;
+
+ static const Param type = Param::INT;
+};
+
+//! @} core_basic
+
+} //namespace cv
+
+#include "opencv2/core/operations.hpp"
+#include "opencv2/core/cvstd.inl.hpp"
+#include "opencv2/core/utility.hpp"
+#include "opencv2/core/optim.hpp"
+#include "opencv2/core/ovx.hpp"
+
+#endif /*OPENCV_CORE_HPP*/
diff --git a/3rdpart/OpenCV/include/opencv2/core/affine.hpp b/3rdpart/OpenCV/include/opencv2/core/affine.hpp
new file mode 100644
index 0000000..1aebf2b
--- /dev/null
+++ b/3rdpart/OpenCV/include/opencv2/core/affine.hpp
@@ -0,0 +1,678 @@
+/*M///////////////////////////////////////////////////////////////////////////////////////
+//
+// IMPORTANT: READ BEFORE DOWNLOADING, COPYING, INSTALLING OR USING.
+//
+// By downloading, copying, installing or using the software you agree to this license.
+// If you do not agree to this license, do not download, install,
+// copy or use the software.
+//
+//
+// License Agreement
+// For Open Source Computer Vision Library
+//
+// Copyright (C) 2000-2008, Intel Corporation, all rights reserved.
+// Copyright (C) 2009, Willow Garage Inc., all rights reserved.
+// Copyright (C) 2013, OpenCV Foundation, all rights reserved.
+// Third party copyrights are property of their respective owners.
+//
+// Redistribution and use in source and binary forms, with or without modification,
+// are permitted provided that the following conditions are met:
+//
+// * Redistribution's of source code must retain the above copyright notice,
+// this list of conditions and the following disclaimer.
+//
+// * Redistribution's in binary form must reproduce the above copyright notice,
+// this list of conditions and the following disclaimer in the documentation
+// and/or other materials provided with the distribution.
+//
+// * The name of the copyright holders may not be used to endorse or promote products
+// derived from this software without specific prior written permission.
+//
+// This software is provided by the copyright holders and contributors "as is" and
+// any express or implied warranties, including, but not limited to, the implied
+// warranties of merchantability and fitness for a particular purpose are disclaimed.
+// In no event shall the Intel Corporation or contributors be liable for any direct,
+// indirect, incidental, special, exemplary, or consequential damages
+// (including, but not limited to, procurement of substitute goods or services;
+// loss of use, data, or profits; or business interruption) however caused
+// and on any theory of liability, whether in contract, strict liability,
+// or tort (including negligence or otherwise) arising in any way out of
+// the use of this software, even if advised of the possibility of such damage.
+//
+//M*/
+
+#ifndef OPENCV_CORE_AFFINE3_HPP
+#define OPENCV_CORE_AFFINE3_HPP
+
+#ifdef __cplusplus
+
+#include
+
+namespace cv
+{
+
+//! @addtogroup core_eigen
+//! @{
+
+ /** @brief Affine transform
+ *
+ * It represents a 4x4 homogeneous transformation matrix \f$T\f$
+ *
+ * \f[T =
+ * \begin{bmatrix}
+ * R & t\\
+ * 0 & 1\\
+ * \end{bmatrix}
+ * \f]
+ *
+ * where \f$R\f$ is a 3x3 rotation matrix and \f$t\f$ is a 3x1 translation vector.
+ *
+ * You can specify \f$R\f$ either by a 3x3 rotation matrix or by a 3x1 rotation vector,
+ * which is converted to a 3x3 rotation matrix by the Rodrigues formula.
+ *
+ * To construct a matrix \f$T\f$ representing first rotation around the axis \f$r\f$ with rotation
+ * angle \f$|r|\f$ in radian (right hand rule) and then translation by the vector \f$t\f$, you can use
+ *
+ * @code
+ * cv::Vec3f r, t;
+ * cv::Affine3f T(r, t);
+ * @endcode
+ *
+ * If you already have the rotation matrix \f$R\f$, then you can use
+ *
+ * @code
+ * cv::Matx33f R;
+ * cv::Affine3f T(R, t);
+ * @endcode
+ *
+ * To extract the rotation matrix \f$R\f$ from \f$T\f$, use
+ *
+ * @code
+ * cv::Matx33f R = T.rotation();
+ * @endcode
+ *
+ * To extract the translation vector \f$t\f$ from \f$T\f$, use
+ *
+ * @code
+ * cv::Vec3f t = T.translation();
+ * @endcode
+ *
+ * To extract the rotation vector \f$r\f$ from \f$T\f$, use
+ *
+ * @code
+ * cv::Vec3f r = T.rvec();
+ * @endcode
+ *
+ * Note that since the mapping from rotation vectors to rotation matrices
+ * is many to one. The returned rotation vector is not necessarily the one
+ * you used before to set the matrix.
+ *
+ * If you have two transformations \f$T = T_1 * T_2\f$, use
+ *
+ * @code
+ * cv::Affine3f T, T1, T2;
+ * T = T2.concatenate(T1);
+ * @endcode
+ *
+ * To get the inverse transform of \f$T\f$, use
+ *
+ * @code
+ * cv::Affine3f T, T_inv;
+ * T_inv = T.inv();
+ * @endcode
+ *
+ */
+ template
+ class Affine3
+ {
+ public:
+ typedef T float_type;
+ typedef Matx Mat3;
+ typedef Matx Mat4;
+ typedef Vec Vec3;
+
+ //! Default constructor. It represents a 4x4 identity matrix.
+ Affine3();
+
+ //! Augmented affine matrix
+ Affine3(const Mat4& affine);
+
+ /**
+ * The resulting 4x4 matrix is
+ *
+ * \f[
+ * \begin{bmatrix}
+ * R & t\\
+ * 0 & 1\\
+ * \end{bmatrix}
+ * \f]
+ *
+ * @param R 3x3 rotation matrix.
+ * @param t 3x1 translation vector.
+ */
+ Affine3(const Mat3& R, const Vec3& t = Vec3::all(0));
+
+ /**
+ * Rodrigues vector.
+ *
+ * The last row of the current matrix is set to [0,0,0,1].
+ *
+ * @param rvec 3x1 rotation vector. Its direction indicates the rotation axis and its length
+ * indicates the rotation angle in radian (using right hand rule).
+ * @param t 3x1 translation vector.
+ */
+ Affine3(const Vec3& rvec, const Vec3& t = Vec3::all(0));
+
+ /**
+ * Combines all constructors above. Supports 4x4, 3x4, 3x3, 1x3, 3x1 sizes of data matrix.
+ *
+ * The last row of the current matrix is set to [0,0,0,1] when data is not 4x4.
+ *
+ * @param data 1-channel matrix.
+ * when it is 4x4, it is copied to the current matrix and t is not used.
+ * When it is 3x4, it is copied to the upper part 3x4 of the current matrix and t is not used.
+ * When it is 3x3, it is copied to the upper left 3x3 part of the current matrix.
+ * When it is 3x1 or 1x3, it is treated as a rotation vector and the Rodrigues formula is used
+ * to compute a 3x3 rotation matrix.
+ * @param t 3x1 translation vector. It is used only when data is neither 4x4 nor 3x4.
+ */
+ explicit Affine3(const Mat& data, const Vec3& t = Vec3::all(0));
+
+ //! From 16-element array
+ explicit Affine3(const float_type* vals);
+
+ //! Create an 4x4 identity transform
+ static Affine3 Identity();
+
+ /**
+ * Rotation matrix.
+ *
+ * Copy the rotation matrix to the upper left 3x3 part of the current matrix.
+ * The remaining elements of the current matrix are not changed.
+ *
+ * @param R 3x3 rotation matrix.
+ *
+ */
+ void rotation(const Mat3& R);
+
+ /**
+ * Rodrigues vector.
+ *
+ * It sets the upper left 3x3 part of the matrix. The remaining part is unaffected.
+ *
+ * @param rvec 3x1 rotation vector. The direction indicates the rotation axis and
+ * its length indicates the rotation angle in radian (using the right thumb convention).
+ */
+ void rotation(const Vec3& rvec);
+
+ /**
+ * Combines rotation methods above. Supports 3x3, 1x3, 3x1 sizes of data matrix.
+ *
+ * It sets the upper left 3x3 part of the matrix. The remaining part is unaffected.
+ *
+ * @param data 1-channel matrix.
+ * When it is a 3x3 matrix, it sets the upper left 3x3 part of the current matrix.
+ * When it is a 1x3 or 3x1 matrix, it is used as a rotation vector. The Rodrigues formula
+ * is used to compute the rotation matrix and sets the upper left 3x3 part of the current matrix.
+ */
+ void rotation(const Mat& data);
+
+ /**
+ * Copy the 3x3 matrix L to the upper left part of the current matrix
+ *
+ * It sets the upper left 3x3 part of the matrix. The remaining part is unaffected.
+ *
+ * @param L 3x3 matrix.
+ */
+ void linear(const Mat3& L);
+
+ /**
+ * Copy t to the first three elements of the last column of the current matrix
+ *
+ * It sets the upper right 3x1 part of the matrix. The remaining part is unaffected.
+ *
+ * @param t 3x1 translation vector.
+ */
+ void translation(const Vec3& t);
+
+ //! @return the upper left 3x3 part
+ Mat3 rotation() const;
+
+ //! @return the upper left 3x3 part
+ Mat3 linear() const;
+
+ //! @return the upper right 3x1 part
+ Vec3 translation() const;
+
+ //! Rodrigues vector.
+ //! @return a vector representing the upper left 3x3 rotation matrix of the current matrix.
+ //! @warning Since the mapping between rotation vectors and rotation matrices is many to one,
+ //! this function returns only one rotation vector that represents the current rotation matrix,
+ //! which is not necessarily the same one set by `rotation(const Vec3& rvec)`.
+ Vec3 rvec() const;
+
+ //! @return the inverse of the current matrix.
+ Affine3 inv(int method = cv::DECOMP_SVD) const;
+
+ //! a.rotate(R) is equivalent to Affine(R, 0) * a;
+ Affine3 rotate(const Mat3& R) const;
+
+ //! a.rotate(rvec) is equivalent to Affine(rvec, 0) * a;
+ Affine3 rotate(const Vec3& rvec) const;
+
+ //! a.translate(t) is equivalent to Affine(E, t) * a, where E is an identity matrix
+ Affine3 translate(const Vec3& t) const;
+
+ //! a.concatenate(affine) is equivalent to affine * a;
+ Affine3 concatenate(const Affine3& affine) const;
+
+ template operator Affine3() const;
+
+ template Affine3 cast() const;
+
+ Mat4 matrix;
+
+#if defined EIGEN_WORLD_VERSION && defined EIGEN_GEOMETRY_MODULE_H
+ Affine3(const Eigen::Transform& affine);
+ Affine3(const Eigen::Transform& affine);
+ operator Eigen::Transform() const;
+ operator Eigen::Transform() const;
+#endif
+ };
+
+ template static
+ Affine3 operator*(const Affine3& affine1, const Affine3& affine2);
+
+ //! V is a 3-element vector with member fields x, y and z
+ template static
+ V operator*(const Affine3& affine, const V& vector);
+
+ typedef Affine3 Affine3f;
+ typedef Affine3 Affine3d;
+
+ static Vec3f operator*(const Affine3f& affine, const Vec3f& vector);
+ static Vec3d operator*(const Affine3d& affine, const Vec3d& vector);
+
+ template class DataType< Affine3<_Tp> >
+ {
+ public:
+ typedef Affine3<_Tp> value_type;
+ typedef Affine3::work_type> work_type;
+ typedef _Tp channel_type;
+
+ enum { generic_type = 0,
+ channels = 16,
+ fmt = traits::SafeFmt::fmt + ((channels - 1) << 8)
+#ifdef OPENCV_TRAITS_ENABLE_DEPRECATED
+ ,depth = DataType::depth
+ ,type = CV_MAKETYPE(depth, channels)
+#endif
+ };
+
+ typedef Vec vec_type;
+ };
+
+ namespace traits {
+ template
+ struct Depth< Affine3<_Tp> > { enum { value = Depth<_Tp>::value }; };
+ template
+ struct Type< Affine3<_Tp> > { enum { value = CV_MAKETYPE(Depth<_Tp>::value, 16) }; };
+ } // namespace
+
+//! @} core
+
+}
+
+//! @cond IGNORED
+
+///////////////////////////////////////////////////////////////////////////////////
+// Implementation
+
+template inline
+cv::Affine3::Affine3()
+ : matrix(Mat4::eye())
+{}
+
+template inline
+cv::Affine3::Affine3(const Mat4& affine)
+ : matrix(affine)
+{}
+
+template inline
+cv::Affine3::Affine3(const Mat3& R, const Vec3& t)
+{
+ rotation(R);
+ translation(t);
+ matrix.val[12] = matrix.val[13] = matrix.val[14] = 0;
+ matrix.val[15] = 1;
+}
+
+template inline
+cv::Affine3::Affine3(const Vec3& _rvec, const Vec3& t)
+{
+ rotation(_rvec);
+ translation(t);
+ matrix.val[12] = matrix.val[13] = matrix.val[14] = 0;
+ matrix.val[15] = 1;
+}
+
+template inline
+cv::Affine3::Affine3(const cv::Mat& data, const Vec3& t)
+{
+ CV_Assert(data.type() == cv::traits::Type::value);
+ CV_Assert(data.channels() == 1);
+
+ if (data.cols == 4 && data.rows == 4)
+ {
+ data.copyTo(matrix);
+ return;
+ }
+ else if (data.cols == 4 && data.rows == 3)
+ {
+ rotation(data(Rect(0, 0, 3, 3)));
+ translation(data(Rect(3, 0, 1, 3)));
+ }
+ else
+ {
+ rotation(data);
+ translation(t);
+ }
+
+ matrix.val[12] = matrix.val[13] = matrix.val[14] = 0;
+ matrix.val[15] = 1;
+}
+
+template inline
+cv::Affine3::Affine3(const float_type* vals) : matrix(vals)
+{}
+
+template inline
+cv::Affine3 cv::Affine3::Identity()
+{
+ return Affine3(cv::Affine3::Mat4::eye());
+}
+
+template inline
+void cv::Affine3::rotation(const Mat3& R)
+{
+ linear(R);
+}
+
+template inline
+void cv::Affine3::rotation(const Vec3& _rvec)
+{
+ double theta = norm(_rvec);
+
+ if (theta < DBL_EPSILON)
+ rotation(Mat3::eye());
+ else
+ {
+ double c = std::cos(theta);
+ double s = std::sin(theta);
+ double c1 = 1. - c;
+ double itheta = (theta != 0) ? 1./theta : 0.;
+
+ Point3_ r = _rvec*itheta;
+
+ Mat3 rrt( r.x*r.x, r.x*r.y, r.x*r.z, r.x*r.y, r.y*r.y, r.y*r.z, r.x*r.z, r.y*r.z, r.z*r.z );
+ Mat3 r_x( 0, -r.z, r.y, r.z, 0, -r.x, -r.y, r.x, 0 );
+
+ // R = cos(theta)*I + (1 - cos(theta))*r*rT + sin(theta)*[r_x]
+ // where [r_x] is [0 -rz ry; rz 0 -rx; -ry rx 0]
+ Mat3 R = c*Mat3::eye() + c1*rrt + s*r_x;
+
+ rotation(R);
+ }
+}
+
+//Combines rotation methods above. Supports 3x3, 1x3, 3x1 sizes of data matrix;
+template inline
+void cv::Affine3::rotation(const cv::Mat& data)
+{
+ CV_Assert(data.type() == cv::traits::Type::value);
+ CV_Assert(data.channels() == 1);
+
+ if (data.cols == 3 && data.rows == 3)
+ {
+ Mat3 R;
+ data.copyTo(R);
+ rotation(R);
+ }
+ else if ((data.cols == 3 && data.rows == 1) || (data.cols == 1 && data.rows == 3))
+ {
+ Vec3 _rvec;
+ data.reshape(1, 3).copyTo(_rvec);
+ rotation(_rvec);
+ }
+ else
+ CV_Error(Error::StsError, "Input matrix can only be 3x3, 1x3 or 3x1");
+}
+
+template inline
+void cv::Affine3::linear(const Mat3& L)
+{
+ matrix.val[0] = L.val[0]; matrix.val[1] = L.val[1]; matrix.val[ 2] = L.val[2];
+ matrix.val[4] = L.val[3]; matrix.val[5] = L.val[4]; matrix.val[ 6] = L.val[5];
+ matrix.val[8] = L.val[6]; matrix.val[9] = L.val[7]; matrix.val[10] = L.val[8];
+}
+
+template inline
+void cv::Affine3::translation(const Vec3& t)
+{
+ matrix.val[3] = t[0]; matrix.val[7] = t[1]; matrix.val[11] = t[2];
+}
+
+template inline
+typename cv::Affine3::Mat3 cv::Affine3::rotation() const
+{
+ return linear();
+}
+
+template inline
+typename cv::Affine3::Mat3 cv::Affine3::linear() const
+{
+ typename cv::Affine3::Mat3 R;
+ R.val[0] = matrix.val[0]; R.val[1] = matrix.val[1]; R.val[2] = matrix.val[ 2];
+ R.val[3] = matrix.val[4]; R.val[4] = matrix.val[5]; R.val[5] = matrix.val[ 6];
+ R.val[6] = matrix.val[8]; R.val[7] = matrix.val[9]; R.val[8] = matrix.val[10];
+ return R;
+}
+
+template inline
+typename cv::Affine3::Vec3 cv::Affine3::translation() const
+{
+ return Vec3(matrix.val[3], matrix.val[7], matrix.val[11]);
+}
+
+template inline
+typename cv::Affine3::Vec3 cv::Affine3::rvec() const
+{
+ cv::Vec3d w;
+ cv::Matx33d u, vt, R = rotation();
+ cv::SVD::compute(R, w, u, vt, cv::SVD::FULL_UV + cv::SVD::MODIFY_A);
+ R = u * vt;
+
+ double rx = R.val[7] - R.val[5];
+ double ry = R.val[2] - R.val[6];
+ double rz = R.val[3] - R.val[1];
+
+ double s = std::sqrt((rx*rx + ry*ry + rz*rz)*0.25);
+ double c = (R.val[0] + R.val[4] + R.val[8] - 1) * 0.5;
+ c = c > 1.0 ? 1.0 : c < -1.0 ? -1.0 : c;
+ double theta = std::acos(c);
+
+ if( s < 1e-5 )
+ {
+ if( c > 0 )
+ rx = ry = rz = 0;
+ else
+ {
+ double t;
+ t = (R.val[0] + 1) * 0.5;
+ rx = std::sqrt(std::max(t, 0.0));
+ t = (R.val[4] + 1) * 0.5;
+ ry = std::sqrt(std::max(t, 0.0)) * (R.val[1] < 0 ? -1.0 : 1.0);
+ t = (R.val[8] + 1) * 0.5;
+ rz = std::sqrt(std::max(t, 0.0)) * (R.val[2] < 0 ? -1.0 : 1.0);
+
+ if( fabs(rx) < fabs(ry) && fabs(rx) < fabs(rz) && (R.val[5] > 0) != (ry*rz > 0) )
+ rz = -rz;
+ theta /= std::sqrt(rx*rx + ry*ry + rz*rz);
+ rx *= theta;
+ ry *= theta;
+ rz *= theta;
+ }
+ }
+ else
+ {
+ double vth = 1/(2*s);
+ vth *= theta;
+ rx *= vth; ry *= vth; rz *= vth;
+ }
+
+ return cv::Vec3d(rx, ry, rz);
+}
+
+template inline
+cv::Affine3 cv::Affine3::inv(int method) const
+{
+ return matrix.inv(method);
+}
+
+template inline
+cv::Affine3 cv::Affine3::rotate(const Mat3& R) const
+{
+ Mat3 Lc = linear();
+ Vec3 tc = translation();
+ Mat4 result;
+ result.val[12] = result.val[13] = result.val[14] = 0;
+ result.val[15] = 1;
+
+ for(int j = 0; j < 3; ++j)
+ {
+ for(int i = 0; i < 3; ++i)
+ {
+ float_type value = 0;
+ for(int k = 0; k < 3; ++k)
+ value += R(j, k) * Lc(k, i);
+ result(j, i) = value;
+ }
+
+ result(j, 3) = R.row(j).dot(tc.t());
+ }
+ return result;
+}
+
+template inline
+cv::Affine3 cv::Affine3::rotate(const Vec3& _rvec) const
+{
+ return rotate(Affine3f(_rvec).rotation());
+}
+
+template inline
+cv::Affine3 cv::Affine3::translate(const Vec3& t) const
+{
+ Mat4 m = matrix;
+ m.val[ 3] += t[0];
+ m.val[ 7] += t[1];
+ m.val[11] += t[2];
+ return m;
+}
+
+template inline
+cv::Affine3 cv::Affine3::concatenate(const Affine3& affine) const
+{
+ return (*this).rotate(affine.rotation()).translate(affine.translation());
+}
+
+template template inline
+cv::Affine3::operator Affine3() const
+{
+ return Affine3(matrix);
+}
+
+template template inline
+cv::Affine3 cv::Affine3::cast() const
+{
+ return Affine3(matrix);
+}
+
+template inline
+cv::Affine3 cv::operator*(const cv::Affine3& affine1, const cv::Affine3& affine2)
+{
+ return affine2.concatenate(affine1);
+}
+
+template inline
+V cv::operator*(const cv::Affine3& affine, const V& v)
+{
+ const typename Affine3::Mat4& m = affine.matrix;
+
+ V r;
+ r.x = m.val[0] * v.x + m.val[1] * v.y + m.val[ 2] * v.z + m.val[ 3];
+ r.y = m.val[4] * v.x + m.val[5] * v.y + m.val[ 6] * v.z + m.val[ 7];
+ r.z = m.val[8] * v.x + m.val[9] * v.y + m.val[10] * v.z + m.val[11];
+ return r;
+}
+
+static inline
+cv::Vec3f cv::operator*(const cv::Affine3f& affine, const cv::Vec3f& v)
+{
+ const cv::Matx44f& m = affine.matrix;
+ cv::Vec3f r;
+ r.val[0] = m.val[0] * v[0] + m.val[1] * v[1] + m.val[ 2] * v[2] + m.val[ 3];
+ r.val[1] = m.val[4] * v[0] + m.val[5] * v[1] + m.val[ 6] * v[2] + m.val[ 7];
+ r.val[2] = m.val[8] * v[0] + m.val[9] * v[1] + m.val[10] * v[2] + m.val[11];
+ return r;
+}
+
+static inline
+cv::Vec3d cv::operator*(const cv::Affine3d& affine, const cv::Vec3d& v)
+{
+ const cv::Matx44d& m = affine.matrix;
+ cv::Vec3d r;
+ r.val[0] = m.val[0] * v[0] + m.val[1] * v[1] + m.val[ 2] * v[2] + m.val[ 3];
+ r.val[1] = m.val[4] * v[0] + m.val[5] * v[1] + m.val[ 6] * v[2] + m.val[ 7];
+ r.val[2] = m.val[8] * v[0] + m.val[9] * v[1] + m.val[10] * v[2] + m.val[11];
+ return r;
+}
+
+
+
+#if defined EIGEN_WORLD_VERSION && defined EIGEN_GEOMETRY_MODULE_H
+
+template inline
+cv::Affine3::Affine3(const Eigen::Transform& affine)
+{
+ cv::Mat(4, 4, cv::traits::Type