Joe Verbout
opencv on mbed
Diff: opencv2/calib3d.hpp
- Revision:
- 0:ea44dc9ed014
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/opencv2/calib3d.hpp Thu Mar 31 21:16:38 2016 +0000
@@ -0,0 +1,2002 @@
+/*M///////////////////////////////////////////////////////////////////////////////////////
+//
+// IMPORTANT: READ BEFORE DOWNLOADING, COPYING, INSTALLING OR USING.
+//
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+// If you do not agree to this license, do not download, install,
+// copy or use the software.
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+//
+// License Agreement
+// For Open Source Computer Vision Library
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+// Copyright (C) 2000-2008, Intel Corporation, all rights reserved.
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+//M*/
+
+#ifndef __OPENCV_CALIB3D_HPP__
+#define __OPENCV_CALIB3D_HPP__
+
+#include "opencv2/core.hpp"
+#include "opencv2/features2d.hpp"
+#include "opencv2/core/affine.hpp"
+
+/**
+ @defgroup calib3d Camera Calibration and 3D Reconstruction
+
+The functions in this section use a so-called pinhole camera model. In this model, a scene view is
+formed by projecting 3D points into the image plane using a perspective transformation.
+
+\f[s \; m' = A [R|t] M'\f]
+
+or
+
+\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_1 \\
+r_{21} & r_{22} & r_{23} & t_2 \\
+r_{31} & r_{32} & r_{33} & t_3
+\end{bmatrix}
+\begin{bmatrix}
+X \\
+Y \\
+Z \\
+1
+\end{bmatrix}\f]
+
+where:
+
+- \f$(X, Y, Z)\f$ are the coordinates of a 3D point in the world coordinate space
+- \f$(u, v)\f$ are the coordinates of the projection point in pixels
+- \f$A\f$ is a camera matrix, or a matrix of intrinsic parameters
+- \f$(cx, cy)\f$ is a principal point that is usually at the image center
+- \f$fx, fy\f$ are the focal lengths expressed in pixel units.
+
+Thus, if an image from the camera is scaled by a factor, all of these parameters should be scaled
+(multiplied/divided, respectively) by the same factor. 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 zoom lens). The joint rotation-translation matrix \f$[R|t]\f$ is called a matrix of
+extrinsic parameters. It is used to describe the camera motion around a static scene, or vice versa,
+rigid motion of an object in front of a still camera. That is, \f$[R|t]\f$ translates coordinates of a
+point \f$(X, Y, Z)\f$ to a coordinate system, fixed with respect to the camera. The transformation above
+is equivalent to the following (when \f$z \ne 0\f$ ):
+
+\f[\begin{array}{l}
+\vecthree{x}{y}{z} = R \vecthree{X}{Y}{Z} + t \\
+x' = x/z \\
+y' = y/z \\
+u = f_x*x' + c_x \\
+v = f_y*y' + c_y
+\end{array}\f]
+
+Real lenses usually have some distortion, mostly radial distortion and slight tangential distortion.
+So, the above model is extended as:
+
+\f[\begin{array}{l}
+\vecthree{x}{y}{z} = R \vecthree{X}{Y}{Z} + t \\
+x' = x/z \\
+y' = y/z \\
+x'' = 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'' = 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 \\
+\text{where} \quad r^2 = x'^2 + y'^2 \\
+u = f_x*x'' + c_x \\
+v = f_y*y'' + c_y
+\end{array}\f]
+
+\f$k_1\f$, \f$k_2\f$, \f$k_3\f$, \f$k_4\f$, \f$k_5\f$, and \f$k_6\f$ are radial distortion coefficients. \f$p_1\f$ and \f$p_2\f$ are
+tangential distortion coefficients. \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.
+
+In some cases the image sensor may be tilted in order to focus an oblique plane in front of the
+camera (Scheimpfug condition). 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 modelled in the following way, see e.g. @cite Louhichi07.
+
+\f[\begin{array}{l}
+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}\\
+u = f_x*x''' + c_x \\
+v = f_y*y''' + c_y
+\end{array}\f]
+
+where 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.
+
+@note
+ - A calibration sample for 3 cameras in 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 sample of an artificially generated camera and chessboard patterns can be
+ found at opencv_source_code/samples/cpp/calibration_artificial.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[x = Xc_1 \\ y = Xc_2 \\ z = Xc_3\f]
+
+ The pinehole projection coordinates of P is [a; b] where
+
+ \f[a = x / z \ and \ b = y / z \\ r^2 = a^2 + b^2 \\ \theta = atan(r)\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[x' = (\theta_d / r) x \\ y' = (\theta_d / r) y \f]
+
+ Finally, conversion into pixel coordinates: The final pixel coordinates vector [u; v] where:
+
+ \f[u = f_x (x' + \alpha y') + c_x \\
+ v = f_y yy + c_y\f]
+
+ @defgroup calib3d_c C API
+
+ @}
+ */
+
+namespace cv
+{
+
+//! @addtogroup calib3d
+//! @{
+
+//! type of the robust estimation algorithm
+enum { LMEDS = 4, //!< least-median algorithm
+ RANSAC = 8, //!< RANSAC algorithm
+ RHO = 16 //!< RHO algorithm
+ };
+
+enum { SOLVEPNP_ITERATIVE = 0,
+ SOLVEPNP_EPNP = 1, //!< EPnP: Efficient Perspective-n-Point Camera Pose Estimation @cite lepetit2009epnp
+ SOLVEPNP_P3P = 2, //!< Complete Solution Classification for the Perspective-Three-Point Problem @cite gao2003complete
+ SOLVEPNP_DLS = 3, //!< A Direct Least-Squares (DLS) Method for PnP @cite hesch2011direct
+ SOLVEPNP_UPNP = 4 //!< Exhaustive Linearization for Robust Camera Pose and Focal Length Estimation @cite penate2013exhaustive
+
+};
+
+enum { CALIB_CB_ADAPTIVE_THRESH = 1,
+ CALIB_CB_NORMALIZE_IMAGE = 2,
+ CALIB_CB_FILTER_QUADS = 4,
+ CALIB_CB_FAST_CHECK = 8
+ };
+
+enum { CALIB_CB_SYMMETRIC_GRID = 1,
+ CALIB_CB_ASYMMETRIC_GRID = 2,
+ CALIB_CB_CLUSTERING = 4
+ };
+
+enum { 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,
+ // 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
+ };
+
+//! 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
+ FM_RANSAC = 8 //!< RANSAC algorithm
+ };
+
+
+
+/** @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 calibrateCamera, stereoCalibrate, or solvePnP .
+ */
+CV_EXPORTS_W void Rodrigues( InputArray src, OutputArray dst, OutputArray jacobian = noArray() );
+
+/** @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\<Point2f\> .
+@param dstPoints Coordinates of the points in the target plane, a matrix of the type CV_32FC2 or
+a vector\<Point2f\> .
+@param method Method used to computed a homography matrix. The following methods are possible:
+- **0** - a regular method using all the points
+- **RANSAC** - RANSAC-based robust method
+- **LMEDS** - Least-Median robust method
+- **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} * \texttt{srcPoints} _i) \| > \texttt{ransacReprojThreshold}\f]
+then the point \f$i\f$ is considered 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, 2000 is the maximum it can be.
+@param confidence Confidence level, between 0 and 1.
+
+The functions find and return 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), estimate the homography matrix
+using this subset and a simple least-square algorithm, and then compute the quality/goodness of the
+computed homography (which is the number of inliers for RANSAC or the 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. Thus, it is normalized so that \f$h_{33}=1\f$. Note that whenever an H matrix
+cannot be estimated, an empty one will be returned.
+
+@sa
+ getAffineTransform, getPerspectiveTransform, estimateRigidTransform, warpPerspective,
+ perspectiveTransform
+
+@note
+ - A example on calculating a homography for image matching can be found at
+ opencv_source_code/samples/cpp/video_homography.cpp
+
+ */
+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 );
+
+/** @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 principle axes that results in the same orientation of an
+object, eg. see @cite Slabaugh . Returned tree rotation matrices and corresponding three Euler angules
+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 matrix.
+
+@param projMatrix 3x4 input projection matrix P.
+@param cameraMatrix Output 3x3 camera matrix K.
+@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
+principle axes that results in the same orientation of an object, eg. see @cite Slabaugh . Returned
+tree rotation matrices and corresponding three Euler angules 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
+@param dr3dt1
+@param dr3dr2
+@param dr3dt2
+@param dt3dr1
+@param dt3dt1
+@param dt3dr2
+@param dt3dt2 Optional output derivatives of rvec3 or tvec3 with regard to rvec1, rvec2, tvec1 and
+tvec2, respectively.
+
+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, 3xN/Nx3 1-channel or 1xN/Nx1 3-channel (or
+vector\<Point3f\> ), where N is the number of points in the view.
+@param rvec Rotation vector. See Rodrigues for details.
+@param tvec Translation vector.
+@param cameraMatrix 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 empty, the zero distortion coefficients are assumed.
+@param imagePoints Output array of image points, 2xN/Nx2 1-channel or 1xN/Nx1 2-channel, or
+vector\<Point2f\> .
+@param jacobian Optional output 2Nx(10+\<numDistCoeffs\>) 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 (*fx/fy*) is fixed and correspondingly adjusts the jacobian
+matrix.
+
+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. The Jacobians are used during the global optimization in
+calibrateCamera, solvePnP, and 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=(0,0,0) or by setting cameraMatrix to a 3x3 identity matrix, or by
+passing zero distortion coefficients, you can get various useful partial cases of the function. This
+means that you 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 );
+
+/** @brief Finds an object pose from 3D-2D point correspondences.
+
+@param objectPoints Array of object points in the object coordinate space, 3xN/Nx3 1-channel or
+1xN/Nx1 3-channel, where N is the number of points. vector\<Point3f\> can be also passed here.
+@param imagePoints Array of corresponding image points, 2xN/Nx2 1-channel or 1xN/Nx1 2-channel,
+where N is the number of points. vector\<Point2f\> can be also passed here.
+@param cameraMatrix Input camera matrix \f$A = \vecthreethree{fx}{0}{cx}{0}{fy}{cy}{0}{0}{1}\f$ .
+@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 rvec Output rotation vector (see 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:
+- **SOLVEPNP_ITERATIVE** Iterative method is based on Levenberg-Marquardt optimization. In
+this case the 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
+projectPoints ) objectPoints .
+- **SOLVEPNP_P3P** Method is based on the paper of X.S. Gao, X.-R. Hou, J. Tang, H.-F. Chang
+"Complete Solution Classification for the Perspective-Three-Point Problem". In this case the
+function requires exactly four object and image points.
+- **SOLVEPNP_EPNP** Method has been introduced by F.Moreno-Noguer, V.Lepetit and P.Fua in the
+paper "EPnP: Efficient Perspective-n-Point Camera Pose Estimation".
+- **SOLVEPNP_DLS** Method is based on the paper of Joel A. Hesch and Stergios I. Roumeliotis.
+"A Direct Least-Squares (DLS) Method for PnP".
+- **SOLVEPNP_UPNP** Method is based on the paper of A.Penate-Sanchez, J.Andrade-Cetto,
+F.Moreno-Noguer. "Exhaustive Linearization for Robust Camera Pose and Focal Length
+Estimation". In this case the function also estimates the parameters \f$f_x\f$ and \f$f_y\f$
+assuming that both have the same value. Then the cameraMatrix is updated with the estimated
+focal length.
+
+The function estimates the object pose given a set of object points, their corresponding image
+projections, as well as the camera matrix and the distortion coefficients.
+
+@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 cv::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))
+ */
+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 from 3D-2D point correspondences using the RANSAC scheme.
+
+@param objectPoints Array of object points in the object coordinate space, 3xN/Nx3 1-channel or
+1xN/Nx1 3-channel, where N is the number of points. vector\<Point3f\> can be also passed here.
+@param imagePoints Array of corresponding image points, 2xN/Nx2 1-channel or 1xN/Nx1 2-channel,
+where N is the number of points. vector\<Point2f\> can be also passed here.
+@param cameraMatrix Input camera matrix \f$A = \vecthreethree{fx}{0}{cx}{0}{fy}{cy}{0}{0}{1}\f$ .
+@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 rvec Output rotation vector (see 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 solvePnP ).
+
+The function estimates an object pose given a set of object points, their corresponding image
+projections, as well as the camera 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 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
+ opencv_source_code/samples/cpp/tutorial_code/calib3d/real_time_pose_estimation/
+ */
+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 );
+
+/** @brief Finds an initial camera 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$f_x = f_y * \texttt{aspectRatio}\f$ .
+
+The function estimates and returns an initial camera 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 = cvSize(points_per_row,points_per_colum) = cvSize(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:
+- **CV_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).
+- **CV_CALIB_CB_NORMALIZE_IMAGE** Normalize the image gamma with equalizeHist before
+applying fixed or adaptive thresholding.
+- **CV_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.
+- **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.
+
+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<Point2f> 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.
+ */
+CV_EXPORTS_W bool findChessboardCorners( InputArray image, Size patternSize, OutputArray corners,
+ int flags = CALIB_CB_ADAPTIVE_THRESH + CALIB_CB_NORMALIZE_IMAGE );
+
+//! finds subpixel-accurate positions of the chessboard corners
+CV_EXPORTS 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 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:
+- **CALIB_CB_SYMMETRIC_GRID** uses symmetric pattern of circles.
+- **CALIB_CB_ASYMMETRIC_GRID** uses asymmetric pattern of circles.
+- **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.
+
+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<Point2f> 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 = CALIB_CB_SYMMETRIC_GRID,
+ const Ptr<FeatureDetector> &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<std::vector<cv::Vec3f>>). The outer
+vector contains as many elements as the number of the 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. The points are 3D, but since they are in a pattern coordinate system,
+then, if the rig is planar, it may make sense to put the model to a XY coordinate plane so that
+Z-coordinate of each input object point is 0.
+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<std::vector<cv::Vec2f>>). imagePoints.size() and
+objectPoints.size() and imagePoints[i].size() must be equal to objectPoints[i].size() for each i.
+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 intrinsic camera matrix.
+@param cameraMatrix Output 3x3 floating-point camera matrix
+\f$A = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}\f$ . If CV\_CALIB\_USE\_INTRINSIC\_GUESS
+and/or CV_CALIB_FIX_ASPECT_RATIO are specified, some or all of fx, fy, cx, cy must be
+initialized before calling the function.
+@param distCoeffs Output 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.
+@param rvecs Output vector of rotation vectors (see Rodrigues ) estimated for each pattern view
+(e.g. std::vector<cv::Mat>>). 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:
+- **CV_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 solvePnP instead.
+- **CV_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
+CV_CALIB_USE_INTRINSIC_GUESS is set too.
+- **CV_CALIB_FIX_ASPECT_RATIO** The functions considers only fy as a free parameter. The
+ratio fx/fy stays the same as in the input cameraMatrix . When
+CV_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.
+- **CV_CALIB_ZERO_TANGENT_DIST** Tangential distortion coefficients \f$(p_1, p_2)\f$ are set
+to zeros and stay zero.
+- **CV_CALIB_FIX_K1,...,CV_CALIB_FIX_K6** The corresponding radial distortion
+coefficient is not changed during the optimization. If CV_CALIB_USE_INTRINSIC_GUESS is
+set, the coefficient from the supplied distCoeffs matrix is used. Otherwise, it is set to 0.
+- **CV_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. If the flag is not
+set, the function computes and returns only 5 distortion coefficients.
+- **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.
+- **CALIB_FIX_S1_S2_S3_S4** The thin prism distortion coefficients are not changed during
+the optimization. If CV_CALIB_USE_INTRINSIC_GUESS is set, the coefficient from the
+supplied distCoeffs matrix is used. Otherwise, it is set to 0.
+- **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.
+- **CALIB_FIX_TAUX_TAUY** The coefficients of the tilted sensor model are not changed during
+the optimization. If CV_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 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 a 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 findChessboardCorners ). Currently, initialization of intrinsic parameters
+(when CV_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 CV_CALIB_FIX_K? are specified.
+
+- Estimate the initial camera pose as if the intrinsic parameters have been already known. This is
+ done using 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 projectPoints for details.
+
+The function returns the final re-projection error.
+
+@note
+ If you use a non-square (=non-NxN) grid and findChessboardCorners for calibration, and
+ calibrateCamera returns bad values (zero distortion coefficients, an image center very far from
+ (w/2-0.5,h/2-0.5), and/or large differences between \f$f_x\f$ and \f$f_y\f$ (ratios of 10:1 or more)),
+ then you have probably used patternSize=cvSize(rows,cols) instead of using
+ patternSize=cvSize(cols,rows) in findChessboardCorners .
+
+@sa
+ findChessboardCorners, solvePnP, initCameraMatrix2D, stereoCalibrate, undistort
+ */
+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 Computes useful camera characteristics from the camera matrix.
+
+@param cameraMatrix Input camera 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 the stereo camera.
+
+@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 cameraMatrix1 Input/output first camera 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 CV_CALIB_USE_INTRINSIC_GUESS , CV_CALIB_FIX_ASPECT_RATIO ,
+CV_CALIB_FIX_INTRINSIC , or CV_CALIB_FIX_FOCAL_LENGTH are specified, some or all of the
+matrix components must be initialized. See the flags description for details.
+@param distCoeffs1 Input/output 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. The output vector length depends on the flags.
+@param cameraMatrix2 Input/output second camera matrix. The parameter is similar to cameraMatrix1
+@param distCoeffs2 Input/output lens distortion coefficients for the second camera. The parameter
+is similar to distCoeffs1 .
+@param imageSize Size of the image used only to initialize intrinsic camera 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 E Output essential matrix.
+@param F Output fundamental matrix.
+@param flags Different flags that may be zero or a combination of the following values:
+- **CV_CALIB_FIX_INTRINSIC** Fix cameraMatrix? and distCoeffs? so that only R, T, E , and F
+matrices are estimated.
+- **CV_CALIB_USE_INTRINSIC_GUESS** Optimize some or all of the intrinsic parameters
+according to the specified flags. Initial values are provided by the user.
+- **CV_CALIB_FIX_PRINCIPAL_POINT** Fix the principal points during the optimization.
+- **CV_CALIB_FIX_FOCAL_LENGTH** Fix \f$f^{(j)}_x\f$ and \f$f^{(j)}_y\f$ .
+- **CV_CALIB_FIX_ASPECT_RATIO** Optimize \f$f^{(j)}_y\f$ . Fix the ratio \f$f^{(j)}_x/f^{(j)}_y\f$
+.
+- **CV_CALIB_SAME_FOCAL_LENGTH** Enforce \f$f^{(0)}_x=f^{(1)}_x\f$ and \f$f^{(0)}_y=f^{(1)}_y\f$ .
+- **CV_CALIB_ZERO_TANGENT_DIST** Set tangential distortion coefficients for each camera to
+zeros and fix there.
+- **CV_CALIB_FIX_K1,...,CV_CALIB_FIX_K6** Do not change the corresponding radial
+distortion coefficient during the optimization. If CV_CALIB_USE_INTRINSIC_GUESS is set,
+the coefficient from the supplied distCoeffs matrix is used. Otherwise, it is set to 0.
+- **CV_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.
+- **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.
+- **CALIB_FIX_S1_S2_S3_S4** The thin prism distortion coefficients are not changed during
+the optimization. If CV_CALIB_USE_INTRINSIC_GUESS is set, the coefficient from the
+supplied distCoeffs matrix is used. Otherwise, it is set to 0.
+- **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.
+- **CALIB_FIX_TAUX_TAUY** The coefficients of the tilted sensor model are not changed during
+the optimization. If CV_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 transformation between two cameras making a stereo pair. If you have a stereo
+camera where the relative position and orientation of two cameras is fixed, and if you computed
+poses of an object relative to the first camera and to the second camera, (R1, T1) and (R2, T2),
+respectively (this can be done with solvePnP ), then those poses definitely relate to each other.
+This means that, given ( \f$R_1\f$,\f$T_1\f$ ), it should be possible to compute ( \f$R_2\f$,\f$T_2\f$ ). You only
+need to know the position and orientation of the second camera relative to the first camera. This is
+what the described function does. It computes ( \f$R\f$,\f$T\f$ ) so that:
+
+\f[R_2=R*R_1
+T_2=R*T_1 + T,\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} E cameraMatrix1^{-1}\f]
+
+Besides the stereo-related information, the function can also perform a full calibration of each of
+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 CV_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
+CV_CALIB_SAME_FOCAL_LENGTH and CV_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_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) );
+
+
+/** @brief Computes rectification transforms for each head of a calibrated stereo camera.
+
+@param cameraMatrix1 First camera matrix.
+@param distCoeffs1 First camera distortion parameters.
+@param cameraMatrix2 Second camera matrix.
+@param distCoeffs2 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 T 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 CV_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). Obviously, 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 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*f \\ 0 & f & cy & 0 \\ 0 & 0 & 1 & 0 \end{bmatrix} ,\f]
+
+ where \f$T_x\f$ is a horizontal shift between the cameras and \f$cx_1=cx_2\f$ if
+ CV_CALIB_ZERO_DISPARITY is set.
+
+- **Vertical stereo**: the first and the second camera views are shifted relative to each other
+ mainly in 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*f \\ 0 & 0 & 1 & 0 \end{bmatrix} ,\f]
+
+ where \f$T_y\f$ is a vertical shift between the cameras and \f$cy_1=cy_2\f$ if 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$|\texttt{points2[i]}^T*\texttt{F}*\texttt{points1[i]}|>\texttt{threshold}\f$ ) 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 matrix based on the free scaling parameter.
+
+@param cameraMatrix Input camera matrix.
+@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 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 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 matrix.
+
+The function computes and returns the optimal new camera 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 undistortion result is likely to have some black pixels corresponding to
+"virtual" pixels outside of the captured distorted image. The original camera matrix, distortion
+coefficients, the computed new camera 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 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.
+- **CV_FM_7POINT** for a 7-point algorithm. \f$N = 7\f$
+- **CV_FM_8POINT** for an 8-point algorithm. \f$N \ge 8\f$
+- **CV_FM_RANSAC** for the RANSAC algorithm. \f$N \ge 8\f$
+- **CV_FM_LMEDS** for the LMedS algorithm. \f$N \ge 8\f$
+@param param1 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 param2 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
+
+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<Point2f> points1(point_count);
+ vector<Point2f> 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 = FM_RANSAC,
+ double param1 = 3., double param2 = 0.99,
+ OutputArray mask = noArray() );
+
+/** @overload */
+CV_EXPORTS Mat findFundamentalMat( InputArray points1, InputArray points2,
+ OutputArray mask, int method = FM_RANSAC,
+ double param1 = 3., double param2 = 0.99 );
+
+/** @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 matrix \f$K = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}\f$ .
+Note that this function assumes that points1 and points2 are feature points from cameras with the
+same camera matrix.
+@param method Method for computing a fundamental matrix.
+- **RANSAC** for the RANSAC algorithm.
+- **MEDS** 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.
+
+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,
+ OutputArray mask = noArray() );
+
+/** @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 principle point.
+@param pp principle point of the camera.
+@param method Method for computing a fundamental matrix.
+- **RANSAC** for the RANSAC algorithm.
+- **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.
+
+This function differs from the one above that it computes camera matrix from focal length and
+principal point:
+
+\f[K =
+\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, OutputArray mask = noArray() );
+
+/** @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 decompose an essential matrix E using svd decomposition @cite HartleyZ00 . Generally 4
+possible poses exists for a given E. They are \f$[R_1, t]\f$, \f$[R_1, -t]\f$, \f$[R_2, t]\f$, \f$[R_2, -t]\f$. By
+decomposing E, you can only get the direction of the translation, so the function returns unit t.
+ */
+CV_EXPORTS_W void decomposeEssentialMat( InputArray E, OutputArray R1, OutputArray R2, OutputArray t );
+
+/** @brief Recover relative camera rotation and translation from an estimated essential matrix and the
+corresponding points in two images, using cheirality check. Returns the number of inliers which 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 matrix \f$K = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}\f$ .
+Note that this function assumes that points1 and points2 are feature points from cameras with the
+same camera matrix.
+@param R Recovered relative rotation.
+@param t Recoverd relative translation.
+@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 decomposeEssentialMat and then verifies possible
+pose hypotheses by doing cheirality check. The cheirality check basically 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 output E and mask from 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<Point2f> points1(point_count);
+ vector<Point2f> 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 Recovered relative rotation.
+@param t Recoverd relative translation.
+@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 principle point.
+@param pp Principle 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 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 differs from the one above that it computes camera matrix from focal length and
+principal point:
+
+\f[K =
+\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() );
+
+/** @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\<Point2f\> .
+@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 Reconstructs points by triangulation.
+
+@param projMatr1 3x4 projection matrix of the first camera.
+@param projMatr2 3x4 projection matrix of the second camera.
+@param projPoints1 2xN array of feature points in the first image. In case of 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 case of 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.
+
+The function reconstructs 3-dimensional points (in homogeneous coordinates) by using their
+observations with a stereo camera. Projections matrices can be obtained from stereoRectify.
+
+@note
+ Keep in mind that all input data should be of float type in order for this function to work.
+
+@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 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$newPoints2^T * F * newPoints1 = 0\f$ .
+ */
+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 cv::stereoRectify())
+CV_EXPORTS_W Rect getValidDisparityROI( Rect roi1, Rect roi2,
+ int minDisparity, int numberOfDisparities,
+ int SADWindowSize );
+
+//! 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. If 16-bit signed format is used, the values are assumed to have no
+fractional bits.
+@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.
+@param Q \f$4 \times 4\f$ perspective transformation matrix that can be obtained with 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) andthe corresponding disparity d=disparity(x,y) , it
+computes:
+
+\f[\begin{array}{l} [X \; Y \; Z \; W]^T = \texttt{Q} *[x \; y \; \texttt{disparity} (x,y) \; 1]^T \\ \texttt{\_3dImage} (x,y) = (X/W, \; Y/W, \; Z/W) \end{array}\f]
+
+The matrix Q can be an arbitrary \f$4 \times 4\f$ matrix (for example, the one computed by
+stereoRectify). 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 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) + (\texttt{F} \cdot \texttt{pt1})(1) + (\texttt{F}^t \cdot \texttt{pt2})(0) + (\texttt{F}^t \cdot \texttt{pt2})(1)}\f]
+The fundamental matrix may be calculated using the cv::findFundamentalMat function. See HZ 11.4.3 for details.
+@param pt1 first homogeneous 2d point
+@param pt2 second homogeneous 2d point
+@param F fundamental matrix
+*/
+CV_EXPORTS_W double sampsonDistance(InputArray pt1, InputArray pt2, InputArray F);
+
+/** @brief Computes an optimal affine transformation between two 3D point sets.
+
+@param src First input 3D point set.
+@param dst Second input 3D point set.
+@param out Output 3D affine transformation matrix \f$3 \times 4\f$ .
+@param inliers Output vector indicating which points are inliers.
+@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 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 intrinsic camera calibration 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 observing a planar object from the
+homography H induced by the plane. The intrinsic camera matrix K must also be provided. The function
+may return up to four mathematical solution sets. At least two of the solutions may further be
+invalidated if point correspondences are available by applying positive depth constraint (all points
+must be in front of the camera). The decomposition method is described in detail in @cite Malis .
+ */
+CV_EXPORTS_W int decomposeHomographyMat(InputArray H,
+ InputArray K,
+ OutputArrayOfArrays rotations,
+ OutputArrayOfArrays translations,
+ OutputArrayOfArrays normals);
+
+/** @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.
+ */
+class CV_EXPORTS_W StereoBM : public StereoMatcher
+{
+public:
+ enum { PREFILTER_NORMALIZED_RESPONSE = 0,
+ PREFILTER_XSOBEL = 1
+ };
+
+ CV_WRAP virtual int getPreFilterType() const = 0;
+ CV_WRAP virtual void setPreFilterType(int preFilterType) = 0;
+
+ CV_WRAP virtual int getPreFilterSize() const = 0;
+ CV_WRAP virtual void setPreFilterSize(int preFilterSize) = 0;
+
+ CV_WRAP virtual int getPreFilterCap() const = 0;
+ CV_WRAP virtual void setPreFilterCap(int preFilterCap) = 0;
+
+ CV_WRAP virtual int getTextureThreshold() const = 0;
+ CV_WRAP virtual void setTextureThreshold(int textureThreshold) = 0;
+
+ CV_WRAP virtual int getUniquenessRatio() const = 0;
+ CV_WRAP virtual void setUniquenessRatio(int uniquenessRatio) = 0;
+
+ CV_WRAP virtual int getSmallerBlockSize() const = 0;
+ CV_WRAP virtual void setSmallerBlockSize(int blockSize) = 0;
+
+ CV_WRAP virtual Rect getROI1() const = 0;
+ CV_WRAP virtual void setROI1(Rect roi1) = 0;
+
+ CV_WRAP virtual Rect getROI2() const = 0;
+ CV_WRAP virtual void setROI2(Rect roi2) = 0;
+
+ /** @brief Creates StereoBM object
+
+ @param numDisparities the disparity search range. For each pixel algorithm will find the best
+ disparity from 0 (default minimum disparity) to numDisparities. The search range can then 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 higher
+ chance for algorithm to find a wrong correspondence.
+
+ The function create StereoBM object. You can then call StereoBM::compute() to compute disparity for
+ a specific stereo pair.
+ */
+ CV_WRAP static Ptr<StereoBM> 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
+ };
+
+ 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\*SADWindowSize\*SADWindowSize and
+ 32\*number_of_image_channels\*SADWindowSize\*SADWindowSize , 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<StereoSGBM> create(int minDisparity, int numDisparities, int blockSize,
+ 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);
+};
+
+//! @} 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,
+ CALIB_RECOMPUTE_EXTRINSIC = 2,
+ CALIB_CHECK_COND = 4,
+ CALIB_FIX_SKEW = 8,
+ CALIB_FIX_K1 = 16,
+ CALIB_FIX_K2 = 32,
+ CALIB_FIX_K3 = 64,
+ CALIB_FIX_K4 = 128,
+ CALIB_FIX_INTRINSIC = 256
+ };
+
+ /** @brief Projects points using fisheye model
+
+ @param objectPoints Array of object points, 1xN/Nx1 3-channel (or vector\<Point3f\> ), 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\<Point2f\>.
+ @param affine
+ @param K Camera matrix \f$K = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{_1}\f$.
+ @param D Input vector of distortion coefficients \f$(k_1, k_2, k_3, k_4)\f$.
+ @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\<Point2f\> ), where N is
+ the number of points in the view.
+ @param K Camera matrix \f$K = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{_1}\f$.
+ @param D Input vector of distortion coefficients \f$(k_1, k_2, k_3, k_4)\f$.
+ @param alpha The skew coefficient.
+ @param distorted Output array of image points, 1xN/Nx1 2-channel, or vector\<Point2f\> .
+ */
+ CV_EXPORTS_W void distortPoints(InputArray undistorted, OutputArray distorted, 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\<Point2f\> ), where N is the
+ number of points in the view.
+ @param K Camera matrix \f$K = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{_1}\f$.
+ @param D Input vector of distortion coefficients \f$(k_1, k_2, k_3, k_4)\f$.
+ @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 matrix (3x3) or new projection matrix (3x4)
+ @param undistorted Output array of image points, 1xN/Nx1 2-channel, or vector\<Point2f\> .
+ */
+ CV_EXPORTS_W void undistortPoints(InputArray distorted, OutputArray undistorted,
+ InputArray K, InputArray D, InputArray R = noArray(), InputArray P = noArray());
+
+ /** @brief Computes undistortion and rectification maps for image transform by cv::remap(). If D is empty zero
+ distortion is used, if R or P is empty identity matrixes are used.
+
+ @param K Camera matrix \f$K = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{_1}\f$.
+ @param D Input vector of distortion coefficients \f$(k_1, k_2, k_3, k_4)\f$.
+ @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 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 matrix \f$K = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{_1}\f$.
+ @param D Input vector of distortion coefficients \f$(k_1, k_2, k_3, k_4)\f$.
+ @param Knew Camera 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 function transforms an image to compensate radial and tangential 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 matrix for undistortion or rectification.
+
+ @param K Camera matrix \f$K = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{_1}\f$.
+ @param image_size
+ @param D Input vector of distortion coefficients \f$(k_1, k_2, k_3, k_4)\f$.
+ @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 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
+ @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 calibaration
+
+ @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 intrinsic camera matrix.
+ @param K Output 3x3 floating-point camera matrix
+ \f$A = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}\f$ . If
+ 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$(k_1, k_2, k_3, k_4)\f$.
+ @param rvecs Output vector of rotation vectors (see 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:
+ - **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.
+ - **fisheye::CALIB_RECOMPUTE_EXTRINSIC** Extrinsic will be recomputed after each iteration
+ of intrinsic optimization.
+ - **fisheye::CALIB_CHECK_COND** The functions will check validity of condition number.
+ - **fisheye::CALIB_FIX_SKEW** Skew coefficient (alpha) is set to zero and stay zero.
+ - **fisheye::CALIB_FIX_K1..4** Selected distortion coefficients are set to zeros and stay
+ zero.
+ @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 matrix.
+ @param D1 First camera distortion parameters.
+ @param K2 Second camera 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 CV_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 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 fisheye::CALIB_USE_INTRINSIC_GUESS , fisheye::CV_CALIB_FIX_INTRINSIC are specified,
+ some or all of the matrix components must be initialized.
+ @param D1 Input/output vector of distortion coefficients \f$(k_1, k_2, k_3, k_4)\f$ of 4 elements.
+ @param K2 Input/output second camera 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 intrinsic camera 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 flags Different flags that may be zero or a combination of the following values:
+ - **fisheye::CV_CALIB_FIX_INTRINSIC** Fix K1, K2? and D1, D2? so that only R, T matrices
+ are estimated.
+ - **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.
+ - **fisheye::CALIB_RECOMPUTE_EXTRINSIC** Extrinsic will be recomputed after each iteration
+ of intrinsic optimization.
+ - **fisheye::CALIB_CHECK_COND** The functions will check validity of condition number.
+ - **fisheye::CALIB_FIX_SKEW** Skew coefficient (alpha) is set to zero and stay zero.
+ - **fisheye::CALIB_FIX_K1..4** 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, int flags = fisheye::CALIB_FIX_INTRINSIC,
+ TermCriteria criteria = TermCriteria(TermCriteria::COUNT + TermCriteria::EPS, 100, DBL_EPSILON));
+
+//! @} calib3d_fisheye
+}
+
+} // cv
+
+#ifndef DISABLE_OPENCV_24_COMPATIBILITY
+#include "opencv2/calib3d/calib3d_c.h"
+#endif
+
+#endif
+