1 \section{Camera Calibration and 3D Reconstruction}
3 The functions in this section use the so-called pinhole camera model. That
4 is, a scene view is formed by projecting 3D points into the image plane
5 using a perspective transformation.
14 s \vecthree{u}{v}{1} = \vecthreethree
19 r_{11} & r_{12} & r_{13} & t_1 \\
20 r_{21} & r_{22} & r_{23} & t_2 \\
21 r_{31} & r_{32} & r_{33} & t_3
23 \begin{bmatrix}X\\Y\\Z\\1 \end{bmatrix}
26 Where $(X, Y, Z)$ are the coordinates of a 3D point in the world
27 coordinate space, $(u, v)$ are the coordinates of the projection point
28 in pixels. $A$ is called a camera matrix, or a matrix of
29 intrinsic parameters. $(cx, cy)$ is a principal point (that is
30 usually at the image center), and $fx, fy$ are the focal lengths
31 expressed in pixel-related units. Thus, if an image from camera is
32 scaled by some factor, all of these parameters should
33 be scaled (multiplied/divided, respectively) by the same factor. The
34 matrix of intrinsic parameters does not depend on the scene viewed and,
35 once estimated, can be re-used (as long as the focal length is fixed (in
36 case of zoom lens)). The joint rotation-translation matrix $[R|t]$
37 is called a matrix of extrinsic parameters. It is used to describe the
38 camera motion around a static scene, or vice versa, rigid motion of an
39 object in front of still camera. That is, $[R|t]$ translates
40 coordinates of a point $(X, Y, Z)$ to some coordinate system,
41 fixed with respect to the camera. The transformation above is equivalent
42 to the following (when $z \ne 0$):
46 \vecthree{x}{y}{z} = R \vecthree{X}{Y}{Z} + t\\
54 Real lenses usually have some distortion, mostly
55 radial distorion and slight tangential distortion. So, the above model
60 \vecthree{x}{y}{z} = R \vecthree{X}{Y}{Z} + t\\
63 x'' = x' (1 + k_1 r^2 + k_2 r^4 + k_3 r^6) + 2 p_1 x' y' + p_2(r^2 + 2 x'^2) \\
64 y'' = y' (1 + k_1 r^2 + k_2 r^4 + k_3 r^6) + p_1 (r^2 + 2 y'^2) + 2 p_2 x' y' \\
65 \text{where} \quad r^2 = x'^2 + y'^2 \\
71 $k_1$, $k_2$, $k_3$ are radial distortion coefficients, $p_1$, $p_2$ are tangential distortion coefficients.
72 Higher-order coefficients are not considered in OpenCV. In the functions below the coefficients are passed or returned as
73 \[ (k_1, k_2, p_1, p_2[, k_3]) \]vector. That is, if the vector contains 4 elements, it means that $k_3=0$.
74 The distortion coefficients do not depend on the scene viewed, thus they also belong to the intrinsic camera parameters.
75 \emph{And they remain the same regardless of the captured image resolution.}
76 That is, if, for example, a camera has been calibrated on images of $320
77 \times 240$ resolution, absolutely the same distortion coefficients can
78 be used for images of $640 \times 480$ resolution from the same camera (while $f_x$,
79 $f_y$, $c_x$ and $c_y$ need to be scaled appropriately).
81 The functions below use the above model to
84 \item Project 3D points to the image plane given intrinsic and extrinsic parameters
85 \item Compute extrinsic parameters given intrinsic parameters, a few 3D points and their projections.
86 \item Estimate intrinsic and extrinsic camera parameters from several views of a known calibration pattern (i.e. every view is described by several 3D-2D point correspodences).
87 \item Estimate the relative position and orientation of the stereo camera "heads" and compute the \emph{rectification} transformation that makes the camera optical axes parallel.
92 \cvCPyFunc{CalcImageHomography}
93 Calculates the homography matrix for an oblong planar object (e.g. arm).
96 void cvCalcImageHomography( \par float* line,\par CvPoint3D32f* center,\par float* intrinsic,\par float* homography );
98 \cvdefPy{CalcImageHomography(line,center)-> (intrinsic,homography)}
101 \cvarg{line}{the main object axis direction (vector (dx,dy,dz))}
102 \cvarg{center}{object center ((cx,cy,cz))}
103 \cvarg{intrinsic}{intrinsic camera parameters (3x3 matrix)}
104 \cvarg{homography}{output homography matrix (3x3)}
107 The function calculates the homography
108 matrix for the initial image transformation from image plane to the
109 plane, defined by a 3D oblong object line (See \_\_Figure 6-10\_\_
110 in the OpenCV Guide 3D Reconstruction Chapter).
114 \cvfunc{CalibrateCamera2}{calibrateCamera}
115 Finds the camera intrinsic and extrinsic parameters from several views of a calibration pattern.
117 \cvdefC{double cvCalibrateCamera2( \par const CvMat* objectPoints,\par const CvMat* imagePoints,\par const CvMat* pointCounts,\par CvSize imageSize,\par CvMat* cameraMatrix,\par CvMat* distCoeffs,\par CvMat* rvecs=NULL,\par CvMat* tvecs=NULL,\par int flags=0 );}
118 \cvdefPy{CalibrateCamera2(objectPoints,imagePoints,pointCounts,imageSize,cameraMatrix,distCoeffs,rvecs,tvecs,flags=0)-> None}
119 \cvdefCpp{double calibrateCamera( const vector<vector<Point3f> >\& objectPoints,\par
120 const vector<vector<Point2f> >\& imagePoints,\par
122 Mat\& cameraMatrix, Mat\& distCoeffs,\par
123 vector<Mat>\& rvecs, vector<Mat>\& tvecs,\par
127 \cvarg{objectPoints}{The joint matrix of object points - calibration pattern features in the model coordinate space. It is floating-point 3xN or Nx3 1-channel, or 1xN or Nx1 3-channel array, where N is the total number of points in all views.}
128 \cvarg{imagePoints}{The joint matrix of object points projections in the camera views. It is floating-point 2xN or Nx2 1-channel, or 1xN or Nx1 2-channel array, where N is the total number of points in all views}
129 \cvarg{pointCounts}{Integer 1xM or Mx1 vector (where M is the number of calibration pattern views) containing the number of points in each particular view. The sum of vector elements must match the size of \texttt{objectPoints} and \texttt{imagePoints} (=N).}
132 \cvarg{objectPoints}{The vector of vectors of points on the calibration pattern in its coordinate system, one vector per view. If the the same calibration pattern is shown in each view and it's fully visible then 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 the pattern coordinate system, then if the rig is planar, it may have sense to put the model to the XY coordinate plane, so that Z-coordinate of each input object point is 0}
133 \cvarg{imagePoints}{The vector of vectors of the object point projections on the calibration pattern views, one vector per a view. The projections must be in the same order as the corresponding object points.}
135 \cvarg{imageSize}{Size of the image, used only to initialize the intrinsic camera matrix}
136 \cvarg{cameraMatrix}{The output 3x3 floating-point camera matrix $A = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}$.\newline
137 If \texttt{CV\_CALIB\_USE\_INTRINSIC\_GUESS} and/or \texttt{CV\_CALIB\_FIX\_ASPECT\_RATIO} are specified, some or all of \texttt{fx, fy, cx, cy} must be initialized before calling the function}
138 \cvarg{distCoeffs}{The output \cvCPy{4x1, 1x4,} 5x1 or 1x5 vector of distortion coefficients $(k_1, k_2, p_1, p_2[, k_3])$}.
139 \cvarg{rvecs}{The output \cvCPy{3x\emph{M} or \emph{M}x3 1-channel, or 1x\emph{M} or \emph{M}x1 3-channel array}\cvCpp{vector} of rotation vectors (see \cvCross{Rodrigues2}{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, i.e. real position of the calibration pattern in the k-th pattern view (k=0..\emph{M}-1)}
140 \cvarg{tvecs}{The output \cvCPy{3x\emph{M} or \emph{M}x3 1-channel, or 1x\emph{M} or \emph{M}x1 3-channel array}\cvCpp{vector} of translation vectors, estimated for each pattern view.}
141 \cvarg{flags}{Different flags, may be 0 or combination of the following values:
143 \cvarg{CV\_CALIB\_USE\_INTRINSIC\_GUESS}{\texttt{cameraMatrix} contains the valid initial values of \texttt{fx, fy, cx, cy} that are optimized further. Otherwise, \texttt{(cx, cy)} is initially set to the image center (\texttt{imageSize} is used here), and focal distances are computed in some least-squares fashion. Note, that if intrinsic parameters are known, there is no need to use this function just to estimate the extrinsic parameters. Use \cvCross{FindExtrinsicCameraParams2}{solvePnP} instead.}
144 \cvarg{CV\_CALIB\_FIX\_PRINCIPAL\_POINT}{The principal point is not changed during the global optimization, it stays at the center or at the other location specified when \newline \texttt{CV\_CALIB\_USE\_INTRINSIC\_GUESS} is set too.}
145 \cvarg{CV\_CALIB\_FIX\_ASPECT\_RATIO}{The functions considers only \texttt{fy} as a free parameter, the ratio \texttt{fx/fy} stays the same as in the input \texttt{cameraMatrix}. \newline When \texttt{CV\_CALIB\_USE\_INTRINSIC\_GUESS} is not set, the actual input values of \texttt{fx} and \texttt{fy} are ignored, only their ratio is computed and used further.}
146 \cvarg{CV\_CALIB\_ZERO\_TANGENT\_DIST}{Tangential distortion coefficients $(p_1, p_2)$ will be set to zeros and stay zero.}}
150 The function estimates the intrinsic camera
151 parameters and extrinsic parameters for each of the views. The
152 coordinates of 3D object points and their correspondent 2D projections
153 in each view must be specified. That may be achieved by using an
154 object with known geometry and easily detectable feature points.
155 Such an object is called a calibration rig or calibration pattern,
156 and OpenCV has built-in support for a chessboard as a calibration
157 rig (see \cvCross{FindChessboardCorners}{findChessboardCorners}). Currently, initialization
158 of intrinsic parameters (when \texttt{CV\_CALIB\_USE\_INTRINSIC\_GUESS}
159 is not set) is only implemented for planar calibration patterns
160 (where z-coordinates of the object points must be all 0's). 3D
161 calibration rigs can also be used as long as initial \texttt{cameraMatrix}
164 The algorithm does the following:
166 \item First, it computes the initial intrinsic parameters (the option only available for planar calibration patterns) or reads them from the input parameters. The distortion coefficients are all set to zeros initially (unless some of \texttt{CV\_CALIB\_FIX\_K?} are specified).
167 \item The the initial camera pose is estimated as if the intrinsic parameters have been already known. This is done using \cvCross{FindExtrinsicCameraParams2}{solvePnP}
168 \item After that the global Levenberg-Marquardt optimization algorithm is run to minimize the reprojection error, i.e. the total sum of squared distances between the observed feature points \texttt{imagePoints} and the projected (using the current estimates for camera parameters and the poses) object points \texttt{objectPoints}; see \cvCross{ProjectPoints2}{projectPoints}.
173 The function returns the final re-projection error.
176 Note: if you're using a non-square (=non-NxN) grid and
177 \cvCppCross{findChessboardCorners} for calibration, and \texttt{calibrateCamera} returns
178 bad values (i.e. zero distortion coefficients, an image center very far from
179 $(w/2-0.5,h/2-0.5)$, and / or large differences between $f_x$ and $f_y$ (ratios of
180 10:1 or more)), then you've probaby used \texttt{patternSize=cvSize(rows,cols)},
181 but should use \texttt{patternSize=cvSize(cols,rows)} in \cvCross{FindChessboardCorners}{findChessboardCorners}.
183 See also: \cvCross{FindChessboardCorners}{findChessboardCorners}, \cvCross{FindExtrinsicCameraParams2}{solvePnP}, \cvCppCross{initCameraMatrix2D}, \cvCross{StereoCalibrate}{stereoCalibrate}, \cvCross{Undistort2}{undistort}
187 \cvCppFunc{calibrationMatrixValues}
188 Computes some useful camera characteristics from the camera matrix
190 \cvdefCpp{void calibrationMatrixValues( const Mat\& cameraMatrix,\par
192 double apertureWidth,\par
193 double apertureHeight,\par
196 double\& focalLength,\par
197 Point2d\& principalPoint,\par
198 double\& aspectRatio );}
200 \cvarg{cameraMatrix}{The input camera matrix that can be estimated by \cvCppCross{calibrateCamera} or \cvCppCross{stereoCalibrate}}
201 \cvarg{imageSize}{The input image size in pixels}
202 \cvarg{apertureWidth}{Physical width of the sensor}
203 \cvarg{apertureHeight}{Physical height of the sensor}
204 \cvarg{fovx}{The output field of view in degrees along the horizontal sensor axis}
205 \cvarg{fovy}{The output field of view in degrees along the vertical sensor axis}
206 \cvarg{focalLength}{The focal length of the lens in mm}
207 \cvarg{prinicialPoint}{The principal point in pixels}
208 \cvarg{aspectRatio}{$f_y/f_x$}
211 The function computes various useful camera characteristics from the previously estimated camera matrix.
213 \cvCppFunc{composeRT}
214 Combines two rotation-and-shift transformations
216 \cvdefCpp{void composeRT( const Mat\& rvec1, const Mat\& tvec1,\par
217 const Mat\& rvec2, const Mat\& tvec2,\par
218 Mat\& rvec3, Mat\& tvec3 );\newline
219 void composeRT( const Mat\& rvec1, const Mat\& tvec1,\par
220 const Mat\& rvec2, const Mat\& tvec2,\par
221 Mat\& rvec3, Mat\& tvec3,\par
222 Mat\& dr3dr1, Mat\& dr3dt1,\par
223 Mat\& dr3dr2, Mat\& dr3dt2,\par
224 Mat\& dt3dr1, Mat\& dt3dt1,\par
225 Mat\& dt3dr2, Mat\& dt3dt2 );}
227 \cvarg{rvec1}{The first rotation vector}
228 \cvarg{tvec1}{The first translation vector}
229 \cvarg{rvec2}{The second rotation vector}
230 \cvarg{tvec2}{The second translation vector}
231 \cvarg{rvec3}{The output rotation vector of the superposition}
232 \cvarg{tvec3}{The output translation vector of the superposition}
233 \cvarg{d??d??}{The optional output derivatives of \texttt{rvec3} or \texttt{tvec3} w.r.t. \texttt{rvec?} or \texttt{tvec?}}
236 The functions compute:
239 \texttt{rvec3} = \mathrm{rodrigues}^{-1}\left(\mathrm{rodrigues}(\texttt{rvec2}) \cdot
240 \mathrm{rodrigues}(\texttt{rvec1})\right) \\
241 \texttt{tvec3} = \mathrm{rodrigues}(\texttt{rvec2}) \cdot \texttt{tvec1} + \texttt{tvec2}
244 where $\mathrm{rodrigues}$ denotes a rotation vector to rotation matrix transformation, and $\mathrm{rodrigues}^{-1}$ denotes the inverse transformation, see \cvCppCross{Rodrigues}.
246 Also, the functions can compute the derivatives of the output vectors w.r.t the input vectors (see \cvCppCross{matMulDeriv}).
247 The functions are used inside \cvCppCross{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 matrix multiplication.
251 \cvfunc{ComputeCorrespondEpilines}{computeCorrespondEpilines}
252 For points in one image of a stereo pair, computes the corresponding epilines in the other image.
254 \cvdefC{void cvComputeCorrespondEpilines( \par const CvMat* points,\par int whichImage,\par const CvMat* F, \par CvMat* lines);}
255 \cvdefPy{ComputeCorrespondEpilines(points, whichImage, F, lines) -> None}
256 \cvdefCpp{void computeCorrespondEpilines( const Mat\& points,\par
257 int whichImage, const Mat\& F,\par
258 vector<Vec3f>\& lines );}
260 \cvCPy{\cvarg{points}{The input points. \texttt{2xN, Nx2, 3xN} or \texttt{Nx3} array (where \texttt{N} number of points). Multi-channel \texttt{1xN} or \texttt{Nx1} array is also acceptable}}
261 \cvCpp{\cvarg{points}{The input points. $N \times 1$ or $1 \times N$ matrix of type \texttt{CV\_32FC2} or \texttt{vector<Point2f>}}}
262 \cvarg{whichImage}{Index of the image (1 or 2) that contains the \texttt{points}}
263 \cvarg{F}{The fundamental matrix that can be estimated using \cvCross{FindFundamentalMat}{findFundamentalMat}
264 or \cvCross{StereoRectify}{stereoRectify}.}
265 \cvarg{lines}{\cvCPy{The output epilines, a \texttt{3xN} or \texttt{Nx3} array.}\cvCpp{The output vector of the corresponding to the points epipolar lines in the other image.} Each line $ax + by + c=0$ is encoded by 3 numbers $(a, b, c)$}
268 For every point in one of the two images of a stereo-pair the function finds the equation of the
269 corresponding epipolar line in the other image.
271 From the fundamental matrix definition (see \cvCross{FindFundamentalMat}{findFundamentalMat}),
272 line $l^{(2)}_i$ in the second image for the point $p^{(1)}_i$ in the first image (i.e. when \texttt{whichImage=1}) is computed as:
274 \[ l^{(2)}_i = F p^{(1)}_i \]
276 and, vice versa, when \texttt{whichImage=2}, $l^{(1)}_i$ is computed from $p^{(2)}_i$ as:
278 \[ l^{(1)}_i = F^T p^{(2)}_i \]
280 Line coefficients are defined up to a scale. They are normalized, such that $a_i^2+b_i^2=1$.
283 \cvfunc{ConvertPointsHomogeneous}{convertPointsHomogeneous}
284 Convert points to/from homogeneous coordinates.
286 \cvdefC{void cvConvertPointsHomogeneous( \par const CvMat* src,\par CvMat* dst );}
288 \cvdefPy{ConvertPointsHomogeneous( src, dst ) -> None}
290 \cvdefCpp{void convertPointsHomogeneous( const Mat\& src, vector<Point3f>\& dst );
292 void convertPointsHomogeneous( const Mat\& src, vector<Point2f>\& dst );}
296 \cvarg{src}{The input point array, \texttt{2xN, Nx2, 3xN, Nx3, 4xN or Nx4 (where \texttt{N} is the number of points)}. Multi-channel \texttt{1xN} or \texttt{Nx1} array is also acceptable}
297 \cvarg{dst}{The output point array, must contain the same number of points as the input; The dimensionality must be the same, 1 less or 1 more than the input, and also within 2 to 4}
299 \cvarg{src}{The input array or vector of 2D or 3D points}
300 \cvarg{dst}{The output vector of 3D or 2D points, respectively}
304 The \cvC{function converts}\cvCpp{functions convert} 2D or 3D points from/to homogeneous coordinates, or simply \cvC{copies or transposes}\cvCpp{copy or transpose} the array. If the input array dimensionality is larger than the output, each coordinate is divided by the last coordinate:
308 (x,y[,z],w) -> (x',y'[,z'])\\
312 z' = z/w \quad \text{(if output is 3D)}
316 If the output array dimensionality is larger, an extra 1 is appended to each point. Otherwise, the input array is simply copied (with optional transposition) to the output.
318 \cvC{\textbf{Note} because the function accepts a large variety of array layouts, it may report an error when input/output array dimensionality is ambiguous. It is always safe to use the function with number of points $\texttt{N} \ge 5$, or to use multi-channel \texttt{Nx1} or \texttt{1xN} arrays.}
322 \cvCPyFunc{CreatePOSITObject}
323 Initializes a structure containing object information.
326 CvPOSITObject* cvCreatePOSITObject( \par CvPoint3D32f* points,\par int point\_count );
327 }\cvdefPy{CreatePOSITObject(points)-> POSITObject}
331 \cvarg{points}{Pointer to the points of the 3D object model}
332 \cvarg{point\_count}{Number of object points}
334 \cvarg{points}{List of 3D points}
338 The function allocates memory for the object structure and computes the object inverse matrix.
340 The preprocessed object data is stored in the structure \cvCPyCross{CvPOSITObject}, internal for OpenCV, which means that the user cannot directly access the structure data. The user may only create this structure and pass its pointer to the function.
342 An object is defined as a set of points given in a coordinate system. The function \cvCPyCross{POSIT} computes a vector that begins at a camera-related coordinate system center and ends at the \texttt{points[0]} of the object.
344 Once the work with a given object is finished, the function \cvCPyCross{ReleasePOSITObject} must be called to free memory.
346 \cvCPyFunc{CreateStereoBMState}
347 Creates block matching stereo correspondence structure.
350 #define CV_STEREO_BM_BASIC 0
351 #define CV_STEREO_BM_FISH_EYE 1
352 #define CV_STEREO_BM_NARROW 2
357 CvStereoBMState* cvCreateStereoBMState( int preset=CV\_STEREO\_BM\_BASIC,
358 int numberOfDisparities=0 );
361 \cvdefPy{CreateStereoBMState(preset=CV\_STEREO\_BM\_BASIC,numberOfDisparities=0)-> StereoBMState}
364 \cvarg{preset}{ID of one of the pre-defined parameter sets. Any of the parameters can be overridden after creating the structure.}
365 \cvarg{numberOfDisparities}{The number of disparities. If the parameter is 0, it is taken from the preset, otherwise the supplied value overrides the one from preset.}
368 The function creates the stereo correspondence structure and initializes it. It is possible to override any of the parameters at any time between the calls to \cvCPyCross{FindStereoCorrespondenceBM}.
370 \cvCPyFunc{CreateStereoGCState}
371 Creates the state of graph cut-based stereo correspondence algorithm.
375 CvStereoGCState* cvCreateStereoGCState( int numberOfDisparities,
379 \cvdefPy{CreateStereoGCState(numberOfDisparities,maxIters)-> StereoGCState}
382 \cvarg{numberOfDisparities}{The number of disparities. The disparity search range will be $\texttt{state->minDisparity} \le disparity < \texttt{state->minDisparity} + \texttt{state->numberOfDisparities}$}
383 \cvarg{maxIters}{Maximum number of iterations. On each iteration all possible (or reasonable) alpha-expansions are tried. The algorithm may terminate earlier if it could not find an alpha-expansion that decreases the overall cost function value. See \href{\#Kolmogorov03}{[Kolmogorov03]} for details. }
386 The function creates the stereo correspondence structure and initializes it. It is possible to override any of the parameters at any time between the calls to \cvCPyCross{FindStereoCorrespondenceGC}.
388 \cvCPyFunc{CvStereoBMState}
389 The structure for block matching stereo correspondence algorithm.
392 typedef struct CvStereoBMState
394 //pre filters (normalize input images):
395 int preFilterType; // 0 for now
396 int preFilterSize; // ~5x5..21x21
397 int preFilterCap; // up to ~31
398 //correspondence using Sum of Absolute Difference (SAD):
399 int SADWindowSize; // Could be 5x5..21x21
400 int minDisparity; // minimum disparity (=0)
401 int numberOfDisparities; // maximum disparity - minimum disparity
402 //post filters (knock out bad matches):
403 int textureThreshold; // areas with no texture are ignored
404 float uniquenessRatio;// filter out pixels if there are other close matches
405 // with different disparity
406 int speckleWindowSize; // the maximum area of speckles to remove
407 // (set to 0 to disable speckle filtering)
408 int speckleRange; // acceptable range of disparity variation in each connected component
415 The block matching stereo correspondence algorithm, by Kurt Konolige, is very fast one-pass stereo matching algorithm that uses sliding sums of absolute differences between pixels in the left image and the pixels in the right image, shifted by some varying amount of pixels (from \texttt{minDisparity} to \texttt{minDisparity+numberOfDisparities}). On a pair of images WxH the algorithm computes disparity in \texttt{O(W*H*numberOfDisparities)} time. In order to improve quality and reability of the disparity map, the algorithm includes pre-filtering and post-filtering procedures.
417 Note that the algorithm searches for the corresponding blocks in x direction only. It means that the supplied stereo pair should be rectified. Vertical stereo layout is not directly supported, but in such a case the images could be transposed by user.
419 \cvCPyFunc{CvStereoGCState}
420 The structure for graph cuts-based stereo correspondence algorithm
423 typedef struct CvStereoGCState
425 int Ithreshold; // threshold for piece-wise linear data cost function (5 by default)
426 int interactionRadius; // radius for smoothness cost function (1 by default; means Potts model)
427 float K, lambda, lambda1, lambda2; // parameters for the cost function
428 // (usually computed adaptively from the input data)
429 int occlusionCost; // 10000 by default
430 int minDisparity; // 0 by default; see CvStereoBMState
431 int numberOfDisparities; // defined by user; see CvStereoBMState
432 int maxIters; // number of iterations; defined by user.
447 The graph cuts stereo correspondence algorithm, described in \href{\#Kolmogrov03}{[Kolmogorov03]} (as \textbf{KZ1}), is non-realtime stereo correpsondence algorithm that usually gives very accurate depth map with well-defined object boundaries. The algorithm represents stereo problem as a sequence of binary optimization problems, each of those is solved using maximum graph flow algorithm. The state structure above should not be allocated and initialized manually; instead, use \cvCPyCross{cvCreateStereoGCState} and then override necessary parameters if needed.
451 \cvfunc{DecomposeProjectionMatrix}{decomposeProjectionMatrix}
452 Decomposes the projection matrix into a rotation matrix and a camera matrix.
455 void cvDecomposeProjectionMatrix( \par const CvMat *projMatrix,\par CvMat *cameraMatrix,\par CvMat *rotMatrix,\par CvMat *transVect,\par CvMat *rotMatrX=NULL,\par CvMat *rotMatrY=NULL,\par CvMat *rotMatrZ=NULL,\par CvPoint3D64f *eulerAngles=NULL);
458 \cvdefPy{DecomposeProjectionMatrix(projMatrix, cameraMatrix, rotMatrix, transVect, rotMatrX = None, rotMatrY = None, rotMatrZ = None) -> eulerAngles}
460 \cvdefCpp{void decomposeProjectionMatrix( const Mat\& projMatrix,\par
461 Mat\& cameraMatrix,\par
462 Mat\& rotMatrix, Mat\& transVect );\newline
463 void decomposeProjectionMatrix( const Mat\& projMatrix, \par
464 Mat\& cameraMatrix,\par
465 Mat\& rotMatrix, Mat\& transVect,\par
466 Mat\& rotMatrixX, Mat\& rotMatrixY,\par
467 Mat\& rotMatrixZ, Vec3d\& eulerAngles );}
469 \cvarg{projMatrix}{The 3x4 input projection matrix P}
470 \cvarg{cameraMatrix}{The output 3x3 camera matrix K}
471 \cvarg{rotMatrix}{The output 3x3 external rotation matrix R}
472 \cvarg{transVect}{The output 4x1 translation vector T}
473 \cvarg{rotMatrX}{Optional 3x3 rotation matrix around x-axis}
474 \cvarg{rotMatrY}{Optional 3x3 rotation matrix around y-axis}
475 \cvarg{rotMatrZ}{Optional 3x3 rotation matrix around z-axis}
476 \cvarg{eulerAngles}{Optional 3 points containing the three Euler angles of rotation}
479 The function computes a decomposition of a projection matrix into a calibration and a rotation matrix and the position of the camera.
481 It optionally returns three rotation matrices, one for each axis, and the three Euler angles that could be used in OpenGL.
483 The function is based on \cvCross{RQDecomp3x3}{RQDecomp3x3}.
485 \cvfunc{DrawChessboardCorners}{drawChessboardCorners}
486 Renders the detected chessboard corners.
489 void cvDrawChessboardCorners( \par CvArr* image,\par CvSize patternSize,\par CvPoint2D32f* corners,\par int count,\par int patternWasFound );
490 }\cvdefPy{DrawChessboardCorners(image,patternSize,corners,patternWasFound)-> None}
491 \cvdefCpp{void drawChessboardCorners( Mat\& image, Size patternSize,\par
492 const Mat\& corners,\par
493 bool patternWasFound );}
495 \cvarg{image}{The destination image; it must be an 8-bit color image}
496 \cvarg{patternSize}{The number of inner corners per chessboard row and column. (patternSize = cvSize(points\_per\_row,points\_per\_colum) = cvSize(columns,rows) )}
497 \cvarg{corners}{The array of corners detected}
498 \cvC{\cvarg{count}{The number of corners}}
499 \cvarg{patternWasFound}{Indicates whether the complete board was found \cvCPy{$(\ne 0)$} or not \cvCPy{$(=0)$}. One may just pass the return value \cvCPyCross{FindChessboardCorners}{findChessboardCorners} here}
502 The function draws the individual chessboard corners detected as red circles if the board was not found or as colored corners connected with lines if the board was found.
504 \cvfunc{FindChessboardCorners}{findChessboardCorners}
505 Finds the positions of the internal corners of the chessboard.
507 \cvdefC{int cvFindChessboardCorners( \par const void* image,\par CvSize patternSize,\par CvPoint2D32f* corners,\par int* cornerCount=NULL,\par int flags=CV\_CALIB\_CB\_ADAPTIVE\_THRESH );}
508 \cvdefPy{FindChessboardCorners(image, patternSize, flags=CV\_CALIB\_CB\_ADAPTIVE\_THRESH) -> corners}
509 \cvdefCpp{bool findChessboardCorners( const Mat\& image, Size patternSize,\par
510 vector<Point2f>\& corners,\par
511 int flags=CV\_CALIB\_CB\_ADAPTIVE\_THRESH+\par
512 CV\_CALIB\_CB\_NORMALIZE\_IMAGE );}
514 \cvarg{image}{Source chessboard view; it must be an 8-bit grayscale or color image}
515 \cvarg{patternSize}{The number of inner corners per chessboard row and column}
516 ( patternSize = cvSize(points\_per\_row,points\_per\_colum) = cvSize(columns,rows) )
517 \cvarg{corners}{The output array of corners detected}
518 \cvC{\cvarg{cornerCount}{The output corner counter. If it is not NULL, it stores the number of corners found}}
519 \cvarg{flags}{Various operation flags, can be 0 or a combination of the following values:
521 \cvarg{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).}
522 \cvarg{CV\_CALIB\_CB\_NORMALIZE\_IMAGE}{normalize the image gamma with \cvCross{EqualizeHist}{equalizeHist} before applying fixed or adaptive thresholding.}
523 \cvarg{CV\_CALIB\_CB\_FILTER\_QUADS}{use additional criteria (like contour area, perimeter, square-like shape) to filter out false quads that are extracted at the contour retrieval stage.}
527 The function attempts to determine
528 whether the input image is a view of the chessboard pattern and
529 locate the internal chessboard corners. The function returns a non-zero
530 value if all of the corners have been found and they have been placed
531 in a certain order (row by row, left to right in every row),
532 otherwise, if the function fails to find all the corners or reorder
533 them, it returns 0. For example, a regular chessboard has 8 x 8
534 squares and 7 x 7 internal corners, that is, points, where the black
535 squares touch each other. The coordinates detected are approximate,
536 and to determine their position more accurately, the user may use
537 the function \cvCross{FindCornerSubPix}{cornerSubPix}.
539 \textbf{Note:} the function requires some white space (like a square-thick border, the wider the better) around the board to make the detection more robust in various environment (otherwise if there is no border and the background is dark, the outer black squares could not be segmented properly and so the square grouping and ordering algorithm will fail).
541 \cvfunc{FindExtrinsicCameraParams2}{solvePnP}
542 Finds the object pose from the 3D-2D point correspondences
544 \cvdefC{void cvFindExtrinsicCameraParams2( \par const CvMat* objectPoints,\par const CvMat* imagePoints,\par const CvMat* cameraMatrix,\par const CvMat* distCoeffs,\par CvMat* rvec,\par CvMat* tvec );}
545 \cvdefPy{FindExtrinsicCameraParams2(objectPoints,imagePoints,cameraMatrix,distCoeffs,rvec,tvec)-> None}
546 \cvdefCpp{void solvePnP( const Mat\& objectPoints,\par
547 const Mat\& imagePoints,\par
548 const Mat\& cameraMatrix,\par
549 const Mat\& distCoeffs,\par
550 Mat\& rvec, Mat\& tvec,\par
551 bool useExtrinsicGuess=false );}
553 \cvarg{objectPoints}{The array of object points in the object coordinate space, 3xN or Nx3 1-channel, or 1xN or Nx1 3-channel, where N is the number of points. \cvCpp{Can also pass \texttt{vector<Point3f>} here.}}
554 \cvarg{imagePoints}{The array of corresponding image points, 2xN or Nx2 1-channel or 1xN or Nx1 2-channel, where N is the number of points. \cvCpp{Can also pass \texttt{vector<Point2f>} here.}}
555 \cvarg{cameraMatrix}{The input camera matrix $A = \vecthreethree{fx}{0}{cx}{0}{fy}{cy}{0}{0}{1} $}
556 \cvarg{distCoeffs}{The input 4x1, 1x4, 5x1 or 1x5 vector of distortion coefficients $(k_1, k_2, p_1, p_2[, k_3])$. If it is NULL, all of the distortion coefficients are set to 0}
557 \cvarg{rvec}{The output rotation vector (see \cvCross{Rodrigues2}{Rodrigues}) that (together with \texttt{tvec}) brings points from the model coordinate system to the camera coordinate system}
558 \cvarg{tvec}{The output translation vector}
561 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. This function finds such a pose that minimizes reprojection error, i.e. the sum of squared distances between the observed projections \texttt{imagePoints} and the projected (using \cvCross{ProjectPoints2}{projectPoints}) \texttt{objectPoints}.
564 \cvfunc{FindFundamentalMat}{findFundamentalMat}
565 Calculates the fundamental matrix from the corresponding points in two images.
568 int cvFindFundamentalMat( \par const CvMat* points1,\par const CvMat* points2,\par CvMat* fundamentalMatrix,\par int method=CV\_FM\_RANSAC,\par double param1=1.,\par double param2=0.99,\par CvMat* status=NULL);
570 \cvdefPy{FindFundamentalMat(points1, points2, fundamentalMatrix, method=CV\_FM\_RANSAC, param1=1., param2=0.99, status = None) -> None}
571 \cvdefCpp{Mat findFundamentalMat( const Mat\& points1, const Mat\& points2,\par
572 vector<uchar>\& status, int method=FM\_RANSAC,\par
573 double param1=3., double param2=0.99 );\newline
574 Mat findFundamentalMat( const Mat\& points1, const Mat\& points2,\par
575 int method=FM\_RANSAC,\par
576 double param1=3., double param2=0.99 );}
578 \cvarg{points1}{Array of \texttt{N} points from the first image.\cvCPy{It can be \texttt{2xN, Nx2, 3xN} or \texttt{Nx3} 1-channel array or \texttt{1xN} or \texttt{Nx1} 2- or 3-channel array}. The point coordinates should be floating-point (single or double precision)}
579 \cvarg{points2}{Array of the second image points of the same size and format as \texttt{points1}}
580 \cvCPy{\cvarg{fundamentalMatrix}{The output fundamental matrix or matrices. The size should be 3x3 or 9x3 (7-point method may return up to 3 matrices)}}
581 \cvarg{method}{Method for computing the fundamental matrix
583 \cvarg{CV\_FM\_7POINT}{for a 7-point algorithm. $N = 7$}
584 \cvarg{CV\_FM\_8POINT}{for an 8-point algorithm. $N \ge 8$}
585 \cvarg{CV\_FM\_RANSAC}{for the RANSAC algorithm. $N \ge 8$}
586 \cvarg{CV\_FM\_LMEDS}{for the LMedS algorithm. $N \ge 8$}
588 \cvarg{param1}{The parameter is used for RANSAC. It is the maximum distance from point to 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}
589 \cvarg{param2}{The parameter is used for RANSAC or LMedS methods only. It specifies the desirable level of confidence (probability) that the estimated matrix is correct}
590 \cvarg{status}{The \cvCPy{optional} 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 RANSAC and LMedS methods. For other methods it is set to all 1's}
593 The epipolar geometry is described by the following equation:
595 \[ [p_2; 1]^T F [p_1; 1] = 0 \]
597 where $F$ is fundamental matrix, $p_1$ and $p_2$ are corresponding points in the first and the second images, respectively.
599 The function calculates the fundamental matrix using one of four methods listed above and returns \cvCpp{the found fundamental matrix}\cvCPy{the number of fundamental matrices found (1 or 3) and 0, if no matrix is found}. Normally just 1 matrix is found, but in the case of 7-point algorithm the function may return up to 3 solutions ($9 \times 3$ matrix that stores all 3 matrices sequentially).
601 The calculated fundamental matrix may be passed further to
602 \cvCross{ComputeCorrespondEpilines}{computeCorrespondEpilines} that finds the epipolar lines
603 corresponding to the specified points. It can also be passed to \cvCross{StereoRectifyUncalibrated}{stereoRectifyUncalibrated} to compute the rectification transformation.
606 \cvfunc{Example. Estimation of fundamental matrix using RANSAC algorithm}
608 int point_count = 100;
612 CvMat* fundamental_matrix;
614 points1 = cvCreateMat(1,point_count,CV_32FC2);
615 points2 = cvCreateMat(1,point_count,CV_32FC2);
616 status = cvCreateMat(1,point_count,CV_8UC1);
618 /* Fill the points here ... */
619 for( i = 0; i < point_count; i++ )
621 points1->data.fl[i*2] = <x,,1,i,,>;
622 points1->data.fl[i*2+1] = <y,,1,i,,>;
623 points2->data.fl[i*2] = <x,,2,i,,>;
624 points2->data.fl[i*2+1] = <y,,2,i,,>;
627 fundamental_matrix = cvCreateMat(3,3,CV_32FC1);
628 int fm_count = cvFindFundamentalMat( points1,points2,fundamental_matrix,
629 CV_FM_RANSAC,1.0,0.99,status );
634 // Example. Estimation of fundamental matrix using RANSAC algorithm
635 int point_count = 100;
636 vector<Point2f> points1(point_count);
637 vector<Point2f> points2(point_count);
639 // initialize the points here ... */
640 for( int i = 0; i < point_count; i++ )
646 Mat fundamental_matrix =
647 findFundamentalMat(points1, points2, FM_RANSAC, 3, 0.99);
651 \cvfunc{FindHomography}{findHomography}
652 Finds the perspective transformation between two planes.
654 \cvdefC{void cvFindHomography( \par const CvMat* srcPoints,\par const CvMat* dstPoints,\par CvMat* H \par
655 int method=0, \par double ransacReprojThreshold=0, \par CvMat* status=NULL);}
656 \cvdefPy{FindHomography(srcPoints,dstPoints,H,method,ransacReprojThreshold=0.0)-> H}
657 \cvdefCpp{Mat findHomography( const Mat\& srcPoints, const Mat\& dstPoints,\par
658 Mat\& status, int method=0,\par
659 double ransacReprojThreshold=0 );\newline
660 Mat findHomography( const Mat\& srcPoints, const Mat\& dstPoints,\par
661 vector<uchar>\& status, int method=0,\par
662 double ransacReprojThreshold=0 );\newline
663 Mat findHomography( const Mat\& srcPoints, const Mat\& dstPoints,\par
664 int method=0, double ransacReprojThreshold=0 );}
668 \cvCPy{\cvarg{srcPoints}{Coordinates of the points in the original plane, 2xN, Nx2, 3xN or Nx3 1-channel array (the latter two are for representation in homogeneous coordinates), where N is the number of points. 1xN or Nx1 2- or 3-channel array can also be passed.}
669 \cvarg{dstPoints}{Point coordinates in the destination plane, 2xN, Nx2, 3xN or Nx3 1-channel, or 1xN or Nx1 2- or 3-channel array.}}
670 \cvCpp{\cvarg{srcPoints}{Coordinates of the points in the original plane, a matrix of type \texttt{CV\_32FC2} or a \texttt{vector<Point2f>}.}
671 \cvarg{dstPoints}{Coordinates of the points in the target plane, a matrix of type \texttt{CV\_32FC2} or a \texttt{vector<Point2f>}.}}
673 \cvCPy{\cvarg{H}{The output 3x3 homography matrix}}
674 \cvarg{method}{ The method used to computed homography matrix; one of the following:
676 \cvarg{0}{a regular method using all the points}
677 \cvarg{CV\_RANSAC}{RANSAC-based robust method}
678 \cvarg{CV\_LMEDS}{Least-Median robust method}
680 \cvarg{ransacReprojThreshold}{The maximum allowed reprojection error to treat a point pair as an inlier (used in the RANSAC method only). That is, if
681 \[\|\texttt{dstPoints}_i - \texttt{convertPointHomogeneous}(\texttt{H} \texttt{srcPoints}_i)\| > \texttt{ransacReprojThreshold}\]
682 then the point $i$ is considered an outlier. If \texttt{srcPoints} and \texttt{dstPoints} are measured in pixels, it usually makes sense to set this parameter somewhere in the range 1 to 10.}
683 \cvarg{status}{The optional output mask set by a robust method (\texttt{CV\_RANSAC} or \texttt{CV\_LMEDS}). \emph{Note that the input mask values are ignored.}}
686 The \cvCPy{function finds}\cvCpp{functions find and return} the perspective transformation $H$ between the source and the destination planes:
689 s_i \vecthree{x'_i}{y'_i}{1} \sim H \vecthree{x_i}{y_i}{1}
692 So that the back-projection error
696 \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+
697 \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
700 is minimized. If the parameter \texttt{method} is set to the default value 0, the function
701 uses all the point pairs to compute the initial homography estimate with a simple least-squares scheme.
703 However, if not all of the point pairs ($srcPoints_i$,
704 $dstPoints_i$) fit the rigid perspective transformation (i.e. there
705 are some outliers), this initial estimate will be poor.
706 In this case one can use one of the 2 robust methods. Both methods,
707 \texttt{RANSAC} and \texttt{LMeDS}, try many different random subsets
708 of the corresponding point pairs (of 4 pairs each), estimate
709 the homography matrix using this subset and a simple least-square
710 algorithm and then compute the quality/goodness of the computed homography
711 (which is the number of inliers for RANSAC or the median re-projection
712 error for LMeDs). The best subset is then used to produce the initial
713 estimate of the homography matrix and the mask of inliers/outliers.
715 Regardless of the method, robust or not, the computed homography
716 matrix is refined further (using inliers only in the case of a robust
717 method) with the Levenberg-Marquardt method in order to reduce the
718 re-projection error even more.
720 The method \texttt{RANSAC} can handle practically any ratio of outliers,
721 but it needs the threshold to distinguish inliers from outliers.
722 The method \texttt{LMeDS} does not need any threshold, but it works
723 correctly only when there are more than 50\% of inliers. Finally,
724 if you are sure in the computed features, where can be only some
725 small noise present, but no outliers, the default method could be the best
728 The function is used to find initial intrinsic and extrinsic matrices.
729 Homography matrix is determined up to a scale, thus it is normalized so that
732 See also: \cvCross{GetAffineTransform}{getAffineTransform}, \cvCross{GetPerspectiveTransform}{getPerspectiveTransform}, \cvCross{EstimateRigidMotion}{estimateRigidMotion}, \cvCross{WarpPerspective}{warpPerspective}, \cvCross{PerspectiveTransform}{perspectiveTransform}
736 \cvCPyFunc{FindStereoCorrespondenceBM}
737 Computes the disparity map using block matching algorithm.
741 void cvFindStereoCorrespondenceBM( \par const CvArr* left, \par const CvArr* right,
742 \par CvArr* disparity, \par CvStereoBMState* state );
744 }\cvdefPy{FindStereoCorrespondenceBM(left,right,disparity,state)-> None}
747 \cvarg{left}{The left single-channel, 8-bit image.}
748 \cvarg{right}{The right image of the same size and the same type.}
749 \cvarg{disparity}{The output single-channel 16-bit signed, or 32-bit floating-point disparity map of the same size as input images. In the first case the computed disparities are represented as fixed-point numbers with 4 fractional bits (i.e. the computed disparity values are multiplied by 16 and rounded to integers).}
750 \cvarg{state}{Stereo correspondence structure.}
753 The function cvFindStereoCorrespondenceBM computes disparity map for the input rectified stereo pair. Invalid pixels (for which disparity can not be computed) are set to \texttt{state->minDisparity - 1} (or to \texttt{(state->minDisparity-1)*16} in the case of 16-bit fixed-point disparity map)
755 \cvCPyFunc{FindStereoCorrespondenceGC}
756 Computes the disparity map using graph cut-based algorithm.
760 void cvFindStereoCorrespondenceGC( \par const CvArr* left, \par const CvArr* right,
761 \par CvArr* dispLeft, \par CvArr* dispRight,
762 \par CvStereoGCState* state,
763 \par int useDisparityGuess = CV\_DEFAULT(0) );
766 \cvdefPy{FindStereoCorrespondenceGC( left, right, dispLeft, dispRight, state, useDisparityGuess=(0))-> None}
769 \cvarg{left}{The left single-channel, 8-bit image.}
770 \cvarg{right}{The right image of the same size and the same type.}
771 \cvarg{dispLeft}{The optional output single-channel 16-bit signed left disparity map of the same size as input images.}
772 \cvarg{dispRight}{The optional output single-channel 16-bit signed right disparity map of the same size as input images.}
773 \cvarg{state}{Stereo correspondence structure.}
774 \cvarg{useDisparityGuess}{If the parameter is not zero, the algorithm will start with pre-defined disparity maps. Both dispLeft and dispRight should be valid disparity maps. Otherwise, the function starts with blank disparity maps (all pixels are marked as occlusions).}
777 The function computes disparity maps for the input rectified stereo pair. Note that the left disparity image will contain values in the following range:
780 -\texttt{state->numberOfDisparities}-\texttt{state->minDisparity}
781 < dispLeft(x,y) \le -\texttt{state->minDisparity},
786 dispLeft(x,y) == \texttt{CV\_STEREO\_GC\_OCCLUSION}
789 and for the right disparity image the following will be true:
792 \texttt{state->minDisparity} \le dispRight(x,y)
793 < \texttt{state->minDisparity} + \texttt{state->numberOfDisparities}
799 dispRight(x,y) == \texttt{CV\_STEREO\_GC\_OCCLUSION}
802 that is, the range for the left disparity image will be inversed,
803 and the pixels for which no good match has been found, will be marked
806 Here is how the function can be called:
809 // image_left and image_right are the input 8-bit single-channel images
810 // from the left and the right cameras, respectively
811 CvSize size = cvGetSize(image_left);
812 CvMat* disparity_left = cvCreateMat( size.height, size.width, CV_16S );
813 CvMat* disparity_right = cvCreateMat( size.height, size.width, CV_16S );
814 CvStereoGCState* state = cvCreateStereoGCState( 16, 2 );
815 cvFindStereoCorrespondenceGC( image_left, image_right,
816 disparity_left, disparity_right, state, 0 );
817 cvReleaseStereoGCState( &state );
818 // now process the computed disparity images as you want ...
821 and this is the output left disparity image computed from the well-known Tsukuba stereo pair and multiplied by -16 (because the values in the left disparity images are usually negative):
824 CvMat* disparity_left_visual = cvCreateMat( size.height, size.width, CV_8U );
825 cvConvertScale( disparity_left, disparity_left_visual, -16 );
826 cvSave( "disparity.pgm", disparity_left_visual );
829 \includegraphics{pics/disparity.png}
834 \cvCppFunc{getDefaultNewCameraMatrix}
835 Returns the default new camera matrix
837 \cvdefCpp{Mat getDefaultNewCameraMatrix(\par
838 const Mat\& cameraMatrix,\par
839 Size imgSize=Size(),\par
840 bool centerPrincipalPoint=false );}
842 \cvarg{cameraMatrix}{The input camera matrix}
843 \cvarg{imageSize}{The camera view image size in pixels}
844 \cvarg{centerPrincipalPoint}{Indicates whether in the new camera matrix the principal point should be at the image center or not}
847 The function returns the camera matrix that is either an exact copy of the input \texttt{cameraMatrix} (when \texttt{centerPrinicipalPoint=false}), or the modified one (when \texttt{centerPrincipalPoint}=true).
849 In the latter case the new camera matrix will be:
852 f_x && 0 && (\texttt{imgSize.width}-1)*0.5 \\
853 0 && f_y && (\texttt{imgSize.height}-1)*0.5 \\
857 where $f_x$ and $f_y$ are $(0,0)$ and $(1,1)$ elements of \texttt{cameraMatrix}, respectively.
859 By default, the undistortion functions in OpenCV (see \texttt{initUndistortRectifyMap}, \texttt{undistort}) do not move the principal point. However, when you work with stereo, it's important to move the principal points in both views to the same y-coordinate (which is required by most of stereo correspondence algorithms), and maybe to the same x-coordinate too. So you can form the new camera matrix for each view, where the principal points will be at the center.
863 \cvfunc{GetOptimalNewCameraMatrix}{getOptimalNewCameraMatrix}
864 Returns the new camera matrix based on the free scaling parameter
866 \cvdefC{void cvGetOptimalNewCameraMatrix(
867 \par const CvMat* cameraMatrix, const CvMat* distCoeffs,
868 \par CvSize imageSize, double alpha,
869 \par CvMat* newCameraMatrix,
870 \par CvSize newImageSize=cvSize(0,0),
871 \par CvRect* validPixROI=0 );}
872 \cvdefPy{GetOptimalNewCameraMatrix(cameraMatrix, distCoeffs, imageSize, alpha, newImgSize=(0,0), validPixROI=0) -> None}
873 \cvdefCpp{Mat getOptimalNewCameraMatrix(
874 \par const Mat\& cameraMatrix, const Mat\& distCoeffs,
875 \par Size imageSize, double alpha, Size newImgSize=Size(),
876 \par Rect* validPixROI=0);}
879 \cvarg{cameraMatrix}{The input camera matrix}
880 \cvarg{distCoeffs}{The input 4x1, 1x4, 5x1 or 1x5 vector of distortion coefficients $(k_1, k_2, p_1, p_2[, k_3])$}.
881 \cvarg{imageSize}{The original image size}
882 \cvarg{alpha}{The free scaling parameter between 0 (when all the pixels in the undistorted image will be valid) and 1 (when all the source image pixels will be retained in the undistorted image); see \cvCross{StereoRectify}{stereoRectify}}
883 \cvC{\cvarg{newCameraMatrix}{The output new camera matrix.}}
884 \cvarg{newImageSize}{The image size after rectification. By default it will be set to \texttt{imageSize}.}
885 \cvarg{validPixROI}{The optional output rectangle that will outline all-good-pixels region in the undistorted image. See \texttt{roi1, roi2} description in \cvCross{StereoRectify}{stereoRectify}}
888 The function computes \cvCpp{and returns} the optimal new camera matrix based on the free scaling parameter. By varying this parameter the user may retrieve only sensible pixels \texttt{alpha=0}, keep all the original image pixels if there is valuable information in the corners \texttt{alpha=1}, or get something in between. When \texttt{alpha>0}, the undistortion result will likely 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 the \text{newImageSize} should be passed to \cvCross{InitUndistortRectifyMap}{initUndistortRectifyMap} to produce the maps for \cvCross{Remap}{remap}.
890 \cvfunc{InitIntrinsicParams2D}{initCameraMatrix2D}
891 Finds the initial camera matrix from the 3D-2D point correspondences
893 \cvdefC{void cvInitIntrinsicParams2D(\par const CvMat* objectPoints,
894 \par const CvMat* imagePoints,
895 \par const CvMat* npoints, CvSize imageSize,
896 \par CvMat* cameraMatrix,
897 \par double aspectRatio=1.);}
898 \cvdefPy{InitCameraMatrix2D( objectPoints, imagePoints, npoints, imageSize, cameraMatrix, aspectRatio=1.) -> None}
899 \cvdefCpp{Mat initCameraMatrix2D( const vector<vector<Point3f> >\& objectPoints,\par
900 const vector<vector<Point2f> >\& imagePoints,\par
901 Size imageSize, double aspectRatio=1.);}
904 \cvarg{objectPoints}{The joint array of object points; see \cvCross{CalibrateCamera2}{calibrateCamera}}
905 \cvarg{imagePoints}{The joint array of object point projections; see \cvCross{CalibrateCamera2}{calibrateCamera}}
906 \cvarg{npoints}{The array of point counts; see \cvCross{CalibrateCamera2}{calibrateCamera}}
909 \cvarg{objectPoints}{The vector of vectors of the object points. See \cvCppCross{calibrateCamera}}
910 \cvarg{imagePoints}{The vector of vectors of the corresponding image points. See \cvCppCross{calibrateCamera}}
912 \cvarg{imageSize}{The image size in pixels; used to initialize the principal point}
913 \cvCPy{\cvarg{cameraMatrix}{The output camera matrix $\vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}$}}
914 \cvarg{aspectRatio}{If it is zero or negative, both $f_x$ and $f_y$ are estimated independently. Otherwise $f_x = f_y * \texttt{aspectRatio}$}
917 The function estimates and returns the initial camera matrix for camera calibration process.
918 Currently, the function only supports planar calibration patterns, i.e. patterns where each object point has z-coordinate =0.
921 \cvfunc{InitUndistortMap}
922 Computes an undistortion map.
924 \cvdefC{void cvInitUndistortMap( \par const CvMat* cameraMatrix,\par const CvMat* distCoeffs,\par CvArr* map1,\par CvArr* map2 );}
925 \cvdefPy{InitUndistortMap(cameraMatrix,distCoeffs,map1,map2)-> None}
928 \cvarg{cameraMatrix}{The input camera matrix $A = \vecthreethree{fx}{0}{cx}{0}{fy}{cy}{0}{0}{1} $}
929 \cvarg{distCoeffs}{The input 4x1, 1x4, 5x1 or 1x5 vector of distortion coefficients $(k_1, k_2, p_1, p_2[, k_3])$}.
930 \cvarg{map1}{The first output map \cvCPy{of type \texttt{CV\_32FC1} or \texttt{CV\_16SC2} - the second variant is more efficient}}
931 \cvarg{map2}{The second output map \cvCPy{of type \texttt{CV\_32FC1} or \texttt{CV\_16UC1} - the second variant is more efficient}}
934 The function is a simplified variant of \cvCross{InitUndistortRectifyMap}{initUndistortRectifyMap} where the rectification transformation \texttt{R} is identity matrix and \texttt{newCameraMatrix=cameraMatrix}.
938 \cvfunc{InitUndistortRectifyMap}{initUndistortRectifyMap}
939 Computes the undistortion and rectification transformation map.
941 \cvdefC{void cvInitUndistortRectifyMap( \par const CvMat* cameraMatrix,
942 \par const CvMat* distCoeffs,
944 \par const CvMat* newCameraMatrix,
945 \par CvArr* map1, \par CvArr* map2 );}
946 \cvdefPy{InitUndistortRectifyMap(cameraMatrix,distCoeffs,R,newCameraMatrix,map1,map2)-> None}
947 \cvdefCpp{void initUndistortRectifyMap( const Mat\& cameraMatrix,\par
948 const Mat\& distCoeffs, const Mat\& R,\par
949 const Mat\& newCameraMatrix,\par
950 Size size, int m1type,\par
951 Mat\& map1, Mat\& map2 );}
953 \cvarg{cameraMatrix}{The input camera matrix $A=\vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}$}
954 \cvarg{distCoeffs}{The input 4x1, 1x4, 5x1 or 1x5 vector of distortion coefficients $(k_1, k_2, p_1, p_2[, k_3])$}.
955 \cvarg{R}{The optional rectification transformation in object space (3x3 matrix). \texttt{R1} or \texttt{R2}, computed by \cvCross{StereoRectify}{stereoRectify} can be passed here. If the matrix is \cvCPy{NULL}\cvCpp{empty}, the identity transformation is assumed}
956 \cvarg{newCameraMatrix}{The new camera matrix $A'=\vecthreethree{f_x'}{0}{c_x'}{0}{f_y'}{c_y'}{0}{0}{1}$}
957 \cvCpp{\cvarg{size}{The undistorted image size}
958 \cvarg{m1type}{The type of the first output map, can be \texttt{CV\_32FC1} or \texttt{CV\_16SC2}. See \cvCppCross{convertMaps}}}
959 \cvarg{map1}{The first output map \cvCPy{of type \texttt{CV\_32FC1} or \texttt{CV\_16SC2} - the second variant is more efficient}}
960 \cvarg{map2}{The second output map \cvCPy{of type \texttt{CV\_32FC1} or \texttt{CV\_16UC1} - the second variant is more efficient}}
963 The function computes the joint undistortion+rectification transformation and represents the result in the form of maps for \cvCross{Remap}{remap}. The undistorted image will look like the original, as if it was captured with a camera with camera matrix \texttt{=newCameraMatrix} and zero distortion. In the case of monocular camera \texttt{newCameraMatrix} is usually equal to \texttt{cameraMatrix}, or it can be computed by \cvCross{GetOptimalNewCameraMatrix}{getOptimalNewCameraMatrix} for a better control over scaling. In the case of stereo camera \texttt{newCameraMatrix} is normally set to \texttt{P1} or \texttt{P2} computed by \cvCross{StereoRectify}{stereoRectify}.
965 Also, this new camera will be oriented differently in the coordinate space, according to \texttt{R}. That, for example, helps to align two heads of a stereo camera so that the epipolar lines on both images become horizontal and have the same y- coordinate (in the case of horizontally aligned stereo camera).
967 The function actually builds the maps for the inverse mapping algorithm that is used by \cvCross{Remap}{remap}. That is, for each pixel $(u, v)$ in the destination (corrected and rectified) image the function computes the corresponding coordinates in the source image (i.e. in the original image from camera). The process is the following:
971 x \leftarrow (u - {c'}_x)/{f'}_x \\
972 y \leftarrow (v - {c'}_y)/{f'}_y \\
973 {[X\,Y\,W]}^T \leftarrow R^{-1}*[x\,y\,1]^T \\
976 x" \leftarrow x' (1 + k_1 r^2 + k_2 r^4 + k_3 r^6) + 2p_1 x' y' + p_2(r^2 + 2 x'^2) \\
977 y" \leftarrow y' (1 + k_1 r^2 + k_2 r^4 + k_3 r^6) + p_1 (r^2 + 2 y'^2) + 2 p_2 x' y' \\
978 map_x(u,v) \leftarrow x" f_x + c_x \\
979 map_y(u,v) \leftarrow y" f_y + c_y
982 where $(k_1, k_2, p_1, p_2[, k_3])$ are the distortion coefficients.
984 In the case of a stereo camera this function is called twice, once for each camera head, after \cvCross{StereoRectify}{stereoRectify}, which in its turn is called after \cvCross{StereoCalibrate}{stereoCalibrate}. But if the stereo camera was not calibrated, it is still possible to compute the rectification transformations directly from the fundamental matrix using \cvCross{StereoRectifyUncalibrated}{stereoRectifyUncalibrated}. For each camera the function computes homography \texttt{H} as the rectification transformation in pixel domain, not a rotation matrix \texttt{R} in 3D space. The \texttt{R} can be computed from \texttt{H} as
986 \[ \texttt{R} = \texttt{cameraMatrix}^{-1} \cdot \texttt{H} \cdot \texttt{cameraMatrix} \]
988 where the \texttt{cameraMatrix} can be chosen arbitrarily.
992 \cvCppFunc{matMulDeriv}
993 Computes partial derivatives of the matrix product w.r.t each multiplied matrix
995 \cvdefCpp{void matMulDeriv( const Mat\& A, const Mat\& B, Mat\& dABdA, Mat\& dABdB );}
997 \cvarg{A}{The first multiplied matrix}
998 \cvarg{B}{The second multiplied matrix}
999 \cvarg{dABdA}{The first output derivative matrix \texttt{d(A*B)/dA} of size $\texttt{A.rows*B.cols} \times {A.rows*A.cols}$}
1000 \cvarg{dABdA}{The second output derivative matrix \texttt{d(A*B)/dB} of size $\texttt{A.rows*B.cols} \times {B.rows*B.cols}$}
1003 The function computes the partial derivatives of the elements of the matrix product $A*B$ w.r.t. the elements of each of the two input matrices. The function is used to compute Jacobian matrices in \cvCppCross{stereoCalibrate}, but can also be used in any other similar optimization function.
1010 Implements the POSIT algorithm.
1013 void cvPOSIT( \par CvPOSITObject* posit\_object,\par CvPoint2D32f* imagePoints,\par double focal\_length,\par CvTermCriteria criteria,\par CvMatr32f rotationMatrix,\par CvVect32f translation\_vector );
1015 \cvdefPy{POSIT(posit\_object,imagePoints,focal\_length,criteria)-> (rotationMatrix,translation\_vector)}
1018 \cvarg{posit\_object}{Pointer to the object structure}
1019 \cvarg{imagePoints}{Pointer to the object points projections on the 2D image plane}
1020 \cvarg{focal\_length}{Focal length of the camera used}
1021 \cvarg{criteria}{Termination criteria of the iterative POSIT algorithm}
1022 \cvarg{rotationMatrix}{Matrix of rotations}
1023 \cvarg{translation\_vector}{Translation vector}
1026 The function implements the POSIT algorithm. Image coordinates are given in a camera-related coordinate system. The focal length may be retrieved using the camera calibration functions. At every iteration of the algorithm a new perspective projection of the estimated pose is computed.
1028 Difference norm between two projections is the maximal distance between corresponding points. The parameter \texttt{criteria.epsilon} serves to stop the algorithm if the difference is small.
1032 \cvfunc{ProjectPoints2}{projectPoints}
1033 Project 3D points on to an image plane.
1035 \cvdefC{void cvProjectPoints2( \par const CvMat* objectPoints,\par const CvMat* rvec,\par const CvMat* tvec,\par const CvMat* cameraMatrix,\par const CvMat* distCoeffs,\par CvMat* imagePoints,\par CvMat* dpdrot=NULL,\par CvMat* dpdt=NULL,\par CvMat* dpdf=NULL,\par CvMat* dpdc=NULL,\par CvMat* dpddist=NULL );}
1037 \cvdefPy{ProjectPoints2(objectPoints,rvec,tvec,cameraMatrix,distCoeffs, imagePoints,dpdrot=NULL,dpdt=NULL,dpdf=NULL,dpdc=NULL,dpddist=NULL)-> None}
1040 \cvdefCpp{void projectPoints( const Mat\& objectPoints,\par
1041 const Mat\& rvec, const Mat\& tvec,\par
1042 const Mat\& cameraMatrix,\par
1043 const Mat\& distCoeffs,\par
1044 vector<Point2f>\& imagePoints );\newline
1045 void projectPoints( const Mat\& objectPoints,\par
1046 const Mat\& rvec, const Mat\& tvec,\par
1047 const Mat\& cameraMatrix,\par
1048 const Mat\& distCoeffs,\par
1049 vector<Point2f>\& imagePoints,\par
1050 Mat\& dpdrot, Mat\& dpdt, Mat\& dpdf,\par
1051 Mat\& dpdc, Mat\& dpddist,\par
1052 double aspectRatio=0 );}
1055 \cvarg{objectPoints}{The array of object points, 3xN or Nx3 1-channel or 1xN or Nx1 3-channel \cvCpp{(or \texttt{vector<Point3f>})}, where N is the number of points in the view}
1056 \cvarg{rvec}{The rotation vector, see \cvCross{Rodrigues2}{Rodrigues}}
1057 \cvarg{tvec}{The translation vector}
1058 \cvarg{cameraMatrix}{The camera matrix $A = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{_1} $}
1059 \cvarg{distCoeffs}{The input 4x1, 1x4, 5x1 or 1x5 vector of distortion coefficients $(k_1, k_2, p_1, p_2[, k_3])$. If it is \cvC{NULL}\cvCpp{empty}\cvPy{None}, all of the distortion coefficients are considered 0's}
1060 \cvarg{imagePoints}{The output array of image points, 2xN or Nx2 1-channel or 1xN or Nx1 2-channel \cvCpp{(or \texttt{vector<Point2f>})}}
1061 \cvarg{dpdrot}{Optional 2Nx3 matrix of derivatives of image points with respect to components of the rotation vector}
1062 \cvarg{dpdt}{Optional 2Nx3 matrix of derivatives of image points with respect to components of the translation vector}
1063 \cvarg{dpdf}{Optional 2Nx2 matrix of derivatives of image points with respect to $f_x$ and $f_y$}
1064 \cvarg{dpdc}{Optional 2Nx2 matrix of derivatives of image points with respect to $c_x$ and $c_y$}
1065 \cvarg{dpddist}{Optional 2Nx4 matrix of derivatives of image points with respect to distortion coefficients}
1068 The function computes projections of 3D
1069 points to the image plane given intrinsic and extrinsic camera
1070 parameters. Optionally, the function computes jacobians - matrices
1071 of partial derivatives of image points coordinates (as functions of all the
1072 input parameters) with respect to the particular parameters, intrinsic and/or
1073 extrinsic. The jacobians are used during the global optimization
1074 in \cvCross{CalibrateCamera2}{calibrateCamera},
1075 \cvCross{FindExtrinsicCameraParams2}{solvePnP} and \cvCross{StereoCalibrate}{stereoCalibrate}. The
1076 function itself can also used to compute re-projection error given the
1077 current intrinsic and extrinsic parameters.
1079 Note, that by setting \texttt{rvec=tvec=(0,0,0)}, or by setting \texttt{cameraMatrix} to 3x3 identity matrix, or by passing zero distortion coefficients, you can get various useful partial cases of the function, i.e. 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 etc.
1082 \cvfunc{ReprojectImageTo3D}{reprojectImageTo3D}
1083 Reprojects disparity image to 3D space.
1085 \cvdefC{void cvReprojectImageTo3D( const CvArr* disparity,\par
1086 CvArr* \_3dImage, const CvMat* Q,\par
1087 int handleMissingValues=0);}
1089 \cvdefPy{ReprojectImageTo3D(disparity, \_3dImage, Q, handleMissingValues=0) -> None}
1091 \cvdefCpp{void reprojectImageTo3D( const Mat\& disparity,\par
1092 Mat\& \_3dImage, const Mat\& Q,\par
1093 bool handleMissingValues=false );}
1095 \cvarg{disparity}{The input single-channel 16-bit signed or 32-bit floating-point disparity image}
1096 \cvarg{\_3dImage}{The output 3-channel floating-point image of the same size as \texttt{disparity}.
1097 Each element of \texttt{\_3dImage(x,y)} will contain the 3D coordinates of the point \texttt{(x,y)}, computed from the disparity map.}
1098 \cvarg{Q}{The $4 \times 4$ perspective transformation matrix that can be obtained with \cvCross{StereoRectify}{stereoRectify}}
1099 \cvarg{handleMissingValues}{If true, when the pixels with the minimal disparity (that corresponds to the ouliers; see \cvCross{FindStereoCorrespondenceBM}{StereoBM}) will be transformed to 3D points with some very large Z value (currently set to 10000)}
1102 The function transforms 1-channel disparity map to 3-channel image representing a 3D surface. That is, for each pixel \texttt{(x,y)} and the corresponding disparity \texttt{d=disparity(x,y)} it computes:
1105 [X\; Y\; Z\; W]^T = \texttt{Q}*[x\; y\; \texttt{disparity}(x,y)\; 1]^T \\
1106 \texttt{\_3dImage}(x,y) = (X/W,\; Y/W,\; Z/W)
1109 The matrix \texttt{Q} can be arbitrary $4 \times 4$ matrix, e.g. the one computed by \cvCross{StereoRectify}{stereoRectify}. To reproject a sparse set of points {(x,y,d),...} to 3D space, use \cvCross{PerspectiveTransform}{perspectiveTransform}.
1112 \cvfunc{RQDecomp3x3}{RQDecomp3x3}
1113 Computes the 'RQ' decomposition of 3x3 matrices.
1116 void cvRQDecomp3x3( \par const CvMat *M,\par CvMat *R,\par CvMat *Q,\par CvMat *Qx=NULL,\par CvMat *Qy=NULL,\par CvMat *Qz=NULL,\par CvPoint3D64f *eulerAngles=NULL);
1118 \cvdefPy{RQDecomp3x3(M, R, Q, Qx = None, Qy = None, Qz = None) -> eulerAngles}
1119 \cvdefCpp{void RQDecomp3x3( const Mat\& M, Mat\& R, Mat\& Q );\newline
1120 Vec3d RQDecomp3x3( const Mat\& M, Mat\& R, Mat\& Q,\par
1121 Mat\& Qx, Mat\& Qy, Mat\& Qz );}
1124 \cvarg{M}{The 3x3 input matrix}
1125 \cvarg{R}{The output 3x3 upper-triangular matrix}
1126 \cvarg{Q}{The output 3x3 orthogonal matrix}
1127 \cvarg{Qx}{Optional 3x3 rotation matrix around x-axis}
1128 \cvarg{Qy}{Optional 3x3 rotation matrix around y-axis}
1129 \cvarg{Qz}{Optional 3x3 rotation matrix around z-axis}
1130 \cvCPy{\cvarg{eulerAngles}{Optional three Euler angles of rotation}}
1133 The function computes a RQ decomposition using the given rotations. This function is used in \cvCross{DecomposeProjectionMatrix}{decomposeProjectionMatrix} to decompose the left 3x3 submatrix of a projection matrix into a camera and a rotation matrix.
1135 It optionally returns three rotation matrices, one for each axis, and the three Euler angles \cvCpp{(as the return value)} that could be used in OpenGL.
1139 \cvCPyFunc{ReleasePOSITObject}
1140 Deallocates a 3D object structure.
1143 void cvReleasePOSITObject( \par CvPOSITObject** posit\_object );
1147 \cvarg{posit\_object}{Double pointer to \texttt{CvPOSIT} structure}
1150 The function releases memory previously allocated by the function \cvCPyCross{CreatePOSITObject}.
1156 \cvCPyFunc{ReleaseStereoBMState}
1157 Releases block matching stereo correspondence structure.
1159 \cvdefC{void cvReleaseStereoBMState( CvStereoBMState** state );}
1160 \cvdefPy{ReleaseStereoBMState(state)-> None}
1163 \cvarg{state}{Double pointer to the released structure.}
1166 The function releases the stereo correspondence structure and all the associated internal buffers.
1168 \cvCPyFunc{ReleaseStereoGCState}
1169 Releases the state structure of the graph cut-based stereo correspondence algorithm.
1171 \cvdefC{void cvReleaseStereoGCState( CvStereoGCState** state );}
1172 \cvdefPy{ReleaseStereoGCState(state)-> None}
1175 \cvarg{state}{Double pointer to the released structure.}
1178 The function releases the stereo correspondence structure and all the associated internal buffers.
1182 \cvfunc{Rodrigues2}{Rodrigues}
1183 Converts a rotation matrix to a rotation vector or vice versa.
1185 \cvdefC{int cvRodrigues2( \par const CvMat* src,\par CvMat* dst,\par CvMat* jacobian=0 );}
1186 \cvdefPy{Rodrigues2(src,dst,jacobian=0)-> None}
1188 \cvdefCpp{void Rodrigues(const Mat\& src, Mat\& dst);\newline
1189 void Rodrigues(const Mat\& src, Mat\& dst, Mat\& jacobian);}
1192 \cvarg{src}{The input rotation vector (3x1 or 1x3) or rotation matrix (3x3)}
1193 \cvarg{dst}{The output rotation matrix (3x3) or rotation vector (3x1 or 1x3), respectively}
1194 \cvarg{jacobian}{Optional output Jacobian matrix, 3x9 or 9x3 - partial derivatives of the output array components with respect to the input array components}
1199 \theta \leftarrow norm(r)\\
1200 r \leftarrow r/\theta\\
1201 R = \cos{\theta} I + (1-\cos{\theta}) r r^T + \sin{\theta}
1209 Inverse transformation can also be done easily, since
1221 A rotation vector is a convenient and most-compact representation of a rotation matrix
1222 (since any rotation matrix has just 3 degrees of freedom). The representation is
1223 used in the global 3D geometry optimization procedures like \cvCross{CalibrateCamera2}{calibrateCamera},
1224 \cvCross{StereoCalibrate}{stereoCalibrate} or \cvCross{FindExtrinsicCameraParams2}{solvePnP}.
1229 \cvCppFunc{StereoBM}
1230 The class for computing stereo correspondence using block matching algorithm.
1233 // Block matching stereo correspondence algorithm\par
1236 enum { NORMALIZED_RESPONSE = CV_STEREO_BM_NORMALIZED_RESPONSE,
1237 BASIC_PRESET=CV_STEREO_BM_BASIC,
1238 FISH_EYE_PRESET=CV_STEREO_BM_FISH_EYE,
1239 NARROW_PRESET=CV_STEREO_BM_NARROW };
1242 // the preset is one of ..._PRESET above.
1243 // ndisparities is the size of disparity range,
1244 // in which the optimal disparity at each pixel is searched for.
1245 // SADWindowSize is the size of averaging window used to match pixel blocks
1246 // (larger values mean better robustness to noise, but yield blurry disparity maps)
1247 StereoBM(int preset, int ndisparities=0, int SADWindowSize=21);
1248 // separate initialization function
1249 void init(int preset, int ndisparities=0, int SADWindowSize=21);
1250 // computes the disparity for the two rectified 8-bit single-channel images.
1251 // the disparity will be 16-bit signed (fixed-point) or 32-bit floating-point image of the same size as left.
1252 void operator()( const Mat& left, const Mat& right, Mat& disparity, int disptype=CV_16S );
1254 Ptr<CvStereoBMState> state;
1260 \cvfunc{StereoCalibrate}{stereoCalibrate}
1261 Calibrates stereo camera.
1263 \cvdefC{double cvStereoCalibrate( \par const CvMat* objectPoints, \par const CvMat* imagePoints1,
1264 \par const CvMat* imagePoints2, \par const CvMat* pointCounts,
1265 \par CvMat* cameraMatrix1, \par CvMat* distCoeffs1,
1266 \par CvMat* cameraMatrix2, \par CvMat* distCoeffs2,
1267 \par CvSize imageSize, \par CvMat* R, \par CvMat* T,
1268 \par CvMat* E=0, \par CvMat* F=0,
1269 \par CvTermCriteria term\_crit=cvTermCriteria(
1270 \par CV\_TERMCRIT\_ITER+CV\_TERMCRIT\_EPS,30,1e-6),
1271 \par int flags=CV\_CALIB\_FIX\_INTRINSIC );}
1273 \cvdefPy{StereoCalibrate( objectPoints, imagePoints1, imagePoints2, pointCounts, cameraMatrix1, distCoeffs1, cameraMatrix2, distCoeffs2, imageSize, R, T, E=NULL, F=NULL, term\_crit=(CV\_TERMCRIT\_ITER+CV\_TERMCRIT\_EPS,30,1e-6), flags=CV\_CALIB\_FIX\_INTRINSIC)-> None}
1275 \cvdefCpp{double stereoCalibrate( const vector<vector<Point3f> >\& objectPoints,\par
1276 const vector<vector<Point2f> >\& imagePoints1,\par
1277 const vector<vector<Point2f> >\& imagePoints2,\par
1278 Mat\& cameraMatrix1, Mat\& distCoeffs1,\par
1279 Mat\& cameraMatrix2, Mat\& distCoeffs2,\par
1280 Size imageSize, Mat\& R, Mat\& T,\par
1281 Mat\& E, Mat\& F,\par
1282 TermCriteria term\_crit = TermCriteria(TermCriteria::COUNT+\par
1283 TermCriteria::EPS, 30, 1e-6),\par
1284 int flags=CALIB\_FIX\_INTRINSIC );}
1288 \cvarg{objectPoints}{The joint matrix of object points - calibration pattern features in the model coordinate space. It is floating-point 3xN or Nx3 1-channel, or 1xN or Nx1 3-channel array, where N is the total number of points in all views.}
1289 \cvarg{imagePoints1}{The joint matrix of object points projections in the first camera views. It is floating-point 2xN or Nx2 1-channel, or 1xN or Nx1 2-channel array, where N is the total number of points in all views}
1290 \cvarg{imagePoints2}{The joint matrix of object points projections in the second camera views. It is floating-point 2xN or Nx2 1-channel, or 1xN or Nx1 2-channel array, where N is the total number of points in all views}
1291 \cvarg{pointCounts}{Integer 1xM or Mx1 vector (where M is the number of calibration pattern views) containing the number of points in each particular view. The sum of vector elements must match the size of \texttt{objectPoints} and \texttt{imagePoints*} (=N).}
1294 \cvarg{objectPoints}{The vector of vectors of points on the calibration pattern in its coordinate system, one vector per view. If the the same calibration pattern is shown in each view and it's fully visible then 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 the pattern coordinate system, then if the rig is planar, it may have sense to put the model to the XY coordinate plane, so that Z-coordinate of each input object point is 0}
1295 \cvarg{imagePoints1}{The vector of vectors of the object point projections on the calibration pattern views from the 1st camera, one vector per a view. The projections must be in the same order as the corresponding object points.}
1296 \cvarg{imagePoints2}{The vector of vectors of the object point projections on the calibration pattern views from the 2nd camera, one vector per a view. The projections must be in the same order as the corresponding object points.}
1298 \cvarg{cameraMatrix1}{The input/output first camera matrix: $ \vecthreethree{f_x^{(j)}}{0}{c_x^{(j)}}{0}{f_y^{(j)}}{c_y^{(j)}}{0}{0}{1}$, $j = 0,\, 1$. If any of \texttt{CV\_CALIB\_USE\_INTRINSIC\_GUESS}, \newline \texttt{CV\_CALIB\_FIX\_ASPECT\_RATIO}, \texttt{CV\_CALIB\_FIX\_INTRINSIC} or \texttt{CV\_CALIB\_FIX\_FOCAL\_LENGTH} are specified, some or all of the matrices' components must be initialized; see the flags description}
1299 \cvarg{cameraMatrix2}{The input/output second camera matrix, as cameraMatrix1.}
1300 \cvarg{distCoeffs1}{The input/output lens distortion coefficients for the first camera, 4x1, 5x1, 1x4 or 1x5 floating-point vectors $(k_1^{(j)}, k_2^{(j)}, p_1^{(j)}, p_2^{(j)}[, k_3^{(j)}])$, $j = 0,\, 1$. If any of \texttt{CV\_CALIB\_FIX\_K1}, \texttt{CV\_CALIB\_FIX\_K2} or \texttt{CV\_CALIB\_FIX\_K3} is specified, then the corresponding elements of the distortion coefficients must be initialized.}
1301 \cvarg{distCoeffs2}{The input/output lens distortion coefficients for the second camera, as distCoeffs1.}
1302 \cvarg{imageSize}{Size of the image, used only to initialize intrinsic camera matrix.}
1303 \cvarg{R}{The output rotation matrix between the 1st and the 2nd cameras' coordinate systems.}
1304 \cvarg{T}{The output translation vector between the cameras' coordinate systems.}
1305 \cvarg{E}{The \cvCPy{optional} output essential matrix.}
1306 \cvarg{F}{The \cvCPy{optional} output fundamental matrix.}
1307 \cvarg{term\_crit}{The termination criteria for the iterative optimization algorithm.}
1308 \cvarg{flags}{Different flags, may be 0 or combination of the following values:
1310 \cvarg{CV\_CALIB\_FIX\_INTRINSIC}{If it is set, \texttt{cameraMatrix?}, as well as \texttt{distCoeffs?} are fixed, so that only \texttt{R, T, E} and \texttt{F} are estimated.}
1311 \cvarg{CV\_CALIB\_USE\_INTRINSIC\_GUESS}{The flag allows the function to optimize some or all of the intrinsic parameters, depending on the other flags, but the initial values are provided by the user.}
1312 \cvarg{CV\_CALIB\_FIX\_PRINCIPAL\_POINT}{The principal points are fixed during the optimization.}
1313 \cvarg{CV\_CALIB\_FIX\_FOCAL\_LENGTH}{$f^{(j)}_x$ and $f^{(j)}_y$ are fixed.}
1314 \cvarg{CV\_CALIB\_FIX\_ASPECT\_RATIO}{$f^{(j)}_y$ is optimized, but the ratio $f^{(j)}_x/f^{(j)}_y$ is fixed.}
1315 \cvarg{CV\_CALIB\_SAME\_FOCAL\_LENGTH}{Enforces $f^{(0)}_x=f^{(1)}_x$ and $f^{(0)}_y=f^{(1)}_y$} \cvarg{CV\_CALIB\_ZERO\_TANGENT\_DIST}{Tangential distortion coefficients for each camera are set to zeros and fixed there.}
1316 \cvarg{CV\_CALIB\_FIX\_K1, CV\_CALIB\_FIX\_K2, CV\_CALIB\_FIX\_K3}{Fixes the corresponding radial distortion coefficient (the coefficient must be passed to the function)}
1320 The function estimates transformation between the 2 cameras making a stereo pair. If we have a stereo camera, where the relative position and orientatation of the 2 cameras is fixed, and if we computed poses of an object relative to the fist camera and to the second camera, (R1, T1) and (R2, T2), respectively (that can be done with \cvCross{FindExtrinsicCameraParams2}{solvePnP}), obviously, those poses will relate to each other, i.e. given ($R_1$, $T_1$) it should be possible to compute ($R_2$, $T_2$) - we only need to know the position and orientation of the 2nd camera relative to the 1st camera. That's what the described function does. It computes ($R$, $T$) such that:
1327 Optionally, it computes the essential matrix E:
1338 where $T_i$ are components of the translation vector $T$: $T=[T_0, T_1, T_2]^T$. And also the function can compute the fundamental matrix F:
1340 \[F = cameraMatrix2^{-T} E cameraMatrix1^{-1}\]
1342 Besides the stereo-related information, the function can also perform full calibration of each of the 2 cameras. However, because of the high dimensionality of the parameter space and noise in the input data the function can diverge from the correct solution. Thus, if intrinsic parameters can be estimated with high accuracy for each of the cameras individually (e.g. using \cvCross{CalibrateCamera2}{calibrateCamera}), it is recommended to do so and then pass \texttt{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, e.g. pass \texttt{CV\_CALIB\_SAME\_FOCAL\_LENGTH} and \texttt{CV\_CALIB\_ZERO\_TANGENT\_DIST} flags, which are usually reasonable assumptions.
1344 Similarly to \cvCross{CalibrateCamera2}{calibrateCamera}, the function minimizes the total re-projection error for all the points in all the available views from both cameras.
1347 The function returns the final value of the re-projection error.
1350 \cvfunc{StereoRectify}{stereoRectify}
1351 Computes rectification transforms for each head of a calibrated stereo camera.
1353 \cvdefC{void cvStereoRectify( \par const CvMat* cameraMatrix1, const CvMat* cameraMatrix2,
1354 \par const CvMat* distCoeffs1, const CvMat* distCoeffs2,
1355 \par CvSize imageSize, const CvMat* R, const CvMat* T,
1356 \par CvMat* R1, CvMat* R2, CvMat* P1, CvMat* P2,
1357 \par CvMat* Q=0, int flags=CV\_CALIB\_ZERO\_DISPARITY,
1358 \par double alpha=-1, CvSize newImageSize=cvSize(0,0),
1359 \par CvRect* roi1=0, CvRect* roi2=0);}
1360 \cvdefPy{StereoRectify( cameraMatrix1, cameraMatrix2, distCoeffs1, distCoeffs2, imageSize, R, T, R1, R2, P1, P2, Q=NULL, flags=CV\_CALIB\_ZERO\_DISPARITY, alpha=-1, newImageSize=(0,0))-> None}
1362 \cvdefCpp{void stereoRectify( const Mat\& cameraMatrix1, const Mat\& distCoeffs1,\par
1363 const Mat\& cameraMatrix2, const Mat\& distCoeffs2,\par
1364 Size imageSize, const Mat\& R, const Mat\& T,\par
1365 Mat\& R1, Mat\& R2, Mat\& P1, Mat\& P2, Mat\& Q,\par
1366 int flags=CALIB\_ZERO\_DISPARITY );\newline
1367 void stereoRectify( const Mat\& cameraMatrix1, const Mat\& distCoeffs1,\par
1368 const Mat\& cameraMatrix2, const Mat\& distCoeffs2,\par
1369 Size imageSize, const Mat\& R, const Mat\& T,\par
1370 Mat\& R1, Mat\& R2, Mat\& P1, Mat\& P2, Mat\& Q,\par
1371 double alpha, Size newImageSize=Size(),\par
1372 Rect* roi1=0, Rect* roi2=0,\par
1373 int flags=CALIB\_ZERO\_DISPARITY );}
1375 \cvarg{cameraMatrix1, cameraMatrix2}{The camera matrices $\vecthreethree{f_x^{(j)}}{0}{c_x^{(j)}}{0}{f_y^{(j)}}{c_y^{(j)}}{0}{0}{1}$.}
1376 \cvarg{distCoeffs1, distCoeffs2}{The input distortion coefficients for each camera, ${k_1}^{(j)}, {k_2}^{(j)}, {p_1}^{(j)}, {p_2}^{(j)} [, {k_3}^{(j)}]$}
1377 \cvarg{imageSize}{Size of the image used for stereo calibration.}
1378 \cvarg{R}{The rotation matrix between the 1st and the 2nd cameras' coordinate systems.}
1379 \cvarg{T}{The translation vector between the cameras' coordinate systems.}
1380 \cvarg{R1, R2}{The output $3 \times 3$ rectification transforms (rotation matrices) for the first and the second cameras, respectively.}
1381 \cvarg{P1, P2}{The output $3 \times 4$ projection matrices in the new (rectified) coordinate systems.}
1382 \cvarg{Q}{The output $4 \times 4$ disparity-to-depth mapping matrix, see \cvCppCross{reprojectImageTo3D}.}
1383 \cvarg{flags}{The operation flags; may be 0 or \texttt{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 horizontal or vertical direction (depending on the orientation of epipolar lines) in order to maximize the useful image area.}
1384 \cvarg{alpha}{The free scaling parameter. If it is -1\cvCpp{ or absent}, the functions performs some default scaling. Otherwise the parameter should be between 0 and 1. \texttt{alpha=0} means that the rectified images will be zoomed and shifted so that only valid pixels are visible (i.e. there will be no black areas after rectification). \texttt{alpha=1} means that the rectified image will be decimated and shifted so that all the pixels from the original images from the cameras are retained in the rectified images, i.e. no source image pixels are lost. Obviously, any intermediate value yields some intermediate result between those two extreme cases.}
1385 \cvarg{newImageSize}{The new image resolution after rectification. The same size should be passed to \cvCross{InitUndistortRectifyMap}{initUndistortRectifyMap}, see the \texttt{stereo\_calib.cpp} sample in OpenCV samples directory. By default, i.e. when (0,0) is passed, it is set to the original \texttt{imageSize}. Setting it to larger value can help you to preserve details in the original image, especially when there is big radial distortion.}
1386 \cvarg{roi1, roi2}{The optional output rectangles inside the rectified images where all the pixels are valid. If \texttt{alpha=0}, the ROIs will cover the whole images, otherwise they likely be smaller, see the picture below}
1389 The function computes the rotation matrices for each camera that (virtually) make both camera image planes the same plane. Consequently, that makes all the epipolar lines parallel and thus simplifies the dense stereo correspondence problem. On input the function takes the matrices computed by \cvCppCross{stereoCalibrate} and on output it gives 2 rotation matrices and also 2 projection matrices in the new coordinates. The 2 cases are distinguished by the function are:
1392 \item Horizontal stereo, when 1st and 2nd camera views are shifted relative to each other mainly along the x axis (with possible small vertical shift). Then in the rectified images the corresponding epipolar lines in left and right cameras will be horizontal and have the same y-coordinate. P1 and P2 will look as:
1403 f & 0 & cx_2 & T_x*f\\
1410 where $T_x$ is horizontal shift between the cameras and $cx_1=cx_2$ if \texttt{CV\_CALIB\_ZERO\_DISPARITY} is set.
1411 \item Vertical stereo, when 1st and 2nd camera views are shifted relative to each other mainly in vertical direction (and probably a bit in the horizontal direction too). Then the epipolar lines in the rectified images will be vertical and have the same x coordinate. P2 and P2 will look as:
1425 0 & f & cy_2 & T_y*f\\
1431 where $T_y$ is vertical shift between the cameras and $cy_1=cy_2$ if \texttt{CALIB\_ZERO\_DISPARITY} is set.
1434 As you can see, the first 3 columns of \texttt{P1} and \texttt{P2} will effectively be the new "rectified" camera matrices.
1435 The matrices, together with \texttt{R1} and \texttt{R2}, can then be passed to \cvCross{InitUndistortRectifyMap}{initUndistortRectifyMap} to initialize the rectification map for each camera.
1437 Below is the screenshot from \texttt{stereo\_calib.cpp} sample. Some red horizontal lines, as you can see, pass through the corresponding image regions, i.e. the images are well rectified (which is what most stereo correspondence algorithms rely on). The green rectangles are \texttt{roi1} and \texttt{roi2} - indeed, their interior are all valid pixels.
1439 \includegraphics[width=0.8\textwidth]{pics/stereo_undistort.jpg}
1442 \cvfunc{StereoRectifyUncalibrated}{stereoRectifyUncalibrated}
1443 Computes rectification transform for uncalibrated stereo camera.
1445 \cvdefC{void cvStereoRectifyUncalibrated( \par const CvMat* points1, \par const CvMat* points2,
1446 \par const CvMat* F, \par CvSize imageSize,
1447 \par CvMat* H1, \par CvMat* H2,
1448 \par double threshold=5 );}
1449 \cvdefPy{StereoRectifyUncalibrated(points1,points2,F,imageSize,H1,H2,threshold=5)-> None}
1450 \cvdefCpp{bool stereoRectifyUncalibrated( const Mat\& points1,\par
1451 const Mat\& points2,\par
1452 const Mat\& F, Size imgSize,\par
1453 Mat\& H1, Mat\& H2,\par
1454 double threshold=5 );}
1456 \cvarg{points1, points2}{The 2 arrays of corresponding 2D points. The same formats as in \cvCross{FindFundamentalMat}{findFundamentalMat} are supported}
1457 \cvarg{F}{The input fundamental matrix. It can be computed from the same set of point pairs using \cvCross{FindFundamentalMat}{findFundamentalMat}.}
1458 \cvarg{imageSize}{Size of the image.}
1459 \cvarg{H1, H2}{The output rectification homography matrices for the first and for the second images.}
1460 \cvarg{threshold}{The optional threshold used to filter out the outliers. If the parameter is greater than zero, then all the point pairs that do not comply the epipolar geometry well enough (that is, the points for which $|\texttt{points2[i]}^T*\texttt{F}*\texttt{points1[i]}|>\texttt{threshold}$) are rejected prior to computing the homographies.
1461 Otherwise all the points are considered inliers.}
1464 The function computes the rectification transformations without knowing intrinsic parameters of the cameras and their relative position in space, hence the suffix "Uncalibrated". Another related difference from \cvCross{StereoRectify}{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 \texttt{H1} and \texttt{H2}. The function implements the algorithm \cite{Hartley99}.
1466 Note that 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 significant distortion, it would better be corrected 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 \cvCross{CalibrateCamera2}{calibrateCamera} and then the images can be corrected using \cvCross{Undistort2}{undistort}, or just the point coordinates can be corrected with \cvCross{UndistortPoints}{undistortPoints}.
1469 \cvfunc{Undistort2}{undistort}
1470 Transforms an image to compensate for lens distortion.
1472 \cvdefC{void cvUndistort2( \par const CvArr* src,\par CvArr* dst,\par const CvMat* cameraMatrix,
1473 \par const CvMat* distCoeffs, \par const CvMat* newCameraMatrix=0 );}
1474 \cvdefPy{Undistort2(src,dst,cameraMatrix,distCoeffs)-> None}
1476 \cvdefCpp{void undistort( const Mat\& src, Mat\& dst, const Mat\& cameraMatrix,\par
1477 const Mat\& distCoeffs, const Mat\& newCameraMatrix=Mat() );}
1479 \cvarg{src}{The input (distorted) image}
1480 \cvarg{dst}{The output (corrected) image; will have the same size and the same type as \texttt{src}}
1481 \cvarg{cameraMatrix}{The input camera matrix $A = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1} $}
1482 \cvarg{distCoeffs}{The vector of distortion coefficients, $(k_1^{(j)}, k_2^{(j)}, p_1^{(j)}, p_2^{(j)}[, k_3^{(j)}])$}
1483 \cvCpp{\cvarg{newCameraMatrix}{Camera matrix of the distorted image. By default it is the same as \texttt{cameraMatrix}, but you may additionally scale and shift the result by using some different matrix}}
1486 The function transforms the image to compensate radial and tangential lens distortion.
1488 The function is simply a combination of \cvCross{InitUndistortRectifyMap}{initUndistortRectifyMap} (with unity \texttt{R}) and \cvCross{Remap}{remap} (with bilinear interpolation). See the former function for details of the transformation being performed.
1490 Those pixels in the destination image, for which there is no correspondent pixels in the source image, are filled with 0's (black color).
1492 The particular subset of the source image that will be visible in the corrected image can be regulated by \texttt{newCameraMatrix}. You can use \cvCross{GetOptimalNewCameraMatrix}{getOptimalNewCameraMatrix} to compute the appropriate \texttt{newCameraMatrix}, depending on your requirements.
1494 The camera matrix and the distortion parameters can be determined using
1495 \cvCross{CalibrateCamera2}{calibrateCamera}. If the resolution of images is different from the used at the calibration stage, $f_x, f_y, c_x$ and $c_y$ need to be scaled accordingly, while the distortion coefficients remain the same.
1498 \cvfunc{UndistortPoints}{undistortPoints}
1499 Computes the ideal point coordinates from the observed point coordinates.
1501 \cvdefC{void cvUndistortPoints( \par const CvMat* src, \par CvMat* dst,
1502 \par const CvMat* cameraMatrix,
1503 \par const CvMat* distCoeffs,
1504 \par const CvMat* R=NULL,
1505 \par const CvMat* P=NULL);}
1506 \cvdefPy{UndistortPoints(src,dst,cameraMatrix,distCoeffs,R=NULL,P=NULL)-> None}
1508 \cvdefCpp{void undistortPoints( const Mat\& src, vector<Point2f>\& dst,\par
1509 const Mat\& cameraMatrix, const Mat\& distCoeffs,\par
1510 const Mat\& R=Mat(), const Mat\& P=Mat());\newline
1511 void undistortPoints( const Mat\& src, Mat\& dst,\par
1512 const Mat\& cameraMatrix, const Mat\& distCoeffs,\par
1513 const Mat\& R=Mat(), const Mat\& P=Mat());}
1516 \cvarg{src}{The observed point coordinates, same format as \texttt{imagePoints} in \cvCross{ProjectPoints2}{projectPoints}}
1517 \cvarg{dst}{The output ideal point coordinates, after undistortion and reverse perspective transformation\cvCPy{, same format as \texttt{src}}.}
1518 \cvarg{cameraMatrix}{The camera matrix $\vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}$}
1519 \cvarg{distCoeffs}{The vector of distortion coefficients, $(k_1^{(j)}, k_2^{(j)}, p_1^{(j)}, p_2^{(j)}[, k_3^{(j)}])$}
1520 \cvarg{R}{The rectification transformation in object space (3x3 matrix). \texttt{R1} or \texttt{R2}, computed by \cvCppCross{StereoRectify} can be passed here. If the matrix is empty, the identity transformation is used}
1521 \cvarg{P}{The new camera matrix (3x3) or the new projection matrix (3x4). \texttt{P1} or \texttt{P2}, computed by \cvCppCross{StereoRectify} can be passed here. If the matrix is empty, the identity new camera matrix is used}
1524 The function is similar to \cvCross{Undistort2}{undistort} and \cvCross{InitUndistortRectifyMap}{initUndistortRectifyMap}, but it operates on a sparse set of points instead of a raster image. Also the function does some kind of reverse transformation to \cvCross{ProjectPoints2}{projectPoints} (in the case of 3D object it will not reconstruct its 3D coordinates, of course; but for a planar object it will, up to a translation vector, if the proper \texttt{R} is specified).
1527 // (u,v) is the input point, (u', v') is the output point
1528 // camera_matrix=[fx 0 cx; 0 fy cy; 0 0 1]
1529 // P=[fx' 0 cx' tx; 0 fy' cy' ty; 0 0 1 tz]
1532 (x',y') = undistort(x",y",dist_coeffs)
1533 [X,Y,W]T = R*[x' y' 1]T
1539 where undistort() is approximate iterative algorithm that estimates the normalized original point coordinates out of the normalized distorted point coordinates ("normalized" means that the coordinates do not depend on the camera matrix).
1541 The function can be used both for a stereo camera head or for monocular camera (when R is \cvC{NULL}\cvPy{None}\cvCpp{empty}).