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.
73 The distortion coefficients do not depend on the scene viewed, thus they also belong to the intrinsic camera parameters.
74 \emph{And they remain the same regardless of the captured image resolution.}
75 That is, if, for example, a camera has been calibrated on images of $320
76 \times 240$ resolution, absolutely the same distortion coefficients can
77 be used for images of $640 \times 480$ resolution from the same camera (while $f_x$,
78 $f_y$, $c_x$ and $c_y$ need to be scaled appropriately).
80 The functions below use the above model to
83 \item Project 3D points to the image plane given intrinsic and extrinsic parameters
84 \item Compute extrinsic parameters given intrinsic parameters, a few 3D points and their projections.
85 \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).
90 \cvCPyFunc{CalcImageHomography}
91 Calculates the homography matrix for an oblong planar object (e.g. arm).
94 void cvCalcImageHomography( \par float* line,\par CvPoint3D32f* center,\par float* intrinsic,\par float* homography );
95 }\cvcodePy{CalcImageHomography(line,points)-> intrinsic,homography}
98 \cvarg{line}{the main object axis direction (vector (dx,dy,dz))}
99 \cvarg{center}{object center ((cx,cy,cz))}
100 \cvarg{intrinsic}{intrinsic camera parameters (3x3 matrix)}
101 \cvarg{homography}{output homography matrix (3x3)}
104 The function calculates the homography
105 matrix for the initial image transformation from image plane to the
106 plane, defined by a 3D oblong object line (See \_\_Figure 6-10\_\_
107 in the OpenCV Guide 3D Reconstruction Chapter).
110 \cvCPyFunc{CalibrateCamera2}
111 Finds the intrinsic and extrinsic camera parameters using a calibration pattern.
114 void cvCalibrateCamera2( \par const CvMat* object\_points,\par const CvMat* image\_points,\par const CvMat* point\_counts,\par CvSize image\_size,\par CvMat* intrinsic\_matrix,\par CvMat* distortion\_coeffs,\par CvMat* rotation\_vectors=NULL,\par CvMat* translation\_vectors=NULL,\par int flags=0 );
115 }\cvcodePy{CalibrateCamera2(object\_points,image\_points,point\_counts,image\_size,intrinsic\_matrix,distortion\_coeffs,rotation\_vectors,translation\_vectors,flags=0)-> None}
118 \cvarg{object\_points}{The joint matrix of object points, 3xN or Nx3, where N is the total number of points in all views}
119 \cvarg{image\_points}{The joint matrix of corresponding image points, 2xN or Nx2, where N is the total number of points in all views}
120 \cvarg{point\_counts}{Vector containing the number of points in each particular view, 1xM or Mx1, where M is the number of points in a scene}
121 \cvarg{image\_size}{Size of the image, used only to initialize the intrinsic camera matrix}
122 \cvarg{intrinsic\_matrix}{The output camera matrix $A = \vecthreethree{fx}{0}{cx}{0}{fy}{cy}{0}{0}{1} $. If \texttt{CV\_CALIB\_USE\_INTRINSIC\_GUESS} and/or \texttt{CV\_CALIB\_FIX\_ASPECT\_RATION} are specified, some or all of \texttt{fx, fy, cx, cy} must be initialized}
123 \cvarg{distortion\_coeffs}{The output 4x1 or 1x4 vector of distortion coefficients $k_1, k_2, k_3, k_4$}
124 \cvarg{rotation\_vectors}{The output 3xM or Mx3 array of rotation vectors (compact representation of rotation matrices, \cvCPyCross{Rodrigues2})}
125 \cvarg{translation\_vectors}{The output 3xM or Mx3 array of translation vectors}
126 \cvarg{flags}{Different flags, may be 0 or combination of the following values:
128 \cvarg{CV\_CALIB\_USE\_INTRINSIC\_GUESS}{\texttt{intrinsic\_matrix} 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{image\_size} 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. Use \cvCPyCross{FindExtrinsicCameraParams2} instead.}
129 \cvarg{CV\_CALIB\_FIX\_PRINCIPAL\_POINT}{The principal point is not changed during the global optimization, it stays at the center and at the other location specified (when \texttt{CV\_CALIB\_USE\_INTRINSIC\_GUESS} is set as well)}
130 \cvarg{CV\_CALIB\_FIX\_ASPECT\_RATIO}{The optimization procedure considers only one of \texttt{fx} and \texttt{fy} as independent variables and keeps the aspect ratio \texttt{fx/fy} the same as it was set initially in \texttt{intrinsic\_matrix}. In this case the actual initial values of \texttt{(fx, fy)} are either taken from the matrix (when \texttt{CV\_CALIB\_USE\_INTRINSIC\_GUESS} is set) or estimated somehow (in the latter case \texttt{fx, fy} may be set to arbitrary values, only their ratio is used).}
131 \cvarg{CV\_CALIB\_ZERO\_TANGENT\_DIST}{Tangential distortion coefficients are set to zeros and do not change during the optimization.}}
135 The function estimates the intrinsic camera
136 parameters and extrinsic parameters for each of the views. The
137 coordinates of 3D object points and their correspondent 2D projections
138 in each view must be specified. That may be achieved by using an
139 object with known geometry and easily detectable feature points.
140 Such an object is called a calibration rig or calibration pattern,
141 and OpenCV has built-in support for a chessboard as a calibration
142 rig (see \cvCPyCross{FindChessboardCornerGuesses}). Currently, initialization
143 of intrinsic parameters (when \texttt{CV\_CALIB\_USE\_INTRINSIC\_GUESS}
144 is not set) is only implemented for planar calibration rigs
145 (z-coordinates of object points must be all 0's or all 1's). 3D
146 rigs can still be used as long as initial \texttt{intrinsic\_matrix}
147 is provided. After the initial values of intrinsic and extrinsic
148 parameters are computed, they are optimized to minimize the total
149 back-projection error - the sum of squared differences between the
150 actual coordinates of image points and the ones computed using
151 \cvCPyCross{ProjectPoints2}.
153 Note: if you're using a non-square (=non-NxN) grid and
154 \cvCPyCross{FindChessboardCorners} for calibration, and cvCalibrateCamera2 returns
155 bad values (i.e. zero distortion coefficients, an image center of
156 (w/2-0.5,h/2-0.5), and / or large differences between $fx$ and $fy$ (ratios of
157 10:1 or more)), then you've probaby used pattern\_size=cvSize(rows,cols),
158 but should use pattern\_size=cvSize(cols,rows) in \cvCPyCross{FindChessboardCorners}.
160 \cvCPyFunc{ComputeCorrespondEpilines}
161 For points in one image of a stereo pair, computes the corresponding epilines in the other image.
164 void cvComputeCorrespondEpilines( \par const CvMat* points,\par int which\_image,\par const CvMat* fundamental\_matrix,\par CvMat* correspondent\_lines);
165 }\cvcodePy{ComputeCorrespondEpilines(points, which\_image, fundamental\_matrix, correspondent\_lines) -> None}
168 \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}
169 \cvarg{which\_image}{Index of the image (1 or 2) that contains the \texttt{points}}
170 \cvarg{fundamental\_matrix}{Fundamental matrix}
171 \cvarg{correspondent\_lines}{Computed epilines, a \texttt{3xN} or \texttt{Nx3} array}
174 For every point in one of the two images of a stereo-pair the function
175 \texttt{ComputeCorrespondEpilines} finds the equation of a line that
176 contains the corresponding point (i.e. projection of the same 3D
177 point) in the other image. Each line is encoded by a vector of 3
178 elements $l = \vecthree{a}{b}{c}$ so that:
180 \[ l^T \vecthree{x}{y}{1} = 0 \]
182 \[ a x + b y + c = 0 \]
184 From the fundamental matrix definition (see \cvCPyCross{FindFundamentalMatrix}
185 discussion), line $l_1$ for a point $p_1$ in the first image
186 $(\texttt{which\_image} =1)$ can be computed as:
190 and the line $l_1$ for a point $p_2$ in the second image $(\texttt{which\_image} =1)$ can be computed as:
194 Line coefficients are defined up to a scale. They are normalized $(a^2+b^2=1)$ are stored into \texttt{correspondent\_lines}.
196 \cvCPyFunc{ConvertPointsHomogenious}
197 Convert points to/from homogenious coordinates.
200 void cvConvertPointsHomogenious( \par const CvMat* src,\par CvMat* dst );
204 \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}
205 \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}
208 The function converts 2D or 3D points from/to homogenious coordinates, or simply copies or transposes the array. If the input array dimensionality is larger than the output, each coordinate is divided by the last coordinate:
212 (x,y[,z],w) -> (x',y'[,z'])\\
216 z' = z/w \quad \text{(if output is 3D)}
220 If the output array dimensionality is larger, an extra 1 is appended to each point. Otherwise, the input array is simply copied (with optional tranposition) to the output.
222 \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.
224 \cvCPyFunc{CreatePOSITObject}
225 Initializes a structure containing object information.
228 CvPOSITObject* cvCreatePOSITObject( \par CvPoint3D32f* points,\par int point\_count );
229 }\cvcodePy{CreatePOSITObject(points)-> POSITObject}
232 \cvarg{points}{Pointer to the points of the 3D object model}
233 \cvarg{point\_count}{Number of object points}
236 The function allocates memory for the object structure and computes the object inverse matrix.
238 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.
240 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.
242 Once the work with a given object is finished, the function \cvCPyCross{ReleasePOSITObject} must be called to free memory.
244 \cvCPyFunc{CreateStereoBMState}
245 Creates block matching stereo correspondence structure.
248 #define CV_STEREO_BM_BASIC 0
249 #define CV_STEREO_BM_FISH_EYE 1
250 #define CV_STEREO_BM_NARROW 2
255 CvStereoBMState* cvCreateStereoBMState( int preset=CV\_STEREO\_BM\_BASIC,
256 int numberOfDisparities=0 );
258 }\cvcodePy{CreateStereoBMState(preset=CV\_STEREO\_BM\_BASIC,numberOfDisparities=0)-> StereoBMState}
261 \cvarg{preset}{ID of one of the pre-defined parameter sets. Any of the parameters can be overridden after creating the structure.}
262 \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.}
265 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{cvFindStereoCorrespondenceBM}.
267 \cvCPyFunc{CreateStereoGCState}
268 Creates the state of graph cut-based stereo correspondence algorithm.
272 CvStereoGCState* cvCreateStereoGCState( int numberOfDisparities,
275 }\cvcodePy{CreateStereoGCState(numberOfDispaities,maxIters)-> StereoGCState}
278 \cvarg{numberOfDisparities}{The number of disparities. The disparity search range will be $\texttt{state->minDisparity} \le disparity < \texttt{state->minDisparity} + \texttt{state->numberOfDisparities}$}
279 \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. }
282 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{cvFindStereoCorrespondenceGC}.
284 \cvCPyFunc{CvStereoBMState}
285 The structure for block matching stereo correspondence algorithm.
288 typedef struct CvStereoBMState
290 //pre filters (normalize input images):
291 int preFilterType; // 0 for now
292 int preFilterSize; // ~5x5..21x21
293 int preFilterCap; // up to ~31
294 //correspondence using Sum of Absolute Difference (SAD):
295 int SADWindowSize; // Could be 5x5..21x21
296 int minDisparity; // minimum disparity (=0)
297 int numberOfDisparities; // maximum disparity - minimum disparity
298 //post filters (knock out bad matches):
299 int textureThreshold; // areas with no texture are ignored
300 float uniquenessRatio;// filter out pixels if there are other close matches
301 // with different disparity
302 int speckleWindowSize;// Disparity variation window (not used)
303 int speckleRange; // Acceptable range of variation in window (not used)
304 // internal buffers, do not modify (!)
305 CvMat* preFilteredImg0;
306 CvMat* preFilteredImg1;
307 CvMat* slidingSumBuf;
312 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.
314 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.
316 \cvCPyFunc{CvStereoGCState}
317 The structure for graph cuts-based stereo correspondence algorithm
320 typedef struct CvStereoGCState
322 int Ithreshold; // threshold for piece-wise linear data cost function (5 by default)
323 int interactionRadius; // radius for smoothness cost function (1 by default; means Potts model)
324 float K, lambda, lambda1, lambda2; // parameters for the cost function
325 // (usually computed adaptively from the input data)
326 int occlusionCost; // 10000 by default
327 int minDisparity; // 0 by default; see CvStereoBMState
328 int numberOfDisparities; // defined by user; see CvStereoBMState
329 int maxIters; // number of iterations; defined by user.
344 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.
346 \cvCPyFunc{DecomposeProjectionMatrix}
347 Computes the `RQ' decomposition of 3x3 matrices.
350 void cvDecomposeProjectionMatrix( \par const CvMat *projMatr,\par CvMat *calibMatr,\par CvMat *rotMatr,\par CvMat *posVect,\par CvMat *rotMatrX=NULL,\par CvMat *rotMatrY=NULL,\par CvMat *rotMatrZ=NULL,\par CvPoint3D64f *eulerAngles=NULL);
351 }\cvcodePy{DecomposeProjectionMatrix(projMatr, calibMatr, rotMatr, posVect, rotMatrX = None, rotMatrY = None, rotMatrZ = None) -> eulerAngles}
354 \cvarg{projMatr}{The 3x4 input projection matrix P}
355 \cvarg{calibMatr}{The output 3x3 internal calibration matrix K}
356 \cvarg{rotMatr}{The output 3x3 external rotation matrix R}
357 \cvarg{posVect}{The output 4x1 external homogenious position vector C}
358 \cvarg{rotMatrX}{Optional 3x3 rotation matrix around x-axis}
359 \cvarg{rotMatrY}{Optional 3x3 rotation matrix around y-axis}
360 \cvarg{rotMatrZ}{Optional 3x3 rotation matrix around z-axis}
361 \cvarg{eulerAngles}{Optional 3 points containing the three Euler angles of rotation}
364 The function computes a decomposition of a projection matrix into a calibration and a rotation matrix and the position of the camera.
366 It optionally returns three rotation matrices, one for each axis, and the three Euler angles that could be used in OpenGL.
369 \cvCPyFunc{DrawChessBoardCorners}
370 Renders the detected chessboard corners.
373 void cvDrawChessboardCorners( \par CvArr* image,\par CvSize pattern\_size,\par CvPoint2D32f* corners,\par int count,\par int pattern\_was\_found );
374 }\cvcodePy{DrawChessboardCorners(image,pattern\_size,corners,pattern\_was\_found)-> None}
377 \cvarg{image}{The destination image; it must be an 8-bit color image}
378 \cvarg{pattern\_size}{The number of inner corners per chessboard row and column. ( pattern\_size = cvSize(points\_per\_row,points\_per\_colum) = cvSize(columns,rows) )}
379 \cvarg{corners}{The array of corners detected}
380 \cvarg{count}{The number of corners}
381 \cvarg{pattern\_was\_found}{Indicates whether the complete board was found $(\ne 0)$ or not $(=0)$. One may just pass the return value \cvCPyCross{FindChessboardCorners} here}
384 The function draws the individual chessboard corners detected as red circles if the board was not found $(\texttt{pattern\_was\_found} =0)$ or as colored corners connected with lines if the board was found $(\texttt{pattern\_was\_found} \ne 0)$.
387 \cvCPyFunc{FindChessboardCorners}
388 Finds the positions of the internal corners of the chessboard.
391 int cvFindChessboardCorners( \par const void* image,\par CvSize pattern\_size,\par CvPoint2D32f* corners,\par int* corner\_count=NULL,\par int flags=CV\_CALIB\_CB\_ADAPTIVE\_THRESH );
392 }\cvcodePy{FindChessboardCorners(image, pattern\_size, flags=CV\_CALIB\_CB\_ADAPTIVE\_THRESH) -> corners}
395 \cvarg{image}{Source chessboard view; it must be an 8-bit grayscale or color image}
396 \cvarg{pattern\_size}{The number of inner corners per chessboard row and column}
397 ( pattern\_size = cvSize(points\_per\_row,points\_per\_colum) = cvSize(columns,rows) )
398 \cvarg{corners}{The output array of corners detected}
399 \cvC{\cvarg{corner\_count}{The output corner counter. If it is not NULL, it stores the number of corners found}}
400 \cvarg{flags}{Various operation flags, can be 0 or a combination of the following values:
402 \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).}
403 \cvarg{CV\_CALIB\_CB\_NORMALIZE\_IMAGE}{normalize the image using \cvCPyCross{NormalizeHist} before applying fixed or adaptive thresholding.}
404 \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.}
408 The function attempts to determine
409 whether the input image is a view of the chessboard pattern and
410 locate the internal chessboard corners. The function returns a non-zero
411 value if all of the corners have been found and they have been placed
412 in a certain order (row by row, left to right in every row),
413 otherwise, if the function fails to find all the corners or reorder
414 them, it returns 0. For example, a regular chessboard has 8 x 8
415 squares and 7 x 7 internal corners, that is, points, where the black
416 squares touch each other. The coordinates detected are approximate,
417 and to determine their position more accurately, the user may use
418 the function \cvCPyCross{FindCornerSubPix}.
420 \cvCPyFunc{FindExtrinsicCameraParams2}
421 Finds the extrinsic camera parameters for a particular view.
424 void cvFindExtrinsicCameraParams2( \par const CvMat* object\_points,\par const CvMat* image\_points,\par const CvMat* intrinsic\_matrix,\par const CvMat* distortion\_coeffs,\par CvMat* rotation\_vector,\par CvMat* translation\_vector );
425 }\cvcodePy{FindExtrinsicCameraParams2(object\_points,image\_points,intrinsic\_matrix,distortion\_coeffs,rotation\_vector,translation\_vector)-> None}
428 \cvarg{object\_points}{The array of object points, 3xN or Nx3, where N is the number of points in the view}
429 \cvarg{image\_points}{The array of corresponding image points, 2xN or Nx2, where N is the number of points in the view}
430 \cvarg{intrinsic\_matrix}{The input camera matrix $A = \vecthreethree{fx}{0}{cx}{0}{fy}{cy}{0}{0}{1} $}
431 \cvarg{distortion\_coeffs}{The input 4x1 or 1x4 vector of distortion coefficients $k_1, k_2, k_3, k_4$. If it is NULL, all of the distortion coefficients are set to 0}
432 \cvarg{rotation\_vector}{The output 3x1 or 1x3 rotation vector (compact representation of a rotation matrix, \cvCPyCross{Rodrigues2}}
433 \cvarg{translation\_vector}{The output 3x1 or 1x3 translation vector}
436 The function estimates the extrinsic camera parameters using known intrinsic parameters and extrinsic parameters for each view. The coordinates of 3D object points and their correspondent 2D projections must be specified. This function also minimizes back-projection error.
438 \cvCPyFunc{FindFundamentalMat}
439 Calculates the fundamental matrix from the corresponding points in two images.
442 int cvFindFundamentalMat( \par const CvMat* points1,\par const CvMat* points2,\par CvMat* fundamental\_matrix,\par int method=CV\_FM\_RANSAC,\par double param1=1.,\par double param2=0.99,\par CvMat* status=NULL);
443 }\cvcodePy{FindFundamentalMat(points1, points2, fundamental\_matrix, method=CV\_FM\_RANSAC, param1=1., double param2=0.99, status = None) -> None}
446 \cvarg{points1}{Array of the first image points of \texttt{2xN, Nx2, 3xN} or \texttt{Nx3} size (where \texttt{N} is number of points). Multi-channel \texttt{1xN} or \texttt{Nx1} array is also acceptable. The point coordinates should be floating-point (single or double precision)}
447 \cvarg{points2}{Array of the second image points of the same size and format as \texttt{points1}}
448 \cvarg{fundamental\_matrix}{The output fundamental matrix or matrices. The size should be 3x3 or 9x3 (7-point method may return up to 3 matrices)}
449 \cvarg{method}{Method for computing the fundamental matrix
451 \cvarg{CV\_FM\_7POINT}{for a 7-point algorithm. $N = 7$}
452 \cvarg{CV\_FM\_8POINT}{for an 8-point algorithm. $N \ge 8$}
453 \cvarg{CV\_FM\_RANSAC}{for the RANSAC algorithm. $N \ge 8$}
454 \cvarg{CV\_FM\_LMEDS}{for the LMedS algorithm. $N \ge 8$}
456 \cvarg{param1}{The parameter is used for RANSAC or LMedS methods only. 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. Usually it is set to 0.5 or 1.0}
457 \cvarg{param2}{The parameter is used for RANSAC or LMedS methods only. It denotes the desirable level of confidence that the matrix is correct}
458 \cvarg{status}{The 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 1}
461 The epipolar geometry is described by the following equation:
465 where $F$ is fundamental matrix, $p_1$ and $p_2$ are corresponding points in the first and the second images, respectively.
467 The function calculates the fundamental
468 matrix using one of four methods listed above and returns the number
469 of fundamental matrices found (1 or 3) and 0, if no matrix is found.
471 The calculated fundamental matrix may be passed further to
472 \texttt{cvComputeCorrespondEpilines} that finds the epipolar lines
473 corresponding to the specified points.
475 \cvfunc{Example. Estimation of fundamental matrix using RANSAC algorithm}
477 int point_count = 100;
481 CvMat* fundamental_matrix;
483 points1 = cvCreateMat(1,point_count,CV_32FC2);
484 points2 = cvCreateMat(1,point_count,CV_32FC2);
485 status = cvCreateMat(1,point_count,CV_8UC1);
487 /* Fill the points here ... */
488 for( i = 0; i < point_count; i++ )
490 points1->data.fl[i*2] = <x,,1,i,,>;
491 points1->data.fl[i*2+1] = <y,,1,i,,>;
492 points2->data.fl[i*2] = <x,,2,i,,>;
493 points2->data.fl[i*2+1] = <y,,2,i,,>;
496 fundamental_matrix = cvCreateMat(3,3,CV_32FC1);
497 int fm_count = cvFindFundamentalMat( points1,points2,fundamental_matrix,
498 CV_FM_RANSAC,1.0,0.99,status );
501 \cvCPyFunc{FindHomography}
502 Finds the perspective transformation between two planes.
505 void cvFindHomography( \par const CvMat* src\_points,\par const CvMat* dst\_points,\par CvMat* homography \par
506 int method=0, \par double ransacReprojThreshold=0, \par CvMat* mask=NULL);
507 }\cvcodePy{FindHomography(src\_points,dst\_points)-> homography}
510 \cvarg{src\_points}{Point coordinates in the original plane, 2xN, Nx2, 3xN or Nx3 array (the latter two are for representation in homogenious coordinates), where N is the number of points}
511 \cvarg{dst\_points}{Point coordinates in the destination plane, 2xN, Nx2, 3xN or Nx3 array (the latter two are for representation in homogenious coordinates)}
512 \cvarg{homography}{Output 3x3 homography matrix}
513 \cvarg{method}{ The method used to computed homography matrix; one of the following:
515 \cvarg{0}{regular method using all the point pairs}
516 \cvarg{CV\_RANSAC}{RANSAC-based robust method}
517 \cvarg{CV\_LMEDS}{Least-Median robust method}
519 \cvarg{ransacReprojThreshold}{The maximum allowed reprojection error to treat a point pair as an inlier. The parameter is only used in RANSAC-based homography estimation. E.g. if \texttt{dst\_points} coordinates are measured in pixels with pixel-accurate precision, it makes sense to set this parameter somewhere in the range 1 to 3. }
520 \cvarg{mask}{The optional output mask set by a robust method (\texttt{CV\_RANSAC} or \texttt{CV\_LMEDS}).}
523 The function finds the perspective transformation $H$ between the source and the destination planes:
526 s_i \vecthree{x'_i}{y'_i}{1} \sim H \vecthree{x_i}{y_i}{1}
529 So that the back-projection error is minimized:
533 \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+
534 \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
537 If the parameter method is set to the default value 0, the function
538 uses all the point pairs and estimates the best suitable homography
539 matrix. However, if not all of the point pairs ($src\_points_i$,
540 $dst\_points_i$) fit the rigid perspective transformation (i.e. there
541 can be outliers), it is still possible to estimate the correct
542 transformation using one of the robust methods available. Both
543 methods, \texttt{CV\_RANSAC} and \texttt{CV\_LMEDS}, try many different random subsets
544 of the corresponding point pairs (of 5 pairs each), estimate
545 the homography matrix using this subset and a simple least-square
546 algorithm and then compute the quality/goodness of the computed homography
547 (which is the number of inliers for RANSAC or the median reprojection
548 error for LMeDs). The best subset is then used to produce the initial
549 estimate of the homography matrix and the mask of inliers/outliers.
551 Regardless of the method, robust or not, the computed homography
552 matrix is refined further (using inliers only in the case of a robust
553 method) with the Levenberg-Marquardt method in order to reduce the
554 reprojection error even more.
556 The method \texttt{CV\_RANSAC} can handle practically any ratio of outliers,
557 but it needs the threshold to distinguish inliers from outliers.
558 The method \texttt{CV\_LMEDS} does not need any threshold, but it works
559 correctly only when there are more than 50\% of inliers. Finally,
560 if you are sure in the computed features and there can be only some
561 small noise, but no outliers, the default method could be the best
564 The function is used to find initial intrinsic and extrinsic matrices.
565 Homography matrix is determined up to a scale, thus it is normalized
568 \cvCPyFunc{FindStereoCorrespondenceBM}
569 Computes the disparity map using block matching algorithm.
573 void cvFindStereoCorrespondenceBM( \par const CvArr* left, \par const CvArr* right,
574 \par CvArr* disparity, \par CvStereoBMState* state );
576 }\cvcodePy{FindStereoCorrespondenceBM(left,right,disparity,state)-> None}
579 \cvarg{left}{The left single-channel, 8-bit image.}
580 \cvarg{right}{The right image of the same size and the same type.}
581 \cvarg{disparity}{The output single-channel 16-bit signed disparity map of the same size as input images. Its elements will be the computed disparities, multiplied by 16 and rounded to integers.}
582 \cvarg{state}{Stereo correspondence structure.}
585 The function cvFindStereoCorrespondenceBM computes disparity map for the input rectified stereo pair.
587 \cvCPyFunc{FindStereoCorrespondenceGC}
588 Computes the disparity map using graph cut-based algorithm.
592 void cvFindStereoCorrespondenceGC( \par const CvArr* left, \par const CvArr* right,
593 \par CvArr* dispLeft, \par CvArr* dispRight,
594 \par CvStereoGCState* state,
595 \par int useDisparityGuess = CV\_DEFAULT(0) );
597 }\cvcodePy{FindStereoCorrespondenceGC(\par left,\par right,\par dispLeft,\par dispRight,\par state,\par useDisparityGuess=CV\_DEFAULT(0))-> None}
600 \cvarg{left}{The left single-channel, 8-bit image.}
601 \cvarg{right}{The right image of the same size and the same type.}
602 \cvarg{dispLeft}{The optional output single-channel 16-bit signed left disparity map of the same size as input images.}
603 \cvarg{dispRight}{The optional output single-channel 16-bit signed right disparity map of the same size as input images.}
604 \cvarg{state}{Stereo correspondence structure.}
605 \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).}
608 The function computes disparity maps for the input rectified stereo pair. Note that the left disparity image will contain values in the following range:
611 -\texttt{state->numberOfDisparities}-\texttt{state->minDisparity}
612 < dispLeft(x,y) \le -\texttt{state->minDisparity},
617 dispLeft(x,y) == \texttt{CV\_STEREO\_GC\_OCCLUSION}
620 and for the right disparity image the following will be true:
623 \texttt{state->minDisparity} \le dispRight(x,y)
624 < \texttt{state->minDisparity} + \texttt{state->numberOfDisparities}
630 dispRight(x,y) == \texttt{CV\_STEREO\_GC\_OCCLUSION}
633 that is, the range for the left disparity image will be inversed,
634 and the pixels for which no good match has been found, will be marked
637 Here is how the function can be called:
640 // image_left and image_right are the input 8-bit single-channel images
641 // from the left and the right cameras, respectively
642 CvSize size = cvGetSize(image_left);
643 CvMat* disparity_left = cvCreateMat( size.height, size.width, CV_16S );
644 CvMat* disparity_right = cvCreateMat( size.height, size.width, CV_16S );
645 CvStereoGCState* state = cvCreateStereoGCState( 16, 2 );
646 cvFindStereoCorrespondenceGC( image_left, image_right,
647 disparity_left, disparity_right, state, 0 );
648 cvReleaseStereoGCState( &state );
649 // now process the computed disparity images as you want ...
652 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):
655 CvMat* disparity_left_visual = cvCreateMat( size.height, size.width, CV_8U );
656 cvConvertScale( disparity_left, disparity_left_visual, -16 );
657 cvSave( "disparity.png", disparity_left_visual );
660 \includegraphics{pics/disparity.png}
663 Implements the POSIT algorithm.
666 void cvPOSIT( \par CvPOSITObject* posit\_object,\par CvPoint2D32f* image\_points,\par double focal\_length,\par CvTermCriteria criteria,\par CvMatr32f rotation\_matrix,\par CvVect32f translation\_vector );
667 }\cvcodePy{POSIT(posit\_object,image\_points,focal\_length,criteria)-> rotation\_matrix,translation\_vector}
670 \cvarg{posit\_object}{Pointer to the object structure}
671 \cvarg{image\_points}{Pointer to the object points projections on the 2D image plane}
672 \cvarg{focal\_length}{Focal length of the camera used}
673 \cvarg{criteria}{Termination criteria of the iterative POSIT algorithm}
674 \cvarg{rotation\_matrix}{Matrix of rotations}
675 \cvarg{translation\_vector}{Translation vector}
678 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.
680 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.
683 \cvCPyFunc{ProjectPoints2}
684 Projects 3D points on to an image plane.
687 void cvProjectPoints2( \par const CvMat* object\_points,\par const CvMat* rotation\_vector,\par const CvMat* translation\_vector,\par const CvMat* intrinsic\_matrix,\par const CvMat* distortion\_coeffs,\par CvMat* image\_points,\par CvMat* dpdrot=NULL,\par CvMat* dpdt=NULL,\par CvMat* dpdf=NULL,\par CvMat* dpdc=NULL,\par CvMat* dpddist=NULL );
688 }\cvcodePy{ProjectPoints2(object\_points,rotation\_vector,translation\_vector,intrinsic\_matrix,distortion\_coeffs, image\_points,dpdrot=NULL,dpdt=NULL,dpdf=NULL,dpdc=NULL,dpddist=NULL)-> None}
691 \cvarg{object\_points}{The array of object points, 3xN or Nx3, where N is the number of points in the view}
692 \cvarg{rotation\_vector}{The rotation vector, 1x3 or 3x1}
693 \cvarg{translation\_vector}{The translation vector, 1x3 or 3x1}
694 \cvarg{intrinsic\_matrix}{The camera matrix $A = \vecthreethree{fx}{0}{cx}{0}{fy}{cy}{0}{0}{1} $}
695 \cvarg{distortion\_coeffs}{The vector of distortion coefficients, 4x1 or 1x4 $k_1, k_2, k_3, k_4$. If it is \texttt{NULL}, all of the distortion coefficients are considered 0's}
696 \cvarg{image\_points}{The output array of image points, 2xN or Nx2, where N is the total number of points in the view}
697 \cvarg{dpdrot}{Optional Nx3 matrix of derivatives of image points with respect to components of the rotation vector}
698 \cvarg{dpdt}{Optional Nx3 matrix of derivatives of image points with respect to components of the translation vector}
699 \cvarg{dpdf}{Optional Nx2 matrix of derivatives of image points with respect to $fx$ and $fy$}
700 \cvarg{dpdc}{Optional Nx2 matrix of derivatives of image points with respect to $cx$ and $cy$}
701 \cvarg{dpddist}{Optional Nx4 matrix of derivatives of image points with respect to distortion coefficients}
704 The function computes projections of 3D
705 points to the image plane given intrinsic and extrinsic camera
706 parameters. Optionally, the function computes jacobians - matrices
707 of partial derivatives of image points as functions of all the
708 input parameters with respect to the particular parameters, intrinsic and/or
709 extrinsic. The jacobians are used during the global optimization
710 in \cvCPyCross{CalibrateCamera2} and
711 \cvCPyCross{FindExtrinsicCameraParams2}. The
712 function itself is also used to compute back-projection error for with
713 current intrinsic and extrinsic parameters.
715 Note, that with intrinsic and/or extrinsic parameters set to special
716 values, the function can be used to compute just an extrinsic transformation
717 or just an intrinsic transformation (i.e. distortion of a sparse set
720 \cvCPyFunc{RQDecomp3x3}
721 Computes the `RQ' decomposition of 3x3 matrices.
724 void cvRQDecomp3x3( \par const CvMat *matrixM,\par CvMat *matrixR,\par CvMat *matrixQ,\par CvMat *matrixQx=NULL,\par CvMat *matrixQy=NULL,\par CvMat *matrixQz=NULL,\par CvPoint3D64f *eulerAngles=NULL);
725 }\cvcodePy{RQDecomp3x3(matrixM, matrixR, matrixQ, matrixQx = None, matrixQy = None, matrixQz = None) -> eulerAngles}
728 \cvarg{matrixM}{The 3x3 input matrix M}
729 \cvarg{matrixR}{The output 3x3 upper-triangular matrix R}
730 \cvarg{matrixQ}{The output 3x3 orthogonal matrix Q}
731 \cvarg{matrixQx}{Optional 3x3 rotation matrix around x-axis}
732 \cvarg{matrixQy}{Optional 3x3 rotation matrix around y-axis}
733 \cvarg{matrixQz}{Optional 3x3 rotation matrix around z-axis}
734 \cvarg{eulerAngles}{Optional 3 points containing the three Euler angles of rotation}
737 The function computes a RQ decomposition using the given rotations. This function is used in \cvCPyCross{DecomposeProjectionMatrix} to decompose the left 3x3 submatrix of a projection matrix into a calibration and a rotation matrix.
739 It optionally returns three rotation matrices, one for each axis, and the three Euler angles that could be used in OpenGL.
742 \cvCPyFunc{ReleasePOSITObject}
743 Deallocates a 3D object structure.
746 void cvReleasePOSITObject( \par CvPOSITObject** posit\_object );
750 \cvarg{posit\_object}{Double pointer to \texttt{CvPOSIT} structure}
753 The function releases memory previously allocated by the function \cvCPyCross{CreatePOSITObject}.
757 \cvCPyFunc{ReleaseStereoBMState}
758 Releases block matching stereo correspondence structure.
762 void cvReleaseStereoBMState( CvStereoBMState** state );
764 }\cvcodePy{ReleaseStereoBMState(state)-> None}
767 \cvarg{state}{Double pointer to the released structure.}
770 The function releases the stereo correspondence structure and all the associated internal buffers.
772 \cvCPyFunc{ReleaseStereoGCState}
773 Releases the state structure of the graph cut-based stereo correspondence algorithm.
777 void cvReleaseStereoGCState( CvStereoGCState** state );
779 }\cvcodePy{ReleaseStereoGCState(state)-> None}
782 \cvarg{state}{Double pointer to the released structure.}
785 The function releases the stereo correspondence structure and all the associated internal buffers.
788 \cvCPyFunc{Rodrigues2}
789 Converts a rotation matrix to a rotation vector or vice versa.
792 int cvRodrigues2( \par const CvMat* src,\par CvMat* dst,\par CvMat* jacobian=0 );
793 }\cvcodePy{Rodrigues2(src,dst,jacobian=0)-> None}
796 \cvarg{src}{The input rotation vector (3x1 or 1x3) or rotation matrix (3x3)}
797 \cvarg{dst}{The output rotation matrix (3x3) or rotation vector (3x1 or 1x3), respectively}
798 \cvarg{jacobian}{Optional output Jacobian matrix, 3x9 or 9x3 - partial derivatives of the output array components with respect to the input array components}
801 The function converts a rotation vector to a rotation matrix or vice versa. A rotation vector is a compact representation of rotation matrix. Direction of the rotation vector is the rotation axis and the length of the vector is the rotation angle around the axis. The rotation matrix $R$, corresponding to the rotation vector $r$, is computed as following:
805 \theta \leftarrow norm(r)\\
806 r \leftarrow r/\theta\\
807 R = \cos{\theta} I + (1-\cos{\theta}) r r^T + \sin{\theta}
815 Inverse transformation can also be done easily as
827 A rotation vector is a convenient representation of a rotation matrix
828 as a matrix with only 3 degrees of freedom. The representation is
829 used in the global optimization procedures inside
830 \cvCPyCross{FindExtrinsicCameraParams2}
831 and \cvCPyCross{CalibrateCamera2}.
834 \cvCPyFunc{StereoCalibrate}
835 Calibrates stereo camera.
839 void cvStereoCalibrate( \par const CvMat* object\_points, \par const CvMat* image\_points1,
840 \par const CvMat* image\_points2, \par const CvMat* point\_counts,
841 \par CvMat* camera\_matrix1, \par CvMat* dist\_coeffs1,
842 \par CvMat* camera\_matrix2, \par CvMat* dist\_coeffs2,
843 \par CvSize image\_size, \par CvMat* R, \par CvMat* T,
844 \par CvMat* E=0, \par CvMat* F=0,
845 \par CvTermCriteria term\_crit=cvTermCriteria(
846 \par CV\_TERMCRIT\_ITER+CV\_TERMCRIT\_EPS,30,1e-6),
847 \par int flags=CV\_CALIB\_FIX\_INTRINSIC );
849 }\cvcodePy{StereoCalibrate(\par object\_points,\par image\_points1,\par image\_points2,\par point\_counts,\par camera\_matrix1,\par dist\_coeffs1,\par camera\_matrix2,\par dist\_coeffs2,\par image\_size,\par R,\par T,\par E=NULL,\par F=NULL,\par term\_crit=cvTermCriteria(CV\_TERMCRIT\_ITER+CV\_TERMCRIT\_EPS,30,1e-6),\par flags=CV\_CALIB\_FIX\_INTRINSIC)-> None}
852 \cvarg{object\_points}{The joint matrix of object points, 3xN or Nx3, where N is the total number of points in all views.}
853 \cvarg{image\_points1}{The joint matrix of corresponding image points in the views from the 1st camera, 2xN or Nx2, where N is the total number of points in all views.}
854 \cvarg{image\_points2}{The joint matrix of corresponding image points in the views from the 2nd camera, 2xN or Nx2, where N is the total number of points in all views.}
855 \cvarg{point\_counts}{Vector containing numbers of points in each view, 1xM or Mx1, where M is the number of views.}
856 \cvarg{camera\_matrix1, camera\_matrix2}{The input/output camera matrices [${fx}_k 0 {cx}_k; 0 {fy}_k {cy}_k; 0 0 1$]. If \texttt{CV\_CALIB\_USE\_INTRINSIC\_GUESS} or \texttt{CV\_CALIB\_FIX\_ASPECT\_RATIO} are specified, some or all of the elements of the matrices must be initialized.}
857 \cvarg{dist\_coeffs1, dist\_coeffs2}{The input/output vectors of distortion coefficients for each camera, \href{\#Pinhole Camera Model, Distortion}{4x1, 1x4, 5x1 or 1x5.}}
858 \cvarg{image\_size}{Size of the image, used only to initialize intrinsic camera matrix.}
859 \cvarg{R}{The rotation matrix between the 1st and the 2nd cameras' coordinate systems.}
860 \cvarg{T}{The translation vector between the cameras' coordinate systems.}
861 \cvarg{E}{The optional output essential matrix.}
862 \cvarg{F}{The optional output fundamental matrix.}
863 \cvarg{term\_crit}{Termination criteria for the iterative optimiziation algorithm.}
864 \cvarg{flags}{Different flags, may be 0 or combination of the following values:
866 \cvarg{CV\_CALIB\_FIX\_INTRINSIC}{If it is set, \texttt{camera\_matrix1,2}, as well as \texttt{dist\_coeffs1,2} are fixed, so that only extrinsic parameters are optimized.}
867 \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.}
868 \cvarg{CV\_CALIB\_FIX\_PRINCIPAL\_POINT}{The principal points are fixed during the optimization.}
869 \cvarg{CV\_CALIB\_FIX\_FOCAL\_LENGTH}{${fx}_k$ and ${fy}_k$ are fixed.}
870 \cvarg{CV\_CALIB\_FIX\_ASPECT\_RATIO}{${fy}_k$ is optimized, but the ratio ${fx}_k/{fy}_k$ is fixed.}
871 \cvarg{CV\_CALIB\_SAME\_FOCAL\_LENGTH}{Enforces ${fx}_0={fx}_1$ and ${fy}_0={fy}_1$. \texttt{CV\_CALIB\_ZERO\_TANGENT\_DIST} - Tangential distortion coefficients for each camera are set to zeros and fixed there.}
872 \cvarg{CV\_CALIB\_FIX\_K1}{The 0-th distortion coefficients (k1) are fixed.}
873 \cvarg{CV\_CALIB\_FIX\_K2}{The 1-st distortion coefficients (k2) are fixed.}
874 \cvarg{CV\_CALIB\_FIX\_K3}{The 4-th distortion coefficients (k3) are fixed.}
878 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 \cvCPyCross{cvFindExtrinsicCameraParams2}), 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:
885 Optionally, it computes the essential matrix E:
896 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:
898 $F = inv(camera\_matrix2)^T*E*inv(camera\_matrix1)$
900 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 \cvCPyCross{cvCalibrateCamera2}), 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.
902 \cvCPyFunc{StereoRectify}
903 Computes rectification transform for stereo camera.
907 void cvStereoRectify( \par const CvMat* camera\_matrix1, \par const CvMat* camera\_matrix2,
908 \par const CvMat* dist\_coeffs1, \par const CvMat* dist\_coeffs2,
909 \par CvSize image\_size, \par const CvMat* R, \par const CvMat* T,
910 \par CvMat* R1, \par CvMat* R2, \par CvMat* P1, \par CvMat* P2,
911 \par CvMat* Q=0, \par int flags=CV\_CALIB\_ZERO\_DISPARITY );
913 }\cvcodePy{StereoRectify(\par camera\_matrix1,\par camera\_matrix2,\par dist\_coeffs1,\par dist\_coeffs2,\par image\_size,\par R,\par T,\par R1,\par R2,\par P1,\par P2,\par Q=NULL,\par flags=CV\_CALIB\_ZERO\_DISPARITY)-> None}
916 \cvarg{camera\_matrix1, camera\_matrix2}{The camera matrices [${fx}_k$ 0 ${cx}_k$; 0 ${fy}_k$ ${cy}_k$; 0 0 1].}
917 \cvarg{dist\_coeffs1, dist\_coeffs2}{The vectors of distortion coefficients for each camera, \href{\#Pinhole Camera Model, Distortion}{4x1, 1x4, 5x1 or 1x5.}}
918 \cvarg{image\_size}{Size of the image used for stereo calibration.}
919 \cvarg{R}{The rotation matrix between the 1st and the 2nd cameras' coordinate systems.}
920 \cvarg{T}{The translation vector between the cameras' coordinate systems.}
921 \cvarg{R1, R2}{3x3 Rectification transforms (rotation matrices) for the first and the second cameras, respectively.}
922 \cvarg{P1, P2}{3x4 Projection matrices in the new (rectified) coordinate systems.}
923 \cvarg{Q}{The optional output disparity-to-depth mapping matrix, 4x4, see \cvCPyCross{cvReprojectImageTo3D}.}
924 \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 can shift one of the image in horizontal or vertical direction (depending on the orientation of epipolar lines) in order to maximise the useful image area. }
927 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 \cvCPyCross{cvStereoCalibrate} and on output it gives 2 rotation matrices and also 2 projection matrices in the new coordinates. The function is normally called after \cvCPyCross{cvStereoCalibrate} that computes both camera matrices, the distortion coefficients, R and T. The 2 cases are distinguished by the function:
930 \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:
950 where $T_x$ is horizontal shift between the cameras and cx1=cx2 if \texttt{CV\_CALIB\_ZERO\_DISPARITY} is set.}
951 \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:
971 where $T_y$ is vertical shift between the cameras and cy1=cy2 if \texttt{CV\_CALIB\_ZERO\_DISPARITY} is set.}
974 As you can see, the first 3 columns of P1 and P2 will effectively be the new "rectified" camera matrices.
976 \cvCPyFunc{StereoRectifyUncalibrated}
977 Computes rectification transform for uncalibrated stereo camera.
981 void cvStereoRectifyUncalibrated( \par const CvMat* points1, \par const CvMat* points2,
982 \par const CvMat* F, \par CvSize image\_size,
983 \par CvMat* H1, \par CvMat* H2,
984 \par double threshold=5 );
986 }\cvcodePy{StereoRectifyUncalibrated(points1,points2,F,image\_size,H1,H2,threshold=5)-> None}
989 \cvarg{points1, points2}{The 2 arrays of corresponding 2D points.}
990 \cvarg{F}{Fundamental matrix. It can be computed using the same set of point pairs points1 and points2 using \cvCPyCross{cvFindFundamentalMat}.}
991 \cvarg{image\_size}{Size of the image.}
992 \cvarg{H1, H2}{The rectification homography matrices for the first and for the second images.}
993 \cvarg{threshold}{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 $fabs(points2[i]^T*F*points1[i])>threshold$) are rejected prior to computing the homographies. }
996 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 \cvCPyCross{cvStereoRectify} 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 following algorithm \href{\#Hartly99}{[Hartley99]}.
998 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 \cvCPyCross{cvCalibrateCamera2} and then the images can be corrected using \cvCPyCross{cvUndistort2}.
1000 \cvCPyFunc{UndistortPoints}
1001 Computes the ideal point coordinates from the observed point coordinates.
1005 void cvUndistortPoints( \par const CvMat* src, \par CvMat* dst,
1006 \par const CvMat* camera\_matrix,
1007 \par const CvMat* dist\_coeffs,
1008 \par const CvMat* R=NULL,
1009 \par const CvMat* P=NULL);
1011 }\cvcodePy{UndistortPoints(src,dst,camera\_matrix,dist\_coeffs,R=NULL,P=NULL)-> None}
1014 \cvarg{src}{The observed point coordinates}
1015 \cvarg{dst}{The ideal point coordinates, after undistortion and reverse perspective transformation}
1016 \cvarg{camera\_matrix}{The camera matrix $A=[fx 0 cx; 0 fy cy; 0 0 1]$}
1017 \cvarg{dist\_coeffs}{he vector of distortion coefficients, \cvCPyCross{4x1, 1x4, 5x1 or 1x5}}
1018 \cvarg{R}{The rectification transformation in object space (3x3 matrix). \texttt{R1} or \texttt{R2}, computed by \cvCPyCross{StereoRectify} can be passed here. If the parameter is NULL, the identity matrix is used}
1019 \cvarg{P}{The new camera matrix (3x3) or the new projection matrix (3x4). \texttt{P1} or \texttt{P2}, computed by \cvCPyCross{StereoRectify} can be passed here. If the parameter is NULL, the identity matrix is used}
1022 The function is similar to \cvCPyCross{InitUndistortRectifyMap} and is opposite to it at the same time. The functions are similar in that they both are used to correct lens distortion and to perform the optional perspective (rectification) transformation. They are opposite because the function \cvCPyCross{InitUndistortRectifyMap} does actually perform the reverse transformation in order to initialize the maps properly, while this function does the forward transformation. That is, in pseudo-code it can be expressed as:
1025 // (u,v) is the input point, (u', v') is the output point
1026 // camera_matrix=[fx 0 cx; 0 fy cy; 0 0 1]
1027 // P=[fx' 0 cx' tx; 0 fy' cy' ty; 0 0 1 tz]
1030 (x',y') = undistort(x",y",dist_coeffs)
1031 [X,Y,W]T = R*[x' y' 1]T
1037 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).
1039 The function can be used as for stereo cameras, as well as for individual cameras when R=NULL.
1046 \cvCppFunc{calibrateCamera}
1047 Finds the camera matrix and the camera poses from several views of the calibration pattern.
1050 void calibrateCamera( const vector<vector<Point3f> >& objectPoints,
1051 const vector<vector<Point2f> >& imagePoints,
1053 Mat& cameraMatrix, Mat& distCoeffs,
1054 vector<Mat>& rvecs, vector<Mat>& tvecs,
1058 CALIB_USE_INTRINSIC_GUESS = CV_CALIB_USE_INTRINSIC_GUESS,
1059 CALIB_FIX_ASPECT_RATIO = CV_CALIB_FIX_ASPECT_RATIO,
1060 CALIB_FIX_PRINCIPAL_POINT = CV_CALIB_FIX_PRINCIPAL_POINT,
1061 CALIB_ZERO_TANGENT_DIST = CV_CALIB_ZERO_TANGENT_DIST,
1062 CALIB_FIX_FOCAL_LENGTH = CV_CALIB_FIX_FOCAL_LENGTH,
1063 CALIB_FIX_K1 = CV_CALIB_FIX_K1,
1064 CALIB_FIX_K2 = CV_CALIB_FIX_K2,
1065 CALIB_FIX_K3 = CV_CALIB_FIX_K3,
1067 CALIB_FIX_INTRINSIC = CV_CALIB_FIX_INTRINSIC,
1068 CALIB_SAME_FOCAL_LENGTH = CV_CALIB_SAME_FOCAL_LENGTH,
1069 // for stereo rectification
1070 CALIB_ZERO_DISPARITY = CV_CALIB_ZERO_DISPARITY
1075 \cvarg{objectPoints}{The vector of vectors of points on the calibration rig in its coordinate system, one vector per a view of the rig. If the the same calibration rig is shown in each view and it's fully visible, all the vectors can be the same (though, you may change the numbering from one view to another). The points are 3D, but since they are in the rig 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}
1076 \cvarg{imagePoints}{The vector of vectors of the object point projections on the calibration rig views, one vector per a view. The projections must be in the same order as the corresponding object points.}
1077 \cvarg{imageSize}{Size of the image, used only to initialize the intrinsic camera matrix}
1078 \cvarg{cameraMatrix}{The input/output matrix of intrinsic camera parameters $A = \vecthreethree{fx}{0}{cx}{0}{fy}{cy}{0}{0}{1}$. If any of \texttt{CALIB\_USE\_INTRINSIC\_GUESS}, \texttt{CALIB\_FIX\_ASPECT\_RATIO}, \texttt{CALIB\_FIX\_FOCAL\_LENGTH} are specified, some or all of \texttt{fx, fy, cx, cy} must be initialized}
1079 \cvarg{distCoeffs}{The input/output lens distortion coefficients, 4x1, 5x1, 1x4 or 1x5 floating-point vector $k_1, k_2, p_1, p_2[, k_3]$. If any of \texttt{CALIB\_FIX\_K1}, \texttt{CALIB\_FIX\_K2} or \texttt{CALIB\_FIX\_K3} is specified, then the corresponding elements of \texttt{distCoeffs} must be initialized.}
1080 \cvarg{rvecs}{The output vector of rotation vectors (see \cvCppCross{Rodrigues}) estimated for each camera view}
1081 \cvarg{tvecsrans}{The output vector of translation vectors estimated for each camera view}
1082 \cvarg{flags}{Different flags, may be 0 or a combination of the following values:
1084 \cvarg{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 (computed from the input \texttt{imageSize}), and focal distances are computed in some least-squares fashion. Note, that if the focal distance initialization is currently supported only for planar calibration rigs. That is, if the calibration rig is 3D, then you must initialize \texttt{cameraMatrix} and pass \texttt{CALIB\_USE\_INTRINSIC\_GUESS} flag. Also, note that distortion coefficients are not regulated by this function; use \texttt{CALIB\_ZERO\_TANGENT\_DIST} and \texttt{CALIB\_FIX\_K?} to fix them}
1085 \cvarg{CALIB\_FIX\_PRINCIPAL\_POINT}{The principal point is not changed during the global optimization, it stays at the center or, when \texttt{CALIB\_USE\_INTRINSIC\_GUESS} is set too, at the other specified location}
1086 \cvarg{CALIB\_FIX\_ASPECT\_RATIO}{The optimization procedure considers only one of \texttt{fx} and \texttt{fy} as independent variables and keeps the aspect ratio \texttt{fx/fy} the same as it was set initially in the input \texttt{cameraMatrix}. In this case the actual initial values of \texttt{(fx, fy)} are either taken from the matrix (when \texttt{CALIB\_USE\_INTRINSIC\_GUESS} is set) or estimated.}
1087 \cvarg{CALIB\_ZERO\_TANGENT\_DIST}{Tangential distortion coefficients are set to zeros and do not change during the optimization.}
1088 \cvarg{CALIB\_FIX\_FOCAL\_LENGTH}{Both \texttt{fx} and \texttt{fy} are fixed (taken from \texttt{cameraMatrix} and do not change during the optimization.}
1089 \cvarg{CALIB\_FIX\_K1, CALIB\_FIX\_K2, CALIB\_FIX\_K3}{The particular distortion coefficients is read from the input \texttt{distCoeffs} and stays the same during optimization}
1093 The function estimates the intrinsic camera
1094 parameters and the extrinsic parameters for each of the views. The
1095 coordinates of 3D object points and their correspondent 2D projections
1096 in each view must be specified. You can use a calibration rig with a known geometry and easily and precisely detectable feature points, e.g. a checkerboard (see \cvCppCross{findChessboardCorners}).
1098 The algorithm does the following:
1100 \item First, it computes the initial intrinsic parameters (only for planar calibration rigs) or reads them from the input parameters. The distortion coefficients are all set to zeros initially (unless some of \texttt{CALIB\_FIX\_K?} are specified).
1101 \item The the initial camera pose is estimated as if the intrinsic parameters have been already known. This is done using \cvCppCross{solvePnP}
1102 \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 \cvCppCross{projectPoints}.
1105 Note: if you're using a non-square (=non-NxN) grid and
1106 \cvCppCross{findChessboardCorners} for calibration, and \texttt{calibrateCamera} returns
1107 bad values (i.e. zero distortion coefficients, an image center very far from
1108 $(w/2-0.5,h/2-0.5)$, and / or large differences between $f_x$ and $f_y$ (ratios of
1109 10:1 or more)), then you've probaby used \texttt{patternSize=cvSize(rows,cols)},
1110 but should use \texttt{patternSize=cvSize(cols,rows)} in \cvCppCross{findChessboardCorners}.
1112 See also: \cvCppCross{findChessboardCorners}, \cvCppCross{solvePnP}, \cvCppCross{initCameraMatrix2D}, \cvCppCross{stereoCalibrate}, \cvCppCross{undistort}
1115 \cvCppFunc{calibrationMatrixValues}
1116 Computes some useful camera characteristics from the camera matrix
1119 void calibrationMatrixValues( const Mat& cameraMatrix,
1121 double apertureWidth,
1122 double apertureHeight,
1125 double& focalLength,
1126 Point2d& principalPoint,
1127 double& aspectRatio );
1130 \cvarg{cameraMatrix}{The input camera matrix that can be estimated by \cvCppCross{calibrateCamera} or \cvCppCross{stereoCalibrate}}
1131 \cvarg{imageSize}{The input image size in pixels}
1132 \cvarg{apertureWidth}{Physical width of the sensor}
1133 \cvarg{apertureHeight}{Physical height of the sensor}
1134 \cvarg{fovx}{The output field of view in degrees along the horizontal sensor axis}
1135 \cvarg{fovy}{The output field of view in degrees along the vertical sensor axis}
1136 \cvarg{focalLength}{The focal length of the lens in mm}
1137 \cvarg{prinicialPoint}{The principal point in pixels}
1138 \cvarg{aspectRatio}{$f_y/f_x$}
1141 The function computes various useful camera characteristics from the previously estimated camera matrix.
1143 \cvCppFunc{composeRT}
1144 Combines two rotation-and-shift transformations
1147 void composeRT( const Mat& rvec1, const Mat& tvec1,
1148 const Mat& rvec2, const Mat& tvec2,
1149 Mat& rvec3, Mat& tvec3 );
1151 void composeRT( const Mat& rvec1, const Mat& tvec1,
1152 const Mat& rvec2, const Mat& tvec2,
1153 Mat& rvec3, Mat& tvec3,
1154 Mat& dr3dr1, Mat& dr3dt1,
1155 Mat& dr3dr2, Mat& dr3dt2,
1156 Mat& dt3dr1, Mat& dt3dt1,
1157 Mat& dt3dr2, Mat& dt3dt2 );
1160 \cvarg{rvec1}{The first rotation vector}
1161 \cvarg{tvec1}{The first translation vector}
1162 \cvarg{rvec2}{The second rotation vector}
1163 \cvarg{tvec2}{The second translation vector}
1164 \cvarg{rvec3}{The output rotation vector of the superposition}
1165 \cvarg{tvec3}{The output translation vector of the superposition}
1166 \cvarg{d??d??}{The optional output derivatives of \texttt{rvec3} or \texttt{tvec3} w.r.t. \texttt{rvec?} or \texttt{tvec?}}
1169 The functions compute:
1172 \texttt{rvec3} = \mathrm{rodrigues}^{-1}\left(\mathrm{rodrigues}(\texttt{rvec2}) \cdot
1173 \mathrm{rodrigues}(\texttt{rvec1})\right) \\
1174 \texttt{tvec3} = \mathrm{rodrigues}(\texttt{rvec2}) \cdot \texttt{tvec1} + \texttt{tvec2}
1177 where $\mathrm{rodrigues}$ denotes a rotation vector to rotation matrix transformation, and $\mathrm{rodrigues}^{-1}$ denotes the inverse transformation, see \cvCppCross{Rodrigues}.
1179 Also, the functions can compute the derivatives of the output vectors w.r.t the input vectors (see \cvCppCross{matMulDeriv}).
1180 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.
1183 \cvCppFunc{computeCorrespondEpilines}
1184 For points in one image of a stereo pair, computes the corresponding epilines in the other image.
1187 void computeCorrespondEpilines( const Mat& points,
1188 int whichImage, const Mat& F,
1189 vector<Vec3f>& lines );
1192 \cvarg{points}{The input points. $N \times 1$ or $1 \times N$ matrix of type \texttt{CV\_32FC2} or \texttt{vector<Point2f>}}
1193 \cvarg{whichImage}{Index of the image (1 or 2) that contains the \texttt{points}}
1194 \cvarg{F}{The fundamental matrix that can be estimated using \cvCppCross{findFundamentalMat} or \texttt{stereoRectify}}
1195 \cvarg{lines}{The output vector of the corresponding to the points epipolar lines in the other image. Each line $ax + by + c=0$ is encoded as 3-element vector $(a, b, c)$}
1198 For every point in one of the two images of a stereo-pair the function
1199 \texttt{computeCorrespondEpilines} finds the equation of the
1200 corresponding epipolar line in the other image.
1202 From the fundamental matrix definition (see \cvCppCross{findFundamentalMatrix}),
1203 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:
1205 \[ l^{(2)}_i = F p^{(1)}_i \]
1207 and, vice versa, when \texttt{whichImage=2}, $l^{(1)}_i$ is computed from $p^{(2)}_i$ as:
1209 \[ l^{(1)}_i = F^T p^{(2)}_i \]
1211 Line coefficients are defined up to a scale. They are normalized, such that $a_i^2+b_i^2=1$.
1213 \cvCppFunc{convertPointHomogeneous}
1214 Converts 2D points to/from homogeneous coordinates.
1217 void convertPointsHomogeneous( const Mat& src, vector<Point3f>& dst );
1218 void convertPointsHomogeneous( const Mat& src, vector<Point2f>& dst );
1220 \cvarg{src}{The input array or vector of 2D or 3D points}
1221 \cvarg{dst}{The output vector of 3D or 2D points, respectively}
1224 The first of the functions converts 2D points to the homogeneous coordinates by adding extra \texttt{1} component to each point. When the input vector already contains 3D points, it is simply copied to \texttt{dst}. The second function converts 3D points to 2D points by dividing 1st and 2nd components by the 3rd one. If the input vector already contains 2D points, it is simply copied to \texttt{dst}.
1226 \cvCppFunc{decomposeProjectionMatrix}
1227 Decomposes the projection matrix into a rotation matrix and a camera matrix.
1230 void decomposeProjectionMatrix( const Mat& projMatrix, Mat& cameraMatrix,
1231 Mat& rotMatrix, Mat& transVect );
1232 void decomposeProjectionMatrix( const Mat& projMatrix, Mat& cameraMatrix,
1233 Mat& rotMatrix, Mat& transVect,
1234 Mat& rotMatrixX, Mat& rotMatrixY,
1235 Mat& rotMatrixZ, Vec3d& eulerAngles );
1238 \cvarg{projMatrix}{The input $3 \times 4$ projection matrix}
1239 \cvarg{cameraMatrix}{The output $3 \times 3$ camera matrix}
1240 \cvarg{rotMatrix}{The output $3 \times 3$ rotation matrix}
1241 \cvarg{transVect}{The output $3 \times 1$ translation vector}
1242 \cvarg{rotMatrixX}{The optional output rotation matrix around x-axis}
1243 \cvarg{rotMatrixY}{The optional output rotation matrix around y-axis}
1244 \cvarg{rotMatrixZ}{The optional output rotation matrix around z-axis}
1245 \cvarg{eulerAngles}{The optional output 3-vector of the Euler rotation angles}
1248 The function computes a decomposition of a projection matrix into a calibration and a rotation matrix and the position of the camera.
1250 It optionally returns three rotation matrices, one for each axis, and the three Euler angles that could be used in OpenGL.
1252 The function is based on \cvCppCross{RQDecomp3x3}.
1254 \cvCppFunc{drawChessboardCorners}
1255 Draws the detected chessboard corners.
1258 void drawChessboardCorners( Mat& image, Size patternSize,
1260 bool patternWasFound );
1263 \cvarg{image}{The destination image; it must be an 8-bit color image}
1264 \cvarg{patternSize}{The number of inner corners per chessboard row and column, i.e. \texttt{Size(<corners per row>, <corners per column>)}}
1265 \cvarg{corners}{The array of detected corners; \texttt{vector<Point2f>} can be passed here as well}
1266 \cvarg{patternWasFound}{Indicates whether the complete board was found. Just pass the return value of \cvCppCross{findChessboardCorners} here}
1269 The function draws the detected chessboard corners. If no complete board was found, the detected corners will be marked with small red circles. Otherwise, a colored board (each board row with a different color) will be drawn.
1271 \cvCppFunc{findFundamentalMat}
1272 Calculates the fundamental matrix from the corresponding points in two images.
1275 Mat findFundamentalMat( const Mat& points1, const Mat& points2,
1276 vector<uchar>& mask, int method=FM_RANSAC,
1277 double param1=3., double param2=0.99 );
1279 Mat findFundamentalMat( const Mat& points1, const Mat& points2,
1280 int method=FM_RANSAC,
1281 double param1=3., double param2=0.99 );
1285 FM_7POINT = CV_FM_7POINT,
1286 FM_8POINT = CV_FM_8POINT,
1287 FM_LMEDS = CV_FM_LMEDS,
1288 FM_RANSAC = CV_FM_RANSAC
1292 \cvarg{points1}{Array of $N$ points in the first image, a matrix of \texttt{CV\_32FC2} type or \texttt{vector<Point2f>}. The points in homogeneous coordinates can also be passed.}
1293 \cvarg{points2}{Array of the corresponding points in the second image of the same size and the same type as \texttt{points1}}
1294 \cvarg{method}{Method for computing the fundamental matrix
1296 \cvarg{FM\_7POINT}{for a 7-point algorithm. $N = 7$}
1297 \cvarg{FM\_8POINT}{for an 8-point algorithm. $N \ge 8$}
1298 \cvarg{FM\_RANSAC}{for the RANSAC algorithm. $N \ge 8$}
1299 \cvarg{FM\_LMEDS}{for the LMedS algorithm. $N \ge 8$}
1301 \cvarg{param1}{The parameter is used for RANSAC only. It is the maximum distance in pixels 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}
1302 \cvarg{param2}{The parameter is used for RANSAC or LMedS methods only. It denotes the desirable level of confidence (between 0 and 1) that the estimated matrix is correct}
1303 \cvarg{mask}{The 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. Other methods set every element to 1}
1306 The epipolar geometry is described by the following equation:
1308 \[ [p_2; 1]^T F [p_1; 1] = 0 \]
1310 where $F$ is fundamental matrix, $p_1$ and $p_2$ are corresponding points in the first and the second images, respectively.
1312 The function calculates the fundamental
1313 matrix using one of four methods listed above and returns the found fundamental matrix. In the case of \texttt{FM\_7POINT} the function may return a $9 \times 3$ matrix. It means that the 3 fundamental matrices are possible and they are all found and stored sequentially.
1315 The calculated fundamental matrix may be passed further to
1316 \texttt{computeCorrespondEpilines} that finds the epipolar lines
1317 corresponding to the specified points. It can also be passed to \cvCppCross{stereoRectifyUncalibrated} to compute the rectification transformation.
1320 // Example. Estimation of fundamental matrix using RANSAC algorithm
1321 int point_count = 100;
1322 vector<Point2f> points1(point_count);
1323 vector<Point2f> points2(point_count);
1325 // initialize the points here ... */
1326 for( int i = 0; i < point_count; i++ )
1332 Mat fundamental_matrix =
1333 findFundamentalMat(points1, points2, FM_RANSAC, 3, 0.99);
1337 \cvCppFunc{findChessboardCorners}
1338 Finds the positions of the internal corners of the chessboard.
1341 bool findChessboardCorners( const Mat& image, Size patternSize,
1342 vector<Point2f>& corners,
1343 int flags=CV_CALIB_CB_ADAPTIVE_THRESH+
1344 CV_CALIB_CB_NORMALIZE_IMAGE );
1345 enum { CALIB_CB_ADAPTIVE_THRESH = CV_CALIB_CB_ADAPTIVE_THRESH,
1346 CALIB_CB_NORMALIZE_IMAGE = CV_CALIB_CB_NORMALIZE_IMAGE,
1347 CALIB_CB_FILTER_QUADS = CV_CALIB_CB_FILTER_QUADS };
1350 \cvarg{image}{The input chessboard (a.k.a. checkerboard) view; it must be an 8-bit grayscale or color image}
1351 \cvarg{patternSize}{The number of inner corners per chessboard row and column, i.e.
1352 \texttt{patternSize = cvSize(<points per row>, <points per column>)}}
1353 \cvarg{corners}{The output vector of the corners detected. If the board is found (the function returned true), the corners should be properly ordered.}
1354 \cvarg{flags}{Various operation flags, can be 0 or a combination of the following values:
1356 \cvarg{CALIB\_CB\_ADAPTIVE\_THRESH}{use adaptive thresholding, instead of a fixed-level threshold, to convert the image to black and white rather than a fixed threshold level}
1357 \cvarg{CALIB\_CB\_NORMALIZE\_IMAGE}{normalize the image brightness and contrast using \cvCppCross{equalizeHist} before applying fixed or adaptive thresholding}
1358 \cvarg{CALIB\_CB\_FILTER\_QUADS}{use some additional criteria (like contour area, perimeter, square-like shape) to filter out false quads that are extracted at the contour retrieval stage. Since the current corner grouping engine is smart enough, usually this parameter is omitted.}
1362 The function attempts to determine
1363 whether the input image is a view of the chessboard pattern and, if yes,
1364 locate the internal chessboard corners. The function returns true if all
1365 of the chessboard corners have been found and they have been placed
1366 in a certain order (row by row, left to right in every row),
1367 otherwise, if the function fails to find all the corners or reorder
1368 them, it returns 0. For example, a regular chessboard has 8 x 8
1369 squares and 7 x 7 internal corners, that is, points, where the black
1370 squares touch each other. The coordinates detected are approximate,
1371 and to determine their position more accurately, the user may use
1372 the function \cvCppCross{cornerSubPix} or other subpixel adjustment technique.
1374 Sometimes the function fails to find the board because the image is too large or too small. If so, try to resize it and then scale the found corners coordinates back (or even scale the computed \texttt{cameraMatrix} back).
1377 \cvCppFunc{getDefaultNewCameraMatrix}
1378 Returns the default new camera matrix
1381 Mat getDefaultNewCameraMatrix( const Mat& cameraMatrix, Size imgSize=Size(),
1382 bool centerPrincipalPoint=false );
1385 \cvarg{cameraMatrix}{The input camera matrix}
1386 \cvarg{imageSize}{The camera view image size in pixels}
1387 \cvarg{centerPrincipalPoint}{Indicates whether in the new camera matrix the principal point should be at the image center or not}
1390 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).
1392 In the latter case the new camera matrix will be:
1395 f_x && 0 && (\texttt{imgSize.width}-1)*0.5 \\
1396 0 && f_y && (\texttt{imgSize.height}-1)*0.5 \\
1400 where $f_x$ and $f_y$ are $(0,0)$ and $(1,1)$ elements of \texttt{cameraMatrix}, respectively.
1402 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.
1404 \cvCppFunc{initCameraMatrix2D}
1405 Finds the initial camera matrix from the 3D-2D point correspondences
1408 Mat initCameraMatrix2D( const vector<vector<Point3f> >& objectPoints,
1409 const vector<vector<Point2f> >& imagePoints,
1410 Size imageSize, double aspectRatio=1. );
1413 \cvarg{objectPoints}{The vector of vectors of the object points. See \cvCppCross{calibrateCamera}}
1414 \cvarg{imagePoints}{The vector of vectors of the corresponding image points. See \cvCppCross{calibrateCamera}}
1415 \cvarg{imageSize}{The image size in pixels; used to initialize the principal point}
1416 \cvarg{aspectRatio}{If it is zero or negative, both $f_x$ and $f_y$ are estimated independently. Otherwise $f_x = f_y * \texttt{aspectRatio}$}
1419 The function estimates and returns the initial camera matrix for camera calibration process.
1420 Currently, the function only supports planar calibration rigs, i.e. the rig for which the $3 \times 3$ covariance matrix of object points is singular.
1423 \cvCppFunc{Rodrigues}
1424 Converts a rotation matrix to a rotation vector or vice versa.
1427 void Rodrigues(const Mat& src, Mat& dst);
1428 void Rodrigues(const Mat& src, Mat& dst, Mat& jacobian);
1432 \cvarg{src}{The input rotation vector (3x1 or 1x3) or a rotation matrix (3x3)}
1433 \cvarg{dst}{The output rotation matrix (3x3) or a rotation vector (3x1 or 1x3), respectively}
1434 \cvarg{jacobian}{The optional output Jacobian matrix, 3x9 or 9x3 - partial derivatives of the output array components with respect to the input array components}
1437 The functions convert a rotation vector to a rotation matrix or vice versa. A rotation vector is a compact representation of rotation matrix. Direction of the rotation vector is the rotation axis and the length of the vector is the rotation angle around the axis. The rotation matrix $R$, corresponding to the rotation vector $r$, is computed as following:
1441 \theta \leftarrow norm(r)\\
1442 r \leftarrow r/\theta\\
1443 R = \cos{\theta} I + (1-\cos{\theta}) r r^T + \sin{\theta}
1451 Inverse transformation can also be done easily, since
1463 A rotation vector is a convenient and most-compact representation of a rotation matrix
1464 (since any rotation matrix has just 3 degrees of freedom). The representation is
1465 used in the global 3D geometry optimization procedures like \cvCppCross{calibrateCamera}, \cvCppCross{stereoCalibrate} or \cvCppCross{solvePnP}.
1468 \cvCppFunc{RQDecomp3x3}
1469 Computes the 'RQ' decomposition of 3x3 matrices.
1472 /* Computes RQ decomposition for 3x3 matrices */
1473 void RQDecomp3x3( const Mat& M, Mat& R, Mat& Q );
1474 Vec3d RQDecomp3x3( const Mat& M, Mat& R, Mat& Q,
1475 Mat& Qx, Mat& Qy, Mat& Qz );
1478 \cvarg{M}{The input $3 \times 3$ floating-point matrix}
1479 \cvarg{R}{The output $3 \times 3$ upper-triangular matrix}
1480 \cvarg{Q}{The output $3 \times 3$ orthogonal matrix}
1481 \cvarg{Qx, Qy, Qz}{The optional output matrices that decompose the rotation matrix Q into separate rotation matrices for each coordinate axis}
1484 The function implements RQ decomposition of a $3 \times 3$ matrix. The function is by \cvCppCross{decomposeProjectionMatrix}.
1486 \cvCppFunc{matMulDeriv}
1487 Computes partial derivatives of the matrix product w.r.t each multiplied matrix
1490 void matMulDeriv( const Mat& A, const Mat& B, Mat& dABdA, Mat& dABdB );
1493 \cvarg{A}{The first multiplied matrix}
1494 \cvarg{B}{The second multiplied matrix}
1495 \cvarg{dABdA}{The first output derivative matrix \texttt{d(A*B)/dA} of size $\texttt{A.rows*B.cols} \times {A.rows*A.cols}$}
1496 \cvarg{dABdA}{The second output derivative matrix \texttt{d(A*B)/dB} of size $\texttt{A.rows*B.cols} \times {B.rows*B.cols}$}
1499 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.
1501 \cvCppFunc{projectPoints}
1502 Projects 3D points on to an image plane.
1505 void projectPoints( const Mat& objectPoints,
1506 const Mat& rvec, const Mat& tvec,
1507 const Mat& cameraMatrix,
1508 const Mat& distCoeffs,
1509 vector<Point2f>& imagePoints );
1511 void projectPoints( const Mat& objectPoints,
1512 const Mat& rvec, const Mat& tvec,
1513 const Mat& cameraMatrix,
1514 const Mat& distCoeffs,
1515 vector<Point2f>& imagePoints,
1516 Mat& dpdrot, Mat& dpdt, Mat& dpdf,
1517 Mat& dpdc, Mat& dpddist,
1518 double aspectRatio=0 );
1521 \cvarg{objectPoints}{The input array of 3D object points, a matrix of type \texttt{CV\_32FC3} or \texttt{vector<Point3f>}}
1522 \cvarg{imagePoints}{The output array of 2D image points}
1523 \cvarg{rvec}{The rotation vector, 1x3 or 3x1}
1524 \cvarg{tvec}{The translation vector, 1x3 or 3x1}
1525 \cvarg{cameraMatrix}{The camera matrix $\vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}$}
1526 \cvarg{distCoeffs}{The array of distortion coefficients, 4x1, 5x1, 1x4 or 1x5 $k_1, k_2, p_1, p_2[, k_3]$. If the matrix is empty, the function uses zero distortion coefficients}
1527 \cvarg{dpdrot, dpdt, dpdf, dpdc, dpdist}{The optional matrices of the partial derivatives of the computed point projections w.r.t the rotation vector, the translation vector, $f_x$ and $f_y$, $c_x$ and $c_y$ and the distortion coefficients respectively. Each matrix has $2*N$ rows (where $N$ is the number of points) - even rows (0th, 2nd ...) are the derivatives of the x-coordinates w.r.t. the camera parameters and odd rows (1st, 3rd ...) are the derivatives of the y-coordinates.}
1528 \cvarg{aspectRatio}{If zero or negative, $f_x$ and $f_y$ are treated as independent variables, otherwise they $f_x = f_y*\texttt{aspectRatio}$, so the derivatives are adjusted appropriately}
1531 The function computes projections of 3D
1532 points to the image plane given intrinsic and extrinsic camera
1533 parameters. Optionally, the function computes jacobians - matrices
1534 of partial derivatives of image points as functions of all the
1535 input parameters with respect to the particular camera parameters, intrinsic and/or
1536 extrinsic. The computed jacobians are used during the global optimization
1537 in \cvCppCross{calibrateCamera}, \cvCppCross{stereoCalibrate} and \cvCppCross{solvePnP}.
1539 Note, that by setting \texttt{rvec=tvec=(0,0,0)} or by setting \texttt{cameraMatrix=Mat::eye(3,3,CV\_64F)} or by setting \texttt{distCoeffs=Mat()} you can get various useful partial cases of the function, i.e. you can computed 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.
1541 \cvCppFunc{reprojectImageTo3D}
1542 Reprojects disparity image to 3D space.
1545 void reprojectImageTo3D( const Mat& disparity,
1546 Mat& _3dImage, const Mat& Q,
1547 bool handleMissingValues=false );
1550 \cvarg{disparity}{The input single-channel 16-bit signed or 32-bit floating-point disparity image}
1551 \cvarg{\_3dImage}{The output 3-channel floating-point image of the same size as \texttt{disparity}.
1552 Each element of \texttt{\_3dImage(x,y)} will contain the 3D coordinates of the point \texttt{(x,y)}, computed from the disparity map.}
1553 \cvarg{Q}{The $4 \times 4$ perspective transformation matrix that can be obtained with \cvCppCross{stereoRectify}}
1554 \cvarg{handleMissingValues}{If true, when the pixels with the minimal disparity (that corresponds to the ouliers; see \cvCppCross{StereoBM}) will be transformed to 3D points with some very large Z value (currently set to 10000)}
1557 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:
1560 [X\; Y\; Z\; W]^T = \texttt{Q}*[x\; y\; \texttt{disparity}(x,y)\; 1]^T \\
1561 \texttt{\_3dImage}(x,y) = (X/W,\; Y/W,\; Z/W)
1564 The matrix \texttt{Q} can be arbitrary $4 \times 4$ matrix, e.g. the one computed by \cvCppCross{stereoRectify}. To reproject a sparse set of points {(x,y,d),...} to 3D space, use \cvCppCross{perspectiveTransform}.
1567 \cvCppFunc{solvePnP}
1568 Finds the camera pose from the 3D-2D point correspondences
1571 void solvePnP( const Mat& objectPoints,
1572 const Mat& imagePoints,
1573 const Mat& cameraMatrix,
1574 const Mat& distCoeffs,
1575 Mat& rvec, Mat& tvec,
1576 bool useExtrinsicGuess=false );
1579 \cvarg{objectPoints}{The array of object points, a matrix of type \texttt{CV\_32FC3} or \texttt{vector<Point3f>}}
1580 \cvarg{imagePoints}{The array of the corresponding image points, a matrix of type{CV\_32FC2} or \texttt{vector<Point2f>}}
1581 \cvarg{cameraMatrix}{The input camera matrix $\vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}$}
1582 \cvarg{distCoeffs}{The input 4x1, 5x1, 1x4 or 1x5 array of distortion coefficients $(k_1, k_2, p_1, p_2[, k3])$. If it is NULL, all of the distortion coefficients are set to 0}
1583 \cvarg{rvec}{The output camera view rotation vector (compact representation of a rotation matrix, \cvCppCross{Rodrigues} that (together with \texttt{tvec}) brings points from the model coordinate system to the camera coordinate system}
1584 \cvarg{tvec}{The output camera view translation vector}
1587 The function estimates the camera 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 back-projection error, i.e. the sum of squared distances between the observed projections \texttt{imagePoints} and the projected with \cvCppCross{projectPoints} \texttt{objectPoints}.
1589 \cvCppFunc{stereoCalibrate}
1590 Calibrates stereo camera.
1593 void stereoCalibrate( const vector<vector<Point3f> >& objectPoints,
1594 const vector<vector<Point2f> >& imagePoints1,
1595 const vector<vector<Point2f> >& imagePoints2,
1596 Mat& cameraMatrix1, Mat& distCoeffs1,
1597 Mat& cameraMatrix2, Mat& distCoeffs2,
1598 Size imageSize, Mat& R, Mat& T,
1600 TermCriteria criteria = TermCriteria(TermCriteria::COUNT+
1601 TermCriteria::EPS, 30, 1e-6),
1602 int flags=CALIB_FIX_INTRINSIC );
1605 \cvarg{objectPoints}{The vector of vectors of points on the calibration rig in its coordinate system, one vector per a view of the rig. See \cvCppCross{calibrateCamera}}
1606 \cvarg{imagePoints1}{The vector of vectors of the object point projections to the first camera views, one vector per a view. The projections must be in the same order as the corresponding object points.}
1607 \cvarg{imagePoints2}{The vector of vectors of the object point projections to the second camera views, one vector per a view. The projections must be in the same order as the corresponding object points.}
1608 \cvarg{imageSize}{Size of the image, used only to initialize the intrinsic camera matrices}
1609 \cvarg{cameraMatrix1, cameraMatrix2}{The input/output first and second camera matrices, respectively: $ \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{CALIB\_USE\_INTRINSIC\_GUESS}, \texttt{CALIB\_FIX\_ASPECT\_RATIO},
1610 \texttt{CALIB\_FIX\_INTRINSIC} or \texttt{CALIB\_FIX\_FOCAL\_LENGTH} are specified, some or all of the matrices' components must be initialized}
1611 \cvarg{distCoeffs1, distCoeffs2}{The input/output lens distortion coefficients for the first and the second cameras, 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{CALIB\_FIX\_K1}, \texttt{CALIB\_FIX\_K2} or \texttt{CALIB\_FIX\_K3} is specified, then the corresponding elements of the distortion coefficients must be initialized.}
1612 \cvarg{R}{The output rotation matrix between the 1st and the 2nd cameras' coordinate systems.}
1613 \cvarg{T}{The output translation vector between the cameras' coordinate systems.}
1614 \cvarg{E}{The output essential matrix.}
1615 \cvarg{F}{The output fundamental matrix.}
1616 \cvarg{criteria}{The termination criteria for the iterative optimiziation algorithm.}
1617 \cvarg{flags}{Different flags, may be 0 or combination of the following values:
1619 \cvarg{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.}
1620 \cvarg{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.}
1621 \cvarg{CALIB\_FIX\_PRINCIPAL\_POINT}{The principal points are fixed during the optimization.}
1622 \cvarg{CALIB\_FIX\_FOCAL\_LENGTH}{$f^{(j)}_x$ and $f^{(j)}_y$ are fixed.}
1623 \cvarg{CALIB\_FIX\_ASPECT\_RATIO}{$f^{(j)}_y$ is optimized, but the ratio $f^{(j)}_x/f^{(j)}_y$ is fixed.}
1624 \cvarg{CALIB\_SAME\_FOCAL\_LENGTH}{Enforces $f^{(0)}_x=f^{(1)}_x$ and $f^{(0)}_y=f^{(1)}_y$} \cvarg{CALIB\_ZERO\_TANGENT\_DIST}{Tangential distortion coefficients for each camera are set to zeros and fixed there.}
1625 \cvarg{CALIB\_FIX\_K1, CALIB\_FIX\_K2, CALIB\_FIX\_K3}{Fixes the corresponding radial distortion coefficient (the coefficient must be passed to the function)}
1629 The function estimates transformation between the 2 cameras - heads of 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, $(R^{(1)}, T^{(1)})$ and $(R^{(2)}, T^{(2)})$, respectively (that can be done with \cvCppCross{solvePnP}), then, obviously, those poses will relate to each other, by knowing only one of $(R^{(j)}, T^{(j)})$ we can compute the other one:
1632 R^{(2)}=R*R^{(1)} \\
1633 T^{(2)}=R*T^{(1)} + T,
1637 And, vice versa, if we computed both $(R^{(1)}, T^{(1)})$ and $(R^{(2)}, T^{(2)})$, we can compute the relative position and orientation of the 2 cameras as following:
1640 R=R^{(2)} {R^{(1)}}^{-1} \\
1641 T=T^{(2)} - R^{(2)} {R^{(1)}}^{-1}*T^{(1)}
1645 The function uses this idea, but the actual algorithm is more complex to take all the available pairs of the camera views into account.
1647 Also, the function computes the essential matrix \texttt{E}:
1658 where $T_i$ are components of the translation vector $T:\,T=[T_0, T_1, T_2]^T$,
1659 and the fundamental matrix \texttt{F}:
1661 \[F = cameraMatrix2^{-T} \cdot E \cdot cameraMatrix1^{-1}\]
1663 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 the intrinsic parameters can be estimated with high accuracy for each of the cameras individually (e.g. using \cvCppCross{calibrateCamera}), it is recommended to do so and then pass \texttt{CALIB\_FIX\_INTRINSIC} flag to the function along with the computed intrinsic parameters. Otherwise, if all the parameters are needed to be estimated at once, it makes sense to restrict some parameters, e.g. pass \texttt{CALIB\_SAME\_FOCAL\_LENGTH} and \texttt{CALIB\_ZERO\_TANGENT\_DIST} flags, which are usually reasonable assumptions.
1666 \cvCppFunc{stereoRectify}
1667 Computes rectification transforms for each head of a calibrated stereo camera.
1670 void stereoRectify( const Mat& cameraMatrix1, const Mat& distCoeffs1,
1671 const Mat& cameraMatrix2, const Mat& distCoeffs2,
1672 Size imageSize, const Mat& R, const Mat& T,
1673 Mat& R1, Mat& R2, Mat& P1, Mat& P2, Mat& Q,
1674 int flags=CALIB_ZERO_DISPARITY );
1677 \cvarg{cameraMatrix1, cameraMatrix2}{The camera matrices $\vecthreethree{f_x^{(j)}}{0}{c_x^{(j)}}{0}{f_y^{(j)}}{c_y^{(j)}}{0}{0}{1}$}
1678 \cvarg{distCoeffs1, distCoeffs2}{The vectors of distortion coefficients for each camera, \cvCppCross{4x1, 1x4, 5x1 or 1x5}}
1679 \cvarg{imageSize}{Size of the image used for stereo calibration.}
1680 \cvarg{R}{The input rotation matrix between the 1st and the 2nd cameras' coordinate systems; can be computed with \cvCppCross{stereoCalibrate}.}
1681 \cvarg{T}{The translation vector between the cameras' coordinate systems; can be computed with \cvCppCross{stereoCalibrate}.}
1682 \cvarg{R1, R2}{The output $3 \times 3$ rectification transforms (rotation matrices) for the first and the second cameras, respectively.}
1683 \cvarg{P1, P2}{The output $3 \times 4$ projection matrices in the new (rectified) coordinate systems.}
1684 \cvarg{Q}{The output $4 \times 4$ disparity-to-depth mapping matrix, see \cvCppCross{reprojectImageTo3D}.}
1685 \cvarg{flags}{The operation flags; may be 0 or \texttt{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.}
1688 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:
1691 \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:
1704 f & 0 & cx_2 & T_x*f\\
1711 where $T_x$ is horizontal shift between the cameras and $cx_1=cx_2$ if \texttt{CALIB\_ZERO\_DISPARITY} is set.}
1712 \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:
1726 0 & f & cy_2 & T_y*f\\
1732 where $T_y$ is vertical shift between the cameras and $cy_1=cy_2$ if \texttt{CALIB\_ZERO\_DISPARITY} is set.}
1735 As you can see, the first 3 columns of \texttt{P1} and \texttt{P2} will effectively be the new "rectified" camera matrices.
1736 The matrices, together with \texttt{R1} and \texttt{R2}, can then be passed to \cvCppCross{initUndistortRectifyMap} to initialize the rectification map for each camera.
1738 \cvCppFunc{stereoRectifyUncalibrated}
1739 Computes rectification transforms for each head of an uncalibrated stereo camera.
1742 bool stereoRectifyUncalibrated( const Mat& points1,
1744 const Mat& F, Size imgSize,
1746 double threshold=5 );
1749 \cvarg{points1, points2}{The two arrays of corresponding 2D points.}
1750 \cvarg{F}{Fundamental matrix. It can be computed using the same set of point pairs \texttt{points1} and \texttt{points2} using \cvCppCross{findFundamentalMat}.}
1751 \cvarg{imageSize}{Size of the image.}
1752 \cvarg{H1, H2}{The output rectification homography matrices for the first and for the second images.}
1753 \cvarg{threshold}{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.}
1756 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 \cvCppCross{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}.
1758 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 \cvCppCross{calibrateCamera} and then the images can be corrected using \cvCppCross{undistort}, or just the point coordinates can be corrected with \cvCppCross{undistortPoints}.
1760 \cvCppFunc{StereoBM}
1761 The class for computing stereo correspondence using block matching algorithm.
1764 // Block matching stereo correspondence algorithm
1767 enum { NORMALIZED_RESPONSE = CV_STEREO_BM_NORMALIZED_RESPONSE,
1768 BASIC_PRESET=CV_STEREO_BM_BASIC,
1769 FISH_EYE_PRESET=CV_STEREO_BM_FISH_EYE,
1770 NARROW_PRESET=CV_STEREO_BM_NARROW };
1773 // the preset is one of ..._PRESET above.
1774 // ndisparities is the size of disparity range,
1775 // in which the optimal disparity at each pixel is searched for.
1776 // SADWindowSize is the size of averaging window used to match pixel blocks
1777 // (larger values mean better robustness to noise, but yield blurry disparity maps)
1778 StereoBM(int preset, int ndisparities=0, int SADWindowSize=21);
1779 // separate initialization function
1780 void init(int preset, int ndisparities=0, int SADWindowSize=21);
1781 // computes the disparity for the two rectified 8-bit single-channel images.
1782 // the disparity will be 16-bit singed image of the same size as left.
1783 void operator()( const Mat& left, const Mat& right, Mat& disparity );
1785 Ptr<CvStereoBMState> state;
1789 \cvCppFunc{undistortPoints}
1790 Computes the ideal point coordinates from the observed point coordinates.
1793 void undistortPoints( const Mat& src, vector<Point2f>& dst,
1794 const Mat& cameraMatrix, const Mat& distCoeffs,
1795 const Mat& R=Mat(), const Mat& P=Mat());
1796 void undistortPoints( const Mat& src, Mat& dst,
1797 const Mat& cameraMatrix, const Mat& distCoeffs,
1798 const Mat& R=Mat(), const Mat& P=Mat());
1801 \cvarg{src}{The observed point coordinates, a matrix or vector of 2D points.}
1802 \cvarg{dst}{The ideal point coordinates, after undistortion and reverse perspective transformation}
1803 \cvarg{cameraMatrix}{The camera matrix $\vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}$}
1804 \cvarg{distCoeffs}{he vector of distortion coefficients, \cvCppCross{4x1, 1x4, 5x1 or 1x5}}
1805 \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}
1806 \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}
1809 The function is similar to \cvCppCross{undistort} and \cvCppCross{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 \cvCppCross{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).