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### Camera Calibration (2)

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## estimateAffine3D

Computes an optimal affine transformation between two 3D point sets.

C++: int estimateAffine3D(InputArray src, InputArray dst, OutputArray out, OutputArray inliers, doubleransacThreshold=3, double confidence=0.99)
Python: cv2.estimateAffine3D(src, dst[, out[, inliers[, ransacThreshold[, confidence]]]]) ¡ú retval, out, inliers
Parameters: src ¨C First input 3D point set.dst ¨C Second input 3D point set.out ¨C Output 3D affine transformation matrix  .inliers ¨C Output vector indicating which points are inliers.ransacThreshold ¨C Maximum reprojection error in the RANSAC algorithm to consider a point as an inlier.confidence ¨C Confidence level, between 0 and 1, for the estimated transformation. Anything between 0.95 and 0.99 is usually good enough. Values too close to 1 can slow down the estimation significantly. Values lower than 0.8-0.9 can result in an incorrectly estimated transformation.

The function estimates an optimal 3D affine transformation between two 3D point sets using the RANSAC algorithm.

## filterSpeckles

Filters off small noise blobs (speckles) in the disparity map

C++: void filterSpeckles(InputOutputArray img, double newVal, int maxSpeckleSize, double maxDiff, InputOutputArraybuf=noArray() )
Python: cv2.filterSpeckles(img, newVal, maxSpeckleSize, maxDiff[, buf]) ¡ú None
Parameters: img ¨C The input 16-bit signed disparity imagenewVal ¨C The disparity value used to paint-off the specklesmaxSpeckleSize ¨C The maximum speckle size to consider it a speckle. Larger blobs are not affected by the algorithmmaxDiff ¨C Maximum difference between neighbor disparity pixels to put them into the same blob. Note that since StereoBM, StereoSGBM and may be other algorithms return a fixed-point disparity map, where disparity values are multiplied by 16, this scale factor should be taken into account when specifying this parameter value.buf ¨C The optional temporary buffer to avoid memory allocation within the function.

## getOptimalNewCameraMatrix

Returns the new camera matrix based on the free scaling parameter.

C++: Mat getOptimalNewCameraMatrix(InputArray cameraMatrix, InputArray distCoeffs, Size imageSize, double alpha, Size newImgSize=Size(), Rect* validPixROI=0, bool centerPrincipalPoint=false )
Python: cv2.getOptimalNewCameraMatrix(cameraMatrix, distCoeffs, imageSize, alpha[, newImgSize[, centerPrincipalPoint]]) ¡ú retval, validPixROI
C: void cvGetOptimalNewCameraMatrix(const CvMat* camera_matrix, const CvMat* dist_coeffs, CvSize image_size, double alpha, CvMat* new_camera_matrix, CvSize new_imag_size=cvSize(0,0), CvRect* valid_pixel_ROI=0, intcenter_principal_point=0 )
Python: cv.GetOptimalNewCameraMatrix(cameraMatrix, distCoeffs, imageSize, alpha, newCameraMatrix, newImageSize=(0, 0), validPixROI=0, centerPrincipalPoint=0) ¡ú None
Parameters: cameraMatrix ¨C Input camera matrix.distCoeffs ¨C Input vector of distortion coefficients  of 4, 5, or 8 elements. If the vector is NULL/empty, the zero distortion coefficients are assumed.imageSize ¨C Original image size.alpha ¨C Free scaling parameter between 0 (when all the pixels in the undistorted image are valid) and 1 (when all the source image pixels are retained in the undistorted image). See stereoRectify() for details.new_camera_matrix ¨C Output new camera matrix.new_imag_size ¨C Image size after rectification. By default,it is set to imageSize .validPixROI ¨C Optional output rectangle that outlines all-good-pixels region in the undistorted image. See roi1, roi2 description in stereoRectify() .centerPrincipalPoint ¨C Optional flag that indicates whether in the new camera matrix the principal point should be at the image center or not. By default, the principal point is chosen to best fit a subset of the source image (determined by alpha) to the corrected image.

The function computes and returns the optimal new camera matrix based on the free scaling parameter. By varying this parameter, you may retrieve only sensible pixels alpha=0 , keep all the original image pixels if there is valuable information in the corners alpha=1 , or get something in between. When alpha>0 , the undistortion result is likely to have some black pixels corresponding to ¡°virtual¡± pixels outside of the captured distorted image. The original camera matrix, distortion coefficients, the computed new camera matrix, and newImageSize should be passed to initUndistortRectifyMap()to produce the maps for remap() .

## initCameraMatrix2D

Finds an initial camera matrix from 3D-2D point correspondences.

C++: Mat initCameraMatrix2D(InputArrayOfArrays objectPoints, InputArrayOfArrays imagePoints, Size imageSize, double aspectRatio=1.)
Python: cv2.initCameraMatrix2D(objectPoints, imagePoints, imageSize[, aspectRatio]) ¡ú retval
C: void cvInitIntrinsicParams2D(const CvMat* object_points, const CvMat* image_points, const CvMat* npoints, CvSize image_size, CvMat* camera_matrix, double aspect_ratio=1. )
Python: cv.InitIntrinsicParams2D(objectPoints, imagePoints, npoints, imageSize, cameraMatrix, aspectRatio=1.) ¡ú None
Parameters: objectPoints ¨C Vector of vectors of the calibration pattern points in the calibration pattern coordinate space. In the old interface all the per-view vectors are concatenated. SeecalibrateCamera() for details.imagePoints ¨C Vector of vectors of the projections of the calibration pattern points. In the old interface all the per-view vectors are concatenated.npoints ¨C The integer vector of point counters for each view.imageSize ¨C Image size in pixels used to initialize the principal point.aspectRatio ¨C If it is zero or negative, both  and  are estimated independently. Otherwise, .

The function estimates and returns an initial camera matrix for the camera calibration process. Currently, the function only supports planar calibration patterns, which are patterns where each object point has z-coordinate =0.

## matMulDeriv

Computes partial derivatives of the matrix product for each multiplied matrix.

C++: void matMulDeriv(InputArray A, InputArray B, OutputArray dABdA, OutputArray dABdB)
Python: cv2.matMulDeriv(A, B[, dABdA[, dABdB]]) ¡ú dABdA, dABdB
Parameters: A ¨C First multiplied matrix.B ¨C Second multiplied matrix.dABdA ¨C First output derivative matrix d(A*B)/dA of size  .dABdB ¨C Second output derivative matrix d(A*B)/dB of size  .

The function computes partial derivatives of the elements of the matrix product
with regard to the elements of each of the two input matrices. The function is used to compute the Jacobian matrices in stereoCalibrate() but can also be used in any other similar optimization function.

## projectPoints

Projects 3D points to an image plane.

C++: void projectPoints(InputArray objectPoints, InputArray rvec, InputArray tvec, InputArray cameraMatrix, InputArray distCoeffs, OutputArray imagePoints, OutputArray jacobian=noArray(), double aspectRatio=0 )
Python: cv2.projectPoints(objectPoints, rvec, tvec, cameraMatrix, distCoeffs[, imagePoints[, jacobian[, aspectRatio]]]) ¡ú imagePoints, jacobian
C: void cvProjectPoints2(const CvMat* object_points, const CvMat* rotation_vector, const CvMat*translation_vector, const CvMat* camera_matrix, const CvMat* distortion_coeffs, CvMat* image_points, CvMat*dpdrot=NULL, CvMat* dpdt=NULL, CvMat* dpdf=NULL, CvMat* dpdc=NULL, CvMat* dpddist=NULL, double aspect_ratio=0 )
Python: cv.ProjectPoints2(objectPoints, rvec, tvec, cameraMatrix, distCoeffs, imagePoints, dpdrot=None, dpdt=None, dpdf=None, dpdc=None, dpddist=None) ¡ú None
Parameters: objectPoints ¨C Array of object points, 3xN/Nx3 1-channel or 1xN/Nx1 3-channel (or vector ), where N is the number of points in the view.rvec ¨C Rotation vector. See Rodrigues() for details.tvec ¨C Translation vector.cameraMatrix ¨C Camera matrix  .distCoeffs ¨C Input vector of distortion coefficients  of 4, 5, or 8 elements. If the vector is NULL/empty, the zero distortion coefficients are assumed.imagePoints ¨C Output array of image points, 2xN/Nx2 1-channel or 1xN/Nx1 2-channel, orvector .jacobian ¨C Optional output 2Nx(10+) jacobian matrix of derivatives of image points with respect to components of the rotation vector, translation vector, focal lengths, coordinates of the principal point and the distortion coefficients. In the old interface different components of the jacobian are returned via different output parameters.aspectRatio ¨C Optional ¡°fixed aspect ratio¡± parameter. If the parameter is not 0, the function assumes that the aspect ratio (fx/fy) is fixed and correspondingly adjusts the jacobian matrix.

The function computes projections of 3D points to the image plane given intrinsic and extrinsic camera parameters. Optionally, the function computes Jacobians - matrices of partial derivatives of image points coordinates (as functions of all the input parameters) with respect to the particular parameters, intrinsic and/or extrinsic. The Jacobians are used during the global optimization in calibrateCamera()solvePnP(), and stereoCalibrate() . The function itself can also be used to compute a re-projection error given the current intrinsic and extrinsic parameters.

Note

By setting rvec=tvec=(0,0,0) or by setting cameraMatrix to a 3x3 identity matrix, or by passing zero distortion coefficients, you can get various useful partial cases of the function. This means that you can compute the distorted coordinates for a sparse set of points or apply a perspective transformation (and also compute the derivatives) in the ideal zero-distortion setup.

## reprojectImageTo3D

Reprojects a disparity image to 3D space.

C++: void reprojectImageTo3D(InputArray disparity, OutputArray _3dImage, InputArray Q, boolhandleMissingValues=false, int ddepth=-1 )
Python: cv2.reprojectImageTo3D(disparity, Q[, _3dImage[, handleMissingValues[, ddepth]]]) ¡ú _3dImage
C: void cvReprojectImageTo3D(const CvArr* disparityImage, CvArr* _3dImage, const CvMat* Q, inthandleMissingValues=0 )
Python: cv.ReprojectImageTo3D(disparity, _3dImage, Q, handleMissingValues=0) ¡ú None
Parameters: disparity ¨C Input single-channel 8-bit unsigned, 16-bit signed, 32-bit signed or 32-bit floating-point disparity image._3dImage ¨C Output 3-channel floating-point image of the same size as disparity . Each element of_3dImage(x,y) contains 3D coordinates of the point (x,y) computed from the disparity map.Q ¨C  perspective transformation matrix that can be obtained with stereoRectify().handleMissingValues ¨C Indicates, whether the function should handle missing values (i.e. points where the disparity was not computed). If handleMissingValues=true, then pixels with the minimal disparity that corresponds to the outliers (see StereoBM::operator() ) are transformed to 3D points with a very large Z value (currently set to 10).ddepth ¨C The optional output array depth. If it is -1, the output image will have CV_32F depth.ddepth can also be set to CV_16S, CV_32S or CV_32F.

The function transforms a single-channel disparity map to a 3-channel image representing a 3D surface. That is, for each pixel (x,y) andthe corresponding disparity d=disparity(x,y) , it computes:

The matrix Q can be an arbitrary
matrix (for example, the one computed by stereoRectify()). To reproject a sparse set of points {(x,y,d),...} to 3D space, use perspectiveTransform() .

## RQDecomp3x3

Computes an RQ decomposition of 3x3 matrices.

C++: Vec3d RQDecomp3x3(InputArray src, OutputArray mtxR, OutputArray mtxQ, OutputArray Qx=noArray(), OutputArrayQy=noArray(), OutputArray Qz=noArray() )
Python: cv2.RQDecomp3x3(src[, mtxR[, mtxQ[, Qx[, Qy[, Qz]]]]]) ¡ú retval, mtxR, mtxQ, Qx, Qy, Qz
C: void cvRQDecomp3x3(const CvMat* matrixM, CvMat* matrixR, CvMat* matrixQ, CvMat* matrixQx=NULL, CvMat*matrixQy=NULL, CvMat* matrixQz=NULL, CvPoint3D64f* eulerAngles=NULL )
Python: cv.RQDecomp3x3(M, R, Q, Qx=None, Qy=None, Qz=None) ¡ú eulerAngles
Parameters: src ¨C 3x3 input matrix.mtxR ¨C Output 3x3 upper-triangular matrix.mtxQ ¨C Output 3x3 orthogonal matrix.Qx ¨C Optional output 3x3 rotation matrix around x-axis.Qy ¨C Optional output 3x3 rotation matrix around y-axis.Qz ¨C Optional output 3x3 rotation matrix around z-axis.

The function computes a RQ decomposition using the given rotations. This function is used in decomposeProjectionMatrix()to decompose the left 3x3 submatrix of a projection matrix into a camera and a rotation matrix.

It optionally returns three rotation matrices, one for each axis, and the three Euler angles in degrees (as the return value) that could be used in OpenGL. Note, there is always more than one sequence of rotations about the three principle axes that results in the same orientation of an object, eg. see [Slabaugh]. Returned tree rotation matrices and corresponding three Euler angules are only one of the possible solutions.

## Rodrigues

Converts a rotation matrix to a rotation vector or vice versa.

C++: void Rodrigues(InputArray src, OutputArray dst, OutputArray jacobian=noArray())
Python: cv2.Rodrigues(src[, dst[, jacobian]]) ¡ú dst, jacobian
C: int cvRodrigues2(const CvMat* src, CvMat* dst, CvMat* jacobian=0 )
Python: cv.Rodrigues2(src, dst, jacobian=0) ¡ú None
Parameters: src ¨C Input rotation vector (3x1 or 1x3) or rotation matrix (3x3).dst ¨C Output rotation matrix (3x3) or rotation vector (3x1 or 1x3), respectively.jacobian ¨C Optional output Jacobian matrix, 3x9 or 9x3, which is a matrix of partial derivatives of the output array components with respect to the input array components.

Inverse transformation can be also done easily, since

A rotation vector is a convenient and most compact representation of a rotation matrix (since any rotation matrix has just 3 degrees of freedom). The representation is used in the global 3D geometry optimization procedures like calibrateCamera(),stereoCalibrate(), or solvePnP() .

## StereoBM

class StereoBM

Class for computing stereo correspondence using the block matching algorithm.

// Block matching stereo correspondence algorithm class StereoBM
{
enum { NORMALIZED_RESPONSE = CV_STEREO_BM_NORMALIZED_RESPONSE,
BASIC_PRESET=CV_STEREO_BM_BASIC,
FISH_EYE_PRESET=CV_STEREO_BM_FISH_EYE,
NARROW_PRESET=CV_STEREO_BM_NARROW };

StereoBM();
// the preset is one of ..._PRESET above.
// ndisparities is the size of disparity range,
// in which the optimal disparity at each pixel is searched for.
// SADWindowSize is the size of averaging window used to match pixel blocks
//    (larger values mean better robustness to noise, but yield blurry disparity maps)
StereoBM(int preset, int ndisparities=0, int SADWindowSize=21);
// separate initialization function
void init(int preset, int ndisparities=0, int SADWindowSize=21);
// computes the disparity for the two rectified 8-bit single-channel images.
// the disparity will be 16-bit signed (fixed-point) or 32-bit floating-point image of the same size as left.
void operator()( InputArray left, InputArray right, OutputArray disparity, int disptype=CV_16S );

Ptr<CvStereoBMState> state;
};


The class is a C++ wrapper for the associated functions. In particular, StereoBM::operator() is the wrapper forcvFindStereoCorrespondenceBM().

## StereoBM::StereoBM

The constructors.

C++: StereoBM::StereoBM()
C++: StereoBM::StereoBM(int preset, int ndisparities=0, int SADWindowSize=21)
Python: cv2.StereoBM([preset[, ndisparities[, SADWindowSize]]]) ¡ú <StereoBM object>
C: CvStereoBMState* cvCreateStereoBMState(int preset=CV_STEREO_BM_BASIC, int numberOfDisparities=0 )
Python: cv.CreateStereoBMState(preset=CV_STEREO_BM_BASIC, numberOfDisparities=0) ¡ú CvStereoBMState
Parameters: preset ¨Cspecifies the whole set of algorithm parameters, one of:BASIC_PRESET - parameters suitable for general camerasFISH_EYE_PRESET - parameters suitable for wide-angle camerasNARROW_PRESET - parameters suitable for narrow-angle camerasAfter constructing the class, you can override any parameters set by the preset.ndisparities ¨C the disparity search range. For each pixel algorithm will find the best disparity from 0 (default minimum disparity) to ndisparities. The search range can then be shifted by changing the minimum disparity.SADWindowSize ¨C the linear size of the blocks compared by the algorithm. The size should be odd (as the block is centered at the current pixel). Larger block size implies smoother, though less accurate disparity map. Smaller block size gives more detailed disparity map, but there is higher chance for algorithm to find a wrong correspondence.

The constructors initialize StereoBM state. You can then call StereoBM::operator() to compute disparity for a specific stereo pair.

Note

In the C API you need to deallocate CvStereoBM state when it is not needed anymore usingcvReleaseStereoBMState(&stereobm).

## StereoBM::operator()

Computes disparity using the BM algorithm for a rectified stereo pair.

C++: void StereoBM::operator()(InputArray left, InputArray right, OutputArray disparity, int disptype=CV_16S )
Python: cv2.StereoBM.compute(left, right[, disparity[, disptype]]) ¡ú disparity
C: void cvFindStereoCorrespondenceBM(const CvArr* left, const CvArr* right, CvArr* disparity, CvStereoBMState*state)
Python: cv.FindStereoCorrespondenceBM(left, right, disparity, state) ¡ú None
Parameters: left ¨C Left 8-bit single-channel image.right ¨C Right image of the same size and the same type as the left one.disparity ¨C Output disparity map. It has the same size as the input images. When disptype==CV_16S, the map is a 16-bit signed single-channel image, containing disparity values scaled by 16. To get the true disparity values from such fixed-point representation, you will need to divide each disp element by 16. If disptype==CV_32F, the disparity map will already contain the real disparity values on output.disptype ¨C Type of the output disparity map, CV_16S (default) or CV_32F.state ¨C The pre-initialized CvStereoBMState structure in the case of the old API.

The method executes the BM algorithm on a rectified stereo pair. See the stereo_match.cpp OpenCV sample on how to prepare images and call the method. Note that the method is not constant, thus you should not use the same StereoBM instance from within different threads simultaneously. The function is parallelized with the TBB library.

## StereoSGBM

class StereoSGBM

Class for computing stereo correspondence using the semi-global block matching algorithm.

class StereoSGBM
{
StereoSGBM();
StereoSGBM(int minDisparity, int numDisparities, int SADWindowSize,
int P1=0, int P2=0, int disp12MaxDiff=0,
int preFilterCap=0, int uniquenessRatio=0,
int speckleWindowSize=0, int speckleRange=0,
bool fullDP=false);
virtual ~StereoSGBM();

virtual void operator()(InputArray left, InputArray right, OutputArray disp);

int minDisparity;
int numberOfDisparities;
int preFilterCap;
int uniquenessRatio;
int P1, P2;
int speckleWindowSize;
int speckleRange;
int disp12MaxDiff;
bool fullDP;

...
};


The class implements the modified H. Hirschmuller algorithm [HH08] that differs from the original one as follows:

• By default, the algorithm is single-pass, which means that you consider only 5 directions instead of 8. SetfullDP=true to run the full variant of the algorithm but beware that it may consume a lot of memory.
• The algorithm matches blocks, not individual pixels. Though, setting SADWindowSize=1 reduces the blocks to single pixels.
• Mutual information cost function is not implemented. Instead, a simpler Birchfield-Tomasi sub-pixel metric from [BT98] is used. Though, the color images are supported as well.
• Some pre- and post- processing steps from K. Konolige algorithm StereoBM::operator() are included, for example: pre-filtering (CV_STEREO_BM_XSOBEL type) and post-filtering (uniqueness check, quadratic interpolation and speckle filtering).

Note

• (Python) An example illustrating the use of the StereoSGBM matching algorithm can be found at opencv_source_code/samples/python2/stereo_match.py

## StereoSGBM::StereoSGBM

C++: StereoSGBM::StereoSGBM()
C++: StereoSGBM::StereoSGBM(int minDisparity, int numDisparities, int SADWindowSize, int P1=0, int P2=0, intdisp12MaxDiff=0, int preFilterCap=0, int uniquenessRatio=0, int speckleWindowSize=0, int speckleRange=0, boolfullDP=false)
Python: cv2.StereoSGBM([minDisparity, numDisparities, SADWindowSize[, P1[, P2[, disp12MaxDiff[, preFilterCap[, uniquenessRatio[, speckleWindowSize[, speckleRange[, fullDP]]]]]]]]]) ¡ú <StereoSGBM object>

Initializes StereoSGBM and sets parameters to custom values.??

Parameters: minDisparity ¨C Minimum possible disparity value. Normally, it is zero but sometimes rectification algorithms can shift images, so this parameter needs to be adjusted accordingly.numDisparities ¨C Maximum disparity minus minimum disparity. The value is always greater than zero. In the current implementation, this parameter must be divisible by 16.SADWindowSize ¨C Matched block size. It must be an odd number >=1 . Normally, it should be somewhere in the 3..11 range.P1 ¨C The first parameter controlling the disparity smoothness. See below.P2 ¨C The second parameter controlling the disparity smoothness. The larger the values are, the smoother the disparity is. P1 is the penalty on the disparity change by plus or minus 1 between neighbor pixels. P2 is the penalty on the disparity change by more than 1 between neighbor pixels. The algorithm requires P2 > P1 . See stereo_match.cpp sample where some reasonably good P1 and P2 values are shown (like 8*number_of_image_channels*SADWindowSize*SADWindowSize and32*number_of_image_channels*SADWindowSize*SADWindowSize , respectively).disp12MaxDiff ¨C Maximum allowed difference (in integer pixel units) in the left-right disparity check. Set it to a non-positive value to disable the check.preFilterCap ¨C Truncation value for the prefiltered image pixels. The algorithm first computes x-derivative at each pixel and clips its value by [-preFilterCap, preFilterCap] interval. The result values are passed to the Birchfield-Tomasi pixel cost function.uniquenessRatio ¨C Margin in percentage by which the best (minimum) computed cost function value should ¡°win¡± the second best value to consider the found match correct. Normally, a value within the 5-15 range is good enough.speckleWindowSize ¨C Maximum size of smooth disparity regions to consider their noise speckles and invalidate. Set it to 0 to disable speckle filtering. Otherwise, set it somewhere in the 50-200 range.speckleRange ¨C Maximum disparity variation within each connected component. If you do speckle filtering, set the parameter to a positive value, it will be implicitly multiplied by 16. Normally, 1 or 2 is good enough.fullDP ¨C Set it to true to run the full-scale two-pass dynamic programming algorithm. It will consume O(W*H*numDisparities) bytes, which is large for 640x480 stereo and huge for HD-size pictures. By default, it is set to false .

The first constructor initializes StereoSGBM with all the default parameters. So, you only have to setStereoSGBM::numberOfDisparities at minimum. The second constructor enables you to set each parameter to a custom value.

## StereoSGBM::operator ()

C++: void StereoSGBM::operator()(InputArray left, InputArray right, OutputArray disp)
Python: cv2.StereoSGBM.compute(left, right[, disp]) ¡ú disp

Computes disparity using the SGBM algorithm for a rectified stereo pair.

Parameters: left ¨C Left 8-bit single-channel or 3-channel image.right ¨C Right image of the same size and the same type as the left one.disp ¨C Output disparity map. It is a 16-bit signed single-channel image of the same size as the input image. It contains disparity values scaled by 16. So, to get the floating-point disparity map, you need to divide each disp element by 16.

The method executes the SGBM algorithm on a rectified stereo pair. See stereo_match.cpp OpenCV sample on how to prepare images and call the method.

Note

The method is not constant, so you should not use the same StereoSGBM instance from different threads simultaneously.

## stereoCalibrate

Calibrates the stereo camera.

C++: double stereoCalibrate(InputArrayOfArrays objectPoints, InputArrayOfArrays imagePoints1, InputArrayOfArraysimagePoints2, InputOutputArray cameraMatrix1, InputOutputArray distCoeffs1, InputOutputArray cameraMatrix2, InputOutputArray distCoeffs2, Size imageSize, OutputArray R, OutputArray T, OutputArray E, OutputArray F, TermCriteriacriteria=TermCriteria(TermCriteria::COUNT+TermCriteria::EPS, 30, 1e-6), int flags=CALIB_FIX_INTRINSIC )
Python: cv2.stereoCalibrate(objectPoints, imagePoints1, imagePoints2, imageSize[, cameraMatrix1[, distCoeffs1[, cameraMatrix2[, distCoeffs2[, R[, T[, E[, F[, criteria[, flags]]]]]]]]]]) ¡ú retval, cameraMatrix1, distCoeffs1, cameraMatrix2, distCoeffs2, R, T, E, F
C: double cvStereoCalibrate(const CvMat* object_points, const CvMat* image_points1, const CvMat* image_points2, const CvMat* npoints, CvMat* camera_matrix1, CvMat* dist_coeffs1, CvMat* camera_matrix2, CvMat* dist_coeffs2, CvSizeimage_size, CvMat* R, CvMat* T, CvMat* E=0, CvMat* F=0, CvTermCriteria term_crit=cvTermCriteria( CV_TERMCRIT_ITER+CV_TERMCRIT_EPS,30,1e-6), int flags=CV_CALIB_FIX_INTRINSIC )
Python: cv.StereoCalibrate(objectPoints, imagePoints1, imagePoints2, pointCounts, cameraMatrix1, distCoeffs1, cameraMatrix2, distCoeffs2, imageSize, R, T, E=None, F=None, term_crit=(CV_TERMCRIT_ITER+CV_TERMCRIT_EPS, 30, 1e-6), flags=CV_CALIB_FIX_INTRINSIC) ¡ú None
Parameters: objectPoints ¨C Vector of vectors of the calibration pattern points.imagePoints1 ¨C Vector of vectors of the projections of the calibration pattern points, observed by the first camera.imagePoints2 ¨C Vector of vectors of the projections of the calibration pattern points, observed by the second camera.cameraMatrix1 ¨C Input/output first camera matrix:  ,  . If any ofCV_CALIB_USE_INTRINSIC_GUESS , CV_CALIB_FIX_ASPECT_RATIO , CV_CALIB_FIX_INTRINSIC , orCV_CALIB_FIX_FOCAL_LENGTH are specified, some or all of the matrix components must be initialized. See the flags description for details.distCoeffs1 ¨C Input/output vector of distortion coefficients  of 4, 5, or 8 elements. The output vector length depends on the flags.cameraMatrix2 ¨C Input/output second camera matrix. The parameter is similar to cameraMatrix1 .distCoeffs2 ¨C Input/output lens distortion coefficients for the second camera. The parameter is similar to distCoeffs1 .imageSize ¨C Size of the image used only to initialize intrinsic camera matrix.R ¨C Output rotation matrix between the 1st and the 2nd camera coordinate systems.T ¨C Output translation vector between the coordinate systems of the cameras.E ¨C Output essential matrix.F ¨C Output fundamental matrix.term_crit ¨C Termination criteria for the iterative optimization algorithm.flags ¨CDifferent flags that may be zero or a combination of the following values:CV_CALIB_FIX_INTRINSIC Fix cameraMatrix? and distCoeffs? so that only R, T, E , and F matrices are estimated.CV_CALIB_USE_INTRINSIC_GUESS Optimize some or all of the intrinsic parameters according to the specified flags. Initial values are provided by the user.CV_CALIB_FIX_PRINCIPAL_POINT Fix the principal points during the optimization.CV_CALIB_FIX_FOCAL_LENGTH Fix  and  .CV_CALIB_FIX_ASPECT_RATIO Optimize  . Fix the ratio  .CV_CALIB_SAME_FOCAL_LENGTH Enforce  and  .CV_CALIB_ZERO_TANGENT_DIST Set tangential distortion coefficients for each camera to zeros and fix there.CV_CALIB_FIX_K1,...,CV_CALIB_FIX_K6 Do not change the corresponding radial distortion coefficient during the optimization. If CV_CALIB_USE_INTRINSIC_GUESS is set, the coefficient from the supplieddistCoeffs matrix is used. Otherwise, it is set to 0.CV_CALIB_RATIONAL_MODEL Enable coefficients k4, k5, and k6. To provide the backward compatibility, this extra flag should be explicitly specified to make the calibration function use the rational model and return 8 coefficients. If the flag is not set, the function computes and returns only 5 distortion coefficients.

The function estimates transformation between two cameras making a stereo pair. If you have a stereo camera where the relative position and orientation of two cameras is fixed, and if you computed poses of an object relative to the first camera and to the second camera, (R1, T1) and (R2, T2), respectively (this can be done with solvePnP() ), then those poses definitely relate to each other. This means that, given (
,:math:T_1 ), it should be possible to compute (
,:math:T_2 ). You only need to know the position and orientation of the second camera relative to the first camera. This is what the described function does. It computes (
,:math:T ) so that:

Optionally, it computes the essential matrix E:

where
are components of the translation vector
:
. And the function can also compute the fundamental matrix F:

Besides the stereo-related information, the function can also perform a full calibration of each of two cameras. However, due to the high dimensionality of the parameter space and noise in the input data, the function can diverge from the correct solution. If the intrinsic parameters can be estimated with high accuracy for each of the cameras individually (for example, using calibrateCamera() ), you are recommended to do so and then pass CV_CALIB_FIX_INTRINSIC flag to the function along with the computed intrinsic parameters. Otherwise, if all the parameters are estimated at once, it makes sense to restrict some parameters, for example, pass CV_CALIB_SAME_FOCAL_LENGTH and CV_CALIB_ZERO_TANGENT_DIST flags, which is usually a reasonable assumption.

Similarly to calibrateCamera() , the function minimizes the total re-projection error for all the points in all the available views from both cameras. The function returns the final value of the re-projection error.

## stereoRectify

Computes rectification transforms for each head of a calibrated stereo camera.

C++: void stereoRectify(InputArray cameraMatrix1, InputArray distCoeffs1, InputArray cameraMatrix2, InputArraydistCoeffs2, Size imageSize, InputArray R, InputArray T, OutputArray R1, OutputArray R2, OutputArray P1, OutputArray P2, OutputArray Q, int flags=CALIB_ZERO_DISPARITY, double alpha=-1, Size newImageSize=Size(), Rect* validPixROI1=0, Rect*validPixROI2=0 )
C: void cvStereoRectify(const CvMat* camera_matrix1, const CvMat* camera_matrix2, const CvMat* dist_coeffs1, const CvMat* dist_coeffs2, CvSize image_size, const CvMat* R, const CvMat* T, CvMat* R1, CvMat* R2, CvMat* P1, CvMat* P2, CvMat* Q=0, int flags=CV_CALIB_ZERO_DISPARITY, double alpha=-1, CvSize new_image_size=cvSize(0,0), CvRect*valid_pix_ROI1=0, CvRect* valid_pix_ROI2=0 )
Python: cv.StereoRectify(cameraMatrix1, cameraMatrix2, distCoeffs1, distCoeffs2, imageSize, R, T, R1, R2, P1, P2, Q=None, flags=CV_CALIB_ZERO_DISPARITY, alpha=-1, newImageSize=(0, 0)) -> (roi1, roi2)
Parameters: cameraMatrix1 ¨C First camera matrix.cameraMatrix2 ¨C Second camera matrix.distCoeffs1 ¨C First camera distortion parameters.distCoeffs2 ¨C Second camera distortion parameters.imageSize ¨C Size of the image used for stereo calibration.R ¨C Rotation matrix between the coordinate systems of the first and the second cameras.T ¨C Translation vector between coordinate systems of the cameras.R1 ¨C Output 3x3 rectification transform (rotation matrix) for the first camera.R2 ¨C Output 3x3 rectification transform (rotation matrix) for the second camera.P1 ¨C Output 3x4 projection matrix in the new (rectified) coordinate systems for the first camera.P2 ¨C Output 3x4 projection matrix in the new (rectified) coordinate systems for the second camera.Q ¨C Output  disparity-to-depth mapping matrix (see reprojectImageTo3D() ).flags ¨C Operation flags that may be zero or CV_CALIB_ZERO_DISPARITY . If the flag is set, the function makes the principal points of each camera have the same pixel coordinates in the rectified views. And if the flag is not set, the function may still shift the images in the horizontal or vertical direction (depending on the orientation of epipolar lines) to maximize the useful image area.alpha ¨C Free scaling parameter. If it is -1 or absent, the function performs the default scaling. Otherwise, the parameter should be between 0 and 1. alpha=0 means that the rectified images are zoomed and shifted so that only valid pixels are visible (no black areas after rectification). alpha=1 means that the rectified image is decimated and shifted so that all the pixels from the original images from the cameras are retained in the rectified images (no source image pixels are lost). Obviously, any intermediate value yields an intermediate result between those two extreme cases.newImageSize ¨C New image resolution after rectification. The same size should be passed toinitUndistortRectifyMap() (see the stereo_calib.cpp sample in OpenCV samples directory). When (0,0) is passed (default), it is set to the original imageSize . Setting it to larger value can help you preserve details in the original image, especially when there is a big radial distortion.validPixROI1 ¨C Optional output rectangles inside the rectified images where all the pixels are valid. If alpha=0 , the ROIs cover the whole images. Otherwise, they are likely to be smaller (see the picture below).validPixROI2 ¨C Optional output rectangles inside the rectified images where all the pixels are valid. If alpha=0 , the ROIs cover the whole images. Otherwise, they are likely to be smaller (see the picture below).

The function computes the rotation matrices for each camera that (virtually) make both camera image planes the same plane. Consequently, this makes all the epipolar lines parallel and thus simplifies the dense stereo correspondence problem. The function takes the matrices computed by stereoCalibrate() as input. As output, it provides two rotation matrices and also two projection matrices in the new coordinates. The function distinguishes the following two cases:

1. Horizontal stereo: the first and the second camera views are shifted relative to each other mainly along the x axis (with possible small vertical shift). In the rectified images, the corresponding epipolar lines in the left and right cameras are horizontal and have the same y-coordinate. P1 and P2 look like:

where
is a horizontal shift between the cameras and
if CV_CALIB_ZERO_DISPARITY is set.

2. Vertical stereo: the first and the second camera views are shifted relative to each other mainly in vertical direction (and probably a bit in the horizontal direction too). The epipolar lines in the rectified images are vertical and have the same x-coordinate. P1 and P2 look like:

where
is a vertical shift between the cameras and
if CALIB_ZERO_DISPARITY is set.

As you can see, the first three columns of P1 and P2 will effectively be the new ¡°rectified¡± camera matrices. The matrices, together with R1 and R2 , can then be passed to initUndistortRectifyMap() to initialize the rectification map for each camera.

See below the screenshot from the stereo_calib.cpp sample. Some red horizontal lines pass through the corresponding image regions. This means that the images are well rectified, which is what most stereo correspondence algorithms rely on. The green rectangles are roi1 and roi2 . You see that their interiors are all valid pixels.

## stereoRectifyUncalibrated

Computes a rectification transform for an uncalibrated stereo camera.

C++: bool stereoRectifyUncalibrated(InputArray points1, InputArray points2, InputArray F, Size imgSize, OutputArray H1, OutputArray H2, double threshold=5 )
Python: cv2.stereoRectifyUncalibrated(points1, points2, F, imgSize[, H1[, H2[, threshold]]]) ¡ú retval, H1, H2
C: int cvStereoRectifyUncalibrated(const CvMat* points1, const CvMat* points2, const CvMat* F, CvSize img_size, CvMat* H1, CvMat* H2, double threshold=5 )
Python: cv.StereoRectifyUncalibrated(points1, points2, F, imageSize, H1, H2, threshold=5) ¡ú None
Parameters: points1 ¨C Array of feature points in the first image.points2 ¨C The corresponding points in the second image. The same formats as infindFundamentalMat() are supported.F ¨C Input fundamental matrix. It can be computed from the same set of point pairs usingfindFundamentalMat() .imgSize ¨C Size of the image.H1 ¨C Output rectification homography matrix for the first image.H2 ¨C Output rectification homography matrix for the second image.threshold ¨C Optional threshold used to filter out the outliers. If the parameter is greater than zero, all the point pairs that do not comply with the epipolar geometry (that is, the points for which ) are rejected prior to computing the homographies. Otherwise,all the points are considered inliers.

The function computes the rectification transformations without knowing intrinsic parameters of the cameras and their relative position in the space, which explains the suffix ¡°uncalibrated¡±. Another related difference fromstereoRectify() is that the function outputs not the rectification transformations in the object (3D) space, but the planar perspective transformations encoded by the homography matrices H1 and H2 . The function implements the algorithm[Hartley99].

Note

While the algorithm does not need to know the intrinsic parameters of the cameras, it heavily depends on the epipolar geometry. Therefore, if the camera lenses have a significant distortion, it would be better to correct it before computing the fundamental matrix and calling this function. For example, distortion coefficients can be estimated for each head of stereo camera separately by using calibrateCamera() . Then, the images can be corrected using undistort() , or just the point coordinates can be corrected with undistortPoints() .

## triangulatePoints

Reconstructs points by triangulation.

C++: void triangulatePoints(InputArray projMatr1, InputArray projMatr2, InputArray projPoints1, InputArrayprojPoints2, OutputArray points4D)
Python: cv2.triangulatePoints(projMatr1, projMatr2, projPoints1, projPoints2[, points4D]) ¡ú points4D
C: void cvTriangulatePoints(CvMat* projMatr1, CvMat* projMatr2, CvMat* projPoints1, CvMat* projPoints2, CvMat*points4D)
Parameters: projMatr1 ¨C 3x4 projection matrix of the first camera.projMatr2 ¨C 3x4 projection matrix of the second camera.projPoints1 ¨C 2xN array of feature points in the first image. In case of c++ version it can be also a vector of feature points or two-channel matrix of size 1xN or Nx1.projPoints2 ¨C 2xN array of corresponding points in the second image. In case of c++ version it can be also a vector of feature points or two-channel matrix of size 1xN or Nx1.points4D ¨C 4xN array of reconstructed points in homogeneous coordinates.

The function reconstructs 3-dimensional points (in homogeneous coordinates) by using their observations with a stereo camera. Projections matrices can be obtained from stereoRectify().

Note

Keep in mind that all input data should be of float type in order for this function to work.

## fisheye

The methods in this namespace use a so-called fisheye camera model.

namespace fisheye
{
//! projects 3D points using fisheye model
void projectPoints(InputArray objectPoints, OutputArray imagePoints, const Affine3d& affine,
InputArray K, InputArray D, double alpha = 0, OutputArray jacobian = noArray());

//! projects points using fisheye model
void projectPoints(InputArray objectPoints, OutputArray imagePoints, InputArray rvec, InputArray tvec,
InputArray K, InputArray D, double alpha = 0, OutputArray jacobian = noArray());

//! distorts 2D points using fisheye model
void distortPoints(InputArray undistorted, OutputArray distorted, InputArray K, InputArray D, double alpha = 0);

//! undistorts 2D points using fisheye model
void undistortPoints(InputArray distorted, OutputArray undistorted,
InputArray K, InputArray D, InputArray R = noArray(), InputArray P  = noArray());

//! computing undistortion and rectification maps for image transform by cv::remap()
//! If D is empty zero distortion is used, if R or P is empty identity matrixes are used
void initUndistortRectifyMap(InputArray K, InputArray D, InputArray R, InputArray P,
const cv::Size& size, int m1type, OutputArray map1, OutputArray map2);

//! undistorts image, optionally changes resolution and camera matrix.
void undistortImage(InputArray distorted, OutputArray undistorted,
InputArray K, InputArray D, InputArray Knew = cv::noArray(), const Size& new_size = Size());

//! estimates new camera matrix for undistortion or rectification
void estimateNewCameraMatrixForUndistortRectify(InputArray K, InputArray D, const Size &image_size, InputArray R,
OutputArray P, double balance = 0.0, const Size& new_size = Size(), double fov_scale = 1.0);

//! performs camera calibaration
double calibrate(InputArrayOfArrays objectPoints, InputArrayOfArrays imagePoints, const Size& image_size,
InputOutputArray K, InputOutputArray D, OutputArrayOfArrays rvecs, OutputArrayOfArrays tvecs, int flags = 0,
TermCriteria criteria = TermCriteria(TermCriteria::COUNT + TermCriteria::EPS, 100, DBL_EPSILON));

//! stereo rectification estimation
void stereoRectify(InputArray K1, InputArray D1, InputArray K2, InputArray D2, const Size &imageSize, InputArray R, InputArray tvec,
OutputArray R1, OutputArray R2, OutputArray P1, OutputArray P2, OutputArray Q, int flags, const Size &newImageSize = Size(),
double balance = 0.0, double fov_scale = 1.0);

//! performs stereo calibration
double stereoCalibrate(InputArrayOfArrays objectPoints, InputArrayOfArrays imagePoints1, InputArrayOfArrays imagePoints2,
InputOutputArray K1, InputOutputArray D1, InputOutputArray K2, InputOutputArray D2, Size imageSize,
OutputArray R, OutputArray T, int flags = CALIB_FIX_INTRINSIC,
TermCriteria criteria = TermCriteria(TermCriteria::COUNT + TermCriteria::EPS, 100, DBL_EPSILON));
};


Definitions: Let P be a point in 3D of coordinates X in the world reference frame (stored in the matrix X) The coordinate vector of P in the camera reference frame is:

class center

where R is the rotation matrix corresponding to the rotation vector om: R = rodrigues(om); call x, y and z the 3 coordinates of Xc:

class center

The pinehole projection coordinates of P is [a; b] where

class center

Fisheye distortion:

class center

The distorted point coordinates are [x¡¯; y¡¯] where

..class:: center .. math:

x' = (\theta_d / r) x \\
y' = (\theta_d / r) y


Finally, conversion into pixel coordinates: The final pixel coordinates vector [u; v] where:

class center

## fisheye::projectPoints

Projects points using fisheye model

C++: void fisheye::projectPoints(InputArray objectPoints, OutputArray imagePoints, const Affine3d& affine, InputArray K, InputArray D, double alpha=0, OutputArray jacobian=noArray())
C++: void fisheye::projectPoints(InputArray objectPoints, OutputArray imagePoints, InputArray rvec, InputArraytvec, InputArray K, InputArray D, double alpha=0, OutputArray jacobian=noArray())
Parameters: objectPoints ¨C Array of object points, 1xN/Nx1 3-channel (or vector ), where N is the number of points in the view.rvec ¨C Rotation vector. See Rodrigues() for details.tvec ¨C Translation vector.K ¨C Camera matrix .D ¨C Input vector of distortion coefficients .alpha ¨C The skew coefficient.imagePoints ¨C Output array of image points, 2xN/Nx2 1-channel or 1xN/Nx1 2-channel, orvector.jacobian ¨C Optional output 2Nx15 jacobian matrix of derivatives of image points with respect to components of the focal lengths, coordinates of the principal point, distortion coefficients, rotation vector, translation vector, and the skew. In the old interface different components of the jacobian are returned via different output parameters.

The function computes projections of 3D points to the image plane given intrinsic and extrinsic camera parameters. Optionally, the function computes Jacobians - matrices of partial derivatives of image points coordinates (as functions of all the input parameters) with respect to the particular parameters, intrinsic and/or extrinsic.

## fisheye::distortPoints

Distorts 2D points using fisheye model.

C++: void fisheye::distortPoints(InputArray undistorted, OutputArray distorted, InputArray K, InputArray D, doublealpha=0)
Parameters: undistorted ¨C Array of object points, 1xN/Nx1 2-channel (or vector ), where N is the number of points in the view.K ¨C Camera matrix .D ¨C Input vector of distortion coefficients .alpha ¨C The skew coefficient.distorted ¨C Output array of image points, 1xN/Nx1 2-channel, or vector .

## fisheye::undistortPoints

Undistorts 2D points using fisheye model

C++: void fisheye::undistortPoints(InputArray distorted, OutputArray undistorted, InputArray K, InputArray D, InputArray R=noArray(), InputArray P=noArray())
Parameters: distorted ¨C Array of object points, 1xN/Nx1 2-channel (or vector ), where N is the number of points in the view.K ¨C Camera matrix .D ¨C Input vector of distortion coefficients .R ¨C Rectification transformation in the object space: 3x3 1-channel, or vector: 3x1/1x3 1-channel or 1x1 3-channelP ¨C New camera matrix (3x3) or new projection matrix (3x4)undistorted ¨C Output array of image points, 1xN/Nx1 2-channel, or vector .

## fisheye::initUndistortRectifyMap

Computes undistortion and rectification maps for image transform by cv::remap(). If D is empty zero distortion is used, if R or P is empty identity matrixes are used.

C++: void fisheye::initUndistortRectifyMap(InputArray K, InputArray D, InputArray R, InputArray P, const cv::Size&size, int m1type, OutputArray map1, OutputArray map2)
Parameters: K ¨C Camera matrix .D ¨C Input vector of distortion coefficients .R ¨C Rectification transformation in the object space: 3x3 1-channel, or vector: 3x1/1x3 1-channel or 1x1 3-channelP ¨C New camera matrix (3x3) or new projection matrix (3x4)size ¨C Undistorted image size.m1type ¨C Type of the first output map that can be CV_32FC1 or CV_16SC2 . See convertMaps() for details.map1 ¨C The first output map.map2 ¨C The second output map.

## fisheye::undistortImage

Transforms an image to compensate for fisheye lens distortion.

C++: void fisheye::undistortImage(InputArray distorted, OutputArray undistorted, InputArray K, InputArray D, InputArray Knew=cv::noArray(), const Size& new_size=Size())
Parameters: distorted ¨C image with fisheye lens distortion.K ¨C Camera matrix .D ¨C Input vector of distortion coefficients .Knew ¨C Camera matrix of the distorted image. By default, it is the identity matrix but you may additionally scale and shift the result by using a different matrix.undistorted ¨C Output image with compensated fisheye lens distortion.

The function transforms an image to compensate radial and tangential lens distortion.

The function is simply a combination of fisheye::initUndistortRectifyMap() (with unity R ) and remap() (with bilinear interpolation). See the former function for details of the transformation being performed.

See below the results of undistortImage.
• a) result of undistort() of perspective camera model (all possible coefficients (k_1, k_2, k_3, k_4, k_5, k_6) of distortion were optimized under calibration)
• b) result of fisheye::undistortImage() of fisheye camera model (all possible coefficients (k_1, k_2, k_3, k_4) of fisheye distortion were optimized under calibration)
• c) original image was captured with fisheye lens

Pictures a) and b) almost the same. But if we consider points of image located far from the center of image, we can notice that on image a) these points are distorted.

## fisheye::estimateNewCameraMatrixForUndistortRectify

Estimates new camera matrix for undistortion or rectification.

C++: void fisheye::estimateNewCameraMatrixForUndistortRectify(InputArray K, InputArray D, const Size&image_size, InputArray R, OutputArray P, double balance=0.0, const Size& new_size=Size(), double fov_scale=1.0)
Parameters: K ¨C Camera matrix .D ¨C Input vector of distortion coefficients .R ¨C Rectification transformation in the object space: 3x3 1-channel, or vector: 3x1/1x3 1-channel or 1x1 3-channelP ¨C New camera matrix (3x3) or new projection matrix (3x4)balance ¨C Sets the new focal length in range between the min focal length and the max focal length. Balance is in range of [0, 1].fov_scale ¨C Divisor for new focal length.

## fisheye::stereoRectify

Stereo rectification for fisheye camera model

C++: void fisheye::stereoRectify(InputArray K1, InputArray D1, InputArray K2, InputArray D2, const Size& imageSize, InputArray R, InputArray tvec, OutputArray R1, OutputArray R2, OutputArray P1, OutputArray P2, OutputArray Q, int flags, const Size& newImageSize=Size(), double balance=0.0, double fov_scale=1.0)
Parameters: K1 ¨C First camera matrix.K2 ¨C Second camera matrix.D1 ¨C First camera distortion parameters.D2 ¨C Second camera distortion parameters.imageSize ¨C Size of the image used for stereo calibration.rotation ¨C Rotation matrix between the coordinate systems of the first and the second cameras.tvec ¨C Translation vector between coordinate systems of the cameras.R1 ¨C Output 3x3 rectification transform (rotation matrix) for the first camera.R2 ¨C Output 3x3 rectification transform (rotation matrix) for the second camera.P1 ¨C Output 3x4 projection matrix in the new (rectified) coordinate systems for the first camera.P2 ¨C Output 3x4 projection matrix in the new (rectified) coordinate systems for the second camera.Q ¨C Output  disparity-to-depth mapping matrix (see reprojectImageTo3D() ).flags ¨C Operation flags that may be zero or CV_CALIB_ZERO_DISPARITY . If the flag is set, the function makes the principal points of each camera have the same pixel coordinates in the rectified views. And if the flag is not set, the function may still shift the images in the horizontal or vertical direction (depending on the orientation of epipolar lines) to maximize the useful image area.alpha ¨C Free scaling parameter. If it is -1 or absent, the function performs the default scaling. Otherwise, the parameter should be between 0 and 1. alpha=0 means that the rectified images are zoomed and shifted so that only valid pixels are visible (no black areas after rectification). alpha=1 means that the rectified image is decimated and shifted so that all the pixels from the original images from the cameras are retained in the rectified images (no source image pixels are lost). Obviously, any intermediate value yields an intermediate result between those two extreme cases.newImageSize ¨C New image resolution after rectification. The same size should be passed toinitUndistortRectifyMap() (see the stereo_calib.cpp sample in OpenCV samples directory). When (0,0) is passed (default), it is set to the original imageSize . Setting it to larger value can help you preserve details in the original image, especially when there is a big radial distortion.roi1 ¨C Optional output rectangles inside the rectified images where all the pixels are valid. Ifalpha=0 , the ROIs cover the whole images. Otherwise, they are likely to be smaller (see the picture below).roi2 ¨C Optional output rectangles inside the rectified images where all the pixels are valid. Ifalpha=0 , the ROIs cover the whole images. Otherwise, they are likely to be smaller (see the picture below).balance ¨C Sets the new focal length in range between the min focal length and the max focal length. Balance is in range of [0, 1].fov_scale ¨C Divisor for new focal length.

## fisheye::calibrate

Performs camera calibaration

C++: double fisheye::calibrate(InputArrayOfArrays objectPoints, InputArrayOfArrays imagePoints, const Size&image_size, InputOutputArray K, InputOutputArray D, OutputArrayOfArrays rvecs, OutputArrayOfArrays tvecs, int flags=0, TermCriteria criteria=TermCriteria(TermCriteria::COUNT + TermCriteria::EPS, 100, DBL_EPSILON))
Parameters: objectPoints ¨C vector of vectors of calibration pattern points in the calibration pattern coordinate space.imagePoints ¨C vector of vectors of the projections of calibration pattern points. imagePoints.size()and objectPoints.size() and imagePoints[i].size() must be equal to objectPoints[i].size() for each i.image_size ¨C Size of the image used only to initialize the intrinsic camera matrix.K ¨C Output 3x3 floating-point camera matrix  . If fisheye::CALIB_USE_INTRINSIC_GUESS/ is specified, some or all of fx, fy, cx, cy must be initialized before calling the function.D ¨C Output vector of distortion coefficients .rvecs ¨C Output vector of rotation vectors (see Rodrigues() ) estimated for each pattern view. That is, each k-th rotation vector together with the corresponding k-th translation vector (see the next output parameter description) brings the calibration pattern from the model coordinate space (in which object points are specified) to the world coordinate space, that is, a real position of the calibration pattern in the k-th pattern view (k=0.. M -1).tvecs ¨C Output vector of translation vectors estimated for each pattern view.flags ¨CDifferent flags that may be zero or a combination of the following values:fisheye::CALIB_USE_INTRINSIC_GUESS cameraMatrix contains valid initial values of fx, fy, cx, cythat are optimized further. Otherwise, (cx, cy) is initially set to the image center ( imageSize is used), and focal distances are computed in a least-squares fashion.fisheye::CALIB_RECOMPUTE_EXTRINSIC Extrinsic will be recomputed after each iteration of intrinsic optimization.fisheye::CALIB_CHECK_COND The functions will check validity of condition number.fisheye::CALIB_FIX_SKEW Skew coefficient (alpha) is set to zero and stay zero.fisheye::CALIB_FIX_K1..4 Selected distortion coefficients are set to zeros and stay zero.criteria ¨C Termination criteria for the iterative optimization algorithm.

## fisheye::stereoCalibrate

Performs stereo calibration

C++: double fisheye::stereoCalibrate(InputArrayOfArrays objectPoints, InputArrayOfArrays imagePoints1, InputArrayOfArrays imagePoints2, InputOutputArray K1, InputOutputArray D1, InputOutputArray K2, InputOutputArray D2, SizeimageSize, OutputArray R, OutputArray T, int flags=CALIB_FIX_INTRINSIC, TermCriteriacriteria=TermCriteria(TermCriteria::COUNT + TermCriteria::EPS, 100, DBL_EPSILON))
Parameters: objectPoints ¨C Vector of vectors of the calibration pattern points.imagePoints1 ¨C Vector of vectors of the projections of the calibration pattern points, observed by the first camera.imagePoints2 ¨C Vector of vectors of the projections of the calibration pattern points, observed by the second camera.K1 ¨C Input/output first camera matrix:  ,  . If any offisheye::CALIB_USE_INTRINSIC_GUESS , fisheye::CV_CALIB_FIX_INTRINSIC are specified, some or all of the matrix components must be initialized.D1 ¨C Input/output vector of distortion coefficients  of 4 elements.K2 ¨C Input/output second camera matrix. The parameter is similar to K1 .D2 ¨C Input/output lens distortion coefficients for the second camera. The parameter is similar to D1.imageSize ¨C Size of the image used only to initialize intrinsic camera matrix.R ¨C Output rotation matrix between the 1st and the 2nd camera coordinate systems.T ¨C Output translation vector between the coordinate systems of the cameras.flags ¨CDifferent flags that may be zero or a combination of the following values:fisheye::CV_CALIB_FIX_INTRINSIC Fix K1, K2? and D1, D2? so that only R, T matrices are estimated.fisheye::CALIB_USE_INTRINSIC_GUESS K1, K2 contains valid initial values of fx, fy, cx, cy that are optimized further. Otherwise, (cx, cy) is initially set to the image center (imageSize is used), and focal distances are computed in a least-squares fashion.fisheye::CALIB_RECOMPUTE_EXTRINSIC Extrinsic will be recomputed after each iteration of intrinsic optimization.fisheye::CALIB_CHECK_COND The functions will check validity of condition number.fisheye::CALIB_FIX_SKEW Skew coefficient (alpha) is set to zero and stay zero.fisheye::CALIB_FIX_K1..4 Selected distortion coefficients are set to zeros and stay zero.criteria ¨C Termination criteria for the iterative optimization algorithm.
 [BT98] Birchfield, S. and Tomasi, C. A pixel dissimilarity measure that is insensitive to image sampling. IEEE Transactions on Pattern Analysis and Machine Intelligence. 1998.
 [BouguetMCT] J.Y.Bouguet. MATLAB calibration tool. http://www.vision.caltech.edu/bouguetj/calib_doc/
 [Hartley99] Hartley, R.I., Theory and Practice of Projective Rectification. IJCV 35 2, pp 115-127 (1)
 [HH08] Hirschmuller, H. Stereo Processing by Semiglobal Matching and Mutual Information, PAMI(30), No. 2, February 2008, pp. 328-341.
 [Slabaugh] (1, 2) Slabaugh, G.G. Computing Euler angles from a rotation matrix.http://www.soi.city.ac.uk/~sbbh653/publications/euler.pdf (verified: 2013-04-15)
 [Zhang2] Zhang. A Flexible New Technique for Camera Calibration. IEEE Transactions on Pattern Analysis and Machine Intelligence, 22(11):1330-1334, 2.
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