The distortion coefficients do not depend on the scene viewed. Thus, they also belong to the intrinsic camera parameters. And they remain the same regardless of the captured image resolution.
* Estimate intrinsic and extrinsic camera parameters from several views of a known calibration pattern (every view is described by several 3D-2D point correspondences).
* Estimate the relative position and orientation of the stereo camera "heads" and compute the *rectification* transformation that makes the camera optical axes parallel.
:param objectPoints:Vector of vectors of calibration pattern points in the calibration pattern coordinate space. The outer vector contains as many elements as the number of the pattern views. If the same calibration pattern is shown in each view and it is fully visible, all the vectors will be the same. Although, it is possible to use partially occluded patterns, or even different patterns in different views. Then, the vectors will be different. The points are 3D, but since they are in a pattern coordinate system, then, if the rig is planar, it may make sense to put the model to a XY coordinate plane so that Z-coordinate of each input object point is 0.
:param imagePoints:Vector of vectors of the projections of calibration pattern points. ``imagePoints.size()`` and ``objectPoints.size()`` and ``imagePoints[i].size()`` must be equal to ``objectPoints[i].size()`` for each ``i``.
:param cameraMatrix:Output 3x3 floating-point camera matrix :math:`A = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}` . If ``CV_CALIB_USE_INTRINSIC_GUESS`` and/or ``CV_CALIB_FIX_ASPECT_RATIO`` are specified, some or all of ``fx, fy, cx, cy`` must be initialized before calling the function.
:param rvecs:Output vector of rotation vectors (see :ref:`Rodrigues` ) estimated for each pattern view. That is, each k-th rotation vector together with the corresponding k-th translation vector (see the next output parameter description) brings the calibration pattern from the model coordinate space (in which object points are specified) to the world coordinate space, that is, a real position of the calibration pattern in the k-th pattern view (k=0.. *M* -1).
***CV_CALIB_USE_INTRINSIC_GUESS**``cameraMatrix`` contains valid initial values of ``fx, fy, cx, cy`` that are optimized further. Otherwise, ``(cx, cy)`` is initially set to the image center ( ``imageSize`` is used), and focal distances are computed in a least-squares fashion. Note, that if intrinsic parameters are known, there is no need to use this function just to estimate extrinsic parameters. Use :ref:`solvePnP` instead.
***CV_CALIB_FIX_PRINCIPAL_POINT** The principal point is not changed during the global optimization. It stays at the center or at a different location specified when ``CV_CALIB_USE_INTRINSIC_GUESS`` is set too.
***CV_CALIB_FIX_ASPECT_RATIO** The functions considers only ``fy`` as a free parameter. The ratio ``fx/fy`` stays the same as in the input ``cameraMatrix`` . When ``CV_CALIB_USE_INTRINSIC_GUESS`` is not set, the actual input values of ``fx`` and ``fy`` are ignored, only their ratio is computed and used further.
***CV_CALIB_FIX_K1,...,CV_CALIB_FIX_K6** The corresponding radial distortion coefficient is not changed during the optimization. If ``CV_CALIB_USE_INTRINSIC_GUESS`` is set, the coefficient from the supplied ``distCoeffs`` matrix is used. Otherwise, it is set to 0.
***CV_CALIB_RATIONAL_MODEL** Coefficients k4, k5, and k6 are enabled. To provide the backward compatibility, this extra flag should be explicitly specified to make the calibration function use the rational model and return 8 coefficients. If the flag is not set, the function computes and returns only 5 distortion coefficients.
Compute the initial intrinsic parameters (the option only available for planar calibration patterns) or read them from the input parameters. The distortion coefficients are all set to zeros initially unless some of ``CV_CALIB_FIX_K?`` are specified.
Run the global Levenberg-Marquardt optimization algorithm to minimize the reprojection error, that is, the total sum of squared distances between the observed feature points ``imagePoints`` and the projected (using the current estimates for camera parameters and the poses) object points ``objectPoints``. See :ref:`projectPoints` for details.
Also, the functions can compute the derivatives of the output vectors with regards to the input vectors (see :ref:`matMulDeriv` ).
The functions are used inside :ref:`stereoCalibrate` but can also be used in your own code where Levenberg-Marquardt or another gradient-based solver is used to optimize a function that contains a matrix multiplication.
:param lines:Output vector of the epipolar lines corresponding to the points in the other image. Each line :math:`ax + by + c=0` is encoded by 3 numbers :math:`(a, b, c)` .
If the output array dimensionality is larger, an extra 1 is appended to each point. Otherwise, the input array is simply copied (with an optional transposition) to the output.
:param patternSize:Number of inner corners per a chessboard row and column. ``(patternSize = cv::Size(points_per_row,points_per_column) = cv::Size(rows,columns) )``
:param patternWasFound:Parameter indicating whether the complete board was found or not. The return value :ref:`FindChessboardCorners` may be passed here.
The function draws individual chessboard corners detected either as red circles if the board was not found, or as colored corners connected with lines if the board was found.
:param patternSize:Number of inner corners per a chessboard row and column. ``( patternSize = cvSize(points_per_row,points_per_colum) = cvSize(columns,rows) )``
***CV_CALIB_CB_ADAPTIVE_THRESH** Use adaptive thresholding to convert the image to black and white, rather than a fixed threshold level (computed from the average image brightness).
***CV_CALIB_CB_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.
***CALIB_CB_FAST_CHECK** Run a fast check on the image that looks for chessboard corners, and shortcut the call if none is found. This can drastically speed up the call in the degenerate condition when no chessboard is observed.
The function requires white space (like a square-thick border, the wider the better) around the board to make the detection more robust in various environments. Otherwise, if there is no border and the background is dark, the outer black squares cannot be segmented properly and so the square grouping and ordering algorithm fails.
The function requires white space (like a square-thick border, the wider the better) around the board to make the detection more robust in various environments.
:param objectPoints:Array of object points in the object coordinate space, 3xN/Nx3 1-channel or 1xN/Nx1 3-channel, where N is the number of points. ``vector<Point3f>`` can be also passed here.
:param imagePoints:Array of corresponding image points, 2xN/Nx2 1-channel or 1xN/Nx1 2-channel, where N is the number of points. ``vector<Point2f>`` can be also passed here.
:param cameraMatrix:Input camera matrix :math:`A = \vecthreethree{fx}{0}{cx}{0}{fy}{cy}{0}{0}{1}` .
:param distCoeffs:Input vector of distortion coefficients :math:`(k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6]])` of 4, 5, or 8 elements. If the vector is NULL/empty, the zero distortion coefficients are assumed.
:param rvec:Output rotation vector (see :ref:`Rodrigues` ) that, together with ``tvec`` , brings points from the model coordinate system to the camera coordinate system.
:param useExtrinsicGuess:If true (1), the function uses the provided ``rvec`` and ``tvec`` values as initial approximations of the rotation and translation vectors, respectively, and further optimizes them.
The function estimates the object pose given a set of object points, their corresponding image projections, as well as the camera matrix and the distortion coefficients. This function finds such a pose that minimizes reprojection error, that is, the sum of squared distances between the observed projections ``imagePoints`` and the projected (using
:param objectPoints:Array of object points in the object coordinate space, 3xN/Nx3 1-channel or 1xN/Nx1 3-channel, where N is the number of points. ``vector<Point3f>`` can be also passed here.
:param imagePoints:Array of corresponding image points, 2xN/Nx2 1-channel or 1xN/Nx1 2-channel, where N is the number of points. ``vector<Point2f>`` can be also passed here.
:param distCoeffs:Input vector of distortion coefficients :math:`(k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6]])` of 4, 5, or 8 elements. If the vector is NULL/empty, the zero distortion coefficients are assumed.
:param rvec:Output rotation vector (see :ref:`Rodrigues` ) that, together with ``tvec`` , brings points from the model coordinate system to the camera coordinate system.
:param useExtrinsicGuess:If true (1), the function uses the provided ``rvec`` and ``tvec`` values as initial approximations of the rotation and translation vectors, respectively, and further optimizes them.
:param reprojectionError:The inlier threshold value used by the RANSAC procedure. That is, the parameter value is the maximum allowed distance between the observed and computed point projections to consider it an inlier.
The function estimates an object pose given a set of object points, their corresponding image projections, as well as the camera matrix and the distortion coefficients. This function finds such a pose that minimizes reprojection error, that is, the sum of squared distances between the observed projections ``imagePoints`` and the projected (using
:ref:`projectPoints` ) ``objectPoints``. The use of RANSAC makes the function resistant to outliers.
:param param1: Parameter used for RANSAC. It is the maximum distance from a point to an epipolar line in pixels, beyond which the point is considered an outlier and is not used for computing the final fundamental matrix. It can be set to something like 1-3, depending on the accuracy of the point localization, image resolution, and the image noise.
:param param2:Parameter used for the RANSAC or LMedS methods only. It specifies a desirable level of confidence (probability) that the estimated matrix is correct.
:param status:Output array of N elements, every element of which is set to 0 for outliers and to 1 for the other points. The array is computed only in the RANSAC and LMedS methods. For other methods, it is set to all 1's.
then the point :math:`i` is considered an outlier. If ``srcPoints`` and ``dstPoints`` are measured in pixels, it usually makes sense to set this parameter somewhere in the range of 1 to 10.
:param centerPrincipalPoint:Location of the principal point in the new camera matrix. The parameter indicates whether this location should be at the image center or not.
The function returns the camera matrix that is either an exact copy of the input ``cameraMatrix`` (when ``centerPrinicipalPoint=false`` ), or the modified one (when ``centerPrincipalPoint`` =true).
By default, the undistortion functions in OpenCV (see
:ref:`initUndistortRectifyMap`,
:ref:`undistort`) do not move the principal point. However, when you work with stereo, it is important to move the principal points in both views to the same y-coordinate (which is required by most of stereo correspondence algorithms), and may be to the same x-coordinate too. So, you can form the new camera matrix for each view where the principal points are located at the center.
:param distCoeffs:Input vector of distortion coefficients :math:`(k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6]])` of 4, 5, or 8 elements. If the vector is NULL/empty, the zero distortion coefficients are assumed.
:param alpha:Free scaling parameter between 0 (when all the pixels in the undistorted image are valid) and 1 (when all the source image pixels are retained in the undistorted image). See :ref:`StereoRectify` for details.
:param validPixROI:Optional output rectangle that outlines all-good-pixels region in the undistorted image. See ``roi1, roi2`` description in :ref:`StereoRectify` .
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
:param objectPoints:Vector of vectors of the calibration pattern points in the calibration pattern coordinate space. See :ref:`calibrateCamera` for details.
:param aspectRatio:If it is zero or negative, both :math:`f_x` and :math:`f_y` are estimated independently. Otherwise, :math:`f_x = f_y * \texttt{aspectRatio}` .
:param distCoeffs:Input vector of distortion coefficients :math:`(k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6]])` of 4, 5, or 8 elements. If the vector is NULL/empty, the zero distortion coefficients are assumed.
:param R:Optional rectification transformation in the object space (3x3 matrix). ``R1`` or ``R2`` , computed by :ref:`StereoRectify` can be passed here. If the matrix is empty, the identity transformation is assumed.
The function computes the joint undistortion and rectification transformation and represents the result in the form of maps for
:ref:`Remap` . The undistorted image looks like original, as if it is captured with a camera using the camera matrix ``=newCameraMatrix`` and zero distortion. In case of a monocular camera, ``newCameraMatrix`` is usually equal to ``cameraMatrix`` , or it can be computed by
:ref:`GetOptimalNewCameraMatrix` for a better control over scaling. In case of a stereo camera, ``newCameraMatrix`` is normally set to ``P1`` or ``P2`` computed by
Also, this new camera is oriented differently in the coordinate space, according to ``R`` . That, for example, helps to align two heads of a stereo camera so that the epipolar lines on both images become horizontal and have the same y- coordinate (in case of a horizontally aligned stereo camera).
:math:`(u, v)` in the destination (corrected and rectified) image, the function computes the corresponding coordinates in the source image (that is, in the original image from camera). The following process is applied:
:ref:`StereoRectify` , which in its turn is called after
:ref:`StereoCalibrate` . But if the stereo camera was not calibrated, it is still possible to compute the rectification transformations directly from the fundamental matrix using
:ref:`StereoRectifyUncalibrated` . For each camera, the function computes homography ``H`` as the rectification transformation in a pixel domain, not a rotation matrix ``R`` in 3D space. ``R`` can be computed from ``H`` as
:param objectPoints:Array of object points, 3xN/Nx3 1-channel or 1xN/Nx1 3-channel (or ``vector<Point3f>`` ), where N is the number of points in the view.
:param distCoeffs:Input vector of distortion coefficients :math:`(k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6]])` of 4, 5, or 8 elements. If the vector is NULL/empty, the zero distortion coefficients are assumed.
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.
:param _3dImage:Output 3-channel floating-point image of the same size as ``disparity`` . Each element of ``_3dImage(x,y)`` contains 3D coordinates of the point ``(x,y)`` computed from the disparity map.
:param handleMissingValues:Indicates, whether the function should handle missing values (i.e. points where the disparity was not computed). If ``handleMissingValues=true``, then pixels with the minimal disparity that corresponds to the outliers (see :ref:`StereoBM::operator ()` ) are transformed to 3D points with a very large Z value (currently set to 10000).
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:
:param jacobian:Optional output Jacobian matrix, 3x9 or 9x3, which is a matrix of partial derivatives of the output array components with respect to the input array components.
:param disp: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.
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.
* By default, the algorithm is single-pass, which means that you consider only 5 directions instead of 8. Set ``fullDP=true`` to run the full variant of the algorithm but beware that it may consume a lot of memory.
* Mutual information cost function is not implemented. Instead, a simpler Birchfield-Tomasi sub-pixel metric from BT96 is used. Though, the color images are supported as well.
* Some pre- and post- processing steps from K. Konolige algorithm :ref:`StereoBM::operator ()` are included, for example: pre-filtering (``CV_STEREO_BM_XSOBEL`` type) and post-filtering (uniqueness check, quadratic interpolation and speckle filtering).
..c:function:: 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)
:param minDisparity:Minimum possible disparity value. Normally, it is zero but sometimes rectification algorithms can shift images, so this parameter needs to be adjusted accordingly.
:param numDisparities:Maximum disparity minus minimum disparity. The value is always greater than zero. In the current implementation, this parameter must be divisible by 16.
:param P1, P2:Parameters that control disparity smoothness. The larger the values are, the smoother the disparity is. ``P1`` is the penalty on the disparity change by plus or minus 1 between neighbor pixels. ``P2`` is the penalty on the disparity change by more than 1 between neighbor pixels. The algorithm requires ``P2 > P1`` . See ``stereo_match.cpp`` sample where some reasonably good ``P1`` and ``P2`` values are shown (like ``8*number_of_image_channels*SADWindowSize*SADWindowSize`` and ``32*number_of_image_channels*SADWindowSize*SADWindowSize`` , respectively).
:param disp12MaxDiff:Maximum allowed difference (in integer pixel units) in the left-right disparity check. Set it to a non-positive value to disable the check.
:param preFilterCap:Truncation value for the prefiltered image pixels. The algorithm first computes x-derivative at each pixel and clips its value by ``[-preFilterCap, preFilterCap]`` interval. The result values are passed to the Birchfield-Tomasi pixel cost function.
:param uniquenessRatio:Margin in percentage by which the best (minimum) computed cost function value should "win" the second best value to consider the found match correct. Normally, a value within the 5-15 range is good enough.
:param speckleWindowSize:Maximum size of smooth disparity regions to consider their noise speckles and invalidate. Set it to 0 to disable speckle filtering. Otherwise, set it somewhere in the 50-200 range.
:param speckleRange:Maximum disparity variation within each connected component. If you do speckle filtering, set the parameter to a positive value, multiple of 16. Normally, 16 or 32 is good enough.
:param fullDP: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 set ``StereoSGBM::numberOfDisparities`` at minimum. The second constructor enables you to set each parameter to a custom value.
:param disp: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.
:param cameraMatrix1:Input/output first camera matrix: :math:`\vecthreethree{f_x^{(j)}}{0}{c_x^{(j)}}{0}{f_y^{(j)}}{c_y^{(j)}}{0}{0}{1}` ,
:math:`j = 0,\, 1` . If any of ``CV_CALIB_USE_INTRINSIC_GUESS`` , ``CV_CALIB_FIX_ASPECT_RATIO`` , ``CV_CALIB_FIX_INTRINSIC`` , or ``CV_CALIB_FIX_FOCAL_LENGTH`` are specified, some or all of the matrix components must be initialized. See the flags description for details.
:param distCoeffs1:Input/output vector of distortion coefficients :math:`(k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6]])` of 4, 5, or 8 elements. The output vector length depends on the flags.
***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_K1,...,CV_CALIB_FIX_K6** Do not change the corresponding radial distortion coefficient during the optimization. If ``CV_CALIB_USE_INTRINSIC_GUESS`` is set, the coefficient from the supplied ``distCoeffs`` matrix is used. Otherwise, it is set to 0.
***CV_CALIB_RATIONAL_MODEL** Enable coefficients k4, k5, and k6. To provide the backward compatibility, this extra flag should be explicitly specified to make the calibration function use the rational model and return 8 coefficients. If the flag is not set, the function computes and returns only 5 distortion coefficients.
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
:ref:`solvePnP` ), then those poses definitely relate to each other. This means that, given (
:math:`R_1`,:math:`T_1` ), it should be possible to compute (
:math:`R_2`,: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 (
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
:ref:`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 :ref:`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.
:param flags:Operation flags that may be zero or ``CV_CALIB_ZERO_DISPARITY`` . If the flag is set, the function makes the principal points of each camera have the same pixel coordinates in the rectified views. And if the flag is not set, the function may still shift the images in the horizontal or vertical direction (depending on the orientation of epipolar lines) to maximize the useful image area.
:param alpha:Free scaling parameter. If it is -1 or absent, the function performs the default scaling. Otherwise, the parameter should be between 0 and 1. ``alpha=0`` means that the rectified images are zoomed and shifted so that only valid pixels are visible (no black areas after rectification). ``alpha=1`` means that the rectified image is decimated and shifted so that all the pixels from the original images from the cameras are retained in the rectified images (no source image pixels are lost). Obviously, any intermediate value yields an intermediate result between those two extreme cases.
:param newImageSize:New image resolution after rectification. The same size should be passed to :ref:`InitUndistortRectifyMap` (see the ``stereo_calib.cpp`` sample in OpenCV samples directory). When (0,0) is passed (default), it is set to the original ``imageSize`` . Setting it to larger value can help you preserve details in the original image, especially when there is a big radial distortion.
:param roi1, roi2: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
:ref:`stereoCalibrate` as input. As output, it provides two rotation matrices and also two projection matrices in the new coordinates. The function distinguishes the following two cases:
**Horizontal stereo**: the first and the second camera views are shifted relative to each other mainly along the x axis (with possible small vertical shift). In the rectified images, the corresponding epipolar lines in the left and right cameras are horizontal and have the same y-coordinate. P1 and P2 look like:
**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:
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.
:param threshold:Optional threshold used to filter out the outliers. If the parameter is greater than zero, all the point pairs that do not comply with the epipolar geometry (that is, the points for which :math:`|\texttt{points2[i]}^T*\texttt{F}*\texttt{points1[i]}|>\texttt{threshold}` ) are rejected prior to computing the homographies. Otherwise,all the points are considered inliers.
The function computes the rectification transformations without knowing intrinsic parameters of the cameras and their relative position in the space, which explains the suffix "uncalibrated". Another related difference from
:ref:`StereoRectify` is that the function outputs not the rectification transformations in the object (3D) space, but the planar perspective transformations encoded by the homography matrices ``H1`` and ``H2`` . The function implements the algorithm
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
:ref:`calibrateCamera` . Then, the images can be corrected using
:param distCoeffs:Input vector of distortion coefficients :math:`(k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6]])` of 4, 5, or 8 elements. If the vector is NULL/empty, the zero distortion coefficients are assumed.
:param newCameraMatrix:Camera matrix of the distorted image. By default, it is the same as ``cameraMatrix`` but you may additionally scale and shift the result by using a different matrix.
:param distCoeffs:Input vector of distortion coefficients :math:`(k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6]])` of 4, 5, or 8 elements. If the vector is NULL/empty, the zero distortion coefficients are assumed.
:param R:Rectification transformation in the object space (3x3 matrix). ``R1`` or ``R2`` computed by :ref:`StereoRectify` can be passed here. If the matrix is empty, the identity transformation is used.
:param P:New camera matrix (3x3) or new projection matrix (3x4). ``P1`` or ``P2`` computed by :ref:`StereoRectify` can be passed here. If the matrix is empty, the identity new camera matrix is used.
:ref:`initUndistortRectifyMap` but it operates on a sparse set of points instead of a raster image. Also the function performs a reverse transformation to
:ref:`projectPoints` . In case of a 3D object, it does not reconstruct its 3D coordinates, but for a planar object, it does, up to a translation vector, if the proper ``R`` is specified. ::
where ``undistort()`` is an approximate iterative algorithm that estimates the normalized original point coordinates out of the normalized distorted point coordinates ("normalized" means that the coordinates do not depend on the camera matrix).
