Camera Calibration and 3D Reconstruction ======================================== .. highlight:: c The functions in this section use the so-called pinhole camera model. That is, a scene view is formed by projecting 3D points into the image plane using a perspective transformation. .. math:: s \; m' = A [R|t] M' or .. math:: s \vecthree{u}{v}{1} = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1} \begin{bmatrix} r_{11} & r_{12} & r_{13} & t_1 \\ r_{21} & r_{22} & r_{23} & t_2 \\ r_{31} & r_{32} & r_{33} & t_3 \end{bmatrix} \begin{bmatrix} X \\ Y \\ Z \\ 1 \end{bmatrix} Where :math:`(X, Y, Z)` are the coordinates of a 3D point in the world coordinate space, :math:`(u, v)` are the coordinates of the projection point in pixels. :math:`A` is called a camera matrix, or a matrix of intrinsic parameters. :math:`(cx, cy)` is a principal point (that is usually at the image center), and :math:`fx, fy` are the focal lengths expressed in pixel-related units. Thus, if an image from camera is scaled by some factor, all of these parameters should be scaled (multiplied/divided, respectively) by the same factor. The matrix of intrinsic parameters does not depend on the scene viewed and, once estimated, can be re-used (as long as the focal length is fixed (in case of zoom lens)). The joint rotation-translation matrix :math:`[R|t]` is called a matrix of extrinsic parameters. It is used to describe the camera motion around a static scene, or vice versa, rigid motion of an object in front of still camera. That is, :math:`[R|t]` translates coordinates of a point :math:`(X, Y, Z)` to some coordinate system, fixed with respect to the camera. The transformation above is equivalent to the following (when :math:`z \ne 0` ): .. math:: \begin{array}{l} \vecthree{x}{y}{z} = R \vecthree{X}{Y}{Z} + t \\ x' = x/z \\ y' = y/z \\ u = f_x*x' + c_x \\ v = f_y*y' + c_y \end{array} Real lenses usually have some distortion, mostly radial distortion and slight tangential distortion. So, the above model is extended as: .. math:: \begin{array}{l} \vecthree{x}{y}{z} = R \vecthree{X}{Y}{Z} + t \\ x' = x/z \\ y' = y/z \\ 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) \\ 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' \\ \text{where} \quad r^2 = x'^2 + y'^2 \\ u = f_x*x'' + c_x \\ v = f_y*y'' + c_y \end{array} :math:`k_1` , :math:`k_2` , :math:`k_3` are radial distortion coefficients, :math:`p_1` , :math:`p_2` are tangential distortion coefficients. Higher-order coefficients are not considered in OpenCV. In the functions below the coefficients are passed or returned as .. math:: (k_1, k_2, p_1, p_2[, k_3]) vector. That is, if the vector contains 4 elements, it means that :math:`k_3=0` . 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.* That is, if, for example, a camera has been calibrated on images of :math:`320 \times 240` resolution, absolutely the same distortion coefficients can be used for images of :math:`640 \times 480` resolution from the same camera (while :math:`f_x` , :math:`f_y` , :math:`c_x` and :math:`c_y` need to be scaled appropriately). The functions below use the above model to * Project 3D points to the image plane given intrinsic and extrinsic parameters * Compute extrinsic parameters given intrinsic parameters, a few 3D points and their projections. * Estimate intrinsic and extrinsic camera parameters from several views of a known calibration pattern (i.e. 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. .. index:: CalcImageHomography .. _CalcImageHomography: CalcImageHomography ------------------- .. cfunction:: void cvCalcImageHomography( float* line, CvPoint3D32f* center, float* intrinsic, float* homography ) Calculates the homography matrix for an oblong planar object (e.g. arm). :param line: the main object axis direction (vector (dx,dy,dz)) :param center: object center ((cx,cy,cz)) :param intrinsic: intrinsic camera parameters (3x3 matrix) :param homography: output homography matrix (3x3) The function calculates the homography matrix for the initial image transformation from image plane to the plane, defined by a 3D oblong object line (See _ _ Figure 6-10 _ _ in the OpenCV Guide 3D Reconstruction Chapter). .. index:: CalibrateCamera2 .. _CalibrateCamera2: CalibrateCamera2 ---------------- .. cfunction:: double cvCalibrateCamera2( const CvMat* objectPoints, const CvMat* imagePoints, const CvMat* pointCounts, CvSize imageSize, CvMat* cameraMatrix, CvMat* distCoeffs, CvMat* rvecs=NULL, CvMat* tvecs=NULL, int flags=0 ) Finds the camera intrinsic and extrinsic parameters from several views of a calibration pattern. :param objectPoints: The joint matrix of object points - calibration pattern features in the model coordinate space. It is floating-point 3xN or Nx3 1-channel, or 1xN or Nx1 3-channel array, where N is the total number of points in all views. :param imagePoints: The joint matrix of object points projections in the camera views. It is floating-point 2xN or Nx2 1-channel, or 1xN or Nx1 2-channel array, where N is the total number of points in all views :param pointCounts: Integer 1xM or Mx1 vector (where M is the number of calibration pattern views) containing the number of points in each particular view. The sum of vector elements must match the size of ``objectPoints`` and ``imagePoints`` (=N). :param imageSize: Size of the image, used only to initialize the intrinsic camera matrix :param cameraMatrix: The 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 distCoeffs: The output 4x1, 1x4, 5x1 or 1x5 vector of distortion coefficients :math:`(k_1, k_2, p_1, p_2[, k_3])` . :param rvecs: The output 3x *M* or *M* x3 1-channel, or 1x *M* or *M* x1 3-channel array of rotation vectors (see :ref:`Rodrigues2` ), estimated for each pattern view. That is, each k-th rotation vector together with the corresponding k-th translation vector (see the next output parameter description) brings the calibration pattern from the model coordinate space (in which object points are specified) to the world coordinate space, i.e. real position of the calibration pattern in the k-th pattern view (k=0.. *M* -1) :param tvecs: The output 3x *M* or *M* x3 1-channel, or 1x *M* or *M* x1 3-channel array of translation vectors, estimated for each pattern view. :param flags: Different flags, may be 0 or combination of the following values: * **CV_CALIB_USE_INTRINSIC_GUESS** ``cameraMatrix`` contains the 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 here), and focal distances are computed in some least-squares fashion. Note, that if intrinsic parameters are known, there is no need to use this function just to estimate the extrinsic parameters. Use :ref:`FindExtrinsicCameraParams2` instead. * **CV_CALIB_FIX_PRINCIPAL_POINT** The principal point is not changed during the global optimization, it stays at the center or at the other location specified when ``CV_CALIB_USE_INTRINSIC_GUESS`` is set too. * **CV_CALIB_FIX_ASPECT_RATIO** The functions considers only ``fy`` as a free parameter, the ratio ``fx/fy`` stays the same as in the input ``cameraMatrix`` . When ``CV_CALIB_USE_INTRINSIC_GUESS`` is not set, the actual input values of ``fx`` and ``fy`` are ignored, only their ratio is computed and used further. * **CV_CALIB_ZERO_TANGENT_DIST** Tangential distortion coefficients :math:`(p_1, p_2)` will be set to zeros and stay zero. The function estimates the intrinsic camera parameters and extrinsic parameters for each of the views. The coordinates of 3D object points and their correspondent 2D projections in each view must be specified. That may be achieved by using an object with known geometry and easily detectable feature points. Such an object is called a calibration rig or calibration pattern, and OpenCV has built-in support for a chessboard as a calibration rig (see :ref:`FindChessboardCorners` ). Currently, initialization of intrinsic parameters (when ``CV_CALIB_USE_INTRINSIC_GUESS`` is not set) is only implemented for planar calibration patterns (where z-coordinates of the object points must be all 0's). 3D calibration rigs can also be used as long as initial ``cameraMatrix`` is provided. The algorithm does the following: #. First, it computes the initial intrinsic parameters (the option only available for planar calibration patterns) or reads them from the input parameters. The distortion coefficients are all set to zeros initially (unless some of ``CV_CALIB_FIX_K?`` are specified). #. The initial camera pose is estimated as if the intrinsic parameters have been already known. This is done using :ref:`FindExtrinsicCameraParams2` #. 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 ``imagePoints`` and the projected (using the current estimates for camera parameters and the poses) object points ``objectPoints`` ; see :ref:`ProjectPoints2` . The function returns the final re-projection error. Note: if you're using a non-square (=non-NxN) grid and :func:`findChessboardCorners` for calibration, and ``calibrateCamera`` returns bad values (i.e. zero distortion coefficients, an image center very far from :math:`(w/2-0.5,h/2-0.5)` , and / or large differences between :math:`f_x` and :math:`f_y` (ratios of 10:1 or more)), then you've probably used ``patternSize=cvSize(rows,cols)`` , but should use ``patternSize=cvSize(cols,rows)`` in :ref:`FindChessboardCorners` . See also: :ref:`FindChessboardCorners` , :ref:`FindExtrinsicCameraParams2` , :func:`initCameraMatrix2D` , :ref:`StereoCalibrate` , :ref:`Undistort2` .. index:: ComputeCorrespondEpilines .. _ComputeCorrespondEpilines: ComputeCorrespondEpilines ------------------------- .. cfunction:: void cvComputeCorrespondEpilines( const CvMat* points, int whichImage, const CvMat* F, CvMat* lines) For points in one image of a stereo pair, computes the corresponding epilines in the other image. :param points: The input points. ``2xN, Nx2, 3xN`` or ``Nx3`` array (where ``N`` number of points). Multi-channel ``1xN`` or ``Nx1`` array is also acceptable :param whichImage: Index of the image (1 or 2) that contains the ``points`` :param F: The fundamental matrix that can be estimated using :ref:`FindFundamentalMat` or :ref:`StereoRectify` . :param lines: The output epilines, a ``3xN`` or ``Nx3`` array. Each line :math:`ax + by + c=0` is encoded by 3 numbers :math:`(a, b, c)` For every point in one of the two images of a stereo-pair the function finds the equation of the corresponding epipolar line in the other image. From the fundamental matrix definition (see :ref:`FindFundamentalMat` ), line :math:`l^{(2)}_i` in the second image for the point :math:`p^{(1)}_i` in the first image (i.e. when ``whichImage=1`` ) is computed as: .. math:: l^{(2)}_i = F p^{(1)}_i and, vice versa, when ``whichImage=2`` , :math:`l^{(1)}_i` is computed from :math:`p^{(2)}_i` as: .. math:: l^{(1)}_i = F^T p^{(2)}_i Line coefficients are defined up to a scale. They are normalized, such that :math:`a_i^2+b_i^2=1` . .. index:: ConvertPointsHomogeneous .. _ConvertPointsHomogeneous: ConvertPointsHomogeneous ------------------------ .. cfunction:: void cvConvertPointsHomogeneous( const CvMat* src, CvMat* dst ) Convert points to/from homogeneous coordinates. :param src: The input point array, ``2xN, Nx2, 3xN, Nx3, 4xN or Nx4 (where ``N`` is the number of points)`` . Multi-channel ``1xN`` or ``Nx1`` array is also acceptable :param 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 The function converts 2D or 3D points from/to homogeneous 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: .. math:: \begin{array}{l} (x,y[,z],w) -> (x',y'[,z']) \\ \text{where} \\ x' = x/w \\ y' = y/w \\ z' = z/w \quad \text{(if output is 3D)} \end{array} If the output array dimensionality is larger, an extra 1 is appended to each point. Otherwise, the input array is simply copied (with optional transposition) to the output. **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 :math:`\texttt{N} \ge 5` , or to use multi-channel ``Nx1`` or ``1xN`` arrays. .. index:: CreatePOSITObject .. _CreatePOSITObject: CreatePOSITObject ----------------- .. cfunction:: CvPOSITObject* cvCreatePOSITObject( CvPoint3D32f* points, int point_count ) Initializes a structure containing object information. :param points: Pointer to the points of the 3D object model :param point_count: Number of object points The function allocates memory for the object structure and computes the object inverse matrix. The preprocessed object data is stored in the structure :ref:`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. An object is defined as a set of points given in a coordinate system. The function :ref:`POSIT` computes a vector that begins at a camera-related coordinate system center and ends at the ``points[0]`` of the object. Once the work with a given object is finished, the function :ref:`ReleasePOSITObject` must be called to free memory. .. index:: CreateStereoBMState .. _CreateStereoBMState: CreateStereoBMState ------------------- .. cfunction:: CvStereoBMState* cvCreateStereoBMState( int preset=CV_STEREO_BM_BASIC, int numberOfDisparities=0 ) Creates block matching stereo correspondence structure. :param preset: ID of one of the pre-defined parameter sets. Any of the parameters can be overridden after creating the structure. Values are * **CV_STEREO_BM_BASIC** Parameters suitable for general cameras * **CV_STEREO_BM_FISH_EYE** Parameters suitable for wide-angle cameras * **CV_STEREO_BM_NARROW** Parameters suitable for narrow-angle cameras :param 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. 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 :ref:`FindStereoCorrespondenceBM` . .. index:: CreateStereoGCState .. _CreateStereoGCState: CreateStereoGCState ------------------- .. cfunction:: CvStereoGCState* cvCreateStereoGCState( int numberOfDisparities, int maxIters ) Creates the state of graph cut-based stereo correspondence algorithm. :param numberOfDisparities: The number of disparities. The disparity search range will be :math:`\texttt{state->minDisparity} \le disparity < \texttt{state->minDisparity} + \texttt{state->numberOfDisparities}` :param 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 [Kolmogorov03]_ for details. 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 :ref:`FindStereoCorrespondenceGC` . .. index:: CvStereoBMState .. _CvStereoBMState: CvStereoBMState --------------- .. ctype:: CvStereoBMState The structure for block matching stereo correspondence algorithm. :: typedef struct CvStereoBMState { //pre filters (normalize input images): int preFilterType; // 0 for now int preFilterSize; // ~5x5..21x21 int preFilterCap; // up to ~31 //correspondence using Sum of Absolute Difference (SAD): int SADWindowSize; // Could be 5x5..21x21 int minDisparity; // minimum disparity (=0) int numberOfDisparities; // maximum disparity - minimum disparity //post filters (knock out bad matches): int textureThreshold; // areas with no texture are ignored int uniquenessRatio;// invalidate disparity at pixels where there are other close matches // with different disparity int speckleWindowSize; // the maximum area of speckles to remove // (set to 0 to disable speckle filtering) int speckleRange; // acceptable range of disparity variation in each connected component int trySmallerWindows; // not used CvRect roi1, roi2; // clipping ROIs int disp12MaxDiff; // maximum allowed disparity difference in the left-right check // internal data ... } CvStereoBMState; .. .. attribute:: preFilterType type of the prefilter, ``CV_STEREO_BM_NORMALIZED_RESPONSE`` or the default and the recommended ``CV_STEREO_BM_XSOBEL`` , int .. attribute:: preFilterSize ~5x5..21x21, int .. attribute:: preFilterCap up to ~31, int .. attribute:: SADWindowSize Could be 5x5..21x21 or higher, but with 21x21 or smaller windows the processing speed is much higher, int .. attribute:: minDisparity minimum disparity (=0), int .. attribute:: numberOfDisparities maximum disparity - minimum disparity, int .. attribute:: textureThreshold the textureness threshold. That is, if the sum of absolute values of x-derivatives computed over ``SADWindowSize`` by ``SADWindowSize`` pixel neighborhood is smaller than the parameter, no disparity is computed at the pixel, int .. attribute:: uniquenessRatio the minimum margin in percents between the best (minimum) cost function value and the second best value to accept the computed disparity, int .. attribute:: speckleWindowSize the maximum area of speckles to remove (set to 0 to disable speckle filtering), int .. attribute:: speckleRange acceptable range of disparity variation in each connected component, int .. attribute:: trySmallerWindows not used currently (0), int .. attribute:: roi1, roi2 These are the clipping ROIs for the left and the right images. The function :ref:`StereoRectify` returns the largest rectangles in the left and right images where after the rectification all the pixels are valid. If you copy those rectangles to the ``CvStereoBMState`` structure, the stereo correspondence function will automatically clear out the pixels outside of the "valid" disparity rectangle computed by :ref:`GetValidDisparityROI` . Thus you will get more "invalid disparity" pixels than usual, but the remaining pixels are more probable to be valid. .. attribute:: disp12MaxDiff The maximum allowed difference between the explicitly computed left-to-right disparity map and the implicitly (by :ref:`ValidateDisparity` ) computed right-to-left disparity. If for some pixel the difference is larger than the specified threshold, the disparity at the pixel is invalidated. By default this parameter is set to (-1), which means that the left-right check is not performed. The block matching stereo correspondence algorithm, by Kurt Konolige, is very fast single-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 ``minDisparity`` to ``minDisparity+numberOfDisparities`` ). On a pair of images WxH the algorithm computes disparity in ``O(W*H*numberOfDisparities)`` time. In order to improve quality and readability of the disparity map, the algorithm includes pre-filtering and post-filtering procedures. 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. .. index:: CvStereoGCState .. _CvStereoGCState: CvStereoGCState --------------- .. ctype:: CvStereoGCState The structure for graph cuts-based stereo correspondence algorithm :: typedef struct CvStereoGCState { int Ithreshold; // threshold for piece-wise linear data cost function (5 by default) int interactionRadius; // radius for smoothness cost function (1 by default; means Potts model) float K, lambda, lambda1, lambda2; // parameters for the cost function // (usually computed adaptively from the input data) int occlusionCost; // 10000 by default int minDisparity; // 0 by default; see CvStereoBMState int numberOfDisparities; // defined by user; see CvStereoBMState int maxIters; // number of iterations; defined by user. // internal buffers CvMat* left; CvMat* right; CvMat* dispLeft; CvMat* dispRight; CvMat* ptrLeft; CvMat* ptrRight; CvMat* vtxBuf; CvMat* edgeBuf; } CvStereoGCState; .. The graph cuts stereo correspondence algorithm, described in [Kolmogorov03]_ (as **KZ1** ), is non-realtime stereo correspondence 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 :ref:`CreateStereoGCState` and then override necessary parameters if needed. .. index:: DecomposeProjectionMatrix .. _DecomposeProjectionMatrix: DecomposeProjectionMatrix ------------------------- .. cfunction:: void cvDecomposeProjectionMatrix( const CvMat *projMatrix, CvMat *cameraMatrix, CvMat *rotMatrix, CvMat *transVect, CvMat *rotMatrX=NULL, CvMat *rotMatrY=NULL, CvMat *rotMatrZ=NULL, CvPoint3D64f *eulerAngles=NULL) Decomposes the projection matrix into a rotation matrix and a camera matrix. :param projMatrix: The 3x4 input projection matrix P :param cameraMatrix: The output 3x3 camera matrix K :param rotMatrix: The output 3x3 external rotation matrix R :param transVect: The output 4x1 translation vector T :param rotMatrX: Optional 3x3 rotation matrix around x-axis :param rotMatrY: Optional 3x3 rotation matrix around y-axis :param rotMatrZ: Optional 3x3 rotation matrix around z-axis :param eulerAngles: Optional 3 points containing the three Euler angles of rotation The function computes a decomposition of a projection matrix into a calibration and a rotation matrix and the position of the camera. It optionally returns three rotation matrices, one for each axis, and the three Euler angles that could be used in OpenGL. The function is based on :ref:`RQDecomp3x3` . .. index:: DrawChessboardCorners .. _DrawChessboardCorners: DrawChessboardCorners --------------------- .. cfunction:: void cvDrawChessboardCorners( CvArr* image, CvSize patternSize, CvPoint2D32f* corners, int count, int patternWasFound ) Renders the detected chessboard corners. :param image: The destination image; it must be an 8-bit color image :param patternSize: The number of inner corners per chessboard row and column. (patternSize = cvSize(points _ per _ row,points _ per _ colum) = cvSize(columns,rows) ) :param corners: The array of corners detected :param count: The number of corners :param patternWasFound: Indicates whether the complete board was found :math:`(\ne 0)` or not :math:`(=0)` . One may just pass the return value :ref:`FindChessboardCorners` here The function draws the individual chessboard corners detected as red circles if the board was not found or as colored corners connected with lines if the board was found. .. index:: FindChessboardCorners .. _FindChessboardCorners: FindChessboardCorners --------------------- .. cfunction:: int cvFindChessboardCorners( const void* image, CvSize patternSize, CvPoint2D32f* corners, int* cornerCount=NULL, int flags=CV_CALIB_CB_ADAPTIVE_THRESH ) Finds the positions of the internal corners of the chessboard. :param image: Source chessboard view; it must be an 8-bit grayscale or color image :param patternSize: The number of inner corners per chessboard row and column ( patternSize = cvSize(points _ per _ row,points _ per _ colum) = cvSize(columns,rows) ) :param corners: The output array of corners detected :param cornerCount: The output corner counter. If it is not NULL, it stores the number of corners found :param flags: Various operation flags, can be 0 or a combination of the following values: * **CV_CALIB_CB_ADAPTIVE_THRESH** use adaptive thresholding to convert the image to black and white, rather than a fixed threshold level (computed from the average image brightness). * **CV_CALIB_CB_NORMALIZE_IMAGE** normalize the image gamma with :ref:`EqualizeHist` before applying fixed or adaptive thresholding. * **CV_CALIB_CB_FILTER_QUADS** use additional criteria (like contour area, perimeter, square-like shape) to filter out false quads that are extracted at the contour retrieval stage. The function attempts to determine whether the input image is a view of the chessboard pattern and locate the internal chessboard corners. The function returns a non-zero value if all of the corners have been found and they have been placed in a certain order (row by row, left to right in every row), otherwise, if the function fails to find all the corners or reorder them, it returns 0. For example, a regular chessboard has 8 x 8 squares and 7 x 7 internal corners, that is, points, where the black squares touch each other. The coordinates detected are approximate, and to determine their position more accurately, the user may use the function :ref:`FindCornerSubPix` . **Note:** the function requires some white space (like a square-thick border, the wider the better) around the board to make the detection more robust in various environment (otherwise if there is no border and the background is dark, the outer black squares could not be segmented properly and so the square grouping and ordering algorithm will fail). .. index:: FindExtrinsicCameraParams2 .. _FindExtrinsicCameraParams2: FindExtrinsicCameraParams2 -------------------------- .. cfunction:: void cvFindExtrinsicCameraParams2( const CvMat* objectPoints, const CvMat* imagePoints, const CvMat* cameraMatrix, const CvMat* distCoeffs, CvMat* rvec, CvMat* tvec, int useExtrinsicGuess=0) Finds the object pose from the 3D-2D point correspondences :param objectPoints: The array of object points in the object coordinate space, 3xN or Nx3 1-channel, or 1xN or Nx1 3-channel, where N is the number of points. :param imagePoints: The array of corresponding image points, 2xN or Nx2 1-channel or 1xN or Nx1 2-channel, where N is the number of points. :param cameraMatrix: The input camera matrix :math:`A = \vecthreethree{fx}{0}{cx}{0}{fy}{cy}{0}{0}{1}` :param distCoeffs: The input 4x1, 1x4, 5x1 or 1x5 vector of distortion coefficients :math:`(k_1, k_2, p_1, p_2[, k_3])` . If it is NULL, all of the distortion coefficients are set to 0 :param rvec: The output rotation vector (see :ref:`Rodrigues2` ) that (together with ``tvec`` ) brings points from the model coordinate system to the camera coordinate system :param tvec: The output translation vector :param useExtrinsicGuess: If true (1), the function will use the provided ``rvec`` and ``tvec`` as the initial approximations of the rotation and translation vectors, respectively, and will further optimize 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, i.e. the sum of squared distances between the observed projections ``imagePoints`` and the projected (using :ref:`ProjectPoints2` ) ``objectPoints`` . .. index:: FindFundamentalMat .. _FindFundamentalMat: FindFundamentalMat ------------------ .. cfunction:: int cvFindFundamentalMat( const CvMat* points1, const CvMat* points2, CvMat* fundamentalMatrix, int method=CV_FM_RANSAC, double param1=1., double param2=0.99, CvMat* status=NULL) Calculates the fundamental matrix from the corresponding points in two images. :param points1: Array of ``N`` points from the first image. It can be ``2xN, Nx2, 3xN`` or ``Nx3`` 1-channel array or ``1xN`` or ``Nx1`` 2- or 3-channel array . The point coordinates should be floating-point (single or double precision) :param points2: Array of the second image points of the same size and format as ``points1`` :param fundamentalMatrix: The output fundamental matrix or matrices. The size should be 3x3 or 9x3 (7-point method may return up to 3 matrices) :param method: Method for computing the fundamental matrix * **CV_FM_7POINT** for a 7-point algorithm. :math:`N = 7` * **CV_FM_8POINT** for an 8-point algorithm. :math:`N \ge 8` * **CV_FM_RANSAC** for the RANSAC algorithm. :math:`N \ge 8` * **CV_FM_LMEDS** for the LMedS algorithm. :math:`N \ge 8` :param param1: The parameter is used for RANSAC. It is the maximum distance from point to epipolar line in pixels, beyond which the point is considered an outlier and is not used for computing the final fundamental matrix. It can be set to something like 1-3, depending on the accuracy of the point localization, image resolution and the image noise :param param2: The parameter is used for RANSAC or LMedS methods only. It specifies the desirable level of confidence (probability) that the estimated matrix is correct :param 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 all 1's The epipolar geometry is described by the following equation: .. math:: [p_2; 1]^T F [p_1; 1] = 0 where :math:`F` is fundamental matrix, :math:`p_1` and :math:`p_2` are corresponding points in the first and the second images, respectively. The function calculates the fundamental matrix using one of four methods listed above and returns the number of fundamental matrices found (1 or 3) and 0, if no matrix is found . Normally just 1 matrix is found, but in the case of 7-point algorithm the function may return up to 3 solutions ( :math:`9 \times 3` matrix that stores all 3 matrices sequentially). The calculated fundamental matrix may be passed further to :ref:`ComputeCorrespondEpilines` that finds the epipolar lines corresponding to the specified points. It can also be passed to :ref:`StereoRectifyUncalibrated` to compute the rectification transformation. :: int point_count = 100; CvMat* points1; CvMat* points2; CvMat* status; CvMat* fundamental_matrix; points1 = cvCreateMat(1,point_count,CV_32FC2); points2 = cvCreateMat(1,point_count,CV_32FC2); status = cvCreateMat(1,point_count,CV_8UC1); /* Fill the points here ... */ for( i = 0; i < point_count; i++ ) { points1->data.fl[i*2] = ; points1->data.fl[i*2+1] = ; points2->data.fl[i*2] = ; points2->data.fl[i*2+1] = ; } fundamental_matrix = cvCreateMat(3,3,CV_32FC1); int fm_count = cvFindFundamentalMat( points1,points2,fundamental_matrix, CV_FM_RANSAC,1.0,0.99,status ); .. .. index:: FindHomography .. _FindHomography: FindHomography -------------- .. cfunction:: void cvFindHomography( const CvMat* srcPoints, const CvMat* dstPoints, CvMat* H int method=0, double ransacReprojThreshold=0, CvMat* status=NULL) Finds the perspective transformation between two planes. :param srcPoints: Coordinates of the points in the original plane, 2xN, Nx2, 3xN or Nx3 1-channel array (the latter two are for representation in homogeneous coordinates), where N is the number of points. 1xN or Nx1 2- or 3-channel array can also be passed. :param dstPoints: Point coordinates in the destination plane, 2xN, Nx2, 3xN or Nx3 1-channel, or 1xN or Nx1 2- or 3-channel array. :param H: The output 3x3 homography matrix :param method: The method used to computed homography matrix; one of the following: * **0** a regular method using all the points * **CV_RANSAC** RANSAC-based robust method * **CV_LMEDS** Least-Median robust method :param ransacReprojThreshold: The maximum allowed reprojection error to treat a point pair as an inlier (used in the RANSAC method only). That is, if .. math:: \| \texttt{dstPoints} _i - \texttt{convertPointHomogeneous} ( \texttt{H} \texttt{srcPoints} _i) \| > \texttt{ransacReprojThreshold} 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 1 to 10. :param status: The optional output mask set by a robust method ( ``CV_RANSAC`` or ``CV_LMEDS`` ). *Note that the input mask values are ignored.* The function finds the perspective transformation :math:`H` between the source and the destination planes: .. math:: s_i \vecthree{x'_i}{y'_i}{1} \sim H \vecthree{x_i}{y_i}{1} So that the back-projection error .. math:: \sum _i \left ( x'_i- \frac{h_{11} x_i + h_{12} y_i + h_{13}}{h_{31} x_i + h_{32} y_i + h_{33}} \right )^2+ \left ( y'_i- \frac{h_{21} x_i + h_{22} y_i + h_{23}}{h_{31} x_i + h_{32} y_i + h_{33}} \right )^2 is minimized. If the parameter ``method`` is set to the default value 0, the function uses all the point pairs to compute the initial homography estimate with a simple least-squares scheme. However, if not all of the point pairs ( :math:`srcPoints_i` , :math:`dstPoints_i` ) fit the rigid perspective transformation (i.e. there are some outliers), this initial estimate will be poor. In this case one can use one of the 2 robust methods. Both methods, ``RANSAC`` and ``LMeDS`` , try many different random subsets of the corresponding point pairs (of 4 pairs each), estimate the homography matrix using this subset and a simple least-square algorithm and then compute the quality/goodness of the computed homography (which is the number of inliers for RANSAC or the median re-projection error for LMeDs). The best subset is then used to produce the initial estimate of the homography matrix and the mask of inliers/outliers. Regardless of the method, robust or not, the computed homography matrix is refined further (using inliers only in the case of a robust method) with the Levenberg-Marquardt method in order to reduce the re-projection error even more. The method ``RANSAC`` can handle practically any ratio of outliers, but it needs the threshold to distinguish inliers from outliers. The method ``LMeDS`` does not need any threshold, but it works correctly only when there are more than 50 % of inliers. Finally, if you are sure in the computed features, where can be only some small noise present, but no outliers, the default method could be the best choice. The function is used to find initial intrinsic and extrinsic matrices. Homography matrix is determined up to a scale, thus it is normalized so that :math:`h_{33}=1` . See also: :ref:`GetAffineTransform` , :ref:`GetPerspectiveTransform` , :ref:`EstimateRigidMotion` , :ref:`WarpPerspective` , :ref:`PerspectiveTransform` .. index:: FindStereoCorrespondenceBM .. _FindStereoCorrespondenceBM: FindStereoCorrespondenceBM -------------------------- .. cfunction:: void cvFindStereoCorrespondenceBM( const CvArr* left, const CvArr* right, CvArr* disparity, CvStereoBMState* state ) Computes the disparity map using block matching algorithm. :param left: The left single-channel, 8-bit image. :param right: The right image of the same size and the same type. :param disparity: The output single-channel 16-bit signed, or 32-bit floating-point disparity map of the same size as input images. In the first case the computed disparities are represented as fixed-point numbers with 4 fractional bits (i.e. the computed disparity values are multiplied by 16 and rounded to integers). :param state: Stereo correspondence structure. The function cvFindStereoCorrespondenceBM computes disparity map for the input rectified stereo pair. Invalid pixels (for which disparity can not be computed) are set to ``state->minDisparity - 1`` (or to ``(state->minDisparity-1)*16`` in the case of 16-bit fixed-point disparity map) .. index:: FindStereoCorrespondenceGC .. _FindStereoCorrespondenceGC: FindStereoCorrespondenceGC -------------------------- .. cfunction:: void cvFindStereoCorrespondenceGC( const CvArr* left, const CvArr* right, CvArr* dispLeft, CvArr* dispRight, CvStereoGCState* state, int useDisparityGuess = CV_DEFAULT(0) ) Computes the disparity map using graph cut-based algorithm. :param left: The left single-channel, 8-bit image. :param right: The right image of the same size and the same type. :param dispLeft: The optional output single-channel 16-bit signed left disparity map of the same size as input images. :param dispRight: The optional output single-channel 16-bit signed right disparity map of the same size as input images. :param state: Stereo correspondence structure. :param 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). The function computes disparity maps for the input rectified stereo pair. Note that the left disparity image will contain values in the following range: .. math:: - \texttt{state->numberOfDisparities} - \texttt{state->minDisparity} < dispLeft(x,y) \le - \texttt{state->minDisparity} , or .. math:: dispLeft(x,y) == \texttt{CV\_STEREO\_GC\_OCCLUSION} and for the right disparity image the following will be true: .. math:: \texttt{state->minDisparity} \le dispRight(x,y) < \texttt{state->minDisparity} + \texttt{state->numberOfDisparities} or .. math:: dispRight(x,y) == \texttt{CV\_STEREO\_GC\_OCCLUSION} that is, the range for the left disparity image will be inversed, and the pixels for which no good match has been found, will be marked as occlusions. Here is how the function can be used: :: // image_left and image_right are the input 8-bit single-channel images // from the left and the right cameras, respectively CvSize size = cvGetSize(image_left); CvMat* disparity_left = cvCreateMat( size.height, size.width, CV_16S ); CvMat* disparity_right = cvCreateMat( size.height, size.width, CV_16S ); CvStereoGCState* state = cvCreateStereoGCState( 16, 2 ); cvFindStereoCorrespondenceGC( image_left, image_right, disparity_left, disparity_right, state, 0 ); cvReleaseStereoGCState( &state ); // now process the computed disparity images as you want ... .. 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): :: CvMat* disparity_left_visual = cvCreateMat( size.height, size.width, CV_8U ); cvConvertScale( disparity_left, disparity_left_visual, -16 ); cvSave( "disparity.pgm", disparity_left_visual ); .. .. image:: ../../pics/disparity.png .. index:: GetOptimalNewCameraMatrix .. _GetOptimalNewCameraMatrix: GetOptimalNewCameraMatrix ------------------------- .. cfunction:: void cvGetOptimalNewCameraMatrix( const CvMat* cameraMatrix, const CvMat* distCoeffs, CvSize imageSize, double alpha, CvMat* newCameraMatrix, CvSize newImageSize=cvSize(0,0), CvRect* validPixROI=0 ) Returns the new camera matrix based on the free scaling parameter :param cameraMatrix: The input camera matrix :param distCoeffs: The input 4x1, 1x4, 5x1 or 1x5 vector of distortion coefficients :math:`(k_1, k_2, p_1, p_2[, k_3])` . :param imageSize: The original image size :param alpha: The free scaling parameter between 0 (when all the pixels in the undistorted image will be valid) and 1 (when all the source image pixels will be retained in the undistorted image); see :ref:`StereoRectify` :param newCameraMatrix: The output new camera matrix. :param newImageSize: The image size after rectification. By default it will be set to ``imageSize`` . :param validPixROI: The optional output rectangle that will outline all-good-pixels region in the undistorted image. See ``roi1, roi2`` description in :ref:`StereoRectify` The function computes the optimal new camera matrix based on the free scaling parameter. By varying this parameter the user 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 will likely have some black pixels corresponding to "virtual" pixels outside of the captured distorted image. The original camera matrix, distortion coefficients, the computed new camera matrix and the ``newImageSize`` should be passed to :ref:`InitUndistortRectifyMap` to produce the maps for :ref:`Remap` . .. index:: InitIntrinsicParams2D .. _InitIntrinsicParams2D: InitIntrinsicParams2D --------------------- .. cfunction:: void cvInitIntrinsicParams2D( const CvMat* objectPoints, const CvMat* imagePoints, const CvMat* npoints, CvSize imageSize, CvMat* cameraMatrix, double aspectRatio=1.) Finds the initial camera matrix from the 3D-2D point correspondences :param objectPoints: The joint array of object points; see :ref:`CalibrateCamera2` :param imagePoints: The joint array of object point projections; see :ref:`CalibrateCamera2` :param npoints: The array of point counts; see :ref:`CalibrateCamera2` :param imageSize: The image size in pixels; used to initialize the principal point :param cameraMatrix: The output camera matrix :math:`\vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}` :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}` The function estimates and returns the initial camera matrix for camera calibration process. Currently, the function only supports planar calibration patterns, i.e. patterns where each object point has z-coordinate =0. .. index:: InitUndistortMap .. _InitUndistortMap: InitUndistortMap ---------------- .. cfunction:: void cvInitUndistortMap( const CvMat* cameraMatrix, const CvMat* distCoeffs, CvArr* map1, CvArr* map2 ) Computes an undistortion map. :param cameraMatrix: The input camera matrix :math:`A = \vecthreethree{fx}{0}{cx}{0}{fy}{cy}{0}{0}{1}` :param distCoeffs: The input 4x1, 1x4, 5x1 or 1x5 vector of distortion coefficients :math:`(k_1, k_2, p_1, p_2[, k_3])` . :param map1: The first output map of type ``CV_32FC1`` or ``CV_16SC2`` - the second variant is more efficient :param map2: The second output map of type ``CV_32FC1`` or ``CV_16UC1`` - the second variant is more efficient The function is a simplified variant of :ref:`InitUndistortRectifyMap` where the rectification transformation ``R`` is identity matrix and ``newCameraMatrix=cameraMatrix`` . .. index:: InitUndistortRectifyMap .. _InitUndistortRectifyMap: InitUndistortRectifyMap ----------------------- .. cfunction:: void cvInitUndistortRectifyMap( const CvMat* cameraMatrix, const CvMat* distCoeffs, const CvMat* R, const CvMat* newCameraMatrix, CvArr* map1, CvArr* map2 ) Computes the undistortion and rectification transformation map. :param cameraMatrix: The input camera matrix :math:`A=\vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}` :param distCoeffs: The input 4x1, 1x4, 5x1 or 1x5 vector of distortion coefficients :math:`(k_1, k_2, p_1, p_2[, k_3])` . :param R: The optional rectification transformation in object space (3x3 matrix). ``R1`` or ``R2`` , computed by :ref:`StereoRectify` can be passed here. If the matrix is NULL , the identity transformation is assumed :param newCameraMatrix: The new camera matrix :math:`A'=\vecthreethree{f_x'}{0}{c_x'}{0}{f_y'}{c_y'}{0}{0}{1}` :param map1: The first output map of type ``CV_32FC1`` or ``CV_16SC2`` - the second variant is more efficient :param map2: The second output map of type ``CV_32FC1`` or ``CV_16UC1`` - the second variant is more efficient The function computes the joint undistortion+rectification transformation and represents the result in the form of maps for :ref:`Remap` . The undistorted image will look like the original, as if it was captured with a camera with camera matrix ``=newCameraMatrix`` and zero distortion. In the case of monocular camera ``newCameraMatrix`` is usually equal to ``cameraMatrix`` , or it can be computed by :ref:`GetOptimalNewCameraMatrix` for a better control over scaling. In the case of stereo camera ``newCameraMatrix`` is normally set to ``P1`` or ``P2`` computed by :ref:`StereoRectify` . Also, this new camera will be 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 the case of horizontally aligned stereo camera). The function actually builds the maps for the inverse mapping algorithm that is used by :ref:`Remap` . That is, for each pixel :math:`(u, v)` in the destination (corrected and rectified) image the function computes the corresponding coordinates in the source image (i.e. in the original image from camera). The process is the following: .. math:: \begin{array}{l} x \leftarrow (u - {c'}_x)/{f'}_x \\ y \leftarrow (v - {c'}_y)/{f'}_y \\{[X\,Y\,W]} ^T \leftarrow R^{-1}*[x \, y \, 1]^T \\ x' \leftarrow X/W \\ y' \leftarrow Y/W \\ x" \leftarrow x' (1 + k_1 r^2 + k_2 r^4 + k_3 r^6) + 2p_1 x' y' + p_2(r^2 + 2 x'^2) \\ y" \leftarrow y' (1 + k_1 r^2 + k_2 r^4 + k_3 r^6) + p_1 (r^2 + 2 y'^2) + 2 p_2 x' y' \\ map_x(u,v) \leftarrow x" f_x + c_x \\ map_y(u,v) \leftarrow y" f_y + c_y \end{array} where :math:`(k_1, k_2, p_1, p_2[, k_3])` are the distortion coefficients. In the case of a stereo camera this function is called twice, once for each camera head, after :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 pixel domain, not a rotation matrix ``R`` in 3D space. The ``R`` can be computed from ``H`` as .. math:: \texttt{R} = \texttt{cameraMatrix} ^{-1} \cdot \texttt{H} \cdot \texttt{cameraMatrix} where the ``cameraMatrix`` can be chosen arbitrarily. .. index:: POSIT .. _POSIT: POSIT ----- .. cfunction:: void cvPOSIT( CvPOSITObject* posit_object, CvPoint2D32f* imagePoints, double focal_length, CvTermCriteria criteria, CvMatr32f rotationMatrix, CvVect32f translation_vector ) Implements the POSIT algorithm. :param posit_object: Pointer to the object structure :param imagePoints: Pointer to the object points projections on the 2D image plane :param focal_length: Focal length of the camera used :param criteria: Termination criteria of the iterative POSIT algorithm :param rotationMatrix: Matrix of rotations :param translation_vector: Translation vector 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. Difference norm between two projections is the maximal distance between corresponding points. The parameter ``criteria.epsilon`` serves to stop the algorithm if the difference is small. .. index:: ProjectPoints2 .. _ProjectPoints2: ProjectPoints2 -------------- .. cfunction:: void cvProjectPoints2( const CvMat* objectPoints, const CvMat* rvec, const CvMat* tvec, const CvMat* cameraMatrix, const CvMat* distCoeffs, CvMat* imagePoints, CvMat* dpdrot=NULL, CvMat* dpdt=NULL, CvMat* dpdf=NULL, CvMat* dpdc=NULL, CvMat* dpddist=NULL ) Project 3D points on to an image plane. :param objectPoints: The array of object points, 3xN or Nx3 1-channel or 1xN or Nx1 3-channel , where N is the number of points in the view :param rvec: The rotation vector, see :ref:`Rodrigues2` :param tvec: The translation vector :param cameraMatrix: The camera matrix :math:`A = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{_1}` :param distCoeffs: The input 4x1, 1x4, 5x1 or 1x5 vector of distortion coefficients :math:`(k_1, k_2, p_1, p_2[, k_3])` . If it is NULL , all of the distortion coefficients are considered 0's :param imagePoints: The output array of image points, 2xN or Nx2 1-channel or 1xN or Nx1 2-channel :param dpdrot: Optional 2Nx3 matrix of derivatives of image points with respect to components of the rotation vector :param dpdt: Optional 2Nx3 matrix of derivatives of image points with respect to components of the translation vector :param dpdf: Optional 2Nx2 matrix of derivatives of image points with respect to :math:`f_x` and :math:`f_y` :param dpdc: Optional 2Nx2 matrix of derivatives of image points with respect to :math:`c_x` and :math:`c_y` :param dpddist: Optional 2Nx4 matrix of derivatives of image points with respect to distortion coefficients 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 :ref:`CalibrateCamera2` , :ref:`FindExtrinsicCameraParams2` and :ref:`StereoCalibrate` . The function itself can also used to compute re-projection error given the current intrinsic and extrinsic parameters. Note, that by setting ``rvec=tvec=(0,0,0)`` , or by setting ``cameraMatrix`` to 3x3 identity matrix, or by passing zero distortion coefficients, you can get various useful partial cases of the function, i.e. you can compute the distorted coordinates for a sparse set of points, or apply a perspective transformation (and also compute the derivatives) in the ideal zero-distortion setup etc. .. index:: ReprojectImageTo3D .. _ReprojectImageTo3D: ReprojectImageTo3D ------------------ .. cfunction:: void cvReprojectImageTo3D( const CvArr* disparity, CvArr* _3dImage, const CvMat* Q, int handleMissingValues=0) Reprojects disparity image to 3D space. :param disparity: The input single-channel 16-bit signed or 32-bit floating-point disparity image :param _3dImage: The output 3-channel floating-point image of the same size as ``disparity`` . Each element of ``_3dImage(x,y)`` will contain the 3D coordinates of the point ``(x,y)`` , computed from the disparity map. :param Q: The :math:`4 \times 4` perspective transformation matrix that can be obtained with :ref:`StereoRectify` :param handleMissingValues: If true, when the pixels with the minimal disparity (that corresponds to the outliers; see :ref:`FindStereoCorrespondenceBM` ) will be transformed to 3D points with some very large Z value (currently set to 10000) The function transforms 1-channel disparity map to 3-channel image representing a 3D surface. That is, for each pixel ``(x,y)`` and the corresponding disparity ``d=disparity(x,y)`` it computes: .. math:: \begin{array}{l} [X \; Y \; Z \; W]^T = \texttt{Q} *[x \; y \; \texttt{disparity} (x,y) \; 1]^T \\ \texttt{\_3dImage} (x,y) = (X/W, \; Y/W, \; Z/W) \end{array} The matrix ``Q`` can be arbitrary :math:`4 \times 4` matrix, e.g. the one computed by :ref:`StereoRectify` . To reproject a sparse set of points {(x,y,d),...} to 3D space, use :ref:`PerspectiveTransform` . .. index:: RQDecomp3x3 .. _RQDecomp3x3: RQDecomp3x3 ----------- .. cfunction:: void cvRQDecomp3x3( const CvMat *M, CvMat *R, CvMat *Q, CvMat *Qx=NULL, CvMat *Qy=NULL, CvMat *Qz=NULL, CvPoint3D64f *eulerAngles=NULL) Computes the 'RQ' decomposition of 3x3 matrices. :param M: The 3x3 input matrix :param R: The output 3x3 upper-triangular matrix :param Q: The output 3x3 orthogonal matrix :param Qx: Optional 3x3 rotation matrix around x-axis :param Qy: Optional 3x3 rotation matrix around y-axis :param Qz: Optional 3x3 rotation matrix around z-axis :param eulerAngles: Optional three Euler angles of rotation The function computes a RQ decomposition using the given rotations. This function is used in :ref:`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 that could be used in OpenGL. .. index:: ReleasePOSITObject .. _ReleasePOSITObject: ReleasePOSITObject ------------------ .. cfunction:: void cvReleasePOSITObject( CvPOSITObject** posit_object ) Deallocates a 3D object structure. :param posit_object: Double pointer to ``CvPOSIT`` structure The function releases memory previously allocated by the function :ref:`CreatePOSITObject` . .. index:: ReleaseStereoBMState .. _ReleaseStereoBMState: ReleaseStereoBMState -------------------- .. cfunction:: void cvReleaseStereoBMState( CvStereoBMState** state ) Releases block matching stereo correspondence structure. :param state: Double pointer to the released structure. The function releases the stereo correspondence structure and all the associated internal buffers. .. index:: ReleaseStereoGCState .. _ReleaseStereoGCState: ReleaseStereoGCState -------------------- .. cfunction:: void cvReleaseStereoGCState( CvStereoGCState** state ) Releases the state structure of the graph cut-based stereo correspondence algorithm. :param state: Double pointer to the released structure. The function releases the stereo correspondence structure and all the associated internal buffers. .. index:: Rodrigues2 .. _Rodrigues2: Rodrigues2 ---------- .. cfunction:: int cvRodrigues2( const CvMat* src, CvMat* dst, CvMat* jacobian=0 ) Converts a rotation matrix to a rotation vector or vice versa. :param src: The input rotation vector (3x1 or 1x3) or rotation matrix (3x3) :param dst: The output rotation matrix (3x3) or rotation vector (3x1 or 1x3), respectively :param jacobian: Optional output Jacobian matrix, 3x9 or 9x3 - partial derivatives of the output array components with respect to the input array components .. math:: \begin{array}{l} \theta \leftarrow norm(r) \\ r \leftarrow r/ \theta \\ R = \cos{\theta} I + (1- \cos{\theta} ) r r^T + \sin{\theta} \vecthreethree{0}{-r_z}{r_y}{r_z}{0}{-r_x}{-r_y}{r_x}{0} \end{array} Inverse transformation can also be done easily, since .. math:: \sin ( \theta ) \vecthreethree{0}{-r_z}{r_y}{r_z}{0}{-r_x}{-r_y}{r_x}{0} = \frac{R - R^T}{2} 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 :ref:`CalibrateCamera2` , :ref:`StereoCalibrate` or :ref:`FindExtrinsicCameraParams2` . .. index:: StereoCalibrate .. _StereoCalibrate: StereoCalibrate --------------- .. cfunction:: double cvStereoCalibrate( const CvMat* objectPoints, const CvMat* imagePoints1, const CvMat* imagePoints2, const CvMat* pointCounts, CvMat* cameraMatrix1, CvMat* distCoeffs1, CvMat* cameraMatrix2, CvMat* distCoeffs2, CvSize imageSize, 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 ) Calibrates stereo camera. :param objectPoints: The joint matrix of object points - calibration pattern features in the model coordinate space. It is floating-point 3xN or Nx3 1-channel, or 1xN or Nx1 3-channel array, where N is the total number of points in all views. :param imagePoints1: The joint matrix of object points projections in the first camera views. It is floating-point 2xN or Nx2 1-channel, or 1xN or Nx1 2-channel array, where N is the total number of points in all views :param imagePoints2: The joint matrix of object points projections in the second camera views. It is floating-point 2xN or Nx2 1-channel, or 1xN or Nx1 2-channel array, where N is the total number of points in all views :param pointCounts: Integer 1xM or Mx1 vector (where M is the number of calibration pattern views) containing the number of points in each particular view. The sum of vector elements must match the size of ``objectPoints`` and ``imagePoints*`` (=N). :param cameraMatrix1: The 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 matrices' components must be initialized; see the flags description :param distCoeffs1: The input/output lens distortion coefficients for the first camera, 4x1, 5x1, 1x4 or 1x5 floating-point vectors :math:`(k_1^{(j)}, k_2^{(j)}, p_1^{(j)}, p_2^{(j)}[, k_3^{(j)}])` , :math:`j = 0,\, 1` . If any of ``CV_CALIB_FIX_K1`` , ``CV_CALIB_FIX_K2`` or ``CV_CALIB_FIX_K3`` is specified, then the corresponding elements of the distortion coefficients must be initialized. :param cameraMatrix2: The input/output second camera matrix, as cameraMatrix1. :param distCoeffs2: The input/output lens distortion coefficients for the second camera, as distCoeffs1. :param imageSize: Size of the image, used only to initialize intrinsic camera matrix. :param R: The output rotation matrix between the 1st and the 2nd cameras' coordinate systems. :param T: The output translation vector between the cameras' coordinate systems. :param E: The optional output essential matrix. :param F: The optional output fundamental matrix. :param term_crit: The termination criteria for the iterative optimization algorithm. :param flags: Different flags, may be 0 or combination of the following values: * **CV_CALIB_FIX_INTRINSIC** If it is set, ``cameraMatrix?`` , as well as ``distCoeffs?`` are fixed, so that only ``R, T, E`` and ``F`` are estimated. * **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. * **CV_CALIB_FIX_PRINCIPAL_POINT** The principal points are fixed during the optimization. * **CV_CALIB_FIX_FOCAL_LENGTH** :math:`f^{(j)}_x` and :math:`f^{(j)}_y` are fixed. * **CV_CALIB_FIX_ASPECT_RATIO** :math:`f^{(j)}_y` is optimized, but the ratio :math:`f^{(j)}_x/f^{(j)}_y` is fixed. * **CV_CALIB_SAME_FOCAL_LENGTH** Enforces :math:`f^{(0)}_x=f^{(1)}_x` and :math:`f^{(0)}_y=f^{(1)}_y` * **CV_CALIB_ZERO_TANGENT_DIST** Tangential distortion coefficients for each camera are set to zeros and fixed there. * **CV_CALIB_FIX_K1, CV_CALIB_FIX_K2, CV_CALIB_FIX_K3** Fixes the corresponding radial distortion coefficient (the coefficient must be passed to the function) The function estimates transformation between the 2 cameras making a stereo pair. If we have a stereo camera, where the relative position and orientation 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 :ref:`FindExtrinsicCameraParams2` ), obviously, those poses will relate to each other, i.e. given ( :math:`R_1` , :math:`T_1` ) it should be possible to compute ( :math:`R_2` , :math:`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 ( :math:`R` , :math:`T` ) such that: .. math:: R_2=R*R_1 T_2=R*T_1 + T, Optionally, it computes the essential matrix E: .. math:: E= \vecthreethree{0}{-T_2}{T_1}{T_2}{0}{-T_0}{-T_1}{T_0}{0} *R where :math:`T_i` are components of the translation vector :math:`T` : :math:`T=[T_0, T_1, T_2]^T` . And also the function can compute the fundamental matrix F: .. math:: F = cameraMatrix2^{-T} E cameraMatrix1^{-1} 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 :ref:`CalibrateCamera2` ), it is 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, e.g. pass ``CV_CALIB_SAME_FOCAL_LENGTH`` and ``CV_CALIB_ZERO_TANGENT_DIST`` flags, which are usually reasonable assumptions. Similarly to :ref:`CalibrateCamera2` , 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. .. index:: StereoRectify .. _StereoRectify: StereoRectify ------------- .. cfunction:: void cvStereoRectify( const CvMat* cameraMatrix1, const CvMat* cameraMatrix2, const CvMat* distCoeffs1, const CvMat* distCoeffs2, CvSize imageSize, 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 newImageSize=cvSize(0,0), CvRect* roi1=0, CvRect* roi2=0) Computes rectification transforms for each head of a calibrated stereo camera. :param cameraMatrix1, cameraMatrix2: The camera matrices :math:`\vecthreethree{f_x^{(j)}}{0}{c_x^{(j)}}{0}{f_y^{(j)}}{c_y^{(j)}}{0}{0}{1}` . :param distCoeffs1, distCoeffs2: The input distortion coefficients for each camera, :math:`{k_1}^{(j)}, {k_2}^{(j)}, {p_1}^{(j)}, {p_2}^{(j)} [, {k_3}^{(j)}]` :param imageSize: Size of the image used for stereo calibration. :param R: The rotation matrix between the 1st and the 2nd cameras' coordinate systems. :param T: The translation vector between the cameras' coordinate systems. :param R1, R2: The output :math:`3 \times 3` rectification transforms (rotation matrices) for the first and the second cameras, respectively. :param P1, P2: The output :math:`3 \times 4` projection matrices in the new (rectified) coordinate systems. :param Q: The output :math:`4 \times 4` disparity-to-depth mapping matrix, see :func:`reprojectImageTo3D` . :param flags: The operation flags; may be 0 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 horizontal or vertical direction (depending on the orientation of epipolar lines) in order to maximize the useful image area. :param alpha: The free scaling parameter. If it is -1 , the functions performs some default scaling. Otherwise the parameter should be between 0 and 1. ``alpha=0`` means that the rectified images will be zoomed and shifted so that only valid pixels are visible (i.e. there will be no black areas after rectification). ``alpha=1`` means that the rectified image will be decimated and shifted so that all the pixels from the original images from the cameras are retained in the rectified images, i.e. no source image pixels are lost. Obviously, any intermediate value yields some intermediate result between those two extreme cases. :param newImageSize: The new image resolution after rectification. The same size should be passed to :ref:`InitUndistortRectifyMap` , see the ``stereo_calib.cpp`` sample in OpenCV samples directory. By default, i.e. when (0,0) is passed, it is set to the original ``imageSize`` . Setting it to larger value can help you to preserve details in the original image, especially when there is big radial distortion. :param roi1, roi2: The optional output rectangles inside the rectified images where all the pixels are valid. If ``alpha=0`` , the ROIs will cover the whole images, otherwise they likely 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, that makes all the epipolar lines parallel and thus simplifies the dense stereo correspondence problem. On input the function takes the matrices computed by :func:`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: #. 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: .. math:: \texttt{P1} = \begin{bmatrix} f & 0 & cx_1 & 0 \\ 0 & f & cy & 0 \\ 0 & 0 & 1 & 0 \end{bmatrix} .. math:: \texttt{P2} = \begin{bmatrix} f & 0 & cx_2 & T_x*f \\ 0 & f & cy & 0 \\ 0 & 0 & 1 & 0 \end{bmatrix} , where :math:`T_x` is horizontal shift between the cameras and :math:`cx_1=cx_2` if ``CV_CALIB_ZERO_DISPARITY`` is set. #. 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: .. math:: \texttt{P1} = \begin{bmatrix} f & 0 & cx & 0 \\ 0 & f & cy_1 & 0 \\ 0 & 0 & 1 & 0 \end{bmatrix} .. math:: \texttt{P2} = \begin{bmatrix} f & 0 & cx & 0 \\ 0 & f & cy_2 & T_y*f \\ 0 & 0 & 1 & 0 \end{bmatrix} , where :math:`T_y` is vertical shift between the cameras and :math:`cy_1=cy_2` if ``CALIB_ZERO_DISPARITY`` is set. As you can see, the first 3 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 :ref:`InitUndistortRectifyMap` to initialize the rectification map for each camera. Below is the screenshot from ``stereo_calib.cpp`` sample. Some red horizontal lines, as you can see, pass through the corresponding image regions, i.e. the images are well rectified (which is what most stereo correspondence algorithms rely on). The green rectangles are ``roi1`` and ``roi2`` - indeed, their interior are all valid pixels. .. image:: ../../pics/stereo_undistort.jpg .. index:: StereoRectifyUncalibrated .. _StereoRectifyUncalibrated: StereoRectifyUncalibrated ------------------------- .. cfunction:: void cvStereoRectifyUncalibrated( const CvMat* points1, const CvMat* points2, const CvMat* F, CvSize imageSize, CvMat* H1, CvMat* H2, double threshold=5 ) Computes rectification transform for uncalibrated stereo camera. :param points1, points2: The 2 arrays of corresponding 2D points. The same formats as in :ref:`FindFundamentalMat` are supported :param F: The input fundamental matrix. It can be computed from the same set of point pairs using :ref:`FindFundamentalMat` . :param imageSize: Size of the image. :param H1, H2: The output rectification homography matrices for the first and for the second images. :param threshold: The optional threshold used to filter out the outliers. If the parameter is greater than zero, then all the point pairs that do not comply the epipolar geometry well enough (that is, the points for which :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 space, hence 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 [Hartley99]_ . 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 :ref:`CalibrateCamera2` and then the images can be corrected using :ref:`Undistort2` , or just the point coordinates can be corrected with :ref:`UndistortPoints` . .. index:: Undistort2 .. _Undistort2: Undistort2 ---------- .. cfunction:: void cvUndistort2( const CvArr* src, CvArr* dst, const CvMat* cameraMatrix, const CvMat* distCoeffs, const CvMat* newCameraMatrix=0 ) Transforms an image to compensate for lens distortion. :param src: The input (distorted) image :param dst: The output (corrected) image; will have the same size and the same type as ``src`` :param cameraMatrix: The input camera matrix :math:`A = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}` :param distCoeffs: The vector of distortion coefficients, :math:`(k_1^{(j)}, k_2^{(j)}, p_1^{(j)}, p_2^{(j)}[, k_3^{(j)}])` The function transforms the image to compensate radial and tangential lens distortion. The function is simply a combination of :ref:`InitUndistortRectifyMap` (with unity ``R`` ) and :ref:`Remap` (with bilinear interpolation). See the former function for details of the transformation being performed. Those pixels in the destination image, for which there is no correspondent pixels in the source image, are filled with 0's (black color). The particular subset of the source image that will be visible in the corrected image can be regulated by ``newCameraMatrix`` . You can use :ref:`GetOptimalNewCameraMatrix` to compute the appropriate ``newCameraMatrix`` , depending on your requirements. The camera matrix and the distortion parameters can be determined using :ref:`CalibrateCamera2` . If the resolution of images is different from the used at the calibration stage, :math:`f_x, f_y, c_x` and :math:`c_y` need to be scaled accordingly, while the distortion coefficients remain the same. .. index:: UndistortPoints .. _UndistortPoints: UndistortPoints --------------- .. cfunction:: void cvUndistortPoints( const CvMat* src, CvMat* dst, const CvMat* cameraMatrix, const CvMat* distCoeffs, const CvMat* R=NULL, const CvMat* P=NULL) Computes the ideal point coordinates from the observed point coordinates. :param src: The observed point coordinates, same format as ``imagePoints`` in :ref:`ProjectPoints2` :param dst: The output ideal point coordinates, after undistortion and reverse perspective transformation , same format as ``src`` . :param cameraMatrix: The camera matrix :math:`\vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}` :param distCoeffs: The vector of distortion coefficients, :math:`(k_1^{(j)}, k_2^{(j)}, p_1^{(j)}, p_2^{(j)}[, k_3^{(j)}])` :param R: The rectification transformation in object space (3x3 matrix). ``R1`` or ``R2`` , computed by :func:`StereoRectify` can be passed here. If the matrix is empty, the identity transformation is used :param P: The new camera matrix (3x3) or the new projection matrix (3x4). ``P1`` or ``P2`` , computed by :func:`StereoRectify` can be passed here. If the matrix is empty, the identity new camera matrix is used The function is similar to :ref:`Undistort2` and :ref:`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 :ref:`ProjectPoints2` (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 ``R`` is specified). :: // (u,v) is the input point, (u', v') is the output point // camera_matrix=[fx 0 cx; 0 fy cy; 0 0 1] // P=[fx' 0 cx' tx; 0 fy' cy' ty; 0 0 1 tz] x" = (u - cx)/fx y" = (v - cy)/fy (x',y') = undistort(x",y",dist_coeffs) [X,Y,W]T = R*[x' y' 1]T x = X/W, y = Y/W u' = x*fx' + cx' v' = y*fy' + cy', .. 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). The function can be used both for a stereo camera head or for monocular camera (when R is NULL ).