摄像头校准和 3D 重建


模块

Fisheye camera model
C API

struct cv::CirclesGridFinderParameters
class cv::LMSolver
class cv::StereoBM
Class for computing stereo correspondence using the block matching algorithm, introduced and contributed to OpenCV by K. Konolige. 更多...
class cv::StereoMatcher
The base class for stereo correspondence algorithms. 更多...
class cv::StereoSGBM
The class implements the modified H. Hirschmuller algorithm [102] that differs from the original one as follows: 更多...

Typedefs

typedef CirclesGridFinderParameters cv::CirclesGridFinderParameters2

枚举

enum {
cv::LMEDS = 4,
cv::RANSAC = 8,
cv::RHO = 16
}
type of the robust estimation algorithm 更多...
enum {
cv::CALIB_CB_ADAPTIVE_THRESH = 1,
cv::CALIB_CB_NORMALIZE_IMAGE = 2,
cv::CALIB_CB_FILTER_QUADS = 4,
cv::CALIB_CB_FAST_CHECK = 8,
cv::CALIB_CB_EXHAUSTIVE = 16,
cv::CALIB_CB_ACCURACY = 32
}
enum {
cv::CALIB_CB_SYMMETRIC_GRID = 1,
cv::CALIB_CB_ASYMMETRIC_GRID = 2,
cv::CALIB_CB_CLUSTERING = 4
}
enum {
cv::CALIB_NINTRINSIC = 18,
cv::CALIB_USE_INTRINSIC_GUESS = 0x00001,
cv::CALIB_FIX_ASPECT_RATIO = 0x00002,
cv::CALIB_FIX_PRINCIPAL_POINT = 0x00004,
cv::CALIB_ZERO_TANGENT_DIST = 0x00008,
cv::CALIB_FIX_FOCAL_LENGTH = 0x00010,
cv::CALIB_FIX_K1 = 0x00020,
cv::CALIB_FIX_K2 = 0x00040,
cv::CALIB_FIX_K3 = 0x00080,
cv::CALIB_FIX_K4 = 0x00800,
cv::CALIB_FIX_K5 = 0x01000,
cv::CALIB_FIX_K6 = 0x02000,
cv::CALIB_RATIONAL_MODEL = 0x04000,
cv::CALIB_THIN_PRISM_MODEL = 0x08000,
cv::CALIB_FIX_S1_S2_S3_S4 = 0x10000,
cv::CALIB_TILTED_MODEL = 0x40000,
cv::CALIB_FIX_TAUX_TAUY = 0x80000,
cv::CALIB_USE_QR = 0x100000,
cv::CALIB_FIX_TANGENT_DIST = 0x200000,
cv::CALIB_FIX_INTRINSIC = 0x00100,
cv::CALIB_SAME_FOCAL_LENGTH = 0x00200,
cv::CALIB_ZERO_DISPARITY = 0x00400,
cv::CALIB_USE_LU = (1 << 17),
cv::CALIB_USE_EXTRINSIC_GUESS = (1 << 22)
}
enum {
cv::FM_7POINT = 1,
cv::FM_8POINT = 2,
cv::FM_LMEDS = 4,
cv::FM_RANSAC = 8
}
the algorithm for finding fundamental matrix 更多...
enum cv::HandEyeCalibrationMethod {
cv::CALIB_HAND_EYE_TSAI = 0,
cv::CALIB_HAND_EYE_PARK = 1,
cv::CALIB_HAND_EYE_HORAUD = 2,
cv::CALIB_HAND_EYE_ANDREFF = 3,
cv::CALIB_HAND_EYE_DANIILIDIS = 4
}
enum cv::SolvePnPMethod {
cv::SOLVEPNP_ITERATIVE = 0,
cv::SOLVEPNP_EPNP = 1,
cv::SOLVEPNP_P3P = 2,
cv::SOLVEPNP_DLS = 3,
cv::SOLVEPNP_UPNP = 4,
cv::SOLVEPNP_AP3P = 5,
cv::SOLVEPNP_IPPE = 6,
cv::SOLVEPNP_IPPE_SQUARE = 7
}
enum cv::UndistortTypes {
cv::PROJ_SPHERICAL_ORTHO = 0,
cv::PROJ_SPHERICAL_EQRECT = 1
}
cv::undistort mode 更多...

函数

double cv::calibrateCamera ( InputArrayOfArrays objectPoints, InputArrayOfArrays imagePoints, Size imageSize, InputOutputArray cameraMatrix, InputOutputArray distCoeffs, OutputArrayOfArrays rvecs, OutputArrayOfArrays tvecs, OutputArray stdDeviationsIntrinsics, OutputArray stdDeviationsExtrinsics, OutputArray perViewErrors, int flags=0, TermCriteria criteria= TermCriteria ( TermCriteria::COUNT + TermCriteria::EPS , 30, DBL_EPSILON))
Finds the camera intrinsic and extrinsic parameters from several views of a calibration pattern. 更多...
double cv::calibrateCamera ( InputArrayOfArrays objectPoints, InputArrayOfArrays imagePoints, Size imageSize, InputOutputArray cameraMatrix, InputOutputArray distCoeffs, OutputArrayOfArrays rvecs, OutputArrayOfArrays tvecs, int flags=0, TermCriteria criteria= TermCriteria ( TermCriteria::COUNT + TermCriteria::EPS , 30, DBL_EPSILON))
double cv::calibrateCameraRO ( InputArrayOfArrays objectPoints, InputArrayOfArrays imagePoints, Size imageSize, int iFixedPoint, InputOutputArray cameraMatrix, InputOutputArray distCoeffs, OutputArrayOfArrays rvecs, OutputArrayOfArrays tvecs, OutputArray newObjPoints, OutputArray stdDeviationsIntrinsics, OutputArray stdDeviationsExtrinsics, OutputArray stdDeviationsObjPoints, OutputArray perViewErrors, int flags=0, TermCriteria criteria= TermCriteria ( TermCriteria::COUNT + TermCriteria::EPS , 30, DBL_EPSILON))
Finds the camera intrinsic and extrinsic parameters from several views of a calibration pattern. 更多...
double cv::calibrateCameraRO ( InputArrayOfArrays objectPoints, InputArrayOfArrays imagePoints, Size imageSize, int iFixedPoint, InputOutputArray cameraMatrix, InputOutputArray distCoeffs, OutputArrayOfArrays rvecs, OutputArrayOfArrays tvecs, OutputArray newObjPoints, int flags=0, TermCriteria criteria= TermCriteria ( TermCriteria::COUNT + TermCriteria::EPS , 30, DBL_EPSILON))
void cv::calibrateHandEye ( InputArrayOfArrays R_gripper2base, InputArrayOfArrays t_gripper2base, InputArrayOfArrays R_target2cam, InputArrayOfArrays t_target2cam, OutputArray R_cam2gripper, OutputArray t_cam2gripper, HandEyeCalibrationMethod method= CALIB_HAND_EYE_TSAI )
Computes Hand-Eye calibration: \(_{}^{g}\textrm{T}_c\). 更多...
void cv::calibrationMatrixValues ( InputArray cameraMatrix, Size imageSize, double apertureWidth, double apertureHeight, double &fovx, double &fovy, double &focalLength, Point2d &principalPoint, double &aspectRatio)
Computes useful camera characteristics from the camera matrix. 更多...
bool cv::checkChessboard ( InputArray img, Size size)
void cv::composeRT ( InputArray rvec1, InputArray tvec1, InputArray rvec2, InputArray tvec2, OutputArray rvec3, OutputArray tvec3, OutputArray dr3dr1= noArray (), OutputArray dr3dt1= noArray (), OutputArray dr3dr2= noArray (), OutputArray dr3dt2= noArray (), OutputArray dt3dr1= noArray (), OutputArray dt3dt1= noArray (), OutputArray dt3dr2= noArray (), OutputArray dt3dt2= noArray ())
Combines two rotation-and-shift transformations. 更多...
void cv::computeCorrespondEpilines ( InputArray points, int whichImage, InputArray F, OutputArray lines)
For points in an image of a stereo pair, computes the corresponding epilines in the other image. 更多...
void cv::convertPointsFromHomogeneous ( InputArray src, OutputArray dst)
Converts points from homogeneous to Euclidean space. 更多...
void cv::convertPointsHomogeneous ( InputArray src, OutputArray dst)
Converts points to/from homogeneous coordinates. 更多...
void cv::convertPointsToHomogeneous ( InputArray src, OutputArray dst)
Converts points from Euclidean to homogeneous space. 更多...
void cv::correctMatches ( InputArray F, InputArray points1, InputArray points2, OutputArray newPoints1, OutputArray newPoints2)
Refines coordinates of corresponding points. 更多...
void cv::decomposeEssentialMat ( InputArray E, OutputArray R1, OutputArray R2, OutputArray t)
Decompose an essential matrix to possible rotations and translation. 更多...
int cv::decomposeHomographyMat ( InputArray H, InputArray K, OutputArrayOfArrays rotations, OutputArrayOfArrays translations, OutputArrayOfArrays normals)
Decompose a homography matrix to rotation(s), translation(s) and plane normal(s). 更多...
void cv::decomposeProjectionMatrix ( InputArray projMatrix, OutputArray cameraMatrix, OutputArray rotMatrix, OutputArray transVect, OutputArray rotMatrixX= noArray (), OutputArray rotMatrixY= noArray (), OutputArray rotMatrixZ= noArray (), OutputArray eulerAngles= noArray ())
Decomposes a projection matrix into a rotation matrix and a camera matrix. 更多...
void cv::drawChessboardCorners ( InputOutputArray image, Size patternSize, InputArray corners, bool patternWasFound)
Renders the detected chessboard corners. 更多...
void cv::drawFrameAxes ( InputOutputArray image, InputArray cameraMatrix, InputArray distCoeffs, InputArray rvec, InputArray tvec, float length, int thickness=3)
Draw axes of the world/object coordinate system from pose estimation. 更多...
cv::Mat cv::estimateAffine2D ( InputArray from, InputArray to, OutputArray inliers= noArray (), int method= RANSAC , double ransacReprojThreshold=3, size_t maxIters=2000, double confidence=0.99, size_t refineIters=10)
Computes an optimal affine transformation between two 2D point sets. 更多...
int cv::estimateAffine3D ( InputArray src, InputArray dst, OutputArray out, OutputArray inliers, double ransacThreshold=3, double confidence=0.99)
Computes an optimal affine transformation between two 3D point sets. 更多...
cv::Mat cv::estimateAffinePartial2D ( InputArray from, InputArray to, OutputArray inliers= noArray (), int method= RANSAC , double ransacReprojThreshold=3, size_t maxIters=2000, double confidence=0.99, size_t refineIters=10)
Computes an optimal limited affine transformation with 4 degrees of freedom between two 2D point sets. 更多...
void cv::filterHomographyDecompByVisibleRefpoints ( InputArrayOfArrays rotations, InputArrayOfArrays normals, InputArray beforePoints, InputArray afterPoints, OutputArray possibleSolutions, InputArray pointsMask= noArray ())
Filters homography decompositions based on additional information. 更多...
void cv::filterSpeckles ( InputOutputArray img, double newVal, int maxSpeckleSize, double maxDiff, InputOutputArray buf= noArray ())
Filters off small noise blobs (speckles) in the disparity map. 更多...
bool cv::find4QuadCornerSubpix ( InputArray img, InputOutputArray corners, Size region_size)
finds subpixel-accurate positions of the chessboard corners 更多...
bool cv::findChessboardCorners ( InputArray image, Size patternSize, OutputArray corners, int flags= CALIB_CB_ADAPTIVE_THRESH + CALIB_CB_NORMALIZE_IMAGE )
Finds the positions of internal corners of the chessboard. 更多...
bool cv::findChessboardCornersSB ( InputArray image, Size patternSize, OutputArray corners, int flags=0)
Finds the positions of internal corners of the chessboard using a sector based approach. 更多...
bool cv::findCirclesGrid ( InputArray image, Size patternSize, OutputArray centers, int flags, const Ptr < FeatureDetector > &blobDetector, const CirclesGridFinderParameters &parameters)
Finds centers in the grid of circles. 更多...
bool cv::findCirclesGrid ( InputArray image, Size patternSize, OutputArray centers, int flags= CALIB_CB_SYMMETRIC_GRID , const Ptr < FeatureDetector > &blobDetector= SimpleBlobDetector::create ())
Mat cv::findEssentialMat ( InputArray points1, InputArray points2, InputArray cameraMatrix, int method= RANSAC , double prob=0.999, double threshold =1.0, OutputArray mask= noArray ())
Calculates an essential matrix from the corresponding points in two images. 更多...
Mat cv::findEssentialMat ( InputArray points1, InputArray points2, double focal=1.0, Point2d pp= Point2d (0, 0), int method= RANSAC , double prob=0.999, double threshold =1.0, OutputArray mask= noArray ())
Mat cv::findFundamentalMat ( InputArray points1, InputArray points2, int method= FM_RANSAC , double ransacReprojThreshold=3., double confidence=0.99, OutputArray mask= noArray ())
Calculates a fundamental matrix from the corresponding points in two images. 更多...
Mat cv::findFundamentalMat ( InputArray points1, InputArray points2, OutputArray mask, int method= FM_RANSAC , double ransacReprojThreshold=3., double confidence=0.99)
Mat cv::findHomography ( InputArray srcPoints, InputArray dstPoints, int method=0, double ransacReprojThreshold=3, OutputArray mask= noArray (), const int maxIters=2000, const double confidence=0.995)
Finds a perspective transformation between two planes. 更多...
Mat cv::findHomography ( InputArray srcPoints, InputArray dstPoints, OutputArray mask, int method=0, double ransacReprojThreshold=3)
Mat cv::getDefaultNewCameraMatrix ( InputArray cameraMatrix, Size imgsize= Size (), bool centerPrincipalPoint=false)
Returns the default new camera matrix. 更多...
Mat cv::getOptimalNewCameraMatrix ( InputArray cameraMatrix, InputArray distCoeffs, Size imageSize, double alpha, Size newImgSize= Size (), Rect *validPixROI=0, bool centerPrincipalPoint=false)
Returns the new camera matrix based on the free scaling parameter. 更多...
Rect cv::getValidDisparityROI ( Rect roi1, Rect roi2, int minDisparity, int numberOfDisparities, int SADWindowSize)
computes valid disparity ROI from the valid ROIs of the rectified images (that are returned by cv::stereoRectify() ) 更多...
Mat cv::initCameraMatrix2D ( InputArrayOfArrays objectPoints, InputArrayOfArrays imagePoints, Size imageSize, double aspectRatio=1.0)
Finds an initial camera matrix from 3D-2D point correspondences. 更多...
void cv::initUndistortRectifyMap ( InputArray cameraMatrix, InputArray distCoeffs, InputArray R, InputArray newCameraMatrix, Size size, int m1type, OutputArray map1, OutputArray map2)
Computes the undistortion and rectification transformation map. 更多...
float cv::initWideAngleProjMap ( InputArray cameraMatrix, InputArray distCoeffs, Size imageSize, int destImageWidth, int m1type, OutputArray map1, OutputArray map2, enum UndistortTypes projType= PROJ_SPHERICAL_EQRECT , double alpha=0)
initializes maps for remap for wide-angle 更多...
static float cv::initWideAngleProjMap ( InputArray cameraMatrix, InputArray distCoeffs, Size imageSize, int destImageWidth, int m1type, OutputArray map1, OutputArray map2, int projType, double alpha=0)
void cv::matMulDeriv ( InputArray A, InputArray B, OutputArray dABdA, OutputArray dABdB)
Computes partial derivatives of the matrix product for each multiplied matrix. 更多...
void cv::projectPoints ( InputArray objectPoints, InputArray rvec, InputArray tvec, InputArray cameraMatrix, InputArray distCoeffs, OutputArray imagePoints, OutputArray jacobian= noArray (), double aspectRatio=0)
Projects 3D points to an image plane. 更多...
int cv::recoverPose ( InputArray E, InputArray points1, InputArray points2, InputArray cameraMatrix, OutputArray R, OutputArray t, InputOutputArray mask= noArray ())
Recover relative camera rotation and translation from an estimated essential matrix and the corresponding points in two images, using cheirality check. Returns the number of inliers which pass the check. 更多...
int cv::recoverPose ( InputArray E, InputArray points1, InputArray points2, OutputArray R, OutputArray t, double focal=1.0, Point2d pp= Point2d (0, 0), InputOutputArray mask= noArray ())
int cv::recoverPose ( InputArray E, InputArray points1, InputArray points2, InputArray cameraMatrix, OutputArray R, OutputArray t, double distanceThresh, InputOutputArray mask= noArray (), OutputArray triangulatedPoints= noArray ())
float cv::rectify3Collinear ( InputArray cameraMatrix1, InputArray distCoeffs1, InputArray cameraMatrix2, InputArray distCoeffs2, InputArray cameraMatrix3, InputArray distCoeffs3, InputArrayOfArrays imgpt1, InputArrayOfArrays imgpt3, Size imageSize, InputArray R12, InputArray T12, InputArray R13, InputArray T13, OutputArray R1, OutputArray R2, OutputArray R3, OutputArray P1, OutputArray P2, OutputArray P3, OutputArray Q, double alpha, Size newImgSize, Rect *roi1, Rect *roi2, int flags)
computes the rectification transformations for 3-head camera, where all the heads are on the same line. 更多...
void cv::reprojectImageTo3D ( InputArray disparity, OutputArray _3dImage, InputArray Q, bool handleMissingValues=false, int ddepth=-1)
Reprojects a disparity image to 3D space. 更多...
void cv::Rodrigues ( InputArray src, OutputArray dst, OutputArray jacobian= noArray ())
Converts a rotation matrix to a rotation vector or vice versa. 更多...
Vec3d cv::RQDecomp3x3 ( InputArray src, OutputArray mtxR, OutputArray mtxQ, OutputArray Qx= noArray (), OutputArray Qy= noArray (), OutputArray Qz= noArray ())
Computes an RQ decomposition of 3x3 matrices. 更多...
double cv::sampsonDistance ( InputArray pt1, InputArray pt2, InputArray F)
Calculates the Sampson Distance between two points. 更多...
int cv::solveP3P ( InputArray objectPoints, InputArray imagePoints, InputArray cameraMatrix, InputArray distCoeffs, OutputArrayOfArrays rvecs, OutputArrayOfArrays tvecs, int flags)
Finds an object pose from 3 3D-2D point correspondences. 更多...
bool cv::solvePnP ( InputArray objectPoints, InputArray imagePoints, InputArray cameraMatrix, InputArray distCoeffs, OutputArray rvec, OutputArray tvec, bool useExtrinsicGuess=false, int flags= SOLVEPNP_ITERATIVE )
Finds an object pose from 3D-2D point correspondences. This function returns the rotation and the translation vectors that transform a 3D point expressed in the object coordinate frame to the camera coordinate frame, using different methods: 更多...
int cv::solvePnPGeneric ( InputArray objectPoints, InputArray imagePoints, InputArray cameraMatrix, InputArray distCoeffs, OutputArrayOfArrays rvecs, OutputArrayOfArrays tvecs, bool useExtrinsicGuess=false, SolvePnPMethod flags= SOLVEPNP_ITERATIVE , InputArray rvec= noArray (), InputArray tvec= noArray (), OutputArray reprojectionError= noArray ())
Finds an object pose from 3D-2D point correspondences. This function returns a list of all the possible solutions (a solution is a <rotation vector, translation vector> couple), depending on the number of input points and the chosen method: 更多...
bool cv::solvePnPRansac ( InputArray objectPoints, InputArray imagePoints, InputArray cameraMatrix, InputArray distCoeffs, OutputArray rvec, OutputArray tvec, bool useExtrinsicGuess=false, int iterationsCount=100, float reprojectionError=8.0, double confidence=0.99, OutputArray inliers= noArray (), int flags= SOLVEPNP_ITERATIVE )
Finds an object pose from 3D-2D point correspondences using the RANSAC scheme. 更多...
void cv::solvePnPRefineLM ( InputArray objectPoints, InputArray imagePoints, InputArray cameraMatrix, InputArray distCoeffs, InputOutputArray rvec, InputOutputArray tvec, TermCriteria criteria= TermCriteria ( TermCriteria::EPS + TermCriteria::COUNT , 20, FLT_EPSILON))
Refine a pose (the translation and the rotation that transform a 3D point expressed in the object coordinate frame to the camera coordinate frame) from a 3D-2D point correspondences and starting from an initial solution. 更多...
void cv::solvePnPRefineVVS ( InputArray objectPoints, InputArray imagePoints, InputArray cameraMatrix, InputArray distCoeffs, InputOutputArray rvec, InputOutputArray tvec, TermCriteria criteria= TermCriteria ( TermCriteria::EPS + TermCriteria::COUNT , 20, FLT_EPSILON), double VVSlambda=1)
Refine a pose (the translation and the rotation that transform a 3D point expressed in the object coordinate frame to the camera coordinate frame) from a 3D-2D point correspondences and starting from an initial solution. 更多...
double cv::stereoCalibrate ( InputArrayOfArrays objectPoints, InputArrayOfArrays imagePoints1, InputArrayOfArrays imagePoints2, InputOutputArray cameraMatrix1, InputOutputArray distCoeffs1, InputOutputArray cameraMatrix2, InputOutputArray distCoeffs2, Size imageSize, InputOutputArray R, InputOutputArray T, OutputArray E, OutputArray F, OutputArray perViewErrors, int flags= CALIB_FIX_INTRINSIC , TermCriteria criteria= TermCriteria ( TermCriteria::COUNT + TermCriteria::EPS , 30, 1e-6))
Calibrates the stereo camera. 更多...
double cv::stereoCalibrate ( InputArrayOfArrays objectPoints, InputArrayOfArrays imagePoints1, InputArrayOfArrays imagePoints2, InputOutputArray cameraMatrix1, InputOutputArray distCoeffs1, InputOutputArray cameraMatrix2, InputOutputArray distCoeffs2, Size imageSize, OutputArray R, OutputArray T, OutputArray E, OutputArray F, int flags= CALIB_FIX_INTRINSIC , TermCriteria criteria= TermCriteria ( TermCriteria::COUNT + TermCriteria::EPS , 30, 1e-6))
void cv::stereoRectify ( InputArray cameraMatrix1, InputArray distCoeffs1, InputArray cameraMatrix2, InputArray distCoeffs2, Size imageSize, InputArray R, InputArray T, OutputArray R1, OutputArray R2, OutputArray P1, OutputArray P2, OutputArray Q, int flags= CALIB_ZERO_DISPARITY , double alpha=-1, Size newImageSize= Size (), Rect *validPixROI1=0, Rect *validPixROI2=0)
Computes rectification transforms for each head of a calibrated stereo camera. 更多...
bool cv::stereoRectifyUncalibrated ( InputArray points1, InputArray points2, InputArray F, Size imgSize, OutputArray H1, OutputArray H2, double threshold =5)
Computes a rectification transform for an uncalibrated stereo camera. 更多...
void cv::triangulatePoints ( InputArray projMatr1, InputArray projMatr2, InputArray projPoints1, InputArray projPoints2, OutputArray points4D)
Reconstructs points by triangulation. 更多...
void cv::undistort ( InputArray src, OutputArray dst, InputArray cameraMatrix, InputArray distCoeffs, InputArray newCameraMatrix= noArray ())
Transforms an image to compensate for lens distortion. 更多...
void cv::undistortPoints ( InputArray src, OutputArray dst, InputArray cameraMatrix, InputArray distCoeffs, InputArray R= noArray (), InputArray P= noArray ())
Computes the ideal point coordinates from the observed point coordinates. 更多...
void cv::undistortPoints ( InputArray src, OutputArray dst, InputArray cameraMatrix, InputArray distCoeffs, InputArray R, InputArray P, TermCriteria criteria)
void cv::validateDisparity ( InputOutputArray disparity, InputArray cost, int minDisparity, int numberOfDisparities, int disp12MaxDisp=1)
validates disparity using the left-right check. The matrix "cost" should be computed by the stereo correspondence algorithm 更多...

详细描述

The functions in this section use a so-called pinhole camera model. In this model, a scene view is formed by projecting 3D points into the image plane using a perspective transformation.

\[s \; m' = A [R|t] M'\]

\[s \vecthree{u}{v}{1} = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1} \begin{bmatrix} r_{11} & r_{12} & r_{13} & t_x \\ r_{21} & r_{22} & r_{23} & t_y \\ r_{31} & r_{32} & r_{33} & t_z \end{bmatrix} \begin{bmatrix} X_w \\ Y_w \\ Z_w \\ 1 \end{bmatrix}\]

where:

  • \((X_w, Y_w, Z_w)\) are the coordinates of a 3D point in the world coordinate space
  • \((u, v)\) are the coordinates of the projection point in pixels
  • \(A\) is a camera matrix, or a matrix of intrinsic parameters
  • \((c_x, c_y)\) is a principal point that is usually at the image center
  • \(f_x, f_y\) are the focal lengths expressed in pixel units.

Thus, if an image from the camera is scaled by a 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. So, once estimated, it can be re-used as long as the focal length is fixed (in case of zoom lens). The joint rotation-translation matrix \([R|t]\) 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 a still camera. That is, \([R|t]\) translates coordinates of a world point \((X_w, Y_w, Z_w)\) to a coordinate system, fixed with respect to the camera. The transformation above is equivalent to the following (when \(z \ne 0\) ):

\[\begin{array}{l} \vecthree{X_c}{Y_c}{Z_c} = R \vecthree{X_w}{Y_w}{Z_w} + t \\ x' = X_c/Z_c \\ y' = Y_c/Z_c \\ u = f_x \times x' + c_x \\ v = f_y \times y' + c_y \end{array}\]

The following figure illustrates the pinhole camera model.

pinhole_camera_model.png
Pinhole camera model

Real lenses usually have some distortion, mostly radial distortion and slight tangential distortion. So, the above model is extended as:

\[\begin{array}{l} \vecthree{X_c}{Y_c}{Z_c} = R \vecthree{X_w}{Y_w}{Z_w} + t \\ x' = X_c/Z_c \\ y' = Y_c/Z_c \\ x'' = x' \frac{1 + k_1 r^2 + k_2 r^4 + k_3 r^6}{1 + k_4 r^2 + k_5 r^4 + k_6 r^6} + 2 p_1 x' y' + p_2(r^2 + 2 x'^2) + s_1 r^2 + s_2 r^4 \\ y'' = y' \frac{1 + k_1 r^2 + k_2 r^4 + k_3 r^6}{1 + k_4 r^2 + k_5 r^4 + k_6 r^6} + p_1 (r^2 + 2 y'^2) + 2 p_2 x' y' + s_3 r^2 + s_4 r^4 \\ \text{where} \quad r^2 = x'^2 + y'^2 \\ u = f_x \times x'' + c_x \\ v = f_y \times y'' + c_y \end{array}\]

\(k_1\), \(k_2\), \(k_3\), \(k_4\), \(k_5\), and \(k_6\) are radial distortion coefficients. \(p_1\) and \(p_2\) are tangential distortion coefficients. \(s_1\), \(s_2\), \(s_3\), and \(s_4\), are the thin prism distortion coefficients. Higher-order coefficients are not considered in OpenCV.

The next figures show two common types of radial distortion: barrel distortion (typically \( k_1 < 0 \)) and pincushion distortion (typically \( k_1 > 0 \)).

distortion_examples.png
distortion_examples2.png

In some cases the image sensor may be tilted in order to focus an oblique plane in front of the camera (Scheimpflug principle). This can be useful for particle image velocimetry (PIV) or triangulation with a laser fan. The tilt causes a perspective distortion of \(x''\) and \(y''\). This distortion can be modelled in the following way, see e.g. [139] .

\[\begin{array}{l} s\vecthree{x'''}{y'''}{1} = \vecthreethree{R_{33}(\tau_x, \tau_y)}{0}{-R_{13}(\tau_x, \tau_y)} {0}{R_{33}(\tau_x, \tau_y)}{-R_{23}(\tau_x, \tau_y)} {0}{0}{1} R(\tau_x, \tau_y) \vecthree{x''}{y''}{1}\\ u = f_x \times x''' + c_x \\ v = f_y \times y''' + c_y \end{array}\]

where the matrix \(R(\tau_x, \tau_y)\) is defined by two rotations with angular parameter \(\tau_x\) and \(\tau_y\), respectively,

\[ R(\tau_x, \tau_y) = \vecthreethree{\cos(\tau_y)}{0}{-\sin(\tau_y)}{0}{1}{0}{\sin(\tau_y)}{0}{\cos(\tau_y)} \vecthreethree{1}{0}{0}{0}{\cos(\tau_x)}{\sin(\tau_x)}{0}{-\sin(\tau_x)}{\cos(\tau_x)} = \vecthreethree{\cos(\tau_y)}{\sin(\tau_y)\sin(\tau_x)}{-\sin(\tau_y)\cos(\tau_x)} {0}{\cos(\tau_x)}{\sin(\tau_x)} {\sin(\tau_y)}{-\cos(\tau_y)\sin(\tau_x)}{\cos(\tau_y)\cos(\tau_x)}. \]

In the functions below the coefficients are passed or returned as

\[(k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6 [, s_1, s_2, s_3, s_4[, \tau_x, \tau_y]]]])\]

vector. That is, if the vector contains four elements, it means that \(k_3=0\) . 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. If, for example, a camera has been calibrated on images of 320 x 240 resolution, absolutely the same distortion coefficients can be used for 640 x 480 images from the same camera while \(f_x\), \(f_y\), \(c_x\), and \(c_y\) need to be scaled appropriately.

The functions below use the above model to do the following:

  • 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 (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.
注意
  • A calibration sample for 3 cameras in horizontal position can be found at opencv_source_code/samples/cpp/3calibration.cpp
  • A calibration sample based on a sequence of images can be found at opencv_source_code/samples/cpp/calibration.cpp
  • A calibration sample in order to do 3D reconstruction can be found at opencv_source_code/samples/cpp/build3dmodel.cpp
  • A calibration example on stereo calibration can be found at opencv_source_code/samples/cpp/stereo_calib.cpp
  • A calibration example on stereo matching can be found at opencv_source_code/samples/cpp/stereo_match.cpp
  • (Python) A camera calibration sample can be found at opencv_source_code/samples/python/calibrate.py

Typedef 文档编制

CirclesGridFinderParameters2

枚举类型文档编制

anonymous enum

anonymous enum

#include < opencv2/calib3d.hpp >

type of the robust estimation algorithm

枚举器
LMEDS
Python: cv.LMEDS

least-median of squares algorithm

RANSAC
Python: cv.RANSAC

RANSAC algorithm.

RHO
Python: cv.RHO

RHO algorithm.

anonymous enum

anonymous enum

#include < opencv2/calib3d.hpp >

枚举器
CALIB_CB_ADAPTIVE_THRESH
Python: cv.CALIB_CB_ADAPTIVE_THRESH
CALIB_CB_NORMALIZE_IMAGE
Python: cv.CALIB_CB_NORMALIZE_IMAGE
CALIB_CB_FILTER_QUADS
Python: cv.CALIB_CB_FILTER_QUADS
CALIB_CB_FAST_CHECK
Python: cv.CALIB_CB_FAST_CHECK
CALIB_CB_EXHAUSTIVE
Python: cv.CALIB_CB_EXHAUSTIVE
CALIB_CB_ACCURACY
Python: cv.CALIB_CB_ACCURACY

anonymous enum

anonymous enum

#include < opencv2/calib3d.hpp >

枚举器
CALIB_CB_SYMMETRIC_GRID
Python: cv.CALIB_CB_SYMMETRIC_GRID
CALIB_CB_ASYMMETRIC_GRID
Python: cv.CALIB_CB_ASYMMETRIC_GRID
CALIB_CB_CLUSTERING
Python: cv.CALIB_CB_CLUSTERING

anonymous enum

anonymous enum

#include < opencv2/calib3d.hpp >

枚举器
CALIB_NINTRINSIC
Python: cv.CALIB_NINTRINSIC
CALIB_USE_INTRINSIC_GUESS
Python: cv.CALIB_USE_INTRINSIC_GUESS
CALIB_FIX_ASPECT_RATIO
Python: cv.CALIB_FIX_ASPECT_RATIO
CALIB_FIX_PRINCIPAL_POINT
Python: cv.CALIB_FIX_PRINCIPAL_POINT
CALIB_ZERO_TANGENT_DIST
Python: cv.CALIB_ZERO_TANGENT_DIST
CALIB_FIX_FOCAL_LENGTH
Python: cv.CALIB_FIX_FOCAL_LENGTH
CALIB_FIX_K1
Python: cv.CALIB_FIX_K1
CALIB_FIX_K2
Python: cv.CALIB_FIX_K2
CALIB_FIX_K3
Python: cv.CALIB_FIX_K3
CALIB_FIX_K4
Python: cv.CALIB_FIX_K4
CALIB_FIX_K5
Python: cv.CALIB_FIX_K5
CALIB_FIX_K6
Python: cv.CALIB_FIX_K6
CALIB_RATIONAL_MODEL
Python: cv.CALIB_RATIONAL_MODEL
CALIB_THIN_PRISM_MODEL
Python: cv.CALIB_THIN_PRISM_MODEL
CALIB_FIX_S1_S2_S3_S4
Python: cv.CALIB_FIX_S1_S2_S3_S4
CALIB_TILTED_MODEL
Python: cv.CALIB_TILTED_MODEL
CALIB_FIX_TAUX_TAUY
Python: cv.CALIB_FIX_TAUX_TAUY
CALIB_USE_QR
Python: cv.CALIB_USE_QR

use QR instead of SVD decomposition for solving. Faster but potentially less precise

CALIB_FIX_TANGENT_DIST
Python: cv.CALIB_FIX_TANGENT_DIST
CALIB_FIX_INTRINSIC
Python: cv.CALIB_FIX_INTRINSIC
CALIB_SAME_FOCAL_LENGTH
Python: cv.CALIB_SAME_FOCAL_LENGTH
CALIB_ZERO_DISPARITY
Python: cv.CALIB_ZERO_DISPARITY
CALIB_USE_LU
Python: cv.CALIB_USE_LU

use LU instead of SVD decomposition for solving. much faster but potentially less precise

CALIB_USE_EXTRINSIC_GUESS
Python: cv.CALIB_USE_EXTRINSIC_GUESS

for stereoCalibrate

anonymous enum

anonymous enum

#include < opencv2/calib3d.hpp >

the algorithm for finding fundamental matrix

枚举器
FM_7POINT
Python: cv.FM_7POINT

7-point algorithm

FM_8POINT
Python: cv.FM_8POINT

8-point algorithm

FM_LMEDS
Python: cv.FM_LMEDS

least-median algorithm. 7-point algorithm is used.

FM_RANSAC
Python: cv.FM_RANSAC

RANSAC algorithm. It needs at least 15 points. 7-point algorithm is used.

HandEyeCalibrationMethod

#include < opencv2/calib3d.hpp >

枚举器
CALIB_HAND_EYE_TSAI
Python: cv.CALIB_HAND_EYE_TSAI

A New Technique for Fully Autonomous and Efficient 3D Robotics Hand/Eye Calibration [229] .

CALIB_HAND_EYE_PARK
Python: cv.CALIB_HAND_EYE_PARK

Robot Sensor Calibration: Solving AX = XB on the Euclidean Group [178] .

CALIB_HAND_EYE_HORAUD
Python: cv.CALIB_HAND_EYE_HORAUD

Hand-eye Calibration [103] .

CALIB_HAND_EYE_ANDREFF
Python: cv.CALIB_HAND_EYE_ANDREFF

On-line Hand-Eye Calibration [7] .

CALIB_HAND_EYE_DANIILIDIS
Python: cv.CALIB_HAND_EYE_DANIILIDIS

Hand-Eye Calibration Using Dual Quaternions [46] .

SolvePnPMethod

#include < opencv2/calib3d.hpp >

枚举器
SOLVEPNP_ITERATIVE
Python: cv.SOLVEPNP_ITERATIVE
SOLVEPNP_EPNP
Python: cv.SOLVEPNP_EPNP

EPnP: Efficient Perspective-n-Point Camera Pose Estimation [128] .

SOLVEPNP_P3P
Python: cv.SOLVEPNP_P3P

Complete Solution Classification for the Perspective-Three-Point Problem [76] .

SOLVEPNP_DLS
Python: cv.SOLVEPNP_DLS

A Direct Least-Squares (DLS) Method for PnP [100] .

SOLVEPNP_UPNP
Python: cv.SOLVEPNP_UPNP

Exhaustive Linearization for Robust Camera Pose and Focal Length Estimation [179] .

SOLVEPNP_AP3P
Python: cv.SOLVEPNP_AP3P

An Efficient Algebraic Solution to the Perspective-Three-Point Problem [117] .

SOLVEPNP_IPPE
Python: cv.SOLVEPNP_IPPE

Infinitesimal Plane-Based Pose Estimation [42]
Object points must be coplanar.

SOLVEPNP_IPPE_SQUARE
Python: cv.SOLVEPNP_IPPE_SQUARE

Infinitesimal Plane-Based Pose Estimation [42]
This is a special case suitable for marker pose estimation.
4 coplanar object points must be defined in the following order:

  • point 0: [-squareLength / 2, squareLength / 2, 0]
  • point 1: [ squareLength / 2, squareLength / 2, 0]
  • point 2: [ squareLength / 2, -squareLength / 2, 0]
  • point 3: [-squareLength / 2, -squareLength / 2, 0]

UndistortTypes

#include < opencv2/calib3d.hpp >

cv::undistort mode

枚举器
PROJ_SPHERICAL_ORTHO
Python: cv.PROJ_SPHERICAL_ORTHO
PROJ_SPHERICAL_EQRECT
Python: cv.PROJ_SPHERICAL_EQRECT

函数文档编制

calibrateCamera() [1/2]

double cv::calibrateCamera ( InputArrayOfArrays objectPoints ,
InputArrayOfArrays imagePoints ,
Size imageSize ,
InputOutputArray cameraMatrix ,
InputOutputArray distCoeffs ,
OutputArrayOfArrays rvecs ,
OutputArrayOfArrays tvecs ,
OutputArray stdDeviationsIntrinsics ,
OutputArray stdDeviationsExtrinsics ,
OutputArray perViewErrors ,
int flags = 0 ,
TermCriteria criteria = TermCriteria ( TermCriteria::COUNT + TermCriteria::EPS , 30, DBL_EPSILON)
)
Python:
retval, cameraMatrix, distCoeffs, rvecs, tvecs = cv.calibrateCamera( objectPoints, imagePoints, imageSize, cameraMatrix, distCoeffs[, rvecs[, tvecs[, flags[, criteria]]]] )
retval, cameraMatrix, distCoeffs, rvecs, tvecs, stdDeviationsIntrinsics, stdDeviationsExtrinsics, perViewErrors = cv.calibrateCameraExtended( objectPoints, imagePoints, imageSize, cameraMatrix, distCoeffs[, rvecs[, tvecs[, stdDeviationsIntrinsics[, stdDeviationsExtrinsics[, perViewErrors[, flags[, criteria]]]]]]] )

#include < opencv2/calib3d.hpp >

Finds the camera intrinsic and extrinsic parameters from several views of a calibration pattern.

Parameters
objectPoints In the new interface it is a vector of vectors of calibration pattern points in the calibration pattern coordinate space (e.g. std::vector<std::vector<cv::Vec3f>>). 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. In the old interface all the vectors of object points from different views are concatenated together.
imagePoints In the new interface it is a vector of vectors of the projections of calibration pattern points (e.g. std::vector<std::vector<cv::Vec2f>>). imagePoints.size() and objectPoints.size() and imagePoints[i].size() must be equal to objectPoints[i].size() for each i. In the old interface all the vectors of object points from different views are concatenated together.
imageSize Size of the image used only to initialize the intrinsic camera matrix.
cameraMatrix Output 3x3 floating-point camera matrix \(A = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}\) . If CV_CALIB_USE_INTRINSIC_GUESS and/or CALIB_FIX_ASPECT_RATIO are specified, some or all of fx, fy, cx, cy must be initialized before calling the function.
distCoeffs Output vector of distortion coefficients \((k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6 [, s_1, s_2, s_3, s_4[, \tau_x, \tau_y]]]])\) of 4, 5, 8, 12 or 14 elements.
rvecs Output vector of rotation vectors (see Rodrigues ) estimated for each pattern view (e.g. std::vector<cv::Mat>>). That is, each k-th rotation vector together with the corresponding k-th translation vector (see the next output parameter description) brings the calibration pattern from the model coordinate space (in which object points are specified) to the world coordinate space, that is, a real position of the calibration pattern in the k-th pattern view (k=0.. M -1).
tvecs Output vector of translation vectors estimated for each pattern view.
stdDeviationsIntrinsics Output vector of standard deviations estimated for intrinsic parameters. Order of deviations values: \((f_x, f_y, c_x, c_y, k_1, k_2, p_1, p_2, k_3, k_4, k_5, k_6 , s_1, s_2, s_3, s_4, \tau_x, \tau_y)\) If one of parameters is not estimated, it's deviation is equals to zero.
stdDeviationsExtrinsics Output vector of standard deviations estimated for extrinsic parameters. Order of deviations values: \((R_1, T_1, \dotsc , R_M, T_M)\) where M is number of pattern views, \(R_i, T_i\) are concatenated 1x3 vectors.
perViewErrors Output vector of the RMS re-projection error estimated for each pattern view.
flags Different flags that may be zero or a combination of the following values:
  • 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 solvePnP instead.
  • 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 CALIB_USE_INTRINSIC_GUESS is set too.
  • 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 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.
  • CALIB_ZERO_TANGENT_DIST Tangential distortion coefficients \((p_1, p_2)\) are set to zeros and stay zero.
  • CALIB_FIX_K1,...,CALIB_FIX_K6 The corresponding radial distortion coefficient is not changed during the optimization. If CALIB_USE_INTRINSIC_GUESS is set, the coefficient from the supplied distCoeffs matrix is used. Otherwise, it is set to 0.
  • 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.
  • CALIB_THIN_PRISM_MODEL Coefficients s1, s2, s3 and s4 are enabled. To provide the backward compatibility, this extra flag should be explicitly specified to make the calibration function use the thin prism model and return 12 coefficients. If the flag is not set, the function computes and returns only 5 distortion coefficients.
  • CALIB_FIX_S1_S2_S3_S4 The thin prism distortion coefficients are not changed during the optimization. If CALIB_USE_INTRINSIC_GUESS is set, the coefficient from the supplied distCoeffs matrix is used. Otherwise, it is set to 0.
  • CALIB_TILTED_MODEL Coefficients tauX and tauY are enabled. To provide the backward compatibility, this extra flag should be explicitly specified to make the calibration function use the tilted sensor model and return 14 coefficients. If the flag is not set, the function computes and returns only 5 distortion coefficients.
  • CALIB_FIX_TAUX_TAUY The coefficients of the tilted sensor model are not changed during the optimization. If CALIB_USE_INTRINSIC_GUESS is set, the coefficient from the supplied distCoeffs matrix is used. Otherwise, it is set to 0.
criteria Termination criteria for the iterative optimization algorithm.
返回
the overall RMS re-projection error.

The function estimates the intrinsic camera parameters and extrinsic parameters for each of the views. The algorithm is based on [266] and [25] . The coordinates of 3D object points and their corresponding 2D projections in each view must be specified. That may be achieved by using an object with a 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 findChessboardCorners ). Currently, initialization of intrinsic parameters (when CALIB_USE_INTRINSIC_GUESS is not set) is only implemented for planar calibration patterns (where Z-coordinates of the object points must be all zeros). 3D calibration rigs can also be used as long as initial cameraMatrix is provided.

The algorithm performs the following steps:

  • 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 CALIB_FIX_K? are specified.
  • Estimate the initial camera pose as if the intrinsic parameters have been already known. This is done using solvePnP .
  • 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 projectPoints for details.
注意
If you use a non-square (=non-NxN) grid and findChessboardCorners for calibration, and calibrateCamera returns bad values (zero distortion coefficients, an image center very far from (w/2-0.5,h/2-0.5), and/or large differences between \(f_x\) and \(f_y\) (ratios of 10:1 or more)), then you have probably used patternSize=cvSize(rows,cols) instead of using patternSize=cvSize(cols,rows) in findChessboardCorners .
另请参阅
calibrateCameraRO , findChessboardCorners , solvePnP , initCameraMatrix2D , stereoCalibrate , undistort

calibrateCamera() [2/2]

double cv::calibrateCamera ( InputArrayOfArrays objectPoints ,
InputArrayOfArrays imagePoints ,
Size imageSize ,
InputOutputArray cameraMatrix ,
InputOutputArray distCoeffs ,
OutputArrayOfArrays rvecs ,
OutputArrayOfArrays tvecs ,
int flags = 0 ,
TermCriteria criteria = TermCriteria ( TermCriteria::COUNT + TermCriteria::EPS , 30, DBL_EPSILON)
)
Python:
retval, cameraMatrix, distCoeffs, rvecs, tvecs = cv.calibrateCamera( objectPoints, imagePoints, imageSize, cameraMatrix, distCoeffs[, rvecs[, tvecs[, flags[, criteria]]]] )
retval, cameraMatrix, distCoeffs, rvecs, tvecs, stdDeviationsIntrinsics, stdDeviationsExtrinsics, perViewErrors = cv.calibrateCameraExtended( objectPoints, imagePoints, imageSize, cameraMatrix, distCoeffs[, rvecs[, tvecs[, stdDeviationsIntrinsics[, stdDeviationsExtrinsics[, perViewErrors[, flags[, criteria]]]]]]] )

#include < opencv2/calib3d.hpp >

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

calibrateCameraRO() [1/2]

double cv::calibrateCameraRO ( InputArrayOfArrays objectPoints ,
InputArrayOfArrays imagePoints ,
Size imageSize ,
int iFixedPoint ,
InputOutputArray cameraMatrix ,
InputOutputArray distCoeffs ,
OutputArrayOfArrays rvecs ,
OutputArrayOfArrays tvecs ,
OutputArray newObjPoints ,
OutputArray stdDeviationsIntrinsics ,
OutputArray stdDeviationsExtrinsics ,
OutputArray stdDeviationsObjPoints ,
OutputArray perViewErrors ,
int flags = 0 ,
TermCriteria criteria = TermCriteria ( TermCriteria::COUNT + TermCriteria::EPS , 30, DBL_EPSILON)
)
Python:
retval, cameraMatrix, distCoeffs, rvecs, tvecs, newObjPoints = cv.calibrateCameraRO( objectPoints, imagePoints, imageSize, iFixedPoint, cameraMatrix, distCoeffs[, rvecs[, tvecs[, newObjPoints[, flags[, criteria]]]]] )
retval, cameraMatrix, distCoeffs, rvecs, tvecs, newObjPoints, stdDeviationsIntrinsics, stdDeviationsExtrinsics, stdDeviationsObjPoints, perViewErrors = cv.calibrateCameraROExtended( objectPoints, imagePoints, imageSize, iFixedPoint, cameraMatrix, distCoeffs[, rvecs[, tvecs[, newObjPoints[, stdDeviationsIntrinsics[, stdDeviationsExtrinsics[, stdDeviationsObjPoints[, perViewErrors[, flags[, criteria]]]]]]]]] )

#include < opencv2/calib3d.hpp >

Finds the camera intrinsic and extrinsic parameters from several views of a calibration pattern.

This function is an extension of calibrateCamera() with the method of releasing object which was proposed in [215] . In many common cases with inaccurate, unmeasured, roughly planar targets (calibration plates), this method can dramatically improve the precision of the estimated camera parameters. Both the object-releasing method and standard method are supported by this function. Use the parameter iFixedPoint for method selection. In the internal implementation, calibrateCamera() is a wrapper for this function.

Parameters
objectPoints Vector of vectors of calibration pattern points in the calibration pattern coordinate space. See calibrateCamera() for details. If the method of releasing object to be used, the identical calibration board must be used in each view and it must be fully visible, and all objectPoints[i] must be the same and all points should be roughly close to a plane. The calibration target has to be rigid, or at least static if the camera (rather than the calibration target) is shifted for grabbing images.
imagePoints Vector of vectors of the projections of calibration pattern points. See calibrateCamera() for details.
imageSize Size of the image used only to initialize the intrinsic camera matrix.
iFixedPoint The index of the 3D object point in objectPoints[0] to be fixed. It also acts as a switch for calibration method selection. If object-releasing method to be used, pass in the parameter in the range of [1, objectPoints[0].size()-2], otherwise a value out of this range will make standard calibration method selected. Usually the top-right corner point of the calibration board grid is recommended to be fixed when object-releasing method being utilized. According to [215] , two other points are also fixed. In this implementation, objectPoints[0].front and objectPoints[0].back.z are used. With object-releasing method, accurate rvecs, tvecs and newObjPoints are only possible if coordinates of these three fixed points are accurate enough.
cameraMatrix Output 3x3 floating-point camera matrix. See calibrateCamera() for details.
distCoeffs Output vector of distortion coefficients. See calibrateCamera() for details.
rvecs Output vector of rotation vectors estimated for each pattern view. See calibrateCamera() for details.
tvecs Output vector of translation vectors estimated for each pattern view.
newObjPoints The updated output vector of calibration pattern points. The coordinates might be scaled based on three fixed points. The returned coordinates are accurate only if the above mentioned three fixed points are accurate. If not needed, noArray() can be passed in. This parameter is ignored with standard calibration method.
stdDeviationsIntrinsics Output vector of standard deviations estimated for intrinsic parameters. See calibrateCamera() for details.
stdDeviationsExtrinsics Output vector of standard deviations estimated for extrinsic parameters. See calibrateCamera() for details.
stdDeviationsObjPoints Output vector of standard deviations estimated for refined coordinates of calibration pattern points. It has the same size and order as objectPoints[0] vector. This parameter is ignored with standard calibration method.
perViewErrors Output vector of the RMS re-projection error estimated for each pattern view.
flags Different flags that may be zero or a combination of some predefined values. See calibrateCamera() for details. If the method of releasing object is used, the calibration time may be much longer. CALIB_USE_QR or CALIB_USE_LU could be used for faster calibration with potentially less precise and less stable in some rare cases.
criteria Termination criteria for the iterative optimization algorithm.
返回
the overall RMS re-projection error.

The function estimates the intrinsic camera parameters and extrinsic parameters for each of the views. The algorithm is based on [266] , [25] and [215] 。请参阅 calibrateCamera() for other detailed explanations.

另请参阅
calibrateCamera , findChessboardCorners , solvePnP , initCameraMatrix2D , stereoCalibrate , undistort

calibrateCameraRO() [2/2]

double cv::calibrateCameraRO ( InputArrayOfArrays objectPoints ,
InputArrayOfArrays imagePoints ,
Size imageSize ,
int iFixedPoint ,
InputOutputArray cameraMatrix ,
InputOutputArray distCoeffs ,
OutputArrayOfArrays rvecs ,
OutputArrayOfArrays tvecs ,
OutputArray newObjPoints ,
int flags = 0 ,
TermCriteria criteria = TermCriteria ( TermCriteria::COUNT + TermCriteria::EPS , 30, DBL_EPSILON)
)
Python:
retval, cameraMatrix, distCoeffs, rvecs, tvecs, newObjPoints = cv.calibrateCameraRO( objectPoints, imagePoints, imageSize, iFixedPoint, cameraMatrix, distCoeffs[, rvecs[, tvecs[, newObjPoints[, flags[, criteria]]]]] )
retval, cameraMatrix, distCoeffs, rvecs, tvecs, newObjPoints, stdDeviationsIntrinsics, stdDeviationsExtrinsics, stdDeviationsObjPoints, perViewErrors = cv.calibrateCameraROExtended( objectPoints, imagePoints, imageSize, iFixedPoint, cameraMatrix, distCoeffs[, rvecs[, tvecs[, newObjPoints[, stdDeviationsIntrinsics[, stdDeviationsExtrinsics[, stdDeviationsObjPoints[, perViewErrors[, flags[, criteria]]]]]]]]] )

#include < opencv2/calib3d.hpp >

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

calibrateHandEye()

void cv::calibrateHandEye ( InputArrayOfArrays R_gripper2base ,
InputArrayOfArrays t_gripper2base ,
InputArrayOfArrays R_target2cam ,
InputArrayOfArrays t_target2cam ,
OutputArray R_cam2gripper ,
OutputArray t_cam2gripper ,
HandEyeCalibrationMethod method = CALIB_HAND_EYE_TSAI
)
Python:
R_cam2gripper, t_cam2gripper = cv.calibrateHandEye( R_gripper2base, t_gripper2base, R_target2cam, t_target2cam[, R_cam2gripper[, t_cam2gripper[, method]]] )

#include < opencv2/calib3d.hpp >

Computes Hand-Eye calibration: \(_{}^{g}\textrm{T}_c\).

Parameters
[in] R_gripper2base Rotation part extracted from the homogeneous matrix that transforms a point expressed in the gripper frame to the robot base frame ( \(_{}^{b}\textrm{T}_g\)). This is a vector ( vector< Mat > ) that contains the rotation matrices for all the transformations from gripper frame to robot base frame.
[in] t_gripper2base Translation part extracted from the homogeneous matrix that transforms a point expressed in the gripper frame to the robot base frame ( \(_{}^{b}\textrm{T}_g\)). This is a vector ( vector< Mat > ) that contains the translation vectors for all the transformations from gripper frame to robot base frame.
[in] R_target2cam Rotation part extracted from the homogeneous matrix that transforms a point expressed in the target frame to the camera frame ( \(_{}^{c}\textrm{T}_t\)). This is a vector ( vector< Mat > ) that contains the rotation matrices for all the transformations from calibration target frame to camera frame.
[in] t_target2cam Rotation part extracted from the homogeneous matrix that transforms a point expressed in the target frame to the camera frame ( \(_{}^{c}\textrm{T}_t\)). This is a vector ( vector< Mat > ) that contains the translation vectors for all the transformations from calibration target frame to camera frame.
[out] R_cam2gripper Estimated rotation part extracted from the homogeneous matrix that transforms a point expressed in the camera frame to the gripper frame ( \(_{}^{g}\textrm{T}_c\)).
[out] t_cam2gripper Estimated translation part extracted from the homogeneous matrix that transforms a point expressed in the camera frame to the gripper frame ( \(_{}^{g}\textrm{T}_c\)).
[in] method One of the implemented Hand-Eye calibration method, see cv::HandEyeCalibrationMethod

The function performs the Hand-Eye calibration using various methods. One approach consists in estimating the rotation then the translation (separable solutions) and the following methods are implemented:

  • R. Tsai, R. Lenz A New Technique for Fully Autonomous and Efficient 3D Robotics Hand/EyeCalibration [229]
  • F. Park, B. Martin Robot Sensor Calibration: Solving AX = XB on the Euclidean Group [178]
  • R. Horaud, F. Dornaika Hand-Eye Calibration [103]

Another approach consists in estimating simultaneously the rotation and the translation (simultaneous solutions), with the following implemented method:

  • N. Andreff, R. Horaud, B. Espiau On-line Hand-Eye Calibration [7]
  • K. Daniilidis Hand-Eye Calibration Using Dual Quaternions [46]

The following picture describes the Hand-Eye calibration problem where the transformation between a camera ("eye") mounted on a robot gripper ("hand") has to be estimated.

hand-eye_figure.png

The calibration procedure is the following:

  • a static calibration pattern is used to estimate the transformation between the target frame and the camera frame
  • the robot gripper is moved in order to acquire several poses
  • for each pose, the homogeneous transformation between the gripper frame and the robot base frame is recorded using for instance the robot kinematics

    \[ \begin{bmatrix} X_b\\ Y_b\\ Z_b\\ 1 \end{bmatrix} = \begin{bmatrix} _{}^{b}\textrm{R}_g & _{}^{b}\textrm{t}_g \\ 0_{1 \times 3} & 1 \end{bmatrix} \begin{bmatrix} X_g\\ Y_g\\ Z_g\\ 1 \end{bmatrix} \]

  • for each pose, the homogeneous transformation between the calibration target frame and the camera frame is recorded using for instance a pose estimation method (PnP) from 2D-3D point correspondences

    \[ \begin{bmatrix} X_c\\ Y_c\\ Z_c\\ 1 \end{bmatrix} = \begin{bmatrix} _{}^{c}\textrm{R}_t & _{}^{c}\textrm{t}_t \\ 0_{1 \times 3} & 1 \end{bmatrix} \begin{bmatrix} X_t\\ Y_t\\ Z_t\\ 1 \end{bmatrix} \]

The Hand-Eye calibration procedure returns the following homogeneous transformation

\[ \begin{bmatrix} X_g\\ Y_g\\ Z_g\\ 1 \end{bmatrix} = \begin{bmatrix} _{}^{g}\textrm{R}_c & _{}^{g}\textrm{t}_c \\ 0_{1 \times 3} & 1 \end{bmatrix} \begin{bmatrix} X_c\\ Y_c\\ Z_c\\ 1 \end{bmatrix} \]

This problem is also known as solving the \(\mathbf{A}\mathbf{X}=\mathbf{X}\mathbf{B}\) equation:

\[ \begin{align*} ^{b}{\textrm{T}_g}^{(1)} \hspace{0.2em} ^{g}\textrm{T}_c \hspace{0.2em} ^{c}{\textrm{T}_t}^{(1)} &= \hspace{0.1em} ^{b}{\textrm{T}_g}^{(2)} \hspace{0.2em} ^{g}\textrm{T}_c \hspace{0.2em} ^{c}{\textrm{T}_t}^{(2)} \\ (^{b}{\textrm{T}_g}^{(2)})^{-1} \hspace{0.2em} ^{b}{\textrm{T}_g}^{(1)} \hspace{0.2em} ^{g}\textrm{T}_c &= \hspace{0.1em} ^{g}\textrm{T}_c \hspace{0.2em} ^{c}{\textrm{T}_t}^{(2)} (^{c}{\textrm{T}_t}^{(1)})^{-1} \\ \textrm{A}_i \textrm{X} &= \textrm{X} \textrm{B}_i \\ \end{align*} \]

注意
Additional information can be found on this website .
A minimum of 2 motions with non parallel rotation axes are necessary to determine the hand-eye transformation. So at least 3 different poses are required, but it is strongly recommended to use many more poses.

calibrationMatrixValues()

void cv::calibrationMatrixValues ( InputArray cameraMatrix ,
Size imageSize ,
double apertureWidth ,
double apertureHeight ,
double & fovx ,
double & fovy ,
double & focalLength ,
Point2d & principalPoint ,
double & aspectRatio
)
Python:
fovx, fovy, focalLength, principalPoint, aspectRatio = cv.calibrationMatrixValues( cameraMatrix, imageSize, apertureWidth, apertureHeight )

#include < opencv2/calib3d.hpp >

Computes useful camera characteristics from the camera matrix.

Parameters
cameraMatrix Input camera matrix that can be estimated by calibrateCamera or stereoCalibrate .
imageSize Input image size in pixels.
apertureWidth Physical width in mm of the sensor.
apertureHeight Physical height in mm of the sensor.
fovx Output field of view in degrees along the horizontal sensor axis.
fovy Output field of view in degrees along the vertical sensor axis.
focalLength Focal length of the lens in mm.
principalPoint Principal point in mm.
aspectRatio \(f_y/f_x\)

The function computes various useful camera characteristics from the previously estimated camera matrix.

注意
Do keep in mind that the unity measure 'mm' stands for whatever unit of measure one chooses for the chessboard pitch (it can thus be any value).

checkChessboard()

bool cv::checkChessboard ( InputArray img ,
Size size
)
Python:
retval = cv.checkChessboard( img, size )

composeRT()

void cv::composeRT ( InputArray rvec1 ,
InputArray tvec1 ,
InputArray rvec2 ,
InputArray tvec2 ,
OutputArray rvec3 ,
OutputArray tvec3 ,
OutputArray dr3dr1 = noArray () ,
OutputArray dr3dt1 = noArray () ,
OutputArray dr3dr2 = noArray () ,
OutputArray dr3dt2 = noArray () ,
OutputArray dt3dr1 = noArray () ,
OutputArray dt3dt1 = noArray () ,
OutputArray dt3dr2 = noArray () ,
OutputArray dt3dt2 = noArray ()
)
Python:
rvec3, tvec3, dr3dr1, dr3dt1, dr3dr2, dr3dt2, dt3dr1, dt3dt1, dt3dr2, dt3dt2 = cv.composeRT( rvec1, tvec1, rvec2, tvec2[, rvec3[, tvec3[, dr3dr1[, dr3dt1[, dr3dr2[, dr3dt2[, dt3dr1[, dt3dt1[, dt3dr2[, dt3dt2]]]]]]]]]] )

#include < opencv2/calib3d.hpp >

Combines two rotation-and-shift transformations.

Parameters
rvec1 First rotation vector.
tvec1 First translation vector.
rvec2 Second rotation vector.
tvec2 Second translation vector.
rvec3 Output rotation vector of the superposition.
tvec3 Output translation vector of the superposition.
dr3dr1 Optional output derivative of rvec3 with regard to rvec1
dr3dt1 Optional output derivative of rvec3 with regard to tvec1
dr3dr2 Optional output derivative of rvec3 with regard to rvec2
dr3dt2 Optional output derivative of rvec3 with regard to tvec2
dt3dr1 Optional output derivative of tvec3 with regard to rvec1
dt3dt1 Optional output derivative of tvec3 with regard to tvec1
dt3dr2 Optional output derivative of tvec3 with regard to rvec2
dt3dt2 Optional output derivative of tvec3 with regard to tvec2

The functions compute:

\[\begin{array}{l} \texttt{rvec3} = \mathrm{rodrigues} ^{-1} \left ( \mathrm{rodrigues} ( \texttt{rvec2} ) \cdot \mathrm{rodrigues} ( \texttt{rvec1} ) \right ) \\ \texttt{tvec3} = \mathrm{rodrigues} ( \texttt{rvec2} ) \cdot \texttt{tvec1} + \texttt{tvec2} \end{array} ,\]

where \(\mathrm{rodrigues}\) denotes a rotation vector to a rotation matrix transformation, and \(\mathrm{rodrigues}^{-1}\) denotes the inverse transformation. See Rodrigues for details.

Also, the functions can compute the derivatives of the output vectors with regards to the input vectors (see matMulDeriv ). The functions are used inside 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.

computeCorrespondEpilines()

void cv::computeCorrespondEpilines ( InputArray points ,
int whichImage ,
InputArray F ,
OutputArray lines
)
Python:
lines = cv.computeCorrespondEpilines( points, whichImage, F[, lines] )

#include < opencv2/calib3d.hpp >

For points in an image of a stereo pair, computes the corresponding epilines in the other image.

Parameters
points Input points. \(N \times 1\) or \(1 \times N\) matrix of type CV_32FC2 or vector<Point2f> .
whichImage Index of the image (1 or 2) that contains the points .
F Fundamental matrix that can be estimated using findFundamentalMat or stereoRectify .
lines Output vector of the epipolar lines corresponding to the points in the other image. Each line \(ax + by + c=0\) is encoded by 3 numbers \((a, b, c)\) .

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 findFundamentalMat ), line \(l^{(2)}_i\) in the second image for the point \(p^{(1)}_i\) in the first image (when whichImage=1 ) is computed as:

\[l^{(2)}_i = F p^{(1)}_i\]

And vice versa, when whichImage=2, \(l^{(1)}_i\) is computed from \(p^{(2)}_i\) as:

\[l^{(1)}_i = F^T p^{(2)}_i\]

Line coefficients are defined up to a scale. They are normalized so that \(a_i^2+b_i^2=1\) .

convertPointsFromHomogeneous()

void cv::convertPointsFromHomogeneous ( InputArray src ,
OutputArray dst
)
Python:
dst = cv.convertPointsFromHomogeneous( src[, dst] )

#include < opencv2/calib3d.hpp >

Converts points from homogeneous to Euclidean space.

Parameters
src Input vector of N-dimensional points.
dst Output vector of N-1-dimensional points.

The function converts points homogeneous to Euclidean space using perspective projection. That is, each point (x1, x2, ... x(n-1), xn) is converted to (x1/xn, x2/xn, ..., x(n-1)/xn). When xn=0, the output point coordinates will be (0,0,0,...).

convertPointsHomogeneous()

void cv::convertPointsHomogeneous ( InputArray src ,
OutputArray dst
)

#include < opencv2/calib3d.hpp >

Converts points to/from homogeneous coordinates.

Parameters
src Input array or vector of 2D, 3D, or 4D points.
dst Output vector of 2D, 3D, or 4D points.

The function converts 2D or 3D points from/to homogeneous coordinates by calling either convertPointsToHomogeneous or convertPointsFromHomogeneous.

注意
The function is obsolete. Use one of the previous two functions instead.

convertPointsToHomogeneous()

void cv::convertPointsToHomogeneous ( InputArray src ,
OutputArray dst
)
Python:
dst = cv.convertPointsToHomogeneous( src[, dst] )

#include < opencv2/calib3d.hpp >

Converts points from Euclidean to homogeneous space.

Parameters
src Input vector of N-dimensional points.
dst Output vector of N+1-dimensional points.

The function converts points from Euclidean to homogeneous space by appending 1's to the tuple of point coordinates. That is, each point (x1, x2, ..., xn) is converted to (x1, x2, ..., xn, 1).

correctMatches()

void cv::correctMatches ( InputArray F ,
InputArray points1 ,
InputArray points2 ,
OutputArray newPoints1 ,
OutputArray newPoints2
)
Python:
newPoints1, newPoints2 = cv.correctMatches( F, points1, points2[, newPoints1[, newPoints2]] )

#include < opencv2/calib3d.hpp >

Refines coordinates of corresponding points.

Parameters
F 3x3 fundamental matrix.
points1 1xN array containing the first set of points.
points2 1xN array containing the second set of points.
newPoints1 The optimized points1.
newPoints2 The optimized points2.

The function implements the Optimal Triangulation Method (see Multiple View Geometry for details). For each given point correspondence points1[i] <-> points2[i], and a fundamental matrix F, it computes the corrected correspondences newPoints1[i] <-> newPoints2[i] that minimize the geometric error \(d(points1[i], newPoints1[i])^2 + d(points2[i],newPoints2[i])^2\) (where \(d(a,b)\) is the geometric distance between points \(a\) and \(b\) ) subject to the epipolar constraint \(newPoints2^T * F * newPoints1 = 0\) .

decomposeEssentialMat()

void cv::decomposeEssentialMat ( InputArray E ,
OutputArray R1 ,
OutputArray R2 ,
OutputArray t
)
Python:
R1, R2, t = cv.decomposeEssentialMat( E[, R1[, R2[, t]]] )

#include < opencv2/calib3d.hpp >

Decompose an essential matrix to possible rotations and translation.

Parameters
E The input essential matrix.
R1 One possible rotation matrix.
R2 Another possible rotation matrix.
t One possible translation.

This function decompose an essential matrix E using svd decomposition [93] . Generally 4 possible poses exists for a given E. They are \([R_1, t]\), \([R_1, -t]\), \([R_2, t]\), \([R_2, -t]\). By decomposing E, you can only get the direction of the translation, so the function returns unit t.

decomposeHomographyMat()

int cv::decomposeHomographyMat ( InputArray H ,
InputArray K ,
OutputArrayOfArrays rotations ,
OutputArrayOfArrays translations ,
OutputArrayOfArrays normals
)
Python:
retval, rotations, translations, normals = cv.decomposeHomographyMat( H, K[, rotations[, translations[, normals]]] )

#include < opencv2/calib3d.hpp >

Decompose a homography matrix to rotation(s), translation(s) and plane normal(s).

Parameters
H The input homography matrix between two images.
K The input intrinsic camera calibration matrix.
rotations Array of rotation matrices.
translations Array of translation matrices.
normals Array of plane normal matrices.

This function extracts relative camera motion between two views observing a planar object from the homography H induced by the plane. The intrinsic camera matrix K must also be provided. The function may return up to four mathematical solution sets. At least two of the solutions may further be invalidated if point correspondences are available by applying positive depth constraint (all points must be in front of the camera). The decomposition method is described in detail in [149] .

范例:
samples/cpp/tutorial_code/features2D/Homography/decompose_homography.cpp .

decomposeProjectionMatrix()

void cv::decomposeProjectionMatrix ( InputArray projMatrix ,
OutputArray cameraMatrix ,
OutputArray rotMatrix ,
OutputArray transVect ,
OutputArray rotMatrixX = noArray () ,
OutputArray rotMatrixY = noArray () ,
OutputArray rotMatrixZ = noArray () ,
OutputArray eulerAngles = noArray ()
)
Python:
cameraMatrix, rotMatrix, transVect, rotMatrixX, rotMatrixY, rotMatrixZ, eulerAngles = cv.decomposeProjectionMatrix( projMatrix[, cameraMatrix[, rotMatrix[, transVect[, rotMatrixX[, rotMatrixY[, rotMatrixZ[, eulerAngles]]]]]]] )

#include < opencv2/calib3d.hpp >

Decomposes a projection matrix into a rotation matrix and a camera matrix.

Parameters
projMatrix 3x4 input projection matrix P.
cameraMatrix Output 3x3 camera matrix K.
rotMatrix Output 3x3 external rotation matrix R.
transVect Output 4x1 translation vector T.
rotMatrixX Optional 3x3 rotation matrix around x-axis.
rotMatrixY Optional 3x3 rotation matrix around y-axis.
rotMatrixZ Optional 3x3 rotation matrix around z-axis.
eulerAngles Optional three-element vector containing three Euler angles of rotation in degrees.

The function computes a decomposition of a projection matrix into a calibration and a rotation matrix and the position of a camera.

It optionally returns three rotation matrices, one for each axis, and three Euler angles that could be used in OpenGL. Note, there is always more than one sequence of rotations about the three principal axes that results in the same orientation of an object, e.g. see [210] . Returned tree rotation matrices and corresponding three Euler angles are only one of the possible solutions.

The function is based on RQDecomp3x3 .

drawChessboardCorners()

void cv::drawChessboardCorners ( InputOutputArray image ,
Size patternSize ,
InputArray corners ,
bool patternWasFound
)
Python:
image = cv.drawChessboardCorners( image, patternSize, corners, patternWasFound )

#include < opencv2/calib3d.hpp >

Renders the detected chessboard corners.

Parameters
image Destination image. It must be an 8-bit color image.
patternSize Number of inner corners per a chessboard row and column (patternSize = cv::Size(points_per_row,points_per_column)).
corners Array of detected corners, the output of findChessboardCorners.
patternWasFound Parameter indicating whether the complete board was found or not. The return value of findChessboardCorners should 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.

范例:
samples/cpp/tutorial_code/features2D/Homography/pose_from_homography.cpp .

drawFrameAxes()

void cv::drawFrameAxes ( InputOutputArray image ,
InputArray cameraMatrix ,
InputArray distCoeffs ,
InputArray rvec ,
InputArray tvec ,
float length ,
int thickness = 3
)
Python:
image = cv.drawFrameAxes( image, cameraMatrix, distCoeffs, rvec, tvec, length[, thickness] )

#include < opencv2/calib3d.hpp >

Draw axes of the world/object coordinate system from pose estimation.

另请参阅
solvePnP
Parameters
image Input/output image. It must have 1 or 3 channels. The number of channels is not altered.
cameraMatrix Input 3x3 floating-point matrix of camera intrinsic parameters. \(A = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}\)
distCoeffs Input vector of distortion coefficients \((k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6 [, s_1, s_2, s_3, s_4[, \tau_x, \tau_y]]]])\) of 4, 5, 8, 12 or 14 elements. If the vector is empty, the zero distortion coefficients are assumed.
rvec Rotation vector (see Rodrigues ) that, together with tvec, brings points from the model coordinate system to the camera coordinate system.
tvec Translation vector.
length Length of the painted axes in the same unit than tvec (usually in meters).
thickness Line thickness of the painted axes.

This function draws the axes of the world/object coordinate system w.r.t. to the camera frame. OX is drawn in red, OY in green and OZ in blue.

范例:
samples/cpp/tutorial_code/features2D/Homography/homography_from_camera_displacement.cpp ,和 samples/cpp/tutorial_code/features2D/Homography/pose_from_homography.cpp .

estimateAffine2D()

cv::Mat cv::estimateAffine2D ( InputArray from ,
InputArray to ,
OutputArray inliers = noArray () ,
int method = RANSAC ,
double ransacReprojThreshold = 3 ,
size_t maxIters = 2000 ,
double confidence = 0.99 ,
size_t refineIters = 10
)
Python:
retval, inliers = cv.estimateAffine2D( from, to[, inliers[, method[, ransacReprojThreshold[, maxIters[, confidence[, refineIters]]]]]] )

#include < opencv2/calib3d.hpp >

Computes an optimal affine transformation between two 2D point sets.

It computes

\[ \begin{bmatrix} x\\ y\\ \end{bmatrix} = \begin{bmatrix} a_{11} & a_{12}\\ a_{21} & a_{22}\\ \end{bmatrix} \begin{bmatrix} X\\ Y\\ \end{bmatrix} + \begin{bmatrix} b_1\\ b_2\\ \end{bmatrix} \]

Parameters
from First input 2D point set containing \((X,Y)\).
to Second input 2D point set containing \((x,y)\).
inliers Output vector indicating which points are inliers (1-inlier, 0-outlier).
method Robust method used to compute transformation. The following methods are possible:
ransacReprojThreshold Maximum reprojection error in the RANSAC algorithm to consider a point as an inlier. Applies only to RANSAC.
maxIters The maximum number of robust method iterations.
confidence Confidence level, between 0 and 1, for the estimated transformation. Anything between 0.95 and 0.99 is usually good enough. Values too close to 1 can slow down the estimation significantly. Values lower than 0.8-0.9 can result in an incorrectly estimated transformation.
refineIters Maximum number of iterations of refining algorithm (Levenberg-Marquardt). Passing 0 will disable refining, so the output matrix will be output of robust method.
返回
Output 2D affine transformation matrix \(2 \times 3\) or empty matrix if transformation could not be estimated. The returned matrix has the following form:

\[ \begin{bmatrix} a_{11} & a_{12} & b_1\\ a_{21} & a_{22} & b_2\\ \end{bmatrix} \]

The function estimates an optimal 2D affine transformation between two 2D point sets using the selected robust algorithm.

The computed transformation is then refined further (using only inliers) with the Levenberg-Marquardt method to reduce the re-projection error even more.

注意
The RANSAC method can handle practically any ratio of outliers but needs a 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.
另请参阅
estimateAffinePartial2D , getAffineTransform

estimateAffine3D()

int cv::estimateAffine3D ( InputArray src ,
InputArray dst ,
OutputArray out ,
OutputArray inliers ,
double ransacThreshold = 3 ,
double confidence = 0.99
)
Python:
retval, out, inliers = cv.estimateAffine3D( src, dst[, out[, inliers[, ransacThreshold[, confidence]]]] )

#include < opencv2/calib3d.hpp >

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

It computes

\[ \begin{bmatrix} x\\ y\\ z\\ \end{bmatrix} = \begin{bmatrix} a_{11} & a_{12} & a_{13}\\ a_{21} & a_{22} & a_{23}\\ a_{31} & a_{32} & a_{33}\\ \end{bmatrix} \begin{bmatrix} X\\ Y\\ Z\\ \end{bmatrix} + \begin{bmatrix} b_1\\ b_2\\ b_3\\ \end{bmatrix} \]

Parameters
src First input 3D point set containing \((X,Y,Z)\).
dst Second input 3D point set containing \((x,y,z)\).
out Output 3D affine transformation matrix \(3 \times 4\) of the form

\[ \begin{bmatrix} a_{11} & a_{12} & a_{13} & b_1\\ a_{21} & a_{22} & a_{23} & b_2\\ a_{31} & a_{32} & a_{33} & b_3\\ \end{bmatrix} \]

inliers Output vector indicating which points are inliers (1-inlier, 0-outlier).
ransacThreshold Maximum reprojection error in the RANSAC algorithm to consider a point as an inlier.
confidence Confidence level, between 0 and 1, for the estimated transformation. Anything between 0.95 and 0.99 is usually good enough. Values too close to 1 can slow down the estimation significantly. Values lower than 0.8-0.9 can result in an incorrectly estimated transformation.

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

estimateAffinePartial2D()

cv::Mat cv::estimateAffinePartial2D ( InputArray from ,
InputArray to ,
OutputArray inliers = noArray () ,
int method = RANSAC ,
double ransacReprojThreshold = 3 ,
size_t maxIters = 2000 ,
double confidence = 0.99 ,
size_t refineIters = 10
)
Python:
retval, inliers = cv.estimateAffinePartial2D( from, to[, inliers[, method[, ransacReprojThreshold[, maxIters[, confidence[, refineIters]]]]]] )

#include < opencv2/calib3d.hpp >

Computes an optimal limited affine transformation with 4 degrees of freedom between two 2D point sets.

Parameters
from First input 2D point set.
to Second input 2D point set.
inliers Output vector indicating which points are inliers.
method Robust method used to compute transformation. The following methods are possible:
ransacReprojThreshold Maximum reprojection error in the RANSAC algorithm to consider a point as an inlier. Applies only to RANSAC.
maxIters The maximum number of robust method iterations.
confidence Confidence level, between 0 and 1, for the estimated transformation. Anything between 0.95 and 0.99 is usually good enough. Values too close to 1 can slow down the estimation significantly. Values lower than 0.8-0.9 can result in an incorrectly estimated transformation.
refineIters Maximum number of iterations of refining algorithm (Levenberg-Marquardt). Passing 0 will disable refining, so the output matrix will be output of robust method.
返回
Output 2D affine transformation (4 degrees of freedom) matrix \(2 \times 3\) or empty matrix if transformation could not be estimated.

The function estimates an optimal 2D affine transformation with 4 degrees of freedom limited to combinations of translation, rotation, and uniform scaling. Uses the selected algorithm for robust estimation.

The computed transformation is then refined further (using only inliers) with the Levenberg-Marquardt method to reduce the re-projection error even more.

Estimated transformation matrix is:

\[ \begin{bmatrix} \cos(\theta) \cdot s & -\sin(\theta) \cdot s & t_x \\ \sin(\theta) \cdot s & \cos(\theta) \cdot s & t_y \end{bmatrix} \]

Where \( \theta \) is the rotation angle, \( s \) the scaling factor and \( t_x, t_y \) are translations in \( x, y \) axes respectively.

注意
The RANSAC method can handle practically any ratio of outliers but need a 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.
另请参阅
estimateAffine2D , getAffineTransform

filterHomographyDecompByVisibleRefpoints()

void cv::filterHomographyDecompByVisibleRefpoints ( InputArrayOfArrays rotations ,
InputArrayOfArrays normals ,
InputArray beforePoints ,
InputArray afterPoints ,
OutputArray possibleSolutions ,
InputArray pointsMask = noArray ()
)
Python:
possibleSolutions = cv.filterHomographyDecompByVisibleRefpoints( rotations, normals, beforePoints, afterPoints[, possibleSolutions[, pointsMask]] )

#include < opencv2/calib3d.hpp >

Filters homography decompositions based on additional information.

Parameters
rotations Vector of rotation matrices.
normals Vector of plane normal matrices.
beforePoints Vector of (rectified) visible reference points before the homography is applied
afterPoints Vector of (rectified) visible reference points after the homography is applied
possibleSolutions Vector of int indices representing the viable solution set after filtering
pointsMask optional Mat/Vector of 8u type representing the mask for the inliers as given by the findHomography function

This function is intended to filter the output of the decomposeHomographyMat based on additional information as described in [149] . The summary of the method: the decomposeHomographyMat function returns 2 unique solutions and their "opposites" for a total of 4 solutions. If we have access to the sets of points visible in the camera frame before and after the homography transformation is applied, we can determine which are the true potential solutions and which are the opposites by verifying which homographies are consistent with all visible reference points being in front of the camera. The inputs are left unchanged; the filtered solution set is returned as indices into the existing one.

filterSpeckles()

void cv::filterSpeckles ( InputOutputArray img ,
double newVal ,
int maxSpeckleSize ,
double maxDiff ,
InputOutputArray buf = noArray ()
)
Python:
img, buf = cv.filterSpeckles( img, newVal, maxSpeckleSize, maxDiff[, buf] )

#include < opencv2/calib3d.hpp >

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

Parameters
img The input 16-bit signed disparity image
newVal The disparity value used to paint-off the speckles
maxSpeckleSize The maximum speckle size to consider it a speckle. Larger blobs are not affected by the algorithm
maxDiff Maximum difference between neighbor disparity pixels to put them into the same blob. Note that since StereoBM , StereoSGBM and may be other algorithms return a fixed-point disparity map, where disparity values are multiplied by 16, this scale factor should be taken into account when specifying this parameter value.
buf The optional temporary buffer to avoid memory allocation within the function.

find4QuadCornerSubpix()

bool cv::find4QuadCornerSubpix ( InputArray img ,
InputOutputArray corners ,
Size region_size
)
Python:
retval, corners = cv.find4QuadCornerSubpix( img, corners, region_size )

#include < opencv2/calib3d.hpp >

finds subpixel-accurate positions of the chessboard corners

findChessboardCorners()

bool cv::findChessboardCorners ( InputArray image ,
Size patternSize ,
OutputArray corners ,
int flags = CALIB_CB_ADAPTIVE_THRESH + CALIB_CB_NORMALIZE_IMAGE
)
Python:
retval, corners = cv.findChessboardCorners( image, patternSize[, corners[, flags]] )

#include < opencv2/calib3d.hpp >

Finds the positions of internal corners of the chessboard.

Parameters
image Source chessboard view. It must be an 8-bit grayscale or color image.
patternSize Number of inner corners per a chessboard row and column ( patternSize = cv::Size(points_per_row,points_per_colum) = cv::Size(columns,rows) ).
corners Output array of detected corners.
flags Various operation flags that can be zero or a combination of the following values:
  • 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).
  • CALIB_CB_NORMALIZE_IMAGE Normalize the image gamma with equalizeHist before applying fixed or adaptive thresholding.
  • CALIB_CB_FILTER_QUADS Use additional criteria (like contour area, perimeter, square-like shape) to filter out false quads 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 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 are found and they are 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 detected coordinates are approximate, and to determine their positions more accurately, the function calls cornerSubPix. You also may use the function cornerSubPix with different parameters if returned coordinates are not accurate enough.

Sample usage of detecting and drawing chessboard corners: :

Size patternsize(8,6); //interior number of corners
Mat gray = ....; //source image
vector<Point2f> corners; //this will be filled by the detected corners
//CALIB_CB_FAST_CHECK saves a lot of time on images
//that do not contain any chessboard corners
bool patternfound = findChessboardCorners (gray, patternsize, corners,
if (patternfound)
cornerSubPix (gray, corners, Size (11, 11), Size (-1, -1),
TermCriteria(CV_TERMCRIT_EPS + CV_TERMCRIT_ITER, 30, 0.1));
drawChessboardCorners (img, patternsize, Mat(corners), patternfound);
注意
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.
范例:
samples/cpp/tutorial_code/features2D/Homography/decompose_homography.cpp , samples/cpp/tutorial_code/features2D/Homography/homography_from_camera_displacement.cpp ,和 samples/cpp/tutorial_code/features2D/Homography/pose_from_homography.cpp .

findChessboardCornersSB()

bool cv::findChessboardCornersSB ( InputArray image ,
Size patternSize ,
OutputArray corners ,
int flags = 0
)
Python:
retval, corners = cv.findChessboardCornersSB( image, patternSize[, corners[, flags]] )

#include < opencv2/calib3d.hpp >

Finds the positions of internal corners of the chessboard using a sector based approach.

Parameters
image Source chessboard view. It must be an 8-bit grayscale or color image.
patternSize Number of inner corners per a chessboard row and column ( patternSize = cv::Size(points_per_row,points_per_colum) = cv::Size(columns,rows) ).
corners Output array of detected corners.
flags Various operation flags that can be zero or a combination of the following values:
  • CALIB_CB_NORMALIZE_IMAGE Normalize the image gamma with equalizeHist before detection.
  • CALIB_CB_EXHAUSTIVE Run an exhaustive search to improve detection rate.
  • CALIB_CB_ACCURACY Up sample input image to improve sub-pixel accuracy due to aliasing effects. This should be used if an accurate camera calibration is required.

The function is analog to findchessboardCorners but uses a localized radon transformation approximated by box filters being more robust to all sort of noise, faster on larger images and is able to directly return the sub-pixel position of the internal chessboard corners. The Method is based on the paper [54] "Accurate Detection and Localization of Checkerboard Corners for Calibration" demonstrating that the returned sub-pixel positions are more accurate than the one returned by cornerSubPix allowing a precise camera calibration for demanding applications.

注意
The function requires a white boarder with roughly the same width as one of the checkerboard fields around the whole board to improve the detection in various environments. In addition, because of the localized radon transformation it is beneficial to use round corners for the field corners which are located on the outside of the board. The following figure illustrates a sample checkerboard optimized for the detection. However, any other checkerboard can be used as well.
checkerboard_radon.png
Checkerboard

findCirclesGrid() [1/2]

bool cv::findCirclesGrid ( InputArray image ,
Size patternSize ,
OutputArray centers ,
int flags ,
const Ptr < FeatureDetector > & blobDetector ,
const CirclesGridFinderParameters & parameters
)
Python:
retval, centers = cv.findCirclesGrid( image, patternSize, flags, blobDetector, parameters[, centers] )
retval, centers = cv.findCirclesGrid( image, patternSize[, centers[, flags[, blobDetector]]] )

#include < opencv2/calib3d.hpp >

Finds centers in the grid of circles.

Parameters
image grid view of input circles; it must be an 8-bit grayscale or color image.
patternSize number of circles per row and column ( patternSize = Size(points_per_row, points_per_colum) ).
centers output array of detected centers.
flags various operation flags that can be one of the following values:
  • CALIB_CB_SYMMETRIC_GRID uses symmetric pattern of circles.
  • CALIB_CB_ASYMMETRIC_GRID uses asymmetric pattern of circles.
  • CALIB_CB_CLUSTERING uses a special algorithm for grid detection. It is more robust to perspective distortions but much more sensitive to background clutter.
blobDetector feature detector that finds blobs like dark circles on light background.
parameters struct for finding circles in a grid pattern.

The function attempts to determine whether the input image contains a grid of circles. If it is, the function locates centers of the circles. The function returns a non-zero value if all of the centers 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.

Sample usage of detecting and drawing the centers of circles: :

Size patternsize(7,7); //number of centers
Mat gray = ....; //source image
vector<Point2f> centers; //this will be filled by the detected centers
bool patternfound = findCirclesGrid (gray, patternsize, centers);
drawChessboardCorners (img, patternsize, Mat(centers), patternfound);
注意
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.

findCirclesGrid() [2/2]

bool cv::findCirclesGrid ( InputArray image ,
Size patternSize ,
OutputArray centers ,
int flags = CALIB_CB_SYMMETRIC_GRID ,
const Ptr < FeatureDetector > & blobDetector = SimpleBlobDetector::create ()
)
Python:
retval, centers = cv.findCirclesGrid( image, patternSize, flags, blobDetector, parameters[, centers] )
retval, centers = cv.findCirclesGrid( image, patternSize[, centers[, flags[, blobDetector]]] )

#include < opencv2/calib3d.hpp >

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

findEssentialMat() [1/2]

Mat cv::findEssentialMat ( InputArray points1 ,
InputArray points2 ,
InputArray cameraMatrix ,
int method = RANSAC ,
double prob = 0.999 ,
double threshold = 1.0 ,
OutputArray mask = noArray ()
)
Python:
retval, mask = cv.findEssentialMat( points1, points2, cameraMatrix[, method[, prob[, threshold[, mask]]]] )
retval, mask = cv.findEssentialMat( points1, points2[, focal[, pp[, method[, prob[, threshold[, mask]]]]]] )

#include < opencv2/calib3d.hpp >

Calculates an essential matrix from the corresponding points in two images.

Parameters
points1 Array of N (N >= 5) 2D points from the first image. The point coordinates should be floating-point (single or double precision).
points2 Array of the second image points of the same size and format as points1 .
cameraMatrix Camera matrix \(K = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}\) . Note that this function assumes that points1 and points2 are feature points from cameras with the same camera matrix.
method Method for computing an essential matrix.
  • RANSAC for the RANSAC algorithm.
  • LMEDS for the LMedS algorithm.
prob Parameter used for the RANSAC or LMedS methods only. It specifies a desirable level of confidence (probability) that the estimated matrix is correct.
threshold 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.
mask 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.

This function estimates essential matrix based on the five-point algorithm solver in [174] . [212] is also a related. The epipolar geometry is described by the following equation:

\[[p_2; 1]^T K^{-T} E K^{-1} [p_1; 1] = 0\]

where \(E\) is an essential matrix, \(p_1\) and \(p_2\) are corresponding points in the first and the second images, respectively. The result of this function may be passed further to decomposeEssentialMat or recoverPose to recover the relative pose between cameras.

findEssentialMat() [2/2]

Mat cv::findEssentialMat ( InputArray points1 ,
InputArray points2 ,
double focal = 1.0 ,
Point2d pp = Point2d (0, 0) ,
int method = RANSAC ,
double prob = 0.999 ,
double threshold = 1.0 ,
OutputArray mask = noArray ()
)
Python:
retval, mask = cv.findEssentialMat( points1, points2, cameraMatrix[, method[, prob[, threshold[, mask]]]] )
retval, mask = cv.findEssentialMat( points1, points2[, focal[, pp[, method[, prob[, threshold[, mask]]]]]] )

#include < opencv2/calib3d.hpp >

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Parameters
points1 Array of N (N >= 5) 2D points from the first image. The point coordinates should be floating-point (single or double precision).
points2 Array of the second image points of the same size and format as points1 .
focal focal length of the camera. Note that this function assumes that points1 and points2 are feature points from cameras with same focal length and principal point.
pp principal point of the camera.
method Method for computing a fundamental matrix.
  • RANSAC for the RANSAC algorithm.
  • LMEDS for the LMedS algorithm.
threshold 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.
prob Parameter used for the RANSAC or LMedS methods only. It specifies a desirable level of confidence (probability) that the estimated matrix is correct.
mask 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.

This function differs from the one above that it computes camera matrix from focal length and principal point:

\[K = \begin{bmatrix} f & 0 & x_{pp} \\ 0 & f & y_{pp} \\ 0 & 0 & 1 \end{bmatrix}\]

findFundamentalMat() [1/2]

Mat cv::findFundamentalMat ( InputArray points1 ,
InputArray points2 ,
int method = FM_RANSAC ,
double ransacReprojThreshold = 3. ,
double confidence = 0.99 ,
OutputArray mask = noArray ()
)
Python:
retval, mask = cv.findFundamentalMat( points1, points2[, method[, ransacReprojThreshold[, confidence[, mask]]]] )

#include < opencv2/calib3d.hpp >

Calculates a fundamental matrix from the corresponding points in two images.

Parameters
points1 Array of N points from the first image. The point coordinates should be floating-point (single or double precision).
points2 Array of the second image points of the same size and format as points1 .
method Method for computing a fundamental matrix.
  • CV_FM_7POINT for a 7-point algorithm. \(N = 7\)
  • CV_FM_8POINT for an 8-point algorithm. \(N \ge 8\)
  • CV_FM_RANSAC for the RANSAC algorithm. \(N \ge 8\)
  • CV_FM_LMEDS for the LMedS algorithm. \(N \ge 8\)
ransacReprojThreshold Parameter used only 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.
confidence Parameter used for the RANSAC and LMedS methods only. It specifies a desirable level of confidence (probability) that the estimated matrix is correct.
mask The epipolar geometry is described by the following equation:

\[[p_2; 1]^T F [p_1; 1] = 0\]

where \(F\) is a fundamental matrix, \(p_1\) and \(p_2\) 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 found fundamental matrix. Normally just one matrix is found. But in case of the 7-point algorithm, the function may return up to 3 solutions ( \(9 \times 3\) matrix that stores all 3 matrices sequentially).

The calculated fundamental matrix may be passed further to computeCorrespondEpilines that finds the epipolar lines corresponding to the specified points. It can also be passed to stereoRectifyUncalibrated to compute the rectification transformation. :

// Example. Estimation of fundamental matrix using the RANSAC algorithm
int point_count = 100;
vector<Point2f> points1(point_count);
vector<Point2f> points2(point_count);
// initialize the points here ...
for ( int i = 0; i < point_count; i++ )
{
points1[i] = ...;
points2[i] = ...;
}
Mat fundamental_matrix =
findFundamentalMat (points1, points2, FM_RANSAC , 3, 0.99);

findFundamentalMat() [2/2]

Mat cv::findFundamentalMat ( InputArray points1 ,
InputArray points2 ,
OutputArray mask ,
int method = FM_RANSAC ,
double ransacReprojThreshold = 3. ,
double confidence = 0.99
)
Python:
retval, mask = cv.findFundamentalMat( points1, points2[, method[, ransacReprojThreshold[, confidence[, mask]]]] )

#include < opencv2/calib3d.hpp >

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

findHomography() [1/2]

Mat cv::findHomography ( InputArray srcPoints ,
InputArray dstPoints ,
int method = 0 ,
double ransacReprojThreshold = 3 ,
OutputArray mask = noArray () ,
const int maxIters = 2000 ,
const double confidence = 0.995
)
Python:
retval, mask = cv.findHomography( srcPoints, dstPoints[, method[, ransacReprojThreshold[, mask[, maxIters[, confidence]]]]] )

#include < opencv2/calib3d.hpp >

Finds a perspective transformation between two planes.

Parameters
srcPoints Coordinates of the points in the original plane, a matrix of the type CV_32FC2 or vector<Point2f> .
dstPoints Coordinates of the points in the target plane, a matrix of the type CV_32FC2 or a vector<Point2f> .
method Method used to compute a homography matrix. The following methods are possible:
  • 0 - a regular method using all the points, i.e., the least squares method
  • RANSAC - RANSAC-based robust method
  • LMEDS - Least-Median robust method
  • RHO - PROSAC-based robust method
ransacReprojThreshold Maximum allowed reprojection error to treat a point pair as an inlier (used in the RANSAC and RHO methods only). That is, if

\[\| \texttt{dstPoints} _i - \texttt{convertPointsHomogeneous} ( \texttt{H} * \texttt{srcPoints} _i) \|_2 > \texttt{ransacReprojThreshold}\]

then the point \(i\) is considered as 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.
mask Optional output mask set by a robust method ( RANSAC or LMEDS ). Note that the input mask values are ignored.
maxIters The maximum number of RANSAC iterations.
confidence Confidence level, between 0 and 1.

The function finds and returns the perspective transformation \(H\) between the source and the destination planes:

\[s_i \vecthree{x'_i}{y'_i}{1} \sim H \vecthree{x_i}{y_i}{1}\]

so that the back-projection error

\[\sum _i \left ( x'_i- \frac{h_{11} x_i + h_{12} y_i + h_{13}}{h_{31} x_i + h_{32} y_i + h_{33}} \right )^2+ \left ( y'_i- \frac{h_{21} x_i + h_{22} y_i + h_{23}}{h_{31} x_i + h_{32} y_i + h_{33}} \right )^2\]

is minimized. If the parameter method is set to the default value 0, the function uses all the point pairs to compute an initial homography estimate with a simple least-squares scheme.

However, if not all of the point pairs ( \(srcPoints_i\), \(dstPoints_i\) ) fit the rigid perspective transformation (that is, there are some outliers), this initial estimate will be poor. In this case, you can use one of the three robust methods. The methods RANSAC, LMeDS and RHO try many different random subsets of the corresponding point pairs (of four pairs each, collinear pairs are discarded), estimate the homography matrix using this subset and a simple least-squares algorithm, and then compute the quality/goodness of the computed homography (which is the number of inliers for RANSAC or the least 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 case of a robust method) with the Levenberg-Marquardt method to reduce the re-projection error even more.

The methods RANSAC and RHO can handle practically any ratio of outliers but need a 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 there are no outliers and the noise is rather small, use the default method (method=0).

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 \(h_{33}=1\). Note that whenever an \(H\) matrix cannot be estimated, an empty one will be returned.

另请参阅
getAffineTransform , estimateAffine2D , estimateAffinePartial2D , getPerspectiveTransform , warpPerspective , perspectiveTransform
范例:
samples/cpp/tutorial_code/features2D/Homography/decompose_homography.cpp , samples/cpp/tutorial_code/features2D/Homography/homography_from_camera_displacement.cpp , samples/cpp/tutorial_code/features2D/Homography/pose_from_homography.cpp ,和 samples/cpp/warpPerspective_demo.cpp .

findHomography() [2/2]

Mat cv::findHomography ( InputArray srcPoints ,
InputArray dstPoints ,
OutputArray mask ,
int method = 0 ,
double ransacReprojThreshold = 3
)
Python:
retval, mask = cv.findHomography( srcPoints, dstPoints[, method[, ransacReprojThreshold[, mask[, maxIters[, confidence]]]]] )

#include < opencv2/calib3d.hpp >

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

getDefaultNewCameraMatrix()

Mat cv::getDefaultNewCameraMatrix ( InputArray cameraMatrix ,
Size imgsize = Size () ,
bool centerPrincipalPoint = false
)
Python:
retval = cv.getDefaultNewCameraMatrix( cameraMatrix[, imgsize[, centerPrincipalPoint]] )

#include < opencv2/calib3d.hpp >

Returns the default new camera matrix.

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).

In the latter case, the new camera matrix will be:

\[\begin{bmatrix} f_x && 0 && ( \texttt{imgSize.width} -1)*0.5 \\ 0 && f_y && ( \texttt{imgSize.height} -1)*0.5 \\ 0 && 0 && 1 \end{bmatrix} ,\]

where \(f_x\) and \(f_y\) are \((0,0)\) and \((1,1)\) elements of cameraMatrix, respectively.

By default, the undistortion functions in OpenCV (see initUndistortRectifyMap , 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.

Parameters
cameraMatrix Input camera matrix.
imgsize Camera view image size in pixels.
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.

getOptimalNewCameraMatrix()

Mat cv::getOptimalNewCameraMatrix ( InputArray cameraMatrix ,
InputArray distCoeffs ,
Size imageSize ,
double alpha ,
Size newImgSize = Size () ,
Rect * validPixROI = 0 ,
bool centerPrincipalPoint = false
)
Python:
retval, validPixROI = cv.getOptimalNewCameraMatrix( cameraMatrix, distCoeffs, imageSize, alpha[, newImgSize[, centerPrincipalPoint]] )

#include < opencv2/calib3d.hpp >

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

Parameters
cameraMatrix Input camera matrix.
distCoeffs Input vector of distortion coefficients \((k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6 [, s_1, s_2, s_3, s_4[, \tau_x, \tau_y]]]])\) of 4, 5, 8, 12 or 14 elements. If the vector is NULL/empty, the zero distortion coefficients are assumed.
imageSize Original image size.
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 stereoRectify for details.
newImgSize Image size after rectification. By default, it is set to imageSize .
validPixROI Optional output rectangle that outlines all-good-pixels region in the undistorted image. See roi1, roi2 description in stereoRectify .
centerPrincipalPoint Optional flag that indicates whether in the new camera matrix the principal point should be at the image center or not. By default, the principal point is chosen to best fit a subset of the source image (determined by alpha) to the corrected image.
返回
new_camera_matrix Output new camera matrix.

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

getValidDisparityROI()

Rect cv::getValidDisparityROI ( Rect roi1 ,
Rect roi2 ,
int minDisparity ,
int numberOfDisparities ,
int SADWindowSize
)
Python:
retval = cv.getValidDisparityROI( roi1, roi2, minDisparity, numberOfDisparities, SADWindowSize )

#include < opencv2/calib3d.hpp >

computes valid disparity ROI from the valid ROIs of the rectified images (that are returned by cv::stereoRectify() )

initCameraMatrix2D()

Mat cv::initCameraMatrix2D ( InputArrayOfArrays objectPoints ,
InputArrayOfArrays imagePoints ,
Size imageSize ,
double aspectRatio = 1.0
)
Python:
retval = cv.initCameraMatrix2D( objectPoints, imagePoints, imageSize[, aspectRatio] )

#include < opencv2/calib3d.hpp >

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

Parameters
objectPoints Vector of vectors of the calibration pattern points in the calibration pattern coordinate space. In the old interface all the per-view vectors are concatenated. See calibrateCamera for details.
imagePoints Vector of vectors of the projections of the calibration pattern points. In the old interface all the per-view vectors are concatenated.
imageSize Image size in pixels used to initialize the principal point.
aspectRatio If it is zero or negative, both \(f_x\) and \(f_y\) are estimated independently. Otherwise, \(f_x = f_y * \texttt{aspectRatio}\) .

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

initUndistortRectifyMap()

void cv::initUndistortRectifyMap ( InputArray cameraMatrix ,
InputArray distCoeffs ,
InputArray R ,
InputArray newCameraMatrix ,
Size size ,
int m1type ,
OutputArray map1 ,
OutputArray map2
)
Python:
map1, map2 = cv.initUndistortRectifyMap( cameraMatrix, distCoeffs, R, newCameraMatrix, size, m1type[, map1[, map2]] )

#include < opencv2/calib3d.hpp >

Computes the undistortion and rectification transformation map.

The function computes the joint undistortion and rectification transformation and represents the result in the form of maps for 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 getOptimalNewCameraMatrix for a better control over scaling. In case of a stereo camera, newCameraMatrix is normally set to P1 or P2 computed by stereoRectify .

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).

The function actually builds the maps for the inverse mapping algorithm that is used by remap. That is, for each pixel \((u, v)\) in the destination (corrected and rectified) image, the function computes the corresponding coordinates in the source image (that is, in the original image from camera). The following process is applied:

\[ \begin{array}{l} x \leftarrow (u - {c'}_x)/{f'}_x \\ y \leftarrow (v - {c'}_y)/{f'}_y \\ {[X\,Y\,W]} ^T \leftarrow R^{-1}*[x \, y \, 1]^T \\ x' \leftarrow X/W \\ y' \leftarrow Y/W \\ r^2 \leftarrow x'^2 + y'^2 \\ x'' \leftarrow x' \frac{1 + k_1 r^2 + k_2 r^4 + k_3 r^6}{1 + k_4 r^2 + k_5 r^4 + k_6 r^6} + 2p_1 x' y' + p_2(r^2 + 2 x'^2) + s_1 r^2 + s_2 r^4\\ y'' \leftarrow y' \frac{1 + k_1 r^2 + k_2 r^4 + k_3 r^6}{1 + k_4 r^2 + k_5 r^4 + k_6 r^6} + p_1 (r^2 + 2 y'^2) + 2 p_2 x' y' + s_3 r^2 + s_4 r^4 \\ s\vecthree{x'''}{y'''}{1} = \vecthreethree{R_{33}(\tau_x, \tau_y)}{0}{-R_{13}((\tau_x, \tau_y)} {0}{R_{33}(\tau_x, \tau_y)}{-R_{23}(\tau_x, \tau_y)} {0}{0}{1} R(\tau_x, \tau_y) \vecthree{x''}{y''}{1}\\ map_x(u,v) \leftarrow x''' f_x + c_x \\ map_y(u,v) \leftarrow y''' f_y + c_y \end{array} \]

where \((k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6[, s_1, s_2, s_3, s_4[, \tau_x, \tau_y]]]])\) are the distortion coefficients.

In case of a stereo camera, this function is called twice: once for each camera head, after stereoRectify, which in its turn is called after stereoCalibrate . But if the stereo camera was not calibrated, it is still possible to compute the rectification transformations directly from the fundamental matrix using 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

\[\texttt{R} = \texttt{cameraMatrix} ^{-1} \cdot \texttt{H} \cdot \texttt{cameraMatrix}\]

where cameraMatrix can be chosen arbitrarily.

Parameters
cameraMatrix Input camera matrix \(A=\vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}\) .
distCoeffs Input vector of distortion coefficients \((k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6[, s_1, s_2, s_3, s_4[, \tau_x, \tau_y]]]])\) of 4, 5, 8, 12 or 14 elements. If the vector is NULL/empty, the zero distortion coefficients are assumed.
R Optional rectification transformation in the object space (3x3 matrix). R1 or R2 , computed by stereoRectify can be passed here. If the matrix is empty, the identity transformation is assumed. In cvInitUndistortMap R assumed to be an identity matrix.
newCameraMatrix New camera matrix \(A'=\vecthreethree{f_x'}{0}{c_x'}{0}{f_y'}{c_y'}{0}{0}{1}\).
size Undistorted image size.
m1type Type of the first output map that can be CV_32FC1, CV_32FC2 or CV_16SC2, see convertMaps
map1 The first output map.
map2 The second output map.

initWideAngleProjMap() [1/2]

float cv::initWideAngleProjMap ( InputArray cameraMatrix ,
InputArray distCoeffs ,
Size imageSize ,
int destImageWidth ,
int m1type ,
OutputArray map1 ,
OutputArray map2 ,
enum UndistortTypes projType = PROJ_SPHERICAL_EQRECT ,
double alpha = 0
)

#include < opencv2/calib3d.hpp >

initializes maps for remap for wide-angle

initWideAngleProjMap() [2/2]

static float cv::initWideAngleProjMap ( InputArray cameraMatrix ,
InputArray distCoeffs ,
Size imageSize ,
int destImageWidth ,
int m1type ,
OutputArray map1 ,
OutputArray map2 ,
int projType ,
double alpha = 0
)
inline static

matMulDeriv()

void cv::matMulDeriv ( InputArray A ,
InputArray B ,
OutputArray dABdA ,
OutputArray dABdB
)
Python:
dABdA, dABdB = cv.matMulDeriv( A, B[, dABdA[, dABdB]] )

#include < opencv2/calib3d.hpp >

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

Parameters
A First multiplied matrix.
B Second multiplied matrix.
dABdA First output derivative matrix d(A*B)/dA of size \(\texttt{A.rows*B.cols} \times {A.rows*A.cols}\) .
dABdB Second output derivative matrix d(A*B)/dB of size \(\texttt{A.rows*B.cols} \times {B.rows*B.cols}\) .

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

projectPoints()

void cv::projectPoints ( InputArray objectPoints ,
InputArray rvec ,
InputArray tvec ,
InputArray cameraMatrix ,
InputArray distCoeffs ,
OutputArray imagePoints ,
OutputArray jacobian = noArray () ,
double aspectRatio = 0
)
Python:
imagePoints, jacobian = cv.projectPoints( objectPoints, rvec, tvec, cameraMatrix, distCoeffs[, imagePoints[, jacobian[, aspectRatio]]] )

#include < opencv2/calib3d.hpp >

Projects 3D points to an image plane.

Parameters
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.
rvec Rotation vector. See Rodrigues for details.
tvec Translation vector.
cameraMatrix Camera matrix \(A = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{_1}\) .
distCoeffs Input vector of distortion coefficients \((k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6 [, s_1, s_2, s_3, s_4[, \tau_x, \tau_y]]]])\) of 4, 5, 8, 12 or 14 elements. If the vector is empty, the zero distortion coefficients are assumed.
imagePoints Output array of image points, 1xN/Nx1 2-channel, or vector<Point2f> .
jacobian Optional output 2Nx(10+<numDistCoeffs>) jacobian matrix of derivatives of image points with respect to components of the rotation vector, translation vector, focal lengths, coordinates of the principal point and the distortion coefficients. In the old interface different components of the jacobian are returned via different output parameters.
aspectRatio Optional "fixed aspect ratio" parameter. If the parameter is not 0, the function assumes that the aspect ratio ( fx/fy ) is fixed and correspondingly adjusts the jacobian matrix.

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

注意
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.

recoverPose() [1/3]

int cv::recoverPose ( InputArray E ,
InputArray points1 ,
InputArray points2 ,
InputArray cameraMatrix ,
OutputArray R ,
OutputArray t ,
InputOutputArray mask = noArray ()
)
Python:
retval, R, t, mask = cv.recoverPose( E, points1, points2, cameraMatrix[, R[, t[, mask]]] )
retval, R, t, mask = cv.recoverPose( E, points1, points2[, R[, t[, focal[, pp[, mask]]]]] )
retval, R, t, mask, triangulatedPoints = cv.recoverPose( E, points1, points2, cameraMatrix, distanceThresh[, R[, t[, mask[, triangulatedPoints]]]] )

#include < opencv2/calib3d.hpp >

Recover relative camera rotation and translation from an estimated essential matrix and the corresponding points in two images, using cheirality check. Returns the number of inliers which pass the check.

Parameters
E The input essential matrix.
points1 Array of N 2D points from the first image. The point coordinates should be floating-point (single or double precision).
points2 Array of the second image points of the same size and format as points1 .
cameraMatrix Camera matrix \(K = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}\) . Note that this function assumes that points1 and points2 are feature points from cameras with the same camera matrix.
R Recovered relative rotation.
t Recovered relative translation.
mask Input/output mask for inliers in points1 and points2. : If it is not empty, then it marks inliers in points1 and points2 for then given essential matrix E. Only these inliers will be used to recover pose. In the output mask only inliers which pass the cheirality check. This function decomposes an essential matrix using decomposeEssentialMat and then verifies possible pose hypotheses by doing cheirality check. The cheirality check basically means that the triangulated 3D points should have positive depth. Some details can be found in [174] .

This function can be used to process output E and mask from findEssentialMat. In this scenario, points1 and points2 are the same input for findEssentialMat. :

// Example. Estimation of fundamental matrix using the RANSAC algorithm
int point_count = 100;
vector<Point2f> points1(point_count);
vector<Point2f> points2(point_count);
// initialize the points here ...
for ( int i = 0; i < point_count; i++ )
{
points1[i] = ...;
points2[i] = ...;
}
// cametra matrix with both focal lengths = 1, and principal point = (0, 0)
Mat cameraMatrix = Mat::eye (3, 3, CV_64F );
Mat E, R, t, mask ;
E = findEssentialMat (points1, points2, cameraMatrix, RANSAC , 0.999, 1.0, mask);
recoverPose (E, points1, points2, cameraMatrix, R, t, mask);

recoverPose() [2/3]

int cv::recoverPose ( InputArray E ,
InputArray points1 ,
InputArray points2 ,
OutputArray R ,
OutputArray t ,
double focal = 1.0 ,
Point2d pp = Point2d (0, 0) ,
InputOutputArray mask = noArray ()
)
Python:
retval, R, t, mask = cv.recoverPose( E, points1, points2, cameraMatrix[, R[, t[, mask]]] )
retval, R, t, mask = cv.recoverPose( E, points1, points2[, R[, t[, focal[, pp[, mask]]]]] )
retval, R, t, mask, triangulatedPoints = cv.recoverPose( E, points1, points2, cameraMatrix, distanceThresh[, R[, t[, mask[, triangulatedPoints]]]] )

#include < opencv2/calib3d.hpp >

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Parameters
E The input essential matrix.
points1 Array of N 2D points from the first image. The point coordinates should be floating-point (single or double precision).
points2 Array of the second image points of the same size and format as points1 .
R Recovered relative rotation.
t Recovered relative translation.
focal Focal length of the camera. Note that this function assumes that points1 and points2 are feature points from cameras with same focal length and principal point.
pp principal point of the camera.
mask Input/output mask for inliers in points1 and points2. : If it is not empty, then it marks inliers in points1 and points2 for then given essential matrix E. Only these inliers will be used to recover pose. In the output mask only inliers which pass the cheirality check.

This function differs from the one above that it computes camera matrix from focal length and principal point:

\[K = \begin{bmatrix} f & 0 & x_{pp} \\ 0 & f & y_{pp} \\ 0 & 0 & 1 \end{bmatrix}\]

recoverPose() [3/3]

int cv::recoverPose ( InputArray E ,
InputArray points1 ,
InputArray points2 ,
InputArray cameraMatrix ,
OutputArray R ,
OutputArray t ,
double distanceThresh ,
InputOutputArray mask = noArray () ,
OutputArray triangulatedPoints = noArray ()
)
Python:
retval, R, t, mask = cv.recoverPose( E, points1, points2, cameraMatrix[, R[, t[, mask]]] )
retval, R, t, mask = cv.recoverPose( E, points1, points2[, R[, t[, focal[, pp[, mask]]]]] )
retval, R, t, mask, triangulatedPoints = cv.recoverPose( E, points1, points2, cameraMatrix, distanceThresh[, R[, t[, mask[, triangulatedPoints]]]] )

#include < opencv2/calib3d.hpp >

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Parameters
E The input essential matrix.
points1 Array of N 2D points from the first image. The point coordinates should be floating-point (single or double precision).
points2 Array of the second image points of the same size and format as points1.
cameraMatrix Camera matrix \(K = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}\) . Note that this function assumes that points1 and points2 are feature points from cameras with the same camera matrix.
R Recovered relative rotation.
t Recovered relative translation.
distanceThresh threshold distance which is used to filter out far away points (i.e. infinite points).
mask Input/output mask for inliers in points1 and points2. : If it is not empty, then it marks inliers in points1 and points2 for then given essential matrix E. Only these inliers will be used to recover pose. In the output mask only inliers which pass the cheirality check.
triangulatedPoints 3d points which were reconstructed by triangulation.

rectify3Collinear()

float cv::rectify3Collinear ( InputArray cameraMatrix1 ,
InputArray distCoeffs1 ,
InputArray cameraMatrix2 ,
InputArray distCoeffs2 ,
InputArray cameraMatrix3 ,
InputArray distCoeffs3 ,
InputArrayOfArrays imgpt1 ,
InputArrayOfArrays imgpt3 ,
Size imageSize ,
InputArray R12 ,
InputArray T12 ,
InputArray R13 ,
InputArray T13 ,
OutputArray R1 ,
OutputArray R2 ,
OutputArray R3 ,
OutputArray P1 ,
OutputArray P2 ,
OutputArray P3 ,
OutputArray Q ,
double alpha ,
Size newImgSize ,
Rect * roi1 ,
Rect * roi2 ,
int flags
)
Python:
retval, R1, R2, R3, P1, P2, P3, Q, roi1, roi2 = cv.rectify3Collinear( cameraMatrix1, distCoeffs1, cameraMatrix2, distCoeffs2, cameraMatrix3, distCoeffs3, imgpt1, imgpt3, imageSize, R12, T12, R13, T13, alpha, newImgSize, flags[, R1[, R2[, R3[, P1[, P2[, P3[, Q]]]]]]] )

#include < opencv2/calib3d.hpp >

computes the rectification transformations for 3-head camera, where all the heads are on the same line.

reprojectImageTo3D()

void cv::reprojectImageTo3D ( InputArray disparity ,
OutputArray _3dImage ,
InputArray Q ,
bool handleMissingValues = false ,
int ddepth = -1
)
Python:
_3dImage = cv.reprojectImageTo3D( disparity, Q[, _3dImage[, handleMissingValues[, ddepth]]] )

#include < opencv2/calib3d.hpp >

Reprojects a disparity image to 3D space.

Parameters
disparity Input single-channel 8-bit unsigned, 16-bit signed, 32-bit signed or 32-bit floating-point disparity image. The values of 8-bit / 16-bit signed formats are assumed to have no fractional bits. If the disparity is 16-bit signed format as computed by StereoBM/StereoSGBM/StereoBinaryBM/StereoBinarySGBM and may be other algorithms, it should be divided by 16 (and scaled to float) before being used here.
_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.
Q \(4 \times 4\) perspective transformation matrix that can be obtained with stereoRectify.
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 StereoMatcher::compute ) are transformed to 3D points with a very large Z value (currently set to 10000).
ddepth The optional output array depth. If it is -1, the output image will have CV_32F depth. ddepth can also be set to CV_16S, CV_32S or CV_32F.

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

\[\begin{array}{l} [X \; Y \; Z \; W]^T = \texttt{Q} *[x \; y \; \texttt{disparity} (x,y) \; 1]^T \\ \texttt{\_3dImage} (x,y) = (X/W, \; Y/W, \; Z/W) \end{array}\]

The matrix Q can be an arbitrary \(4 \times 4\) matrix (for example, the one computed by stereoRectify). To reproject a sparse set of points {(x,y,d),...} to 3D space, use perspectiveTransform .

Rodrigues()

void cv::Rodrigues ( InputArray src ,
OutputArray dst ,
OutputArray jacobian = noArray ()
)
Python:
dst, jacobian = cv.Rodrigues( src[, dst[, jacobian]] )

#include < opencv2/calib3d.hpp >

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

Parameters
src Input rotation vector (3x1 or 1x3) or rotation matrix (3x3).
dst Output rotation matrix (3x3) or rotation vector (3x1 or 1x3), respectively.
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.

\[\begin{array}{l} \theta \leftarrow norm(r) \\ r \leftarrow r/ \theta \\ R = \cos(\theta) I + (1- \cos{\theta} ) r r^T + \sin(\theta) \vecthreethree{0}{-r_z}{r_y}{r_z}{0}{-r_x}{-r_y}{r_x}{0} \end{array}\]

Inverse transformation can be also done easily, since

\[\sin ( \theta ) \vecthreethree{0}{-r_z}{r_y}{r_z}{0}{-r_x}{-r_y}{r_x}{0} = \frac{R - R^T}{2}\]

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 calibrateCamera , stereoCalibrate ,或 solvePnP .

注意
More information about the computation of the derivative of a 3D rotation matrix with respect to its exponential coordinate can be found in:
  • A Compact Formula for the Derivative of a 3-D Rotation in Exponential Coordinates, Guillermo Gallego, Anthony J. Yezzi [75]
Useful information on SE(3) and Lie Groups can be found in:
  • A tutorial on SE(3) transformation parameterizations and on-manifold optimization, Jose-Luis Blanco [20]
  • Lie Groups for 2D and 3D Transformation, Ethan Eade [58]
  • A micro Lie theory for state estimation in robotics, Joan Solà, Jérémie Deray, Dinesh Atchuthan [211]
范例:
samples/cpp/tutorial_code/features2D/Homography/decompose_homography.cpp , samples/cpp/tutorial_code/features2D/Homography/homography_from_camera_displacement.cpp ,和 samples/cpp/tutorial_code/features2D/Homography/pose_from_homography.cpp .

RQDecomp3x3()

Vec3d cv::RQDecomp3x3 (