1. 旋转矩阵与旋转向量的相互转换1.1. 罗德里格斯公式符号^是向量到反对称的转换符。反之我们也可以计算从一个旋转矩阵到旋转向量的转换。对于转角θ有因此关于转轴n由于旋转轴上的向量在旋转后不发生改变说明转轴 n 是矩阵 R 特征值 1 对应的特征向量。求解此方程再归一化就得到了旋转轴。1.2. 转换函数void Rodrigues(const cv::Mat srccv::Mat dstcv::Mat jacobian0);参数说明src——为输入的旋转向量3x1或者1x3或者旋转矩阵3x3。该参数向量表示其旋转的角度用向量长度表示。dst——为输出的旋转矩阵3x3或者旋转向量3x1或者1x3。jacobian——为可选的输出雅可比矩阵3x9或者9x3是输入与输出数组的偏导数。2. 图像变换2.1. 去畸变2.1.1. 针孔相机调用方法std::vectorcv::Point2f inputDistortedPoints ... std::vectorcv::Point2f outputUndistortedPoints; cv::Mat cameraMatrix ... cv::Mat distCoeffs ... cv::undistortPoints(inputDistortedPoints, outputUndistortedPoints, cameraMatrix, distCoeffs, cv::noArray(), cameraMatrix);不要像下面这样调用输出的点不正确cv::undistortPoints(inputDistortedPoints, outputUndistortedPoints, cameraMatrix, distCoeffs2.1.2. 鱼眼相机cv::fisheye::undistortPoints(inputDistortedPoints, outputUndistortedPoints, cameraMatrix, distCoeffs, cv::noArray(), cameraMatrix);2.2. 投影2.2.1. 针孔相机函数void cv::projectPoints(InputArray objectPoints, InputArray rvec, InputArray tvec, InputArray cameraMatrix, InputArray distCoeffs, OutputArray imagePoints, OutputArray jacobian noArray(), double aspectRatio 0)ParametersobjectPointsArray of object points expressed wrt. the world coordinate frame. A 3xN/Nx3 1-channel or 1xN/Nx1 3-channel (or vectorPoint3f), where N is the number of points in the view.rvecThe rotation vector (Rodrigues) that, together with tvec, performs a change of basis from world to camera coordinate system, see calibrateCamera for details.tvecThe translation vector, see parameter description above.cameraMatrixCamera intrinsic matrixdistCoeffsInput vector of distortion coefficients (k1,k2,p1,p2[,k3[,k4,k5,k6[,s1,s2,s3,s4[,τx,τy]]]]) of 4, 5, 8, 12 or 14 elements . If the vector is empty, the zero distortion coefficients are assumed.imagePointsOutput array of image points, 1xN/Nx1 2-channel, or vectorPoint2f .jacobianOptional output 2Nx(10numDistCoeffs) 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.aspectRatioOptional 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.示例#include opencv2/core/core.hpp #include opencv2/imgproc/imgproc.hpp #include opencv2/calib3d/calib3d.hpp #include opencv2/highgui/highgui.hpp #include iostream #include string using namespace std; vectorcv::Point3f Generate3DPoints(); int main(int argc, char* argv[]) { // Read 3D points vectorcv::Point3f objectPoints Generate3DPoints(); vectorcv::Point2f imagePoints; cv::Mat intrisicMat(3, 3, cv::DataTypefloat::type); // Intrisic matrix intrisicMat.atfloat(0, 0) 1.6415318549788924e003; intrisicMat.atfloat(1, 0) 0; intrisicMat.atfloat(2, 0) 0; intrisicMat.atfloat(0, 1) 0; intrisicMat.atfloat(1, 1) 1.7067753507885654e003; intrisicMat.atfloat(2, 1) 0; intrisicMat.atfloat(0, 2) 5.3262822453148601e002; intrisicMat.atfloat(1, 2) 3.8095355839052968e002; intrisicMat.atfloat(2, 2) 1; cv::Mat rVec(3, 1, cv::DataTypefloat::type); // Rotation vector rVec.atfloat(0) -3.9277902400761393e-002; rVec.atfloat(1) 3.7803824407602084e-002; rVec.atfloat(2) 2.6445674487856268e-002; cv::Mat tVec(3, 1, cv::DataTypefloat::type); // Translation vector tVec.atfloat(0) 2.1158489381208221e000; tVec.atfloat(1) -7.6847683212704716e000; tVec.atfloat(2) 2.6169795190294256e001; cv::Mat distCoeffs(5, 1, cv::DataTypefloat::type); // Distortion vector distCoeffs.atfloat(0) -7.9134632415085826e-001; distCoeffs.atfloat(1) 1.5623584435644169e000; distCoeffs.atfloat(2) -3.3916502741726508e-002; distCoeffs.atfloat(3) -1.3921577146136694e-002; distCoeffs.atfloat(4) 1.1430734623697941e-002; cout Intrisic matrix: intrisicMat endl endl; cout Rotation vector: rVec endl endl; cout Translation vector: tVec endl endl; cout Distortion coef: distCoeffs endl endl; std::vectorcv::Point2f projectedPoints; cv::projectPoints(objectPoints, rVec, tVec, intrisicMat, distCoeffs, projectedPoints); cout Press any key to exit.; cin.ignore(); cin.get(); return 0; } vectorcv::Point3f Generate3DPoints() { vectorcv::Point3f points; points.push_back(cv::Point3f(.5, .5, -.5)); points.push_back(cv::Point3f(.5, .5, .5)); points.push_back(cv::Point3f(-.5, .5, .5)); points.push_back(cv::Point3f(-.5, .5, -.5)); points.push_back(cv::Point3f(.5, -.5, -.5)); points.push_back(cv::Point3f(-.5, -.5, -.5)); points.push_back(cv::Point3f(-.5, -.5, .5)); for(unsigned int i 0; i points.size(); i) { cout points[i] endl endl; } return points; }2.2.2. 鱼眼相机函数// 提供了两个重载函数经验上第一个容易崩溃建议使用第二个 void cv::fisheye::projectPoints(InputArray objectPoints, OutputArray imagePoints, InputArray rvec, InputArray tvec, InputArray K, InputArray D, double alpha 0, OutputArray jacobian noArray()) void cv::fisheye::projectPoints(InputArray objectPoints, OutputArray imagePoints, const Affine3d affine, InputArray K, InputArray D, double alpha 0, OutputArray jacobian noArray())ParametersobjectPointsArray of object points, 1xN/Nx1 3-channel (or vectorPoint3f), where N is the number of points in the view.imagePointsOutput array of image points, 2xN/Nx2 1-channel or 1xN/Nx1 2-channel, or vectorPoint2f.affine仿射变换可以使用位姿矩阵进行初始化KCamera intrinsic matrix cameramatrixK.DInput vector of distortion coefficients (k1,k2,k3,k4).alphaThe skew coefficient.jacobianOptional output 2Nx15 jacobian matrix of derivatives of image points with respect to components of the focal lengths, coordinates of the principal point, distortion coefficients, rotation vector, translation vector, and the skew. In the old interface different components of the jacobian are returned via different output parameters.参考文献OpenCV的projectPoints函数用法_JIN_嫣熙的博客-CSDN博客_projectpointsOpencv学习12——cv::Rodrigues()函数_令狐少侠、的博客-CSDN博客_rodrigues函数OpenCV: Camera Calibration and 3D ReconstructionOpenCV: Fisheye camera modelundistortPoints opencv_cvml的博客-CSDN博客
1. 旋转矩阵与旋转向量的相互转换1.1. 罗德里格斯公式符号^是向量到反对称的转换符。反之我们也可以计算从一个旋转矩阵到旋转向量的转换。对于转角θ有因此关于转轴n由于旋转轴上的向量在旋转后不发生改变说明转轴 n 是矩阵 R 特征值 1 对应的特征向量。求解此方程再归一化就得到了旋转轴。1.2. 转换函数void Rodrigues(const cv::Mat srccv::Mat dstcv::Mat jacobian0);参数说明src——为输入的旋转向量3x1或者1x3或者旋转矩阵3x3。该参数向量表示其旋转的角度用向量长度表示。dst——为输出的旋转矩阵3x3或者旋转向量3x1或者1x3。jacobian——为可选的输出雅可比矩阵3x9或者9x3是输入与输出数组的偏导数。2. 图像变换2.1. 去畸变2.1.1. 针孔相机调用方法std::vectorcv::Point2f inputDistortedPoints ... std::vectorcv::Point2f outputUndistortedPoints; cv::Mat cameraMatrix ... cv::Mat distCoeffs ... cv::undistortPoints(inputDistortedPoints, outputUndistortedPoints, cameraMatrix, distCoeffs, cv::noArray(), cameraMatrix);不要像下面这样调用输出的点不正确cv::undistortPoints(inputDistortedPoints, outputUndistortedPoints, cameraMatrix, distCoeffs2.1.2. 鱼眼相机cv::fisheye::undistortPoints(inputDistortedPoints, outputUndistortedPoints, cameraMatrix, distCoeffs, cv::noArray(), cameraMatrix);2.2. 投影2.2.1. 针孔相机函数void cv::projectPoints(InputArray objectPoints, InputArray rvec, InputArray tvec, InputArray cameraMatrix, InputArray distCoeffs, OutputArray imagePoints, OutputArray jacobian noArray(), double aspectRatio 0)ParametersobjectPointsArray of object points expressed wrt. the world coordinate frame. A 3xN/Nx3 1-channel or 1xN/Nx1 3-channel (or vectorPoint3f), where N is the number of points in the view.rvecThe rotation vector (Rodrigues) that, together with tvec, performs a change of basis from world to camera coordinate system, see calibrateCamera for details.tvecThe translation vector, see parameter description above.cameraMatrixCamera intrinsic matrixdistCoeffsInput vector of distortion coefficients (k1,k2,p1,p2[,k3[,k4,k5,k6[,s1,s2,s3,s4[,τx,τy]]]]) of 4, 5, 8, 12 or 14 elements . If the vector is empty, the zero distortion coefficients are assumed.imagePointsOutput array of image points, 1xN/Nx1 2-channel, or vectorPoint2f .jacobianOptional output 2Nx(10numDistCoeffs) 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.aspectRatioOptional 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.示例#include opencv2/core/core.hpp #include opencv2/imgproc/imgproc.hpp #include opencv2/calib3d/calib3d.hpp #include opencv2/highgui/highgui.hpp #include iostream #include string using namespace std; vectorcv::Point3f Generate3DPoints(); int main(int argc, char* argv[]) { // Read 3D points vectorcv::Point3f objectPoints Generate3DPoints(); vectorcv::Point2f imagePoints; cv::Mat intrisicMat(3, 3, cv::DataTypefloat::type); // Intrisic matrix intrisicMat.atfloat(0, 0) 1.6415318549788924e003; intrisicMat.atfloat(1, 0) 0; intrisicMat.atfloat(2, 0) 0; intrisicMat.atfloat(0, 1) 0; intrisicMat.atfloat(1, 1) 1.7067753507885654e003; intrisicMat.atfloat(2, 1) 0; intrisicMat.atfloat(0, 2) 5.3262822453148601e002; intrisicMat.atfloat(1, 2) 3.8095355839052968e002; intrisicMat.atfloat(2, 2) 1; cv::Mat rVec(3, 1, cv::DataTypefloat::type); // Rotation vector rVec.atfloat(0) -3.9277902400761393e-002; rVec.atfloat(1) 3.7803824407602084e-002; rVec.atfloat(2) 2.6445674487856268e-002; cv::Mat tVec(3, 1, cv::DataTypefloat::type); // Translation vector tVec.atfloat(0) 2.1158489381208221e000; tVec.atfloat(1) -7.6847683212704716e000; tVec.atfloat(2) 2.6169795190294256e001; cv::Mat distCoeffs(5, 1, cv::DataTypefloat::type); // Distortion vector distCoeffs.atfloat(0) -7.9134632415085826e-001; distCoeffs.atfloat(1) 1.5623584435644169e000; distCoeffs.atfloat(2) -3.3916502741726508e-002; distCoeffs.atfloat(3) -1.3921577146136694e-002; distCoeffs.atfloat(4) 1.1430734623697941e-002; cout Intrisic matrix: intrisicMat endl endl; cout Rotation vector: rVec endl endl; cout Translation vector: tVec endl endl; cout Distortion coef: distCoeffs endl endl; std::vectorcv::Point2f projectedPoints; cv::projectPoints(objectPoints, rVec, tVec, intrisicMat, distCoeffs, projectedPoints); cout Press any key to exit.; cin.ignore(); cin.get(); return 0; } vectorcv::Point3f Generate3DPoints() { vectorcv::Point3f points; points.push_back(cv::Point3f(.5, .5, -.5)); points.push_back(cv::Point3f(.5, .5, .5)); points.push_back(cv::Point3f(-.5, .5, .5)); points.push_back(cv::Point3f(-.5, .5, -.5)); points.push_back(cv::Point3f(.5, -.5, -.5)); points.push_back(cv::Point3f(-.5, -.5, -.5)); points.push_back(cv::Point3f(-.5, -.5, .5)); for(unsigned int i 0; i points.size(); i) { cout points[i] endl endl; } return points; }2.2.2. 鱼眼相机函数// 提供了两个重载函数经验上第一个容易崩溃建议使用第二个 void cv::fisheye::projectPoints(InputArray objectPoints, OutputArray imagePoints, InputArray rvec, InputArray tvec, InputArray K, InputArray D, double alpha 0, OutputArray jacobian noArray()) void cv::fisheye::projectPoints(InputArray objectPoints, OutputArray imagePoints, const Affine3d affine, InputArray K, InputArray D, double alpha 0, OutputArray jacobian noArray())ParametersobjectPointsArray of object points, 1xN/Nx1 3-channel (or vectorPoint3f), where N is the number of points in the view.imagePointsOutput array of image points, 2xN/Nx2 1-channel or 1xN/Nx1 2-channel, or vectorPoint2f.affine仿射变换可以使用位姿矩阵进行初始化KCamera intrinsic matrix cameramatrixK.DInput vector of distortion coefficients (k1,k2,k3,k4).alphaThe skew coefficient.jacobianOptional output 2Nx15 jacobian matrix of derivatives of image points with respect to components of the focal lengths, coordinates of the principal point, distortion coefficients, rotation vector, translation vector, and the skew. In the old interface different components of the jacobian are returned via different output parameters.参考文献OpenCV的projectPoints函数用法_JIN_嫣熙的博客-CSDN博客_projectpointsOpencv学习12——cv::Rodrigues()函数_令狐少侠、的博客-CSDN博客_rodrigues函数OpenCV: Camera Calibration and 3D ReconstructionOpenCV: Fisheye camera modelundistortPoints opencv_cvml的博客-CSDN博客
