Camera Projection Matrix with Eigen
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void projectFromCameraCoordinateToCameraPlane( Eigen::Matrix3Xd &pointsInCameraCoordinate, Eigen::Matrix3d &cameraIntrinsicMatrix,Eigen::Matrix2Xd &pointsInCameraPlane) { /* Intrinsic camera Matrix is something like this: focalLength ===> unit is mm mx= ==>unit is Pixel/mm U0= ===> unit is Pixel my=-(numberOfPixelInHeight)/heightOfSensor ; U0=(numberOfPixelInHeight)/2 ; mx=(numberOfPixelInWidth)/heightOfSensor; V0=(numberOfPixelInWidth)/2; Gamma=0 X,Y,Z,W are homogeneous position of point in camera coordinate ┌ ┐ ┌ ┐┌ ┐ v` |f*mx Gamma V0 0||X| u` =|0 f*my U0 0||Y| w` |0 0 1 0||Z| └ ┘ └ ┘└W┘ ▲y | ----►V | | ____________________|_____________________ | |__|__|__|__|__|__|__|__|__|__|__|__|__|__| U ▼ |__|__|__|__|__|__|__|__|__|__|__|__|__|__| |__|__|__|__|__|__|__|__|__|__|__|__|__|__| |__|__|__|__|__|__|__|__|__|__|__|__|__|__| |__|__|__|__|__|__|__|__|__|__|__|__|__|__|____________► x |__|__|__|__|__|__|__|__|__|__|__|__|__|__| |__|__|__|__|__|__|__|__|__|__|__|__|__|__| |__|__|__|__|__|__|__|__|__|__|__|__|__|__| |__|__|__|__|__|__|__|__|__|__|__|__|__|__| |__|__|__|__|__|__|__|__|__|__|__|__|__|__| To project points from camera coordinate to camera plane: V`=X*f*mx + V0*Z U`=Y*f*my + U0*Z W`=Z U=U`/W` ,V=V`/W` V=f*mx*X/Z + V0 U=f*my*Y/Z + U0 (U,V) is the index of corresponding point in the image */ Eigen::Matrix3Xd pointsInCameraPlaneHomogeneous(pointsInCameraCoordinate.rows(),pointsInCameraCoordinate.cols()); pointsInCameraPlaneHomogeneous=cameraIntrinsicMatrix*pointsInCameraCoordinate; std::cout<<"pointsInCameraPlaneHomogeneous"<<std::endl; std::cout<<pointsInCameraPlaneHomogeneous<<std::endl; for(int i=0;i<pointsInCameraPlaneHomogeneous.cols();i++ ) { pointsInCameraPlaneHomogeneous(0,i)=pointsInCameraPlaneHomogeneous(0,i)/pointsInCameraPlaneHomogeneous(2,i); pointsInCameraPlaneHomogeneous(1,i)=pointsInCameraPlaneHomogeneous(1,i)/pointsInCameraPlaneHomogeneous(2,i); } pointsInCameraPlane=pointsInCameraPlaneHomogeneous.block(0,0,pointsInCameraPlaneHomogeneous.rows()-1,pointsInCameraPlaneHomogeneous.cols()); } void transformPoints(Eigen::Matrix3Xd &points, Eigen::Matrix3d &rotationMatrix, Eigen::Vector3d &translationVector,Eigen::Matrix3Xd &transformedPoints) { transformedPoints=(rotationMatrix*points).colwise() + translationVector ; } void projectFromCameraCoordinateToCameraPlane_Example() { /* OpenCV coordinate system ▲ / / Z/ / / ------------------------------► X | | | | Y | ▼ */ int numberOfPixelInHeight,numberOfPixelInWidth; double heightOfSensor, widthOfSensor; double focalLength=1.5; double mx, my, U0, V0; numberOfPixelInHeight=600; numberOfPixelInWidth=600; heightOfSensor=10; widthOfSensor=10; my=(numberOfPixelInHeight)/heightOfSensor ; U0=(numberOfPixelInHeight)/2 ; mx=(numberOfPixelInWidth)/widthOfSensor; V0=(numberOfPixelInWidth)/2; double L = 0.2; Eigen::Matrix3Xd controlPointsInWorldCoordinate(3,6); Eigen::Matrix3Xd controlPointsInCameraCoordinate(3,6); Eigen::Matrix3d cameraIntrinsicMatrix; cameraIntrinsicMatrix<<focalLength*mx, 0, V0, 0,focalLength*my,U0, 0,0,1; controlPointsInWorldCoordinate.col(0)= Eigen::Vector3d(-L, -L, 0); controlPointsInWorldCoordinate.col(1)= Eigen::Vector3d(2 * L, -L, 0.2); controlPointsInWorldCoordinate.col(2)= Eigen::Vector3d(L, L, 0.2); controlPointsInWorldCoordinate.col(3)= Eigen::Vector3d(-L, L, 0); controlPointsInWorldCoordinate.col(4)= Eigen::Vector3d(-2 * L, L, 0); controlPointsInWorldCoordinate.col(5)= Eigen::Vector3d(0, 0, 0.5); Eigen::Matrix3d rotationMatrix; rotationMatrix<< 1,0,0 ,0,1,0 ,0,0,1; Eigen::Vector3d translationVector(3,1); translationVector<<-0.1, 0.1, 1.2; transformPoints(controlPointsInWorldCoordinate, rotationMatrix, translationVector, controlPointsInCameraCoordinate ); Eigen::Matrix2Xd pointsInCameraPlane(2,controlPointsInCameraCoordinate.cols()); projectFromCameraCoordinateToCameraPlane(controlPointsInCameraCoordinate,cameraIntrinsicMatrix,pointsInCameraPlane); std::vector<cv::Point3d> cvPointsInCameraCoordinate; std::vector<cv::Point2d> cvpointsInCameraPlane; cvPointsInCameraCoordinate.push_back(cv::Point3d(-L, -L, 0)); cvPointsInCameraCoordinate.push_back(cv::Point3d(2 * L, -L, 0.2)); cvPointsInCameraCoordinate.push_back(cv::Point3d(L, L, 0.2)); cvPointsInCameraCoordinate.push_back(cv::Point3d(-L, L, 0)); cvPointsInCameraCoordinate.push_back(cv::Point3d(-2 * L, L, 0)); cvPointsInCameraCoordinate.push_back(cv::Point3d(0, 0, 0.5)); cv::Mat cameraMatrix= (cv::Mat_<double>(3,3) << focalLength*mx, 0, V0, 0,focalLength*my,U0, 0,0,1); cv::Mat rvec= cv::Mat::eye(3,3, CV_64F); cv::Mat tvec=(cv::Mat_<double>(3,1)<<-0.1, 0.1, 1.2); cv::projectPoints(cvPointsInCameraCoordinate,rvec,tvec,cameraMatrix,cv::noArray(),cvpointsInCameraPlane); std::cout<<"cameraIntrinsicMatrix" <<std::endl; std::cout<<cameraIntrinsicMatrix <<std::endl; std::cout<<cameraMatrix <<std::endl; Eigen::MatrixXd image(numberOfPixelInHeight,numberOfPixelInWidth); image=MatrixXd::Zero(numberOfPixelInHeight,numberOfPixelInWidth); int U,V; for(int i=0;i<pointsInCameraPlane.cols();i++) { U=int(pointsInCameraPlane(0,i)); V=int(pointsInCameraPlane(1,i)); std::cout<<U<<","<<V <<std::endl; image(U,V)=255; std::cout<<cvpointsInCameraPlane.at(i)<<std::endl; } Mat dst; eigen2cv(image, dst); std::string fileName=std::string("eigen_camera_projection_result_focal_")+std::to_string(focalLength)+ std::string("_.jpg"); cv::imwrite(fileName,dst); } |
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