Decomposing Projection Using OpenCV and C++
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#include <opencv/cv.hpp> #include <opencv2/core.hpp> #include <opencv2/calib3d.hpp> #include "transformation.hpp" //https://www.cnblogs.com/shengguang/p/5932522.html void HouseHolderQR(const cv::Mat &A, cv::Mat &Q, cv::Mat &R) { assert ( A.channels() == 1 ); assert ( A.rows >= A.cols ); auto sign = [](double value) { return value >= 0 ? 1: -1; }; const auto totalRows = A.rows; const auto totalCols = A.cols; R = A.clone(); Q = cv::Mat::eye ( totalRows, totalRows, A.type() ); for ( int col = 0; col < A.cols; ++ col ) { cv::Mat matAROI = cv::Mat ( R, cv::Range ( col, totalRows ), cv::Range ( col, totalCols ) ); cv::Mat y = matAROI.col ( 0 ); auto yNorm = norm ( y ); cv::Mat e1 = cv::Mat::eye ( y.rows, 1, A.type() ); cv::Mat w = y + sign(y.at<double>(0,0)) * yNorm * e1; cv::Mat v = w / norm( w ); cv::Mat vT; cv::transpose(v, vT ); cv::Mat I = cv::Mat::eye( matAROI.rows, matAROI.rows, A.type() ); cv::Mat I_2VVT = I - 2 * v * vT; cv::Mat matH = cv::Mat::eye ( totalRows, totalRows, A.type() ); cv::Mat matHROI = cv::Mat(matH, cv::Range ( col, totalRows ), cv::Range ( col, totalRows ) ); I_2VVT.copyTo ( matHROI ); R = matH * R; Q = Q * matH; } } int main() { /* Thera are two notations for Projection Matrix 1)P=K[R|t] ┌X┐ ┌R,t┐ |Y| X_Cam=R*X+t ==> Homogeneous Coordinate ==> X_Cam=|0,1| |Z| └ ┘4x4└1┘4x1 ┌X┐ ┌ ┐ |Y| image plane <--x=K[I|0]3x4 |R,t| |Z| └0,1┘4x4 └1┘4x1 P=K[R|t] 2)P=KR[I|-X0] ┌X┐ ┌R -Rc┐|Y| X_Cam=R*[X_w-C] ==> Homogeneous Coordinate ==> | ||Z| └0 1 ┘└1┘ ┌X┐ ┌R -Rc┐|Y| image plane <--x=K[I|0]3x4 |0 1 ||Z| └ ┘└1┘ P=K[R|-RC]= KR[I|-C] (1) and (2) ==> t=-RC */ int numberOfPixelInHeight,numberOfPixelInWidth; double heightOfSensor, widthOfSensor; double focalLength=1.50; double mx, my, U0, V0; numberOfPixelInHeight=600; numberOfPixelInWidth=800; heightOfSensor=10; widthOfSensor=10; my=(numberOfPixelInHeight)/heightOfSensor ; U0=(numberOfPixelInHeight)/2 ; mx=(numberOfPixelInWidth)/widthOfSensor; V0=(numberOfPixelInWidth)/2; cv::Mat cameraMatrix = (cv::Mat_<double>(3,3) << focalLength*mx, 0, V0, 0,focalLength*my,U0, 0,0,1); double tx,ty,tz,roll,pitch,yaw; tx=1.0; ty=2.1; tz=-1.4; cv::Mat translation = (cv::Mat_<double>(3,1) <<tx,ty,tz); cv::Vec3d theta; roll=+M_PI/4 ; pitch=+M_PI/10; yaw=-+M_PI/6; theta[0]=roll; theta[1]=pitch; theta[2]=yaw; cv::Mat rotation=eulerAnglesToRotationMatrix(theta); //1)P=K[R|t] cv::Mat R_T; cv::hconcat(rotation, translation, R_T); cv::Mat projectionMatrix=cameraMatrix*R_T; cv::Mat calculatedCameraMatrix,calculatedRotation,calculatedTranslation; cv::decomposeProjectionMatrix(projectionMatrix,calculatedCameraMatrix,calculatedRotation,calculatedTranslation); std::cout<<"==============================Ground Truth==============================" <<std::endl; std::cout<<"Rotation Matrix (Ground Truth)" <<std::endl; std::cout<<rotation <<std::endl; std::cout<<"Translation Matrix (Ground Truth)" <<std::endl; std::cout<<translation <<std::endl; std::cout<<"Camera Matrix (Ground Truth)" <<std::endl; std::cout<<cameraMatrix <<std::endl; std::cout<<"==============================Decomposing Using OpenCV==============================" <<std::endl; std::cout<<"Computed Rotation Matrix (OpenCV)" <<std::endl; std::cout<<calculatedRotation <<std::endl; std::cout<<"Computed Translation Matrix (OpenCV)" <<std::endl; //std::cout<<calculatedTranslation/calculatedTranslation.at<double>(3,0) <<std::endl; cv::Mat tempT=(cv::Mat_<double>(3,1)<< calculatedTranslation.at<double>(0,0)/calculatedTranslation.at<double>(3,0), calculatedTranslation.at<double>(1,0)/calculatedTranslation.at<double>(3,0), calculatedTranslation.at<double>(2,0)/calculatedTranslation.at<double>(3,0)); std::cout<<-rotation*tempT<<std::endl; std::cout<<"Computed Camera Matrix (OpenCV)" <<std::endl; std::cout<<calculatedCameraMatrix <<std::endl; ///////////////////////////////////////decomposing the projection matrix/////////////////////////////////////////// /* P=KR[I|-X0]=[H_inf3x3|h3x1] KR=H_inf3x3 1)X0 -KRX0=h3x1 => X0=-(KR)^-1*h3x1 ==>X0=-(H_inf3x3)^-1*h3x1 2)K,R KR=H_inf3x3 =>(KR)^-1= H_inf3x3^-1 =>R^-1*K^-1=H_inf3x3^-1 | R^-1*K^-1=Q*R => R=Q^-1, K=R^-1 H_inf3x3^-1=Q*R | */ cv::Mat H_inf3x3=(cv::Mat_<double>(3,3)<< projectionMatrix.at<double>(0,0),projectionMatrix.at<double>(0,1),projectionMatrix.at<double>(0,2) ,projectionMatrix.at<double>(1,0),projectionMatrix.at<double>(1,1),projectionMatrix.at<double>(1,2) ,projectionMatrix.at<double>(2,0),projectionMatrix.at<double>(2,1),projectionMatrix.at<double>(2,2)); cv::Mat h3x1=(cv::Mat_<double>(3,1)<<projectionMatrix.at<double>(0,3),projectionMatrix.at<double>(1,3),projectionMatrix.at<double>(2,3) ); cv::Mat Q,R; cv::Mat H_inf3x3_inv=H_inf3x3.inv(); //R=Q^-1, K=R^-1 HouseHolderQR(H_inf3x3_inv, Q, R); cv::Mat K=R.inv(); std::cout<<"==============================Decomposing Using My Code==============================" <<std::endl; //due to homogeneity we divide it by last element std::cout<<"Estimated Camera Matrix\n"<<K/K.at<double>(2,2) <<std::endl; cv::Mat rotationMatrix=Q.inv(); std::cout<<"Estimated Camera Rotation\n"<<rotationMatrix*-1 <<std::endl; std::cout<<"Estimated Camera Translation" <<std::endl; //t=-R*C, Q.inv()=R std::cout<<-1*(-Q.inv()*(-H_inf3x3.inv()*h3x1 ))<<std::endl; |
And the output is:
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==============================Ground Truth============================== Rotation Matrix (Ground Truth) [0.823639103546332, 0.5427868801100539, -0.1643199010764935; -0.4755282581475767, 0.5031184295835893, -0.7216264418079997; -0.3090169943749474, 0.6724985119639573, 0.6724985119639574] Translation Matrix (Ground Truth) [1; 2.1; -1.4] Camera Matrix (Ground Truth) [120, 0, 400; 0, 90, 300; 0, 0, 1] ==============================Decomposing Using OpenCV============================== Computed Rotation Matrix (OpenCV) [0.823639103546332, 0.5427868801100539, -0.1643199010764936; -0.4755282581475769, 0.5031184295835893, -0.7216264418079997; -0.3090169943749474, 0.6724985119639573, 0.6724985119639574] Computed Translation Matrix (OpenCV) [0.9999999999999988; 2.1; -1.4] Computed Camera Matrix (OpenCV) [120, -1.4210854715202e-14, 400; 0, 90.00000000000001, 300; 0, 0, 1] ==============================Decomposing Using My Code============================== Estimated Camera Matrix [120, -5.776629175002766e-14, 399.9999999999999; -5.608036291626306e-15, 89.99999999999994, 299.9999999999999; -1.49192016182457e-17, -1.561251128379126e-16, 1] Estimated Camera Rotation [0.8236391035463322, 0.5427868801100542, -0.1643199010764936; -0.4755282581475767, 0.5031184295835892, -0.7216264418079998; -0.3090169943749475, 0.6724985119639573, 0.6724985119639575] Estimated Camera Translation [1; 2.099999999999999; -1.4] |
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