WebSVN – seema-scanner – Diff – /src/cvtools.cpp


#include "cvtools.h"
 
#ifdef _WIN32
#include <cstdint>
#endif
 
#include <stdio.h>
 
namespace cvtools{
 
// Create a mask for feature matching which disallows matches not satisfying the epipolar constraint.
// Works like cv::windowedMatchingMask in conjunction with cv::BFMatcher::match().
// F is the fundamental matrix.
// maxD is the maximum point to line distance permissible.
cv::Mat epipolarMatchingMask(const cv::vector<cv::KeyPoint> &keypoints1, const cv::vector<cv::KeyPoint> &keypoints2, cv::Matx33f F, float maxD){
 
    if(keypoints1.empty() || keypoints2.empty())
        return cv::Mat();
 
    int n1 = (int)keypoints1.size(), n2 = (int)keypoints2.size();
    cv::Mat mask(n1, n2, CV_8UC1);
 
    // Point to line distance
//    for( int i = 0; i < n1; i++ ){
//        cv::Vec3f p1 = cv::Vec3f(keypoints1[i].pt.x, keypoints1[i].pt.y, 1.0);
//        // Epipolar line defined by p1
//        cv::Vec3f l = F*p1;
//        l /= sqrt(l(0)*l(0) + l(1)*l(1));
//        for( int j = 0; j < n2; j++ ){
//            cv::Vec3f p2 = cv::Vec3f(keypoints2[j].pt.x, keypoints2[j].pt.y, 1.0);
//            // Signed distance to line
//            float d = l.dot(p2);
//            mask.at<uchar>(i, j) = fabs(d) < maxD;
//        }
//    }
 
    // Symmetric epipolar distance
    std::vector<cv::Point2f> q1, q2;
    cvtools::keypointsToPoints(keypoints1, q1);
    cvtools::keypointsToPoints(keypoints2, q2);
    std::vector<cv::Point3f> l1, l2;
    cv::computeCorrespondEpilines(q1, 1, F, l1);
    cv::computeCorrespondEpilines(q2, 2, F, l2);
 
    for( int i = 0; i < n1; i++ ){
        cv::Vec3f p1 = cv::Vec3f(q1[i].x, q1[i].y, 1.0);
        for( int j = 0; j < n2; j++ ){
            cv::Vec3f p2 = cv::Vec3f(q2[j].x, q2[j].y, 1.0);
            float d12 = l1[i].dot(p2);
            float d21 = l2[j].dot(p1);
            float d = d12*d12 + d21*d21;
            mask.at<uchar>(i, j) = d < maxD;
        }
    }
 
//    // Sampson Error (H&Z, p. 287) (expensive...)
//    std::vector<cv::Point2f> q1, q2;
//    cvtools::keypointsToPoints(keypoints1, q1);
//    cvtools::keypointsToPoints(keypoints2, q2);
//    std::vector<cv::Point3f> p1, p2;
//    cv::convertPointsToHomogeneous(q1, p1);
//    cv::convertPointsToHomogeneous(q2, p2);
//    cv::Mat Fp1Mat = cv::Mat(F)*cv::Mat(p1).reshape(1).t();
//    cv::Mat FTp2Mat = cv::Mat(F.t())*cv::Mat(p2).reshape(1).t();
//    for( int i = 0; i < n1; i++ ){
//        cv::Vec3f Fp1 = Fp1Mat.col(i);
//        for( int j = 0; j < n2; j++ ){
//            cv::Vec3f FTp2 = FTp2Mat.col(j);
//            cv::Matx<float,1,1> p2TFp1 = cv::Matx31f(p2[j]).t()*F*cv::Matx31f(p1[i]);
//            float d = p2TFp1(0)*p2TFp1(0) / (Fp1(0)*Fp1(0) + Fp1(1)*Fp1(1) + FTp2(0)*FTp2(0) + FTp2(1)*FTp2(1));
//            mask.at<uchar>(i, j) = d < maxD;
//        }
//    }
 
    return mask;
}
 
 
// Remove correspondences which have a distance metric above thresh.
void matchingThreshold(const std::vector<cv::DMatch> &matchesIn, std::vector<cv::DMatch> &matchesOut, float thresh){
 
    int nMatches = matchesIn.size();
    matchesOut.clear();
    matchesOut.reserve(nMatches);
 
    for(int i=0; i<nMatches; i++){
        if(matchesIn[i].distance < thresh)
            matchesOut.push_back(matchesIn[i]);
    }
 
}
 
// Lightly modified OpenCV function which accepts a line width argument
void drawChessboardCorners(cv::InputOutputArray _image, cv::Size patternSize, cv::InputArray _corners, bool patternWasFound, int line_width){
    cv::Mat corners = _corners.getMat();
    if( corners.empty() )
        return;
    cv::Mat image = _image.getMat(); CvMat c_image = _image.getMat();
    int nelems = corners.checkVector(2, CV_32F, true);
    CV_Assert(nelems >= 0);
    cvDrawChessboardCorners( &c_image, patternSize, (CvPoint2D32f*)corners.data,
                             nelems, patternWasFound, line_width);
}
 
void rshift(cv::Mat& I, unsigned int shift){
 
    int nRows = I.rows;
    int nCols = I.cols;
 
    if (I.isContinuous()){
        nCols *= nRows;
        nRows = 1;
    }
 
    int i,j;
    unsigned short* p;
    for( i = 0; i < nRows; ++i){
        p = I.ptr<unsigned short>(i);
        for ( j = 0; j < nCols; ++j){
            p[j] = p[j]>>shift;
        }
    }
}
 
void cvDrawChessboardCorners(CvArr* _image, CvSize pattern_size, CvPoint2D32f* corners, int count, int found, int line_width){
    const int shift = 0;
    const int radius = 12;
    const int r = radius*(1 << shift);
    int i;
    CvMat stub, *image;
    double scale = 1;
    int type, cn, line_type;
 
    image = cvGetMat( _image, &stub );
 
    type = CV_MAT_TYPE(image->type);
    cn = CV_MAT_CN(type);
    if( cn != 1 && cn != 3 && cn != 4 )
        CV_Error( CV_StsUnsupportedFormat, "Number of channels must be 1, 3 or 4" );
 
    switch( CV_MAT_DEPTH(image->type) )
    {
    case CV_8U:
        scale = 1;
        break;
    case CV_16U:
        scale = 256;
        break;
    case CV_32F:
        scale = 1./255;
        break;
    default:
        CV_Error( CV_StsUnsupportedFormat,
            "Only 8-bit, 16-bit or floating-point 32-bit images are supported" );
    }
 
    line_type = type == CV_8UC1 || type == CV_8UC3 ? CV_AA : 8;
 
    if( !found )
    {
        CvScalar color = {{0,0,255}};
        if( cn == 1 )
            color = cvScalarAll(200);
        color.val[0] *= scale;
        color.val[1] *= scale;
        color.val[2] *= scale;
        color.val[3] *= scale;
 
        for( i = 0; i < count; i++ )
        {
            CvPoint pt;
            pt.x = cvRound(corners[i].x*(1 << shift));
            pt.y = cvRound(corners[i].y*(1 << shift));
            cvLine( image, cvPoint( pt.x - r, pt.y - r ),
                    cvPoint( pt.x + r, pt.y + r ), color, line_width, line_type, shift );
            cvLine( image, cvPoint( pt.x - r, pt.y + r),
                    cvPoint( pt.x + r, pt.y - r), color, line_width, line_type, shift );
            cvCircle( image, pt, r+(1<<shift), color, line_width, line_type, shift );
        }
    }
    else
    {
        int x, y;
        CvPoint prev_pt = {0, 0};
        const int line_max = 7;
        static const CvScalar line_colors[line_max] =
        {
            {{0,0,255}},
            {{0,128,255}},
            {{0,200,200}},
            {{0,255,0}},
            {{200,200,0}},
            {{255,0,0}},
            {{255,0,255}}
        };
 
        for( y = 0, i = 0; y < pattern_size.height; y++ )
        {
            CvScalar color = line_colors[y % line_max];
            if( cn == 1 )
                color = cvScalarAll(200);
            color.val[0] *= scale;
            color.val[1] *= scale;
            color.val[2] *= scale;
            color.val[3] *= scale;
 
            for( x = 0; x < pattern_size.width; x++, i++ )
            {
                CvPoint pt;
                pt.x = cvRound(corners[i].x*(1 << shift));
                pt.y = cvRound(corners[i].y*(1 << shift));
 
                if( i != 0 )
                    cvLine( image, prev_pt, pt, color, 1, line_type, shift );
 
                cvLine( image, cvPoint(pt.x - r, pt.y - r),
                        cvPoint(pt.x + r, pt.y + r), color, line_width, line_type, shift );
                cvLine( image, cvPoint(pt.x - r, pt.y + r),
                        cvPoint(pt.x + r, pt.y - r), color, line_width, line_type, shift );
                cvCircle( image, pt, r+(1<<shift), color, line_width, line_type, shift );
                prev_pt = pt;
            }
        }
    }
}
 
// Returns the result of mod(mat(x,y), moduli) for each matrix element
cv::Mat modulo(const cv::Mat &mat, float n){
 
    cv::Mat ret(mat.rows, mat.cols, mat.type());
 
    for(int row=0; row<ret.rows; row++){
        for(int col=0; col<ret.cols; col++){
            float val = mat.at<float>(row, col);
            // note: std::fmod calculates the remainder, not arithmetic modulo
            ret.at<float>(row, col) = val - n * std::floor(val / n);
        }
    }
 
    return ret;
}
 
// Convert a 3xN matrix to a vector of Point3fs.
void matToPoints3f(const cv::Mat &mat, std::vector<cv::Point3f> &points){
 
    unsigned int nPoints = mat.cols;
    points.resize(nPoints);
 
    for(unsigned int i=0; i<nPoints; i++)
        points[i] = cv::Point3f(mat.at<float>(0, i), mat.at<float>(1, i), mat.at<float>(2, i));
}
 
// Convert a (Dim+1)xN matrix of homogenous points to a DimxN matrix of points in non-homogenous coordinates.
void convertMatFromHomogeneous(cv::Mat &src, cv::Mat &dst){
    unsigned int N = src.cols;
    unsigned int Dim = src.rows-1;
    dst.create(Dim, N, src.type());
    for(unsigned int i=0; i<N; i++){
        for(unsigned int j=0; j<Dim; j++)
            dst.at<float>(j,i) = src.at<float>(j,i)/src.at<float>(Dim,i);
    }
 
}
 
// Function to solve the hand-eye (or eye-in-hand) calibration problem.
// Finds [Omega | tau], to minimize ||[R_mark | t_mark][Omega | tau] - [Omega | tau][R | t]||^2
// Algorithm according to Tsai, Lenz, A new technique for fully autonomous and efficient 3d robotics hand-eye calibration
// DTU, 2014, Jakob Wilm
void handEyeCalibrationTsai(const std::vector<cv::Matx33f> R, const std::vector<cv::Vec3f> t, const std::vector<cv::Matx33f> R_mark, const std::vector<cv::Vec3f> t_mark, cv::Matx33f &Omega, cv::Vec3f &tau){
 
    int N = R.size();
    assert(N == R_mark.size());
    assert(N == t.size());
    assert(N == t_mark.size());
 
    // construct equations for rotation
    cv::Mat A(3*N, 3, CV_32F);
    cv::Mat b(3*N, 1, CV_32F);
    for(int i=0; i<N; i++){
        // angle axis representations
        cv::Vec3f rot;
        cv::Vec3f rot_mark;
        cv::Rodrigues(R[i], rot);
        cv::Rodrigues(R_mark[i], rot_mark);
 
        cv::Vec3f P = 2.0*sin(cv::norm(rot)/2.0)*cv::normalize(rot);
//std::cout << "P: " << std::endl << P << std::endl;
        cv::Vec3f P_mark = 2.0*sin(cv::norm(rot_mark)/2.0)*cv::normalize(rot_mark);
//std::cout << "P_mark: " << std::endl << P_mark << std::endl;
        cv::Vec3f sum = P+P_mark;
        cv::Mat crossProduct = (cv::Mat_<float>(3,3) << 0.0, -sum(2), sum(1), sum(2), 0.0, -sum(0), -sum(1), sum(0), 0.0);
//std::cout << "crossProduct: " << std::endl << crossProduct << std::endl;
        crossProduct.copyTo(A.rowRange(i*3, i*3+3));
 
        cv::Mat(P-P_mark).copyTo(b.rowRange(i*3, i*3+3));
    }
 
    // solve for rotation
    cv::Vec3f P_prime;
    cv::solve(A, b, P_prime, cv::DECOMP_SVD);
    cv::Vec3f P = 2.0*P_prime/(cv::sqrt(1.0 + cv::norm(P_prime)*cv::norm(P_prime)));
    float nP = cv::norm(P);
    cv::Mat crossProduct = (cv::Mat_<float>(3,3) << 0.0, -P(2), P(1), P(2), 0.0, -P(0), -P(1), P(0), 0.0);
    cv::Mat OmegaMat = (1.0-nP*nP/2.0)*cv::Mat::eye(3,3,CV_32F) + 0.5*(cv::Mat(P)*cv::Mat(P).t() + cv::sqrt(4.0 - nP*nP)*crossProduct);
    Omega = cv::Matx33f(OmegaMat);
 
    // construct equations for translation
    A.setTo(0.0);
    b.setTo(0.0);
    for(int i=0; i<N; i++){
 
        cv::Mat diff = cv::Mat(R_mark[i]) - cv::Mat::eye(3, 3, CV_32F);
        diff.copyTo(A.rowRange(i*3, i*3+3));
 
        cv::Mat diff_mark = cv::Mat(Omega*t[i] - t_mark[i]);
        diff_mark.copyTo(b.rowRange(i*3, i*3+3));
    }
 
    // solve for translation
    cv::solve(A, b, tau, cv::DECOMP_SVD);
 
    cv::Mat err_tau = b - (A*cv::Mat(tau));
    std::cout << err_tau << std::endl;
}
 
// Function to solve for the rotation axis from sets of 3D point coordinates of flat pattern feature points
// Algorithm according to Chen et al., Rotation axis calibration of a turntable using constrained global optimization, Optik 2014
// DTU, 2014, Jakob Wilm
void rotationAxisCalibration(const std::vector< std::vector<cv::Point3f> > Qcam, const std::vector<cv::Point3f> Qobj, cv::Vec3f &axis, cv::Vec3f &point){
 
    // number of frames (points on each arch)
    int l = Qcam.size();
 
    // number of points in each frame
    int mn = Qobj.size();
 
    assert(mn == Qcam[0].size());
 
    // construct matrix for axis determination
    cv::Mat M(6, 6, CV_32F, cv::Scalar(0));
 
    for(int k=0; k<l; k++){
        for(int idx=0; idx<mn; idx++){
 
//            float i = Qobj[idx].x+4;
//            float j = Qobj[idx].y+4;
            float i = Qobj[idx].x;
            float j = Qobj[idx].y;
 
            float x = Qcam[k][idx].x;
            float y = Qcam[k][idx].y;
            float z = Qcam[k][idx].z;
 
            M += (cv::Mat_<float>(6,6) << x*x, x*y, x*z, x, i*x, j*x,
                                            0, y*y, y*z, y, i*y, j*y,
                                            0,   0, z*z, z, i*z, j*z,
                                            0,   0,   0, 1,   i,   j,
                                            0,   0,   0, 0, i*i, i*j,
                                            0,   0,   0, 0,   0, j*j);
 
        }
    }
 
    cv::completeSymm(M, false);
 
    // solve for axis
    std::vector<float> lambda;
    cv::Mat u;
    cv::eigen(M, lambda, u);
 
    float minLambda = abs(lambda[0]);
    int idx = 0;
    for(int i=1; i<lambda.size(); i++){
        if(abs(lambda[i]) < minLambda){
            minLambda = lambda[i];
            idx = i;
        }
    }
 
    axis = u.row(idx).colRange(0, 3);
    axis = cv::normalize(axis);
 
    float nx = u.at<float>(idx, 0);
    float ny = u.at<float>(idx, 1);
    float nz = u.at<float>(idx, 2);
    float d  = u.at<float>(idx, 3);
    float dh = u.at<float>(idx, 4);
    float dv = u.at<float>(idx, 5);
 
//    // Paper version: c is initially eliminated
//    cv::Mat A(l*mn, mn+2, CV_32F, cv::Scalar(0.0));
//    cv::Mat bb(l*mn, 1, CV_32F);
 
//    for(int k=0; k<l; k++){
//        for(int idx=0; idx<mn; idx++){
 
//            float i = Qobj[idx].x;
//            float j = Qobj[idx].y;
 
//            float x = Qcam[k][idx].x;
//            float y = Qcam[k][idx].y;
//            float z = Qcam[k][idx].z;
 
//            float f = x*x + y*y + z*z + (2*x*nx + 2*y*ny + 2*z*nz)*(i*dh + j*dv);
 
//            int row = k*mn+idx;
//            A.at<float>(row, 0) = 2*x - (2*z*nx)/nz;
//            A.at<float>(row, 1) = 2*y - (2*z*ny)/nz;
//            A.at<float>(row, idx+2) = 1.0;
 
//            bb.at<float>(row, 0) = f + (2*z*d)/nz;
//        }
//    }
 
//    // solve for point
//    cv::Mat abe;
//    cv::solve(A, bb, abe, cv::DECOMP_SVD);
 
//    float a = abe.at<float>(0, 0);
//    float b = abe.at<float>(1, 0);
//    float c = -(nx*a+ny*b+d)/nz;
 
    // Our version: solve simultanously for a,b,c
    cv::Mat A(l*mn, mn+3, CV_32F, cv::Scalar(0.0));
    cv::Mat bb(l*mn, 1, CV_32F);
 
    for(int k=0; k<l; k++){
        for(int idx=0; idx<mn; idx++){
 
            float i = Qobj[idx].x;
            float j = Qobj[idx].y;
 
            float x = Qcam[k][idx].x;
            float y = Qcam[k][idx].y;
            float z = Qcam[k][idx].z;
 
            float f = x*x + y*y + z*z + (2*x*nx + 2*y*ny + 2*z*nz)*(i*dh + j*dv);
 
            int row = k*mn+idx;
            A.at<float>(row, 0) = 2*x;
            A.at<float>(row, 1) = 2*y;
            A.at<float>(row, 2) = 2*z;
            A.at<float>(row, idx+3) = 1.0;
 
            bb.at<float>(row, 0) = f;
        }
    }
 
    // solve for point
    cv::Mat abe;
    cv::solve(A, bb, abe, cv::DECOMP_SVD);
 
    float a = abe.at<float>(0, 0);
    float b = abe.at<float>(1, 0);
    float c = abe.at<float>(2, 0);
 
    point[0] = a;
    point[1] = b;
    point[2] = c;
 
}
 
// Function to fit two sets of corresponding pose data.
// Finds [Omega | tau], to minimize ||[R_mark | t_mark] - [Omega | tau][R | t]||^2
// Algorithm and notation according to Mili Shah, Comparing two sets of corresponding six degree of freedom data, CVIU 2011.
// DTU, 2013, Oline V. Olesen, Jakob Wilm
void fitSixDofData(const std::vector<cv::Matx33f> R, const std::vector<cv::Vec3f> t, const std::vector<cv::Matx33f> R_mark, const std::vector<cv::Vec3f> t_mark, cv::Matx33f &Omega, cv::Vec3f &tau){
 
    int N = R.size();
    assert(N == R_mark.size());
    assert(N == t.size());
    assert(N == t_mark.size());
 
    // Mean translations
    cv::Vec3f t_mean;
    cv::Vec3f t_mark_mean;
    for(int i=0; i<N; i++){
        t_mean += 1.0/N * t[i];
        t_mark_mean += 1.0/N * t_mark[i];
    }
 
    // Data with mean adjusted translations
    cv::Mat X_bar(3, 4*N, CV_32F);
    cv::Mat X_mark_bar(3, 4*N, CV_32F);
    for(int i=0; i<N; i++){
        cv::Mat(R[i]).copyTo(X_bar.colRange(i*4,i*4+3));
        cv::Mat(t[i] - t_mean).copyTo(X_bar.col(i*4+3));
        cv::Mat(R_mark[i]).copyTo(X_mark_bar.colRange(i*4,i*4+3));
        cv::Mat(t_mark[i] - t_mark_mean).copyTo(X_mark_bar.col(i*4+3));
    }
    //std::cout << X_bar << std::endl;
    // SVD
    cv::Mat W, U, VT;
    cv::SVDecomp(X_bar*X_mark_bar.t(), W, U, VT);
 
    cv::Matx33f D = cv::Matx33f::eye();
    if(cv::determinant(VT*U) < 0)
        D(3,3) = -1;
 
    // Best rotation
    Omega = cv::Matx33f(cv::Mat(VT.t()))*D*cv::Matx33f(cv::Mat(U.t()));
 
    // Best translation
    tau = t_mark_mean - Omega*t_mean;
 
}
 
// Forward distortion of points. The inverse of the undistortion in cv::initUndistortRectifyMap().
// Inspired by Pascal Thomet, http://code.opencv.org/issues/1387#note-11
// Convention for distortion parameters: http://www.vision.caltech.edu/bouguetj/calib_doc/htmls/parameters.html
void initDistortMap(const cv::Matx33f cameraMatrix, const cv::Vec<float, 5> distCoeffs, const cv::Size size, cv::Mat &map1, cv::Mat &map2){
 
    float fx = cameraMatrix(0,0);
    float fy = cameraMatrix(1,1);
    float ux = cameraMatrix(0,2);
    float uy = cameraMatrix(1,2);
 
    float k1 = distCoeffs[0];
    float k2 = distCoeffs[1];
    float p1 = distCoeffs[2];
    float p2 = distCoeffs[3];
    float k3 = distCoeffs[4];
 
    map1.create(size, CV_32F);
    map2.create(size, CV_32F);
 
    for(int col = 0; col < size.width; col++){
        for(int row = 0; row < size.height; row++){
 
            // move origo to principal point and convert using focal length
            float x = (col-ux)/fx;
            float y = (row-uy)/fy;
 
            float xCorrected, yCorrected;
 
            //Step 1 : correct distortion
            float r2 = x*x + y*y;
            //radial
            xCorrected = x * (1. + k1*r2 + k2*r2*r2 + k3*r2*r2*r2);
            yCorrected = y * (1. + k1*r2 + k2*r2*r2 + k3*r2*r2*r2);
            //tangential
            xCorrected = xCorrected + (2.*p1*x*y + p2*(r2+2.*x*x));
            yCorrected = yCorrected + (p1*(r2+2.*y*y) + 2.*p2*x*y);
 
            //convert back to pixel coordinates
            float col_displaced = xCorrected * fx + ux;
            float row_displaced = yCorrected * fy + uy;
 
            // correct the vector in the opposite direction
            map1.at<float>(row,col) = col+(col-col_displaced);
            map2.at<float>(row,col) = row +(row-row_displaced);
        }
    }
}
 
// Downsample a texture which was created in virtual column/row space for a diamond pixel array projector
cv::Mat diamondDownsample(cv::Mat &pattern){
 
    cv::Mat pattern_diamond(pattern.rows,pattern.cols/2,CV_8UC3);
 
    for(unsigned int col = 0; col < pattern_diamond.cols; col++){
        for(unsigned int row = 0; row < pattern_diamond.rows; row++){
 
            pattern_diamond.at<cv::Vec3b>(row,col)=pattern.at<cv::Vec3b>(row,col*2+row%2);
        }
    }
 
    return pattern_diamond;
 
}
 
 
void mouseCallback(int evt, int x, int y, int flags, void* param){
    cv::Mat *im = (cv::Mat*) param;
    if (evt == CV_EVENT_LBUTTONDOWN) {
        if(im->type() == CV_8UC3){
            printf("%d %d: %d, %d, %d\n",
                   x, y,
                   (int)(*im).at<cv::Vec3b>(y, x)[0],
                    (int)(*im).at<cv::Vec3b>(y, x)[1],
                    (int)(*im).at<cv::Vec3b>(y, x)[2]);
        } else if (im->type() == CV_32F) {
            printf("%d %d: %f\n",
                   x, y,
                   im->at<float>(y, x));
        }
    }
}
 
void imshow(const char *windowName, cv::Mat im, unsigned int x, unsigned int y){
 
    // Imshow
    if(!cvGetWindowHandle(windowName)){
        int windowFlags = CV_GUI_EXPANDED | CV_WINDOW_KEEPRATIO;
        cv::namedWindow(windowName, windowFlags);
        cv::moveWindow(windowName, x, y);
    }
    cv::imshow(windowName, im);
}
 
void imagesc(const char *windowName, cv::Mat im){
 
    // Imshow with scaled image
 
 
}
 
cv::Mat histimage(cv::Mat histogram){
 
    cv::Mat histImage(512, 640, CV_8UC3, cv::Scalar(0));
 
    // Normalize the result to [ 2, histImage.rows-2 ]
    cv::normalize(histogram, histogram, 2, histImage.rows-2, cv::NORM_MINMAX, -1, cv::Mat());
 
    float bin_w = (float)histImage.cols/(float)histogram.rows;
 
    // Draw main histogram
    for(int i = 1; i < histogram.rows-10; i++){
        cv::line(histImage, cv::Point( bin_w*(i-1), histImage.rows - cvRound(histogram.at<float>(i-1)) ),
                 cv::Point( bin_w*(i), histImage.rows - cvRound(histogram.at<float>(i)) ),
                 cv::Scalar(255, 255, 255), 2, 4);
    }
 
    // Draw red max
    for(int i = histogram.rows-10; i < histogram.rows; i++){
        cv::line(histImage, cv::Point( bin_w*(i-1), histImage.rows - cvRound(histogram.at<float>(i-1)) ),
                 cv::Point( bin_w*(i), histImage.rows - cvRound(histogram.at<float>(i)) ),
                 cv::Scalar(0, 0, 255), 2, 4);
    }
 
    return histImage;
}
 
void hist(const char *windowName, cv::Mat histogram, unsigned int x, unsigned int y){
 
    // Display
    imshow(windowName, histimage(histogram), x, y);
    cv::Point(1,2);
}
 
 
void writeMat(cv::Mat const& mat, const char* filename, const char* varName, bool bgr2rgb){
    /*!
         *  \author Philip G. Lee <rocketman768@gmail.com>
         *  Write \b mat into \b filename
         *  in uncompressed .mat format (Level 5 MATLAB) for Matlab.
         *  The variable name in matlab will be \b varName. If
         *  \b bgr2rgb is true and there are 3 channels, swaps 1st and 3rd
         *  channels in the output. This is needed because OpenCV matrices
         *  are bgr, while Matlab is rgb. This has been tested to work with
         *  3-channel single-precision floating point matrices, and I hope
         *  it works on other types/channels, but not exactly sure.
         *  Documentation at <http://www.mathworks.com/help/pdf_doc/matlab/matfile_format.pdf>
         */
    int textLen = 116;
    char* text;
    int subsysOffsetLen = 8;
    char* subsysOffset;
    int verLen = 2;
    char* ver;
    char flags;
    int bytes;
    int padBytes;
    int bytesPerElement;
    int i,j,k,k2;
    bool doBgrSwap;
    char mxClass;
    int32_t miClass;
    uchar const* rowPtr;
    uint32_t tmp32;
    float tmp;
    FILE* fp;
 
    // Matlab constants.
    const uint16_t MI = 0x4d49; // Contains "MI" in ascii.
    const int32_t miINT8 = 1;
    const int32_t miUINT8 = 2;
    const int32_t miINT16 = 3;
    const int32_t miUINT16 = 4;
    const int32_t miINT32 = 5;
    const int32_t miUINT32 = 6;
    const int32_t miSINGLE = 7;
    const int32_t miDOUBLE = 9;
    const int32_t miMATRIX = 14;
    const char mxDOUBLE_CLASS = 6;
    const char mxSINGLE_CLASS = 7;
    const char mxINT8_CLASS = 8;
    const char mxUINT8_CLASS = 9;
    const char mxINT16_CLASS = 10;
    const char mxUINT16_CLASS = 11;
    const char mxINT32_CLASS = 12;
    const char mxUINT32_CLASS = 13;
    const uint64_t zero = 0; // Used for padding.
 
    fp = fopen( filename, "wb" );
 
    if( fp == 0 )
        return;
 
    const int rows = mat.rows;
    const int cols = mat.cols;
    const int chans = mat.channels();
 
    doBgrSwap = (chans==3) && bgr2rgb;
 
    // I hope this mapping is right :-/
    switch( mat.depth() ){
    case CV_8U:
        mxClass = mxUINT8_CLASS;
        miClass = miUINT8;
        bytesPerElement = 1;
        break;
    case CV_8S:
        mxClass = mxINT8_CLASS;
        miClass = miINT8;
        bytesPerElement = 1;
        break;
    case CV_16U:
        mxClass = mxUINT16_CLASS;
        miClass = miUINT16;
        bytesPerElement = 2;
        break;
    case CV_16S:
        mxClass = mxINT16_CLASS;
        miClass = miINT16;
        bytesPerElement = 2;
        break;
    case CV_32S:
        mxClass = mxINT32_CLASS;
        miClass = miINT32;
        bytesPerElement = 4;
        break;
    case CV_32F:
        mxClass = mxSINGLE_CLASS;
        miClass = miSINGLE;
        bytesPerElement = 4;
        break;
    case CV_64F:
        mxClass = mxDOUBLE_CLASS;
        miClass = miDOUBLE;
        bytesPerElement = 8;
        break;
    default:
        return;
    }
 
    //==================Mat-file header (128 bytes, page 1-5)==================
    text = new char[textLen]; // Human-readable text.
    memset( text, ' ', textLen );
    text[textLen-1] = '\0';
    const char* t = "MATLAB 5.0 MAT-file, Platform: PCWIN";
    memcpy( text, t, strlen(t) );
 
    subsysOffset = new char[subsysOffsetLen]; // Zeros for us.
    memset( subsysOffset, 0x00, subsysOffsetLen );
    ver = new char[verLen];
    ver[0] = 0x00;
    ver[1] = 0x01;
 
    fwrite( text, 1, textLen, fp );
    fwrite( subsysOffset, 1, subsysOffsetLen, fp );
    fwrite( ver, 1, verLen, fp );
    // Endian indicator. MI will show up as "MI" on big-endian
    // systems and "IM" on little-endian systems.
    fwrite( &MI, 2, 1, fp );
    //+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 
    //===================Data element tag (8 bytes, page 1-8)==================
    bytes = 16 + 24 + (8 + strlen(varName) + (8-(strlen(varName)%8))%8)
            + (8 + rows*cols*chans*bytesPerElement);
    fwrite( &miMATRIX, 4, 1, fp ); // Data type.
    fwrite( &bytes, 4, 1, fp); // Data size in bytes.
    //+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 
    //====================Array flags (16 bytes, page 1-15)====================
    bytes = 8;
    fwrite( &miUINT32, 4, 1, fp );
    fwrite( &bytes, 4, 1, fp );
    flags = 0x00; // Complex, logical, and global flags all off.
 
    tmp32 = 0;
    tmp32 = (flags << 8 ) | (mxClass);
    fwrite( &tmp32, 4, 1, fp );
 
    fwrite( &zero, 4, 1, fp ); // Padding to 64-bit boundary.
    //+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 
    //===============Dimensions subelement (24 bytes, page 1-17)===============
    bytes = 12;
    fwrite( &miINT32, 4, 1, fp );
    fwrite( &bytes, 4, 1, fp );
 
    fwrite( &rows, 4, 1, fp );
    fwrite( &cols, 4, 1, fp );
    fwrite( &chans, 4, 1, fp );
    fwrite( &zero, 4, 1, fp ); // Padding to 64-bit boundary.
    //+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 
    //==Array name (8 + strlen(varName) + (8-(strlen(varName)%8))%8 bytes, page 1-17)==
    bytes = strlen(varName);
 
    fwrite( &miINT8, 4, 1, fp );
    fwrite( &bytes, 4, 1, fp );
    fwrite( varName, 1, bytes, fp );
 
    // Pad to nearest 64-bit boundary.
    padBytes = (8-(bytes%8))%8;
    fwrite( &zero, 1, padBytes, fp );
    //+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 
    //====Matrix data (rows*cols*chans*bytesPerElement+8 bytes, page 1-20)=====
    bytes = rows*cols*chans*bytesPerElement;
    fwrite( &miClass, 4, 1, fp );
    fwrite( &bytes, 4, 1, fp );
 
    for( k = 0; k < chans; ++k )
    {
        if( doBgrSwap )
        {
            k2 = (k==0)? 2 : ((k==2)? 0 : 1);
        }
        else
            k2 = k;
 
        for( j = 0; j < cols; ++j )
        {
            for( i = 0; i < rows; ++i )
            {
                rowPtr = mat.data + mat.step*i;
                fwrite( rowPtr + (chans*j + k2)*bytesPerElement, bytesPerElement, 1, fp );
            }
        }
    }
 
    // Pad to 64-bit boundary.
    padBytes = (8-(bytes%8))%8;
    fwrite( &zero, 1, padBytes, fp );
    //+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 
    fclose(fp);
    delete[] text;
    delete[] subsysOffset;
    delete[] ver;
}
 
 
 
 
 
}
 

Rev 119	Rev 120
1	`#include "cvtools.h"`	1	`#include "cvtools.h"`
2		2
3	`#ifdef _WIN32`	3	`#ifdef _WIN32`
4	`#include <cstdint>`	4	`#include <cstdint>`
5	`#endif`	5	`#endif`
6		6
7	`#include <stdio.h>`	7	`#include <stdio.h>`
8		8
9	`namespace cvtools{`	9	`namespace cvtools{`
10		10
11	`// Create a mask for feature matching which disallows matches not satisfying the epipolar constraint.`	11	`// Create a mask for feature matching which disallows matches not satisfying the epipolar constraint.`
12	`// Works like cv::windowedMatchingMask in conjunction with cv::BFMatcher::match().`	12	`// Works like cv::windowedMatchingMask in conjunction with cv::BFMatcher::match().`
13	`// F is the fundamental matrix.`	13	`// F is the fundamental matrix.`
14	`// maxD is the maximum point to line distance permissible.`	14	`// maxD is the maximum point to line distance permissible.`
15	`cv::Mat epipolarMatchingMask(const cv::vector<cv::KeyPoint> &keypoints1, const cv::vector<cv::KeyPoint> &keypoints2, cv::Matx33f F, float maxD){`	15	`cv::Mat epipolarMatchingMask(const cv::vector<cv::KeyPoint> &keypoints1, const cv::vector<cv::KeyPoint> &keypoints2, cv::Matx33f F, float maxD){`
16		16
17	`if(keypoints1.empty() \|\| keypoints2.empty())`	17	`if(keypoints1.empty() \|\| keypoints2.empty())`
18	`return cv::Mat();`	18	`return cv::Mat();`
19		19
20	`int n1 = (int)keypoints1.size(), n2 = (int)keypoints2.size();`	20	`int n1 = (int)keypoints1.size(), n2 = (int)keypoints2.size();`
21	`cv::Mat mask(n1, n2, CV_8UC1);`	21	`cv::Mat mask(n1, n2, CV_8UC1);`
22		22
23	`// Point to line distance`	23	`// Point to line distance`
24	`// for( int i = 0; i < n1; i++ ){`	24	`// for( int i = 0; i < n1; i++ ){`
25	`// cv::Vec3f p1 = cv::Vec3f(keypoints1[i].pt.x, keypoints1[i].pt.y, 1.0);`	25	`// cv::Vec3f p1 = cv::Vec3f(keypoints1[i].pt.x, keypoints1[i].pt.y, 1.0);`
26	`// // Epipolar line defined by p1`	26	`// // Epipolar line defined by p1`
27	`// cv::Vec3f l = F*p1;`	27	`// cv::Vec3f l = F*p1;`
28	`// l /= sqrt(l(0)l(0) + l(1)l(1));`	28	`// l /= sqrt(l(0)l(0) + l(1)l(1));`
29	`// for( int j = 0; j < n2; j++ ){`	29	`// for( int j = 0; j < n2; j++ ){`
30	`// cv::Vec3f p2 = cv::Vec3f(keypoints2[j].pt.x, keypoints2[j].pt.y, 1.0);`	30	`// cv::Vec3f p2 = cv::Vec3f(keypoints2[j].pt.x, keypoints2[j].pt.y, 1.0);`
31	`// // Signed distance to line`	31	`// // Signed distance to line`
32	`// float d = l.dot(p2);`	32	`// float d = l.dot(p2);`
33	`// mask.at<uchar>(i, j) = fabs(d) < maxD;`	33	`// mask.at<uchar>(i, j) = fabs(d) < maxD;`
34	`// }`	34	`// }`
35	`// }`	35	`// }`
36		36
37	`// Symmetric epipolar distance`	37	`// Symmetric epipolar distance`
38	`std::vector<cv::Point2f> q1, q2;`	38	`std::vector<cv::Point2f> q1, q2;`
39	`cvtools::keypointsToPoints(keypoints1, q1);`	39	`cvtools::keypointsToPoints(keypoints1, q1);`
40	`cvtools::keypointsToPoints(keypoints2, q2);`	40	`cvtools::keypointsToPoints(keypoints2, q2);`
41	`std::vector<cv::Point3f> l1, l2;`	41	`std::vector<cv::Point3f> l1, l2;`
42	`cv::computeCorrespondEpilines(q1, 1, F, l1);`	42	`cv::computeCorrespondEpilines(q1, 1, F, l1);`
43	`cv::computeCorrespondEpilines(q2, 2, F, l2);`	43	`cv::computeCorrespondEpilines(q2, 2, F, l2);`
44		44
45	`for( int i = 0; i < n1; i++ ){`	45	`for( int i = 0; i < n1; i++ ){`
46	`cv::Vec3f p1 = cv::Vec3f(q1[i].x, q1[i].y, 1.0);`	46	`cv::Vec3f p1 = cv::Vec3f(q1[i].x, q1[i].y, 1.0);`
47	`for( int j = 0; j < n2; j++ ){`	47	`for( int j = 0; j < n2; j++ ){`
48	`cv::Vec3f p2 = cv::Vec3f(q2[j].x, q2[j].y, 1.0);`	48	`cv::Vec3f p2 = cv::Vec3f(q2[j].x, q2[j].y, 1.0);`
49	`float d12 = l1[i].dot(p2);`	49	`float d12 = l1[i].dot(p2);`
50	`float d21 = l2[j].dot(p1);`	50	`float d21 = l2[j].dot(p1);`
51	`float d = d12d12 + d21d21;`	51	`float d = d12d12 + d21d21;`
52	`mask.at<uchar>(i, j) = d < maxD;`	52	`mask.at<uchar>(i, j) = d < maxD;`
53	`}`	53	`}`
54	`}`	54	`}`
55		55
56	`// // Sampson Error (H&Z, p. 287) (expensive...)`	56	`// // Sampson Error (H&Z, p. 287) (expensive...)`
57	`// std::vector<cv::Point2f> q1, q2;`	57	`// std::vector<cv::Point2f> q1, q2;`
58	`// cvtools::keypointsToPoints(keypoints1, q1);`	58	`// cvtools::keypointsToPoints(keypoints1, q1);`
59	`// cvtools::keypointsToPoints(keypoints2, q2);`	59	`// cvtools::keypointsToPoints(keypoints2, q2);`
60	`// std::vector<cv::Point3f> p1, p2;`	60	`// std::vector<cv::Point3f> p1, p2;`
61	`// cv::convertPointsToHomogeneous(q1, p1);`	61	`// cv::convertPointsToHomogeneous(q1, p1);`
62	`// cv::convertPointsToHomogeneous(q2, p2);`	62	`// cv::convertPointsToHomogeneous(q2, p2);`
63	`// cv::Mat Fp1Mat = cv::Mat(F)*cv::Mat(p1).reshape(1).t();`	63	`// cv::Mat Fp1Mat = cv::Mat(F)*cv::Mat(p1).reshape(1).t();`
64	`// cv::Mat FTp2Mat = cv::Mat(F.t())*cv::Mat(p2).reshape(1).t();`	64	`// cv::Mat FTp2Mat = cv::Mat(F.t())*cv::Mat(p2).reshape(1).t();`
65	`// for( int i = 0; i < n1; i++ ){`	65	`// for( int i = 0; i < n1; i++ ){`
66	`// cv::Vec3f Fp1 = Fp1Mat.col(i);`	66	`// cv::Vec3f Fp1 = Fp1Mat.col(i);`
67	`// for( int j = 0; j < n2; j++ ){`	67	`// for( int j = 0; j < n2; j++ ){`
68	`// cv::Vec3f FTp2 = FTp2Mat.col(j);`	68	`// cv::Vec3f FTp2 = FTp2Mat.col(j);`
69	`// cv::Matx<float,1,1> p2TFp1 = cv::Matx31f(p2[j]).t()Fcv::Matx31f(p1[i]);`	69	`// cv::Matx<float,1,1> p2TFp1 = cv::Matx31f(p2[j]).t()Fcv::Matx31f(p1[i]);`
70	`// float d = p2TFp1(0)p2TFp1(0) / (Fp1(0)Fp1(0) + Fp1(1)Fp1(1) + FTp2(0)FTp2(0) + FTp2(1)*FTp2(1));`	70	`// float d = p2TFp1(0)p2TFp1(0) / (Fp1(0)Fp1(0) + Fp1(1)Fp1(1) + FTp2(0)FTp2(0) + FTp2(1)*FTp2(1));`
71	`// mask.at<uchar>(i, j) = d < maxD;`	71	`// mask.at<uchar>(i, j) = d < maxD;`
72	`// }`	72	`// }`
73	`// }`	73	`// }`
74		74
75	`return mask;`	75	`return mask;`
76	`}`	76	`}`
77		77
78		78
79	`// Remove correspondences which have a distance metric above thresh.`	79	`// Remove correspondences which have a distance metric above thresh.`
80	`void matchingThreshold(const std::vector<cv::DMatch> &matchesIn, std::vector<cv::DMatch> &matchesOut, float thresh){`	80	`void matchingThreshold(const std::vector<cv::DMatch> &matchesIn, std::vector<cv::DMatch> &matchesOut, float thresh){`
81		81
82	`int nMatches = matchesIn.size();`	82	`int nMatches = matchesIn.size();`
83	`matchesOut.clear();`	83	`matchesOut.clear();`
84	`matchesOut.reserve(nMatches);`	84	`matchesOut.reserve(nMatches);`
85		85
86	`for(int i=0; i<nMatches; i++){`	86	`for(int i=0; i<nMatches; i++){`
87	`if(matchesIn[i].distance < thresh)`	87	`if(matchesIn[i].distance < thresh)`
88	`matchesOut.push_back(matchesIn[i]);`	88	`matchesOut.push_back(matchesIn[i]);`
89	`}`	89	`}`
90		90
91	`}`	91	`}`
92		92
93	`// Lightly modified OpenCV function which accepts a line width argument`	93	`// Lightly modified OpenCV function which accepts a line width argument`
94	`void drawChessboardCorners(cv::InputOutputArray _image, cv::Size patternSize, cv::InputArray _corners, bool patternWasFound, int line_width){`	94	`void drawChessboardCorners(cv::InputOutputArray _image, cv::Size patternSize, cv::InputArray _corners, bool patternWasFound, int line_width){`
95	`cv::Mat corners = _corners.getMat();`	95	`cv::Mat corners = _corners.getMat();`
96	`if( corners.empty() )`	96	`if( corners.empty() )`
97	`return;`	97	`return;`
98	`cv::Mat image = _image.getMat(); CvMat c_image = _image.getMat();`	98	`cv::Mat image = _image.getMat(); CvMat c_image = _image.getMat();`
99	`int nelems = corners.checkVector(2, CV_32F, true);`	99	`int nelems = corners.checkVector(2, CV_32F, true);`
100	`CV_Assert(nelems >= 0);`	100	`CV_Assert(nelems >= 0);`
101	`cvDrawChessboardCorners( &c_image, patternSize, (CvPoint2D32f*)corners.data,`	101	`cvDrawChessboardCorners( &c_image, patternSize, (CvPoint2D32f*)corners.data,`
102	`nelems, patternWasFound, line_width);`	102	`nelems, patternWasFound, line_width);`
103	`}`	103	`}`
104		104
-		105	`void rshift(cv::Mat& I, unsigned int shift){`
-		106
-		107	`int nRows = I.rows;`
-		108	`int nCols = I.cols;`
-		109
-		110	`if (I.isContinuous()){`
-		111	`nCols *= nRows;`
-		112	`nRows = 1;`
-		113	`}`
-		114
-		115	`int i,j;`
-		116	`unsigned short* p;`
-		117	`for( i = 0; i < nRows; ++i){`
-		118	`p = I.ptr<unsigned short>(i);`
-		119	`for ( j = 0; j < nCols; ++j){`
-		120	`p[j] = p[j]>>shift;`
-		121	`}`
-		122	`}`
-		123	`}`
-		124
105	`void cvDrawChessboardCorners(CvArr* _image, CvSize pattern_size, CvPoint2D32f* corners, int count, int found, int line_width){`	125	`void cvDrawChessboardCorners(CvArr* _image, CvSize pattern_size, CvPoint2D32f* corners, int count, int found, int line_width){`
106	`const int shift = 0;`	126	`const int shift = 0;`
107	`const int radius = 12;`	127	`const int radius = 12;`
108	`const int r = radius*(1 << shift);`	128	`const int r = radius*(1 << shift);`
109	`int i;`	129	`int i;`
110	`CvMat stub, *image;`	130	`CvMat stub, *image;`
111	`double scale = 1;`	131	`double scale = 1;`
112	`int type, cn, line_type;`	132	`int type, cn, line_type;`
113		133
114	`image = cvGetMat( _image, &stub );`	134	`image = cvGetMat( _image, &stub );`
115		135
116	`type = CV_MAT_TYPE(image->type);`	136	`type = CV_MAT_TYPE(image->type);`
117	`cn = CV_MAT_CN(type);`	137	`cn = CV_MAT_CN(type);`
118	`if( cn != 1 && cn != 3 && cn != 4 )`	138	`if( cn != 1 && cn != 3 && cn != 4 )`
119	`CV_Error( CV_StsUnsupportedFormat, "Number of channels must be 1, 3 or 4" );`	139	`CV_Error( CV_StsUnsupportedFormat, "Number of channels must be 1, 3 or 4" );`
120		140
121	`switch( CV_MAT_DEPTH(image->type) )`	141	`switch( CV_MAT_DEPTH(image->type) )`
122	`{`	142	`{`
123	`case CV_8U:`	143	`case CV_8U:`
124	`scale = 1;`	144	`scale = 1;`
125	`break;`	145	`break;`
126	`case CV_16U:`	146	`case CV_16U:`
127	`scale = 256;`	147	`scale = 256;`
128	`break;`	148	`break;`
129	`case CV_32F:`	149	`case CV_32F:`
130	`scale = 1./255;`	150	`scale = 1./255;`
131	`break;`	151	`break;`
132	`default:`	152	`default:`
133	`CV_Error( CV_StsUnsupportedFormat,`	153	`CV_Error( CV_StsUnsupportedFormat,`
134	`"Only 8-bit, 16-bit or floating-point 32-bit images are supported" );`	154	`"Only 8-bit, 16-bit or floating-point 32-bit images are supported" );`
135	`}`	155	`}`
136		156
137	`line_type = type == CV_8UC1 \|\| type == CV_8UC3 ? CV_AA : 8;`	157	`line_type = type == CV_8UC1 \|\| type == CV_8UC3 ? CV_AA : 8;`
138		158
139	`if( !found )`	159	`if( !found )`
140	`{`	160	`{`
141	`CvScalar color = {{0,0,255}};`	161	`CvScalar color = {{0,0,255}};`
142	`if( cn == 1 )`	162	`if( cn == 1 )`
143	`color = cvScalarAll(200);`	163	`color = cvScalarAll(200);`
144	`color.val[0] *= scale;`	164	`color.val[0] *= scale;`
145	`color.val[1] *= scale;`	165	`color.val[1] *= scale;`
146	`color.val[2] *= scale;`	166	`color.val[2] *= scale;`
147	`color.val[3] *= scale;`	167	`color.val[3] *= scale;`
148		168
149	`for( i = 0; i < count; i++ )`	169	`for( i = 0; i < count; i++ )`
150	`{`	170	`{`
151	`CvPoint pt;`	171	`CvPoint pt;`
152	`pt.x = cvRound(corners[i].x*(1 << shift));`	172	`pt.x = cvRound(corners[i].x*(1 << shift));`
153	`pt.y = cvRound(corners[i].y*(1 << shift));`	173	`pt.y = cvRound(corners[i].y*(1 << shift));`
154	`cvLine( image, cvPoint( pt.x - r, pt.y - r ),`	174	`cvLine( image, cvPoint( pt.x - r, pt.y - r ),`
155	`cvPoint( pt.x + r, pt.y + r ), color, line_width, line_type, shift );`	175	`cvPoint( pt.x + r, pt.y + r ), color, line_width, line_type, shift );`
156	`cvLine( image, cvPoint( pt.x - r, pt.y + r),`	176	`cvLine( image, cvPoint( pt.x - r, pt.y + r),`
157	`cvPoint( pt.x + r, pt.y - r), color, line_width, line_type, shift );`	177	`cvPoint( pt.x + r, pt.y - r), color, line_width, line_type, shift );`
158	`cvCircle( image, pt, r+(1<<shift), color, line_width, line_type, shift );`	178	`cvCircle( image, pt, r+(1<<shift), color, line_width, line_type, shift );`
159	`}`	179	`}`
160	`}`	180	`}`
161	`else`	181	`else`
162	`{`	182	`{`
163	`int x, y;`	183	`int x, y;`
164	`CvPoint prev_pt = {0, 0};`	184	`CvPoint prev_pt = {0, 0};`
165	`const int line_max = 7;`	185	`const int line_max = 7;`
166	`static const CvScalar line_colors[line_max] =`	186	`static const CvScalar line_colors[line_max] =`
167	`{`	187	`{`
168	`{{0,0,255}},`	188	`{{0,0,255}},`
169	`{{0,128,255}},`	189	`{{0,128,255}},`
170	`{{0,200,200}},`	190	`{{0,200,200}},`
171	`{{0,255,0}},`	191	`{{0,255,0}},`
172	`{{200,200,0}},`	192	`{{200,200,0}},`
173	`{{255,0,0}},`	193	`{{255,0,0}},`
174	`{{255,0,255}}`	194	`{{255,0,255}}`
175	`};`	195	`};`
176		196
177	`for( y = 0, i = 0; y < pattern_size.height; y++ )`	197	`for( y = 0, i = 0; y < pattern_size.height; y++ )`
178	`{`	198	`{`
179	`CvScalar color = line_colors[y % line_max];`	199	`CvScalar color = line_colors[y % line_max];`
180	`if( cn == 1 )`	200	`if( cn == 1 )`
181	`color = cvScalarAll(200);`	201	`color = cvScalarAll(200);`
182	`color.val[0] *= scale;`	202	`color.val[0] *= scale;`
183	`color.val[1] *= scale;`	203	`color.val[1] *= scale;`
184	`color.val[2] *= scale;`	204	`color.val[2] *= scale;`
185	`color.val[3] *= scale;`	205	`color.val[3] *= scale;`
186		206
187	`for( x = 0; x < pattern_size.width; x++, i++ )`	207	`for( x = 0; x < pattern_size.width; x++, i++ )`
188	`{`	208	`{`
189	`CvPoint pt;`	209	`CvPoint pt;`
190	`pt.x = cvRound(corners[i].x*(1 << shift));`	210	`pt.x = cvRound(corners[i].x*(1 << shift));`
191	`pt.y = cvRound(corners[i].y*(1 << shift));`	211	`pt.y = cvRound(corners[i].y*(1 << shift));`
192		212
193	`if( i != 0 )`	213	`if( i != 0 )`
194	`cvLine( image, prev_pt, pt, color, 1, line_type, shift );`	214	`cvLine( image, prev_pt, pt, color, 1, line_type, shift );`
195		215
196	`cvLine( image, cvPoint(pt.x - r, pt.y - r),`	216	`cvLine( image, cvPoint(pt.x - r, pt.y - r),`
197	`cvPoint(pt.x + r, pt.y + r), color, line_width, line_type, shift );`	217	`cvPoint(pt.x + r, pt.y + r), color, line_width, line_type, shift );`
198	`cvLine( image, cvPoint(pt.x - r, pt.y + r),`	218	`cvLine( image, cvPoint(pt.x - r, pt.y + r),`
199	`cvPoint(pt.x + r, pt.y - r), color, line_width, line_type, shift );`	219	`cvPoint(pt.x + r, pt.y - r), color, line_width, line_type, shift );`
200	`cvCircle( image, pt, r+(1<<shift), color, line_width, line_type, shift );`	220	`cvCircle( image, pt, r+(1<<shift), color, line_width, line_type, shift );`
201	`prev_pt = pt;`	221	`prev_pt = pt;`
202	`}`	222	`}`
203	`}`	223	`}`
204	`}`	224	`}`
205	`}`	225	`}`
206		226
207	`// Returns the result of mod(mat(x,y), moduli) for each matrix element`	227	`// Returns the result of mod(mat(x,y), moduli) for each matrix element`
208	`cv::Mat modulo(const cv::Mat &mat, float n){`	228	`cv::Mat modulo(const cv::Mat &mat, float n){`
209		229
210	`cv::Mat ret(mat.rows, mat.cols, mat.type());`	230	`cv::Mat ret(mat.rows, mat.cols, mat.type());`
211		231
212	`for(int row=0; row<ret.rows; row++){`	232	`for(int row=0; row<ret.rows; row++){`
213	`for(int col=0; col<ret.cols; col++){`	233	`for(int col=0; col<ret.cols; col++){`
214	`float val = mat.at<float>(row, col);`	234	`float val = mat.at<float>(row, col);`
215	`// note: std::fmod calculates the remainder, not arithmetic modulo`	235	`// note: std::fmod calculates the remainder, not arithmetic modulo`
216	`ret.at<float>(row, col) = val - n * std::floor(val / n);`	236	`ret.at<float>(row, col) = val - n * std::floor(val / n);`
217	`}`	237	`}`
218	`}`	238	`}`
219		239
220	`return ret;`	240	`return ret;`
221	`}`	241	`}`
222		242
223	`// Convert a 3xN matrix to a vector of Point3fs.`	243	`// Convert a 3xN matrix to a vector of Point3fs.`
224	`void matToPoints3f(const cv::Mat &mat, std::vector<cv::Point3f> &points){`	244	`void matToPoints3f(const cv::Mat &mat, std::vector<cv::Point3f> &points){`
225		245
226	`unsigned int nPoints = mat.cols;`	246	`unsigned int nPoints = mat.cols;`
227	`points.resize(nPoints);`	247	`points.resize(nPoints);`
228		248
229	`for(unsigned int i=0; i<nPoints; i++)`	249	`for(unsigned int i=0; i<nPoints; i++)`
230	`points[i] = cv::Point3f(mat.at<float>(0, i), mat.at<float>(1, i), mat.at<float>(2, i));`	250	`points[i] = cv::Point3f(mat.at<float>(0, i), mat.at<float>(1, i), mat.at<float>(2, i));`
231	`}`	251	`}`
232		252
233	`// Convert a (Dim+1)xN matrix of homogenous points to a DimxN matrix of points in non-homogenous coordinates.`	253	`// Convert a (Dim+1)xN matrix of homogenous points to a DimxN matrix of points in non-homogenous coordinates.`
234	`void convertMatFromHomogeneous(cv::Mat &src, cv::Mat &dst){`	254	`void convertMatFromHomogeneous(cv::Mat &src, cv::Mat &dst){`
235	`unsigned int N = src.cols;`	255	`unsigned int N = src.cols;`
236	`unsigned int Dim = src.rows-1;`	256	`unsigned int Dim = src.rows-1;`
237	`dst.create(Dim, N, src.type());`	257	`dst.create(Dim, N, src.type());`
238	`for(unsigned int i=0; i<N; i++){`	258	`for(unsigned int i=0; i<N; i++){`
239	`for(unsigned int j=0; j<Dim; j++)`	259	`for(unsigned int j=0; j<Dim; j++)`
240	`dst.at<float>(j,i) = src.at<float>(j,i)/src.at<float>(Dim,i);`	260	`dst.at<float>(j,i) = src.at<float>(j,i)/src.at<float>(Dim,i);`
241	`}`	261	`}`
242		262
243	`}`	263	`}`
244		264
245	`// Function to solve the hand-eye (or eye-in-hand) calibration problem.`	265	`// Function to solve the hand-eye (or eye-in-hand) calibration problem.`
246	`// Finds [Omega \| tau], to minimize \|\|[R_mark \| t_mark][Omega \| tau] - [Omega \| tau][R \| t]\|\|^2`	266	`// Finds [Omega \| tau], to minimize \|\|[R_mark \| t_mark][Omega \| tau] - [Omega \| tau][R \| t]\|\|^2`
247	`// Algorithm according to Tsai, Lenz, A new technique for fully autonomous and efficient 3d robotics hand-eye calibration`	267	`// Algorithm according to Tsai, Lenz, A new technique for fully autonomous and efficient 3d robotics hand-eye calibration`
248	`// DTU, 2014, Jakob Wilm`	268	`// DTU, 2014, Jakob Wilm`
249	`void handEyeCalibrationTsai(const std::vector<cv::Matx33f> R, const std::vector<cv::Vec3f> t, const std::vector<cv::Matx33f> R_mark, const std::vector<cv::Vec3f> t_mark, cv::Matx33f &Omega, cv::Vec3f &tau){`	269	`void handEyeCalibrationTsai(const std::vector<cv::Matx33f> R, const std::vector<cv::Vec3f> t, const std::vector<cv::Matx33f> R_mark, const std::vector<cv::Vec3f> t_mark, cv::Matx33f &Omega, cv::Vec3f &tau){`
250		270
251	`int N = R.size();`	271	`int N = R.size();`
252	`assert(N == R_mark.size());`	272	`assert(N == R_mark.size());`
253	`assert(N == t.size());`	273	`assert(N == t.size());`
254	`assert(N == t_mark.size());`	274	`assert(N == t_mark.size());`
255		275
256	`// construct equations for rotation`	276	`// construct equations for rotation`
257	`cv::Mat A(3*N, 3, CV_32F);`	277	`cv::Mat A(3*N, 3, CV_32F);`
258	`cv::Mat b(3*N, 1, CV_32F);`	278	`cv::Mat b(3*N, 1, CV_32F);`
259	`for(int i=0; i<N; i++){`	279	`for(int i=0; i<N; i++){`
260	`// angle axis representations`	280	`// angle axis representations`
261	`cv::Vec3f rot;`	281	`cv::Vec3f rot;`
262	`cv::Vec3f rot_mark;`	282	`cv::Vec3f rot_mark;`
263	`cv::Rodrigues(R[i], rot);`	283	`cv::Rodrigues(R[i], rot);`
264	`cv::Rodrigues(R_mark[i], rot_mark);`	284	`cv::Rodrigues(R_mark[i], rot_mark);`
265		285
266	`cv::Vec3f P = 2.0sin(cv::norm(rot)/2.0)cv::normalize(rot);`	286	`cv::Vec3f P = 2.0sin(cv::norm(rot)/2.0)cv::normalize(rot);`
267	`//std::cout << "P: " << std::endl << P << std::endl;`	287	`//std::cout << "P: " << std::endl << P << std::endl;`
268	`cv::Vec3f P_mark = 2.0sin(cv::norm(rot_mark)/2.0)cv::normalize(rot_mark);`	288	`cv::Vec3f P_mark = 2.0sin(cv::norm(rot_mark)/2.0)cv::normalize(rot_mark);`
269	`//std::cout << "P_mark: " << std::endl << P_mark << std::endl;`	289	`//std::cout << "P_mark: " << std::endl << P_mark << std::endl;`
270	`cv::Vec3f sum = P+P_mark;`	290	`cv::Vec3f sum = P+P_mark;`
271	`cv::Mat crossProduct = (cv::Mat_<float>(3,3) << 0.0, -sum(2), sum(1), sum(2), 0.0, -sum(0), -sum(1), sum(0), 0.0);`	291	`cv::Mat crossProduct = (cv::Mat_<float>(3,3) << 0.0, -sum(2), sum(1), sum(2), 0.0, -sum(0), -sum(1), sum(0), 0.0);`
272	`//std::cout << "crossProduct: " << std::endl << crossProduct << std::endl;`	292	`//std::cout << "crossProduct: " << std::endl << crossProduct << std::endl;`
273	`crossProduct.copyTo(A.rowRange(i3, i3+3));`	293	`crossProduct.copyTo(A.rowRange(i3, i3+3));`
274		294
275	`cv::Mat(P-P_mark).copyTo(b.rowRange(i3, i3+3));`	295	`cv::Mat(P-P_mark).copyTo(b.rowRange(i3, i3+3));`
276	`}`	296	`}`
277		297
278	`// solve for rotation`	298	`// solve for rotation`
279	`cv::Vec3f P_prime;`	299	`cv::Vec3f P_prime;`
280	`cv::solve(A, b, P_prime, cv::DECOMP_SVD);`	300	`cv::solve(A, b, P_prime, cv::DECOMP_SVD);`
281	`cv::Vec3f P = 2.0P_prime/(cv::sqrt(1.0 + cv::norm(P_prime)cv::norm(P_prime)));`	301	`cv::Vec3f P = 2.0P_prime/(cv::sqrt(1.0 + cv::norm(P_prime)cv::norm(P_prime)));`
282	`float nP = cv::norm(P);`	302	`float nP = cv::norm(P);`
283	`cv::Mat crossProduct = (cv::Mat_<float>(3,3) << 0.0, -P(2), P(1), P(2), 0.0, -P(0), -P(1), P(0), 0.0);`	303	`cv::Mat crossProduct = (cv::Mat_<float>(3,3) << 0.0, -P(2), P(1), P(2), 0.0, -P(0), -P(1), P(0), 0.0);`
284	`cv::Mat OmegaMat = (1.0-nPnP/2.0)cv::Mat::eye(3,3,CV_32F) + 0.5(cv::Mat(P)cv::Mat(P).t() + cv::sqrt(4.0 - nPnP)crossProduct);`	304	`cv::Mat OmegaMat = (1.0-nPnP/2.0)cv::Mat::eye(3,3,CV_32F) + 0.5(cv::Mat(P)cv::Mat(P).t() + cv::sqrt(4.0 - nPnP)crossProduct);`
285	`Omega = cv::Matx33f(OmegaMat);`	305	`Omega = cv::Matx33f(OmegaMat);`
286		306
287	`// construct equations for translation`	307	`// construct equations for translation`
288	`A.setTo(0.0);`	308	`A.setTo(0.0);`
289	`b.setTo(0.0);`	309	`b.setTo(0.0);`
290	`for(int i=0; i<N; i++){`	310	`for(int i=0; i<N; i++){`
291		311
292	`cv::Mat diff = cv::Mat(R_mark[i]) - cv::Mat::eye(3, 3, CV_32F);`	312	`cv::Mat diff = cv::Mat(R_mark[i]) - cv::Mat::eye(3, 3, CV_32F);`
293	`diff.copyTo(A.rowRange(i3, i3+3));`	313	`diff.copyTo(A.rowRange(i3, i3+3));`
294		314
295	`cv::Mat diff_mark = cv::Mat(Omega*t[i] - t_mark[i]);`	315	`cv::Mat diff_mark = cv::Mat(Omega*t[i] - t_mark[i]);`
296	`diff_mark.copyTo(b.rowRange(i3, i3+3));`	316	`diff_mark.copyTo(b.rowRange(i3, i3+3));`
297	`}`	317	`}`
298		318
299	`// solve for translation`	319	`// solve for translation`
300	`cv::solve(A, b, tau, cv::DECOMP_SVD);`	320	`cv::solve(A, b, tau, cv::DECOMP_SVD);`
301		321
302	`cv::Mat err_tau = b - (A*cv::Mat(tau));`	322	`cv::Mat err_tau = b - (A*cv::Mat(tau));`
303	`std::cout << err_tau << std::endl;`	323	`std::cout << err_tau << std::endl;`
304	`}`	324	`}`
305		325
306	`// Function to solve for the rotation axis from sets of 3D point coordinates of flat pattern feature points`	326	`// Function to solve for the rotation axis from sets of 3D point coordinates of flat pattern feature points`
307	`// Algorithm according to Chen et al., Rotation axis calibration of a turntable using constrained global optimization, Optik 2014`	327	`// Algorithm according to Chen et al., Rotation axis calibration of a turntable using constrained global optimization, Optik 2014`
308	`// DTU, 2014, Jakob Wilm`	328	`// DTU, 2014, Jakob Wilm`
309	`void rotationAxisCalibration(const std::vector< std::vector<cv::Point3f> > Qcam, const std::vector<cv::Point3f> Qobj, cv::Vec3f &axis, cv::Vec3f &point){`	329	`void rotationAxisCalibration(const std::vector< std::vector<cv::Point3f> > Qcam, const std::vector<cv::Point3f> Qobj, cv::Vec3f &axis, cv::Vec3f &point){`
310		330
311	`// number of frames (points on each arch)`	331	`// number of frames (points on each arch)`
312	`int l = Qcam.size();`	332	`int l = Qcam.size();`
313		333
314	`// number of points in each frame`	334	`// number of points in each frame`
315	`int mn = Qobj.size();`	335	`int mn = Qobj.size();`
316		336
317	`assert(mn == Qcam[0].size());`	337	`assert(mn == Qcam[0].size());`
318		338
319	`// construct matrix for axis determination`	339	`// construct matrix for axis determination`
320	`cv::Mat M(6, 6, CV_32F, cv::Scalar(0));`	340	`cv::Mat M(6, 6, CV_32F, cv::Scalar(0));`
321		341
322	`for(int k=0; k<l; k++){`	342	`for(int k=0; k<l; k++){`
323	`for(int idx=0; idx<mn; idx++){`	343	`for(int idx=0; idx<mn; idx++){`
324		344
325	`// float i = Qobj[idx].x+4;`	345	`// float i = Qobj[idx].x+4;`
326	`// float j = Qobj[idx].y+4;`	346	`// float j = Qobj[idx].y+4;`
327	`float i = Qobj[idx].x;`	347	`float i = Qobj[idx].x;`
328	`float j = Qobj[idx].y;`	348	`float j = Qobj[idx].y;`
329		349
330	`float x = Qcam[k][idx].x;`	350	`float x = Qcam[k][idx].x;`
331	`float y = Qcam[k][idx].y;`	351	`float y = Qcam[k][idx].y;`
332	`float z = Qcam[k][idx].z;`	352	`float z = Qcam[k][idx].z;`
333		353
334	`M += (cv::Mat_<float>(6,6) << xx, xy, xz, x, ix, j*x,`	354	`M += (cv::Mat_<float>(6,6) << xx, xy, xz, x, ix, j*x,`
335	`0, yy, yz, y, iy, jy,`	355	`0, yy, yz, y, iy, jy,`
336	`0, 0, zz, z, iz, j*z,`	356	`0, 0, zz, z, iz, j*z,`
337	`0, 0, 0, 1, i, j,`	357	`0, 0, 0, 1, i, j,`
338	`0, 0, 0, 0, ii, ij,`	358	`0, 0, 0, 0, ii, ij,`
339	`0, 0, 0, 0, 0, j*j);`	359	`0, 0, 0, 0, 0, j*j);`
340		360
341	`}`	361	`}`
342	`}`	362	`}`
343		363
344	`cv::completeSymm(M, false);`	364	`cv::completeSymm(M, false);`
345		365
346	`// solve for axis`	366	`// solve for axis`
347	`std::vector<float> lambda;`	367	`std::vector<float> lambda;`
348	`cv::Mat u;`	368	`cv::Mat u;`
349	`cv::eigen(M, lambda, u);`	369	`cv::eigen(M, lambda, u);`
350		370
351	`float minLambda = abs(lambda[0]);`	371	`float minLambda = abs(lambda[0]);`
352	`int idx = 0;`	372	`int idx = 0;`
353	`for(int i=1; i<lambda.size(); i++){`	373	`for(int i=1; i<lambda.size(); i++){`
354	`if(abs(lambda[i]) < minLambda){`	374	`if(abs(lambda[i]) < minLambda){`
355	`minLambda = lambda[i];`	375	`minLambda = lambda[i];`
356	`idx = i;`	376	`idx = i;`
357	`}`	377	`}`
358	`}`	378	`}`
359		379
360	`axis = u.row(idx).colRange(0, 3);`	380	`axis = u.row(idx).colRange(0, 3);`
361	`axis = cv::normalize(axis);`	381	`axis = cv::normalize(axis);`
362		382
363	`float nx = u.at<float>(idx, 0);`	383	`float nx = u.at<float>(idx, 0);`
364	`float ny = u.at<float>(idx, 1);`	384	`float ny = u.at<float>(idx, 1);`
365	`float nz = u.at<float>(idx, 2);`	385	`float nz = u.at<float>(idx, 2);`
366	`float d = u.at<float>(idx, 3);`	386	`float d = u.at<float>(idx, 3);`
367	`float dh = u.at<float>(idx, 4);`	387	`float dh = u.at<float>(idx, 4);`
368	`float dv = u.at<float>(idx, 5);`	388	`float dv = u.at<float>(idx, 5);`
369		389
370	`// // Paper version: c is initially eliminated`	390	`// // Paper version: c is initially eliminated`
371	`// cv::Mat A(l*mn, mn+2, CV_32F, cv::Scalar(0.0));`	391	`// cv::Mat A(l*mn, mn+2, CV_32F, cv::Scalar(0.0));`
372	`// cv::Mat bb(l*mn, 1, CV_32F);`	392	`// cv::Mat bb(l*mn, 1, CV_32F);`
373		393
374	`// for(int k=0; k<l; k++){`	394	`// for(int k=0; k<l; k++){`
375	`// for(int idx=0; idx<mn; idx++){`	395	`// for(int idx=0; idx<mn; idx++){`
376		396
377	`// float i = Qobj[idx].x;`	397	`// float i = Qobj[idx].x;`
378	`// float j = Qobj[idx].y;`	398	`// float j = Qobj[idx].y;`
379		399
380	`// float x = Qcam[k][idx].x;`	400	`// float x = Qcam[k][idx].x;`
381	`// float y = Qcam[k][idx].y;`	401	`// float y = Qcam[k][idx].y;`
382	`// float z = Qcam[k][idx].z;`	402	`// float z = Qcam[k][idx].z;`
383		403
384	`// float f = xx + yy + zz + (2xnx + 2yny + 2znz)(idh + jdv);`	404	`// float f = xx + yy + zz + (2xnx + 2yny + 2znz)(idh + jdv);`
385		405
386	`// int row = k*mn+idx;`	406	`// int row = k*mn+idx;`
387	`// A.at<float>(row, 0) = 2x - (2z*nx)/nz;`	407	`// A.at<float>(row, 0) = 2x - (2z*nx)/nz;`
388	`// A.at<float>(row, 1) = 2y - (2z*ny)/nz;`	408	`// A.at<float>(row, 1) = 2y - (2z*ny)/nz;`
389	`// A.at<float>(row, idx+2) = 1.0;`	409	`// A.at<float>(row, idx+2) = 1.0;`
390		410
391	`// bb.at<float>(row, 0) = f + (2zd)/nz;`	411	`// bb.at<float>(row, 0) = f + (2zd)/nz;`
392	`// }`	412	`// }`
393	`// }`	413	`// }`
394		414
395	`// // solve for point`	415	`// // solve for point`
396	`// cv::Mat abe;`	416	`// cv::Mat abe;`
397	`// cv::solve(A, bb, abe, cv::DECOMP_SVD);`	417	`// cv::solve(A, bb, abe, cv::DECOMP_SVD);`
398		418
399	`// float a = abe.at<float>(0, 0);`	419	`// float a = abe.at<float>(0, 0);`
400	`// float b = abe.at<float>(1, 0);`	420	`// float b = abe.at<float>(1, 0);`
401	`// float c = -(nxa+nyb+d)/nz;`	421	`// float c = -(nxa+nyb+d)/nz;`
402		422
403	`// Our version: solve simultanously for a,b,c`	423	`// Our version: solve simultanously for a,b,c`
404	`cv::Mat A(l*mn, mn+3, CV_32F, cv::Scalar(0.0));`	424	`cv::Mat A(l*mn, mn+3, CV_32F, cv::Scalar(0.0));`
405	`cv::Mat bb(l*mn, 1, CV_32F);`	425	`cv::Mat bb(l*mn, 1, CV_32F);`
406		426
407	`for(int k=0; k<l; k++){`	427	`for(int k=0; k<l; k++){`
408	`for(int idx=0; idx<mn; idx++){`	428	`for(int idx=0; idx<mn; idx++){`
409		429
410	`float i = Qobj[idx].x;`	430	`float i = Qobj[idx].x;`
411	`float j = Qobj[idx].y;`	431	`float j = Qobj[idx].y;`
412		432
413	`float x = Qcam[k][idx].x;`	433	`float x = Qcam[k][idx].x;`
414	`float y = Qcam[k][idx].y;`	434	`float y = Qcam[k][idx].y;`
415	`float z = Qcam[k][idx].z;`	435	`float z = Qcam[k][idx].z;`
416		436
417	`float f = xx + yy + zz + (2xnx + 2yny + 2znz)(idh + jdv);`	437	`float f = xx + yy + zz + (2xnx + 2yny + 2znz)(idh + jdv);`
418		438
419	`int row = k*mn+idx;`	439	`int row = k*mn+idx;`
420	`A.at<float>(row, 0) = 2*x;`	440	`A.at<float>(row, 0) = 2*x;`
421	`A.at<float>(row, 1) = 2*y;`	441	`A.at<float>(row, 1) = 2*y;`
422	`A.at<float>(row, 2) = 2*z;`	442	`A.at<float>(row, 2) = 2*z;`
423	`A.at<float>(row, idx+3) = 1.0;`	443	`A.at<float>(row, idx+3) = 1.0;`
424		444
425	`bb.at<float>(row, 0) = f;`	445	`bb.at<float>(row, 0) = f;`
426	`}`	446	`}`
427	`}`	447	`}`
428		448
429	`// solve for point`	449	`// solve for point`
430	`cv::Mat abe;`	450	`cv::Mat abe;`
431	`cv::solve(A, bb, abe, cv::DECOMP_SVD);`	451	`cv::solve(A, bb, abe, cv::DECOMP_SVD);`
432		452
433	`float a = abe.at<float>(0, 0);`	453	`float a = abe.at<float>(0, 0);`
434	`float b = abe.at<float>(1, 0);`	454	`float b = abe.at<float>(1, 0);`
435	`float c = abe.at<float>(2, 0);`	455	`float c = abe.at<float>(2, 0);`
436		456
437	`point[0] = a;`	457	`point[0] = a;`
438	`point[1] = b;`	458	`point[1] = b;`
439	`point[2] = c;`	459	`point[2] = c;`
440		460
441	`}`	461	`}`
442		462
443	`// Function to fit two sets of corresponding pose data.`	463	`// Function to fit two sets of corresponding pose data.`
444	`// Finds [Omega \| tau], to minimize \|\|[R_mark \| t_mark] - [Omega \| tau][R \| t]\|\|^2`	464	`// Finds [Omega \| tau], to minimize \|\|[R_mark \| t_mark] - [Omega \| tau][R \| t]\|\|^2`
445	`// Algorithm and notation according to Mili Shah, Comparing two sets of corresponding six degree of freedom data, CVIU 2011.`	465	`// Algorithm and notation according to Mili Shah, Comparing two sets of corresponding six degree of freedom data, CVIU 2011.`
446	`// DTU, 2013, Oline V. Olesen, Jakob Wilm`	466	`// DTU, 2013, Oline V. Olesen, Jakob Wilm`
447	`void fitSixDofData(const std::vector<cv::Matx33f> R, const std::vector<cv::Vec3f> t, const std::vector<cv::Matx33f> R_mark, const std::vector<cv::Vec3f> t_mark, cv::Matx33f &Omega, cv::Vec3f &tau){`	467	`void fitSixDofData(const std::vector<cv::Matx33f> R, const std::vector<cv::Vec3f> t, const std::vector<cv::Matx33f> R_mark, const std::vector<cv::Vec3f> t_mark, cv::Matx33f &Omega, cv::Vec3f &tau){`
448		468
449	`int N = R.size();`	469	`int N = R.size();`
450	`assert(N == R_mark.size());`	470	`assert(N == R_mark.size());`
451	`assert(N == t.size());`	471	`assert(N == t.size());`
452	`assert(N == t_mark.size());`	472	`assert(N == t_mark.size());`
453		473
454	`// Mean translations`	474	`// Mean translations`
455	`cv::Vec3f t_mean;`	475	`cv::Vec3f t_mean;`
456	`cv::Vec3f t_mark_mean;`	476	`cv::Vec3f t_mark_mean;`
457	`for(int i=0; i<N; i++){`	477	`for(int i=0; i<N; i++){`
458	`t_mean += 1.0/N * t[i];`	478	`t_mean += 1.0/N * t[i];`
459	`t_mark_mean += 1.0/N * t_mark[i];`	479	`t_mark_mean += 1.0/N * t_mark[i];`
460	`}`	480	`}`
461		481
462	`// Data with mean adjusted translations`	482	`// Data with mean adjusted translations`
463	`cv::Mat X_bar(3, 4*N, CV_32F);`	483	`cv::Mat X_bar(3, 4*N, CV_32F);`
464	`cv::Mat X_mark_bar(3, 4*N, CV_32F);`	484	`cv::Mat X_mark_bar(3, 4*N, CV_32F);`
465	`for(int i=0; i<N; i++){`	485	`for(int i=0; i<N; i++){`
466	`cv::Mat(R[i]).copyTo(X_bar.colRange(i4,i4+3));`	486	`cv::Mat(R[i]).copyTo(X_bar.colRange(i4,i4+3));`
467	`cv::Mat(t[i] - t_mean).copyTo(X_bar.col(i*4+3));`	487	`cv::Mat(t[i] - t_mean).copyTo(X_bar.col(i*4+3));`
468	`cv::Mat(R_mark[i]).copyTo(X_mark_bar.colRange(i4,i4+3));`	488	`cv::Mat(R_mark[i]).copyTo(X_mark_bar.colRange(i4,i4+3));`
469	`cv::Mat(t_mark[i] - t_mark_mean).copyTo(X_mark_bar.col(i*4+3));`	489	`cv::Mat(t_mark[i] - t_mark_mean).copyTo(X_mark_bar.col(i*4+3));`
470	`}`	490	`}`
471	`//std::cout << X_bar << std::endl;`	491	`//std::cout << X_bar << std::endl;`
472	`// SVD`	492	`// SVD`
473	`cv::Mat W, U, VT;`	493	`cv::Mat W, U, VT;`
474	`cv::SVDecomp(X_bar*X_mark_bar.t(), W, U, VT);`	494	`cv::SVDecomp(X_bar*X_mark_bar.t(), W, U, VT);`
475		495
476	`cv::Matx33f D = cv::Matx33f::eye();`	496	`cv::Matx33f D = cv::Matx33f::eye();`
477	`if(cv::determinant(VT*U) < 0)`	497	`if(cv::determinant(VT*U) < 0)`
478	`D(3,3) = -1;`	498	`D(3,3) = -1;`
479		499
480	`// Best rotation`	500	`// Best rotation`

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