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 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 91	Rev 119
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.`
-		12	`// Works like cv::windowedMatchingMask in conjunction with cv::BFMatcher::match().`
-		13	`// F is the fundamental matrix.`
-		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){`
-		16
-		17	`if(keypoints1.empty() \|\| keypoints2.empty())`
-		18	`return cv::Mat();`
-		19
-		20	`int n1 = (int)keypoints1.size(), n2 = (int)keypoints2.size();`
-		21	`cv::Mat mask(n1, n2, CV_8UC1);`
-		22
-		23	`// Point to line distance`
-		24	`// for( int i = 0; i < n1; i++ ){`
-		25	`// cv::Vec3f p1 = cv::Vec3f(keypoints1[i].pt.x, keypoints1[i].pt.y, 1.0);`
-		26	`// // Epipolar line defined by p1`
-		27	`// cv::Vec3f l = F*p1;`
-		28	`// l /= sqrt(l(0)l(0) + l(1)l(1));`
-		29	`// for( int j = 0; j < n2; j++ ){`
-		30	`// cv::Vec3f p2 = cv::Vec3f(keypoints2[j].pt.x, keypoints2[j].pt.y, 1.0);`
-		31	`// // Signed distance to line`
-		32	`// float d = l.dot(p2);`
-		33	`// mask.at<uchar>(i, j) = fabs(d) < maxD;`
-		34	`// }`
-		35	`// }`
-		36
-		37	`// Symmetric epipolar distance`
-		38	`std::vector<cv::Point2f> q1, q2;`
-		39	`cvtools::keypointsToPoints(keypoints1, q1);`
-		40	`cvtools::keypointsToPoints(keypoints2, q2);`
-		41	`std::vector<cv::Point3f> l1, l2;`
-		42	`cv::computeCorrespondEpilines(q1, 1, F, l1);`
-		43	`cv::computeCorrespondEpilines(q2, 2, F, l2);`
-		44
-		45	`for( int i = 0; i < n1; i++ ){`
-		46	`cv::Vec3f p1 = cv::Vec3f(q1[i].x, q1[i].y, 1.0);`
-		47	`for( int j = 0; j < n2; j++ ){`
-		48	`cv::Vec3f p2 = cv::Vec3f(q2[j].x, q2[j].y, 1.0);`
-		49	`float d12 = l1[i].dot(p2);`
-		50	`float d21 = l2[j].dot(p1);`
-		51	`float d = d12d12 + d21d21;`
-		52	`mask.at<uchar>(i, j) = d < maxD;`
-		53	`}`
-		54	`}`
-		55
-		56	`// // Sampson Error (H&Z, p. 287) (expensive...)`
-		57	`// std::vector<cv::Point2f> q1, q2;`
-		58	`// cvtools::keypointsToPoints(keypoints1, q1);`
-		59	`// cvtools::keypointsToPoints(keypoints2, q2);`
-		60	`// std::vector<cv::Point3f> p1, p2;`
-		61	`// cv::convertPointsToHomogeneous(q1, p1);`
-		62	`// cv::convertPointsToHomogeneous(q2, p2);`
-		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();`
-		65	`// for( int i = 0; i < n1; i++ ){`
-		66	`// cv::Vec3f Fp1 = Fp1Mat.col(i);`
-		67	`// for( int j = 0; j < n2; j++ ){`
-		68	`// cv::Vec3f FTp2 = FTp2Mat.col(j);`
-		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));`
-		71	`// mask.at<uchar>(i, j) = d < maxD;`
-		72	`// }`
-		73	`// }`
-		74
-		75	`return mask;`
-		76	`}`
-		77
-		78
-		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){`
-		81
-		82	`int nMatches = matchesIn.size();`
-		83	`matchesOut.clear();`
-		84	`matchesOut.reserve(nMatches);`
-		85
-		86	`for(int i=0; i<nMatches; i++){`
-		87	`if(matchesIn[i].distance < thresh)`
-		88	`matchesOut.push_back(matchesIn[i]);`
-		89	`}`
-		90
-		91	`}`
-		92
11	`// Lightly modified OpenCV function which accepts a line width argument`	93	`// Lightly modified OpenCV function which accepts a line width argument`
12	`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){`
13	`cv::Mat corners = _corners.getMat();`	95	`cv::Mat corners = _corners.getMat();`
14	`if( corners.empty() )`	96	`if( corners.empty() )`
15	`return;`	97	`return;`
16	`cv::Mat image = _image.getMat(); CvMat c_image = _image.getMat();`	98	`cv::Mat image = _image.getMat(); CvMat c_image = _image.getMat();`
17	`int nelems = corners.checkVector(2, CV_32F, true);`	99	`int nelems = corners.checkVector(2, CV_32F, true);`
18	`CV_Assert(nelems >= 0);`	100	`CV_Assert(nelems >= 0);`
19	`cvDrawChessboardCorners( &c_image, patternSize, (CvPoint2D32f*)corners.data,`	101	`cvDrawChessboardCorners( &c_image, patternSize, (CvPoint2D32f*)corners.data,`
20	`nelems, patternWasFound, line_width);`	102	`nelems, patternWasFound, line_width);`
21	`}`	103	`}`
22		104
23	`void cvDrawChessboardCorners(CvArr* _image, CvSize pattern_size, CvPoint2D32f* corners, int count, int found, int line_width){`	105	`void cvDrawChessboardCorners(CvArr* _image, CvSize pattern_size, CvPoint2D32f* corners, int count, int found, int line_width){`
24	`const int shift = 0;`	106	`const int shift = 0;`
25	`const int radius = 12;`	107	`const int radius = 12;`
26	`const int r = radius*(1 << shift);`	108	`const int r = radius*(1 << shift);`
27	`int i;`	109	`int i;`
28	`CvMat stub, *image;`	110	`CvMat stub, *image;`
29	`double scale = 1;`	111	`double scale = 1;`
30	`int type, cn, line_type;`	112	`int type, cn, line_type;`
31		113
32	`image = cvGetMat( _image, &stub );`	114	`image = cvGetMat( _image, &stub );`
33		115
34	`type = CV_MAT_TYPE(image->type);`	116	`type = CV_MAT_TYPE(image->type);`
35	`cn = CV_MAT_CN(type);`	117	`cn = CV_MAT_CN(type);`
36	`if( cn != 1 && cn != 3 && cn != 4 )`	118	`if( cn != 1 && cn != 3 && cn != 4 )`
37	`CV_Error( CV_StsUnsupportedFormat, "Number of channels must be 1, 3 or 4" );`	119	`CV_Error( CV_StsUnsupportedFormat, "Number of channels must be 1, 3 or 4" );`
38		120
39	`switch( CV_MAT_DEPTH(image->type) )`	121	`switch( CV_MAT_DEPTH(image->type) )`
40	`{`	122	`{`
41	`case CV_8U:`	123	`case CV_8U:`
42	`scale = 1;`	124	`scale = 1;`
43	`break;`	125	`break;`
44	`case CV_16U:`	126	`case CV_16U:`
45	`scale = 256;`	127	`scale = 256;`
46	`break;`	128	`break;`
47	`case CV_32F:`	129	`case CV_32F:`
48	`scale = 1./255;`	130	`scale = 1./255;`
49	`break;`	131	`break;`
50	`default:`	132	`default:`
51	`CV_Error( CV_StsUnsupportedFormat,`	133	`CV_Error( CV_StsUnsupportedFormat,`
52	`"Only 8-bit, 16-bit or floating-point 32-bit images are supported" );`	134	`"Only 8-bit, 16-bit or floating-point 32-bit images are supported" );`
53	`}`	135	`}`
54		136
55	`line_type = type == CV_8UC1 \|\| type == CV_8UC3 ? CV_AA : 8;`	137	`line_type = type == CV_8UC1 \|\| type == CV_8UC3 ? CV_AA : 8;`
56		138
57	`if( !found )`	139	`if( !found )`
58	`{`	140	`{`
59	`CvScalar color = {{0,0,255}};`	141	`CvScalar color = {{0,0,255}};`
60	`if( cn == 1 )`	142	`if( cn == 1 )`
61	`color = cvScalarAll(200);`	143	`color = cvScalarAll(200);`
62	`color.val[0] *= scale;`	144	`color.val[0] *= scale;`
63	`color.val[1] *= scale;`	145	`color.val[1] *= scale;`
64	`color.val[2] *= scale;`	146	`color.val[2] *= scale;`
65	`color.val[3] *= scale;`	147	`color.val[3] *= scale;`
66		148
67	`for( i = 0; i < count; i++ )`	149	`for( i = 0; i < count; i++ )`
68	`{`	150	`{`
69	`CvPoint pt;`	151	`CvPoint pt;`
70	`pt.x = cvRound(corners[i].x*(1 << shift));`	152	`pt.x = cvRound(corners[i].x*(1 << shift));`
71	`pt.y = cvRound(corners[i].y*(1 << shift));`	153	`pt.y = cvRound(corners[i].y*(1 << shift));`
72	`cvLine( image, cvPoint( pt.x - r, pt.y - r ),`	154	`cvLine( image, cvPoint( pt.x - r, pt.y - r ),`
73	`cvPoint( pt.x + r, pt.y + r ), color, line_width, line_type, shift );`	155	`cvPoint( pt.x + r, pt.y + r ), color, line_width, line_type, shift );`
74	`cvLine( image, cvPoint( pt.x - r, pt.y + r),`	156	`cvLine( image, cvPoint( pt.x - r, pt.y + r),`
75	`cvPoint( pt.x + r, pt.y - r), color, line_width, line_type, shift );`	157	`cvPoint( pt.x + r, pt.y - r), color, line_width, line_type, shift );`
76	`cvCircle( image, pt, r+(1<<shift), color, line_width, line_type, shift );`	158	`cvCircle( image, pt, r+(1<<shift), color, line_width, line_type, shift );`
77	`}`	159	`}`
78	`}`	160	`}`
79	`else`	161	`else`
80	`{`	162	`{`
81	`int x, y;`	163	`int x, y;`
82	`CvPoint prev_pt = {0, 0};`	164	`CvPoint prev_pt = {0, 0};`
83	`const int line_max = 7;`	165	`const int line_max = 7;`
84	`static const CvScalar line_colors[line_max] =`	166	`static const CvScalar line_colors[line_max] =`
85	`{`	167	`{`
86	`{{0,0,255}},`	168	`{{0,0,255}},`
87	`{{0,128,255}},`	169	`{{0,128,255}},`
88	`{{0,200,200}},`	170	`{{0,200,200}},`
89	`{{0,255,0}},`	171	`{{0,255,0}},`
90	`{{200,200,0}},`	172	`{{200,200,0}},`
91	`{{255,0,0}},`	173	`{{255,0,0}},`
92	`{{255,0,255}}`	174	`{{255,0,255}}`
93	`};`	175	`};`
94		176
95	`for( y = 0, i = 0; y < pattern_size.height; y++ )`	177	`for( y = 0, i = 0; y < pattern_size.height; y++ )`
96	`{`	178	`{`
97	`CvScalar color = line_colors[y % line_max];`	179	`CvScalar color = line_colors[y % line_max];`
98	`if( cn == 1 )`	180	`if( cn == 1 )`
99	`color = cvScalarAll(200);`	181	`color = cvScalarAll(200);`
100	`color.val[0] *= scale;`	182	`color.val[0] *= scale;`
101	`color.val[1] *= scale;`	183	`color.val[1] *= scale;`
102	`color.val[2] *= scale;`	184	`color.val[2] *= scale;`
103	`color.val[3] *= scale;`	185	`color.val[3] *= scale;`
104		186
105	`for( x = 0; x < pattern_size.width; x++, i++ )`	187	`for( x = 0; x < pattern_size.width; x++, i++ )`
106	`{`	188	`{`
107	`CvPoint pt;`	189	`CvPoint pt;`
108	`pt.x = cvRound(corners[i].x*(1 << shift));`	190	`pt.x = cvRound(corners[i].x*(1 << shift));`
109	`pt.y = cvRound(corners[i].y*(1 << shift));`	191	`pt.y = cvRound(corners[i].y*(1 << shift));`
110		192
111	`if( i != 0 )`	193	`if( i != 0 )`
112	`cvLine( image, prev_pt, pt, color, 1, line_type, shift );`	194	`cvLine( image, prev_pt, pt, color, 1, line_type, shift );`
113		195
114	`cvLine( image, cvPoint(pt.x - r, pt.y - r),`	196	`cvLine( image, cvPoint(pt.x - r, pt.y - r),`
115	`cvPoint(pt.x + r, pt.y + r), color, line_width, line_type, shift );`	197	`cvPoint(pt.x + r, pt.y + r), color, line_width, line_type, shift );`
116	`cvLine( image, cvPoint(pt.x - r, pt.y + r),`	198	`cvLine( image, cvPoint(pt.x - r, pt.y + r),`
117	`cvPoint(pt.x + r, pt.y - r), color, line_width, line_type, shift );`	199	`cvPoint(pt.x + r, pt.y - r), color, line_width, line_type, shift );`
118	`cvCircle( image, pt, r+(1<<shift), color, line_width, line_type, shift );`	200	`cvCircle( image, pt, r+(1<<shift), color, line_width, line_type, shift );`
119	`prev_pt = pt;`	201	`prev_pt = pt;`
120	`}`	202	`}`
121	`}`	203	`}`
122	`}`	204	`}`
123	`}`	205	`}`
124		206
125	`// Returns the result of mod(mat(x,y), moduli) for each matrix element`	207	`// Returns the result of mod(mat(x,y), moduli) for each matrix element`
126	`cv::Mat modulo(const cv::Mat &mat, float n){`	208	`cv::Mat modulo(const cv::Mat &mat, float n){`
127		209
128	`cv::Mat ret(mat.rows, mat.cols, mat.type());`	210	`cv::Mat ret(mat.rows, mat.cols, mat.type());`
129		211
130	`for(int row=0; row<ret.rows; row++){`	212	`for(int row=0; row<ret.rows; row++){`
131	`for(int col=0; col<ret.cols; col++){`	213	`for(int col=0; col<ret.cols; col++){`
132	`float val = mat.at<float>(row, col);`	214	`float val = mat.at<float>(row, col);`
133	`// note: std::fmod calculates the remainder, not arithmetic modulo`	215	`// note: std::fmod calculates the remainder, not arithmetic modulo`
134	`ret.at<float>(row, col) = val - n * std::floor(val / n);`	216	`ret.at<float>(row, col) = val - n * std::floor(val / n);`
135	`}`	217	`}`
136	`}`	218	`}`
137		219
138	`return ret;`	220	`return ret;`
139	`}`	221	`}`
140		222
141	`// Convert a 3xN matrix to a vector of Point3fs.`	223	`// Convert a 3xN matrix to a vector of Point3fs.`
142	`void matToPoints3f(const cv::Mat &mat, std::vector<cv::Point3f> &points){`	224	`void matToPoints3f(const cv::Mat &mat, std::vector<cv::Point3f> &points){`
143		225
144	`unsigned int nPoints = mat.cols;`	226	`unsigned int nPoints = mat.cols;`
145	`points.resize(nPoints);`	227	`points.resize(nPoints);`
146		228
147	`for(unsigned int i=0; i<nPoints; i++)`	229	`for(unsigned int i=0; i<nPoints; i++)`
148	`points[i] = cv::Point3f(mat.at<float>(0, i), mat.at<float>(1, i), mat.at<float>(2, i));`	230	`points[i] = cv::Point3f(mat.at<float>(0, i), mat.at<float>(1, i), mat.at<float>(2, i));`
149	`}`	231	`}`
150		232
151	`// Convert a (Dim+1)xN matrix of homogenous points to a DimxN matrix of points in non-homogenous coordinates.`	233	`// Convert a (Dim+1)xN matrix of homogenous points to a DimxN matrix of points in non-homogenous coordinates.`
152	`void convertMatFromHomogeneous(cv::Mat &src, cv::Mat &dst){`	234	`void convertMatFromHomogeneous(cv::Mat &src, cv::Mat &dst){`
153	`unsigned int N = src.cols;`	235	`unsigned int N = src.cols;`
154	`unsigned int Dim = src.rows-1;`	236	`unsigned int Dim = src.rows-1;`
155	`dst.create(Dim, N, src.type());`	237	`dst.create(Dim, N, src.type());`
156	`for(unsigned int i=0; i<N; i++){`	238	`for(unsigned int i=0; i<N; i++){`
157	`for(unsigned int j=0; j<Dim; j++)`	239	`for(unsigned int j=0; j<Dim; j++)`
158	`dst.at<float>(j,i) = src.at<float>(j,i)/src.at<float>(Dim,i);`	240	`dst.at<float>(j,i) = src.at<float>(j,i)/src.at<float>(Dim,i);`
159	`}`	241	`}`
160		242
161	`}`	243	`}`
162		244
163	`// Function to solve the hand-eye (or eye-in-hand) calibration problem.`	245	`// Function to solve the hand-eye (or eye-in-hand) calibration problem.`
164	`// Finds [Omega \| tau], to minimize \|\|[R_mark \| t_mark][Omega \| tau] - [Omega \| tau][R \| t]\|\|^2`	246	`// Finds [Omega \| tau], to minimize \|\|[R_mark \| t_mark][Omega \| tau] - [Omega \| tau][R \| t]\|\|^2`
165	`// Algorithm according to Tsai, Lenz, A new technique for fully autonomous and efficient 3d robotics hand-eye calibration`	247	`// Algorithm according to Tsai, Lenz, A new technique for fully autonomous and efficient 3d robotics hand-eye calibration`
166	`// DTU, 2014, Jakob Wilm`	248	`// DTU, 2014, Jakob Wilm`
167	`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){`	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){`
168		250
169	`int N = R.size();`	251	`int N = R.size();`
170	`assert(N == R_mark.size());`	252	`assert(N == R_mark.size());`
171	`assert(N == t.size());`	253	`assert(N == t.size());`
172	`assert(N == t_mark.size());`	254	`assert(N == t_mark.size());`
173		255
174	`// construct equations for rotation`	256	`// construct equations for rotation`
175	`cv::Mat A(3*N, 3, CV_32F);`	257	`cv::Mat A(3*N, 3, CV_32F);`
176	`cv::Mat b(3*N, 1, CV_32F);`	258	`cv::Mat b(3*N, 1, CV_32F);`
177	`for(int i=0; i<N; i++){`	259	`for(int i=0; i<N; i++){`
178	`// angle axis representations`	260	`// angle axis representations`
179	`cv::Vec3f rot;`	261	`cv::Vec3f rot;`
180	`cv::Vec3f rot_mark;`	262	`cv::Vec3f rot_mark;`
181	`cv::Rodrigues(R[i], rot);`	263	`cv::Rodrigues(R[i], rot);`
182	`cv::Rodrigues(R_mark[i], rot_mark);`	264	`cv::Rodrigues(R_mark[i], rot_mark);`
183		265
184	`cv::Vec3f P = 2.0sin(cv::norm(rot)/2.0)cv::normalize(rot);`	266	`cv::Vec3f P = 2.0sin(cv::norm(rot)/2.0)cv::normalize(rot);`
185	`//std::cout << "P: " << std::endl << P << std::endl;`	267	`//std::cout << "P: " << std::endl << P << std::endl;`
186	`cv::Vec3f P_mark = 2.0sin(cv::norm(rot_mark)/2.0)cv::normalize(rot_mark);`	268	`cv::Vec3f P_mark = 2.0sin(cv::norm(rot_mark)/2.0)cv::normalize(rot_mark);`
187	`//std::cout << "P_mark: " << std::endl << P_mark << std::endl;`	269	`//std::cout << "P_mark: " << std::endl << P_mark << std::endl;`
188	`cv::Vec3f sum = P+P_mark;`	270	`cv::Vec3f sum = P+P_mark;`
189	`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);`	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);`
190	`//std::cout << "crossProduct: " << std::endl << crossProduct << std::endl;`	272	`//std::cout << "crossProduct: " << std::endl << crossProduct << std::endl;`
191	`crossProduct.copyTo(A.rowRange(i3, i3+3));`	273	`crossProduct.copyTo(A.rowRange(i3, i3+3));`
192		274
193	`cv::Mat(P-P_mark).copyTo(b.rowRange(i3, i3+3));`	275	`cv::Mat(P-P_mark).copyTo(b.rowRange(i3, i3+3));`
194	`}`	276	`}`
195		277
196	`// solve for rotation`	278	`// solve for rotation`
197	`cv::Vec3f P_prime;`	279	`cv::Vec3f P_prime;`
198	`cv::solve(A, b, P_prime, cv::DECOMP_SVD);`	280	`cv::solve(A, b, P_prime, cv::DECOMP_SVD);`
199	`cv::Vec3f P = 2.0P_prime/(cv::sqrt(1.0 + cv::norm(P_prime)cv::norm(P_prime)));`	281	`cv::Vec3f P = 2.0P_prime/(cv::sqrt(1.0 + cv::norm(P_prime)cv::norm(P_prime)));`
200	`float nP = cv::norm(P);`	282	`float nP = cv::norm(P);`
201	`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);`	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);`
202	`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);`	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);`
203	`Omega = cv::Matx33f(OmegaMat);`	285	`Omega = cv::Matx33f(OmegaMat);`
204		286
205	`// construct equations for translation`	287	`// construct equations for translation`
206	`A.setTo(0.0);`	288	`A.setTo(0.0);`
207	`b.setTo(0.0);`	289	`b.setTo(0.0);`
208	`for(int i=0; i<N; i++){`	290	`for(int i=0; i<N; i++){`
209		291
210	`cv::Mat diff = cv::Mat(R_mark[i]) - cv::Mat::eye(3, 3, CV_32F);`	292	`cv::Mat diff = cv::Mat(R_mark[i]) - cv::Mat::eye(3, 3, CV_32F);`
211	`diff.copyTo(A.rowRange(i3, i3+3));`	293	`diff.copyTo(A.rowRange(i3, i3+3));`
212		294
213	`cv::Mat diff_mark = cv::Mat(Omega*t[i] - t_mark[i]);`	295	`cv::Mat diff_mark = cv::Mat(Omega*t[i] - t_mark[i]);`
214	`diff_mark.copyTo(b.rowRange(i3, i3+3));`	296	`diff_mark.copyTo(b.rowRange(i3, i3+3));`
215	`}`	297	`}`
216		298
217	`// solve for translation`	299	`// solve for translation`
218	`cv::solve(A, b, tau, cv::DECOMP_SVD);`	300	`cv::solve(A, b, tau, cv::DECOMP_SVD);`
219		301
220	`cv::Mat err_tau = b - (A*cv::Mat(tau));`	302	`cv::Mat err_tau = b - (A*cv::Mat(tau));`
221	`std::cout << err_tau << std::endl;`	303	`std::cout << err_tau << std::endl;`
222	`}`	304	`}`
223		305
224	`// Function to solve for the rotation axis from sets of 3D point coordinates of flat pattern feature points`	306	`// Function to solve for the rotation axis from sets of 3D point coordinates of flat pattern feature points`
225	`// Algorithm according to Chen et al., Rotation axis calibration of a turntable using constrained global optimization, Optik 2014`	307	`// Algorithm according to Chen et al., Rotation axis calibration of a turntable using constrained global optimization, Optik 2014`
226	`// DTU, 2014, Jakob Wilm`	308	`// DTU, 2014, Jakob Wilm`
227	`void rotationAxisCalibration(const std::vector< std::vector<cv::Point3f> > Qcam, const std::vector<cv::Point3f> Qobj, cv::Vec3f &axis, cv::Vec3f &point){`	309	`void rotationAxisCalibration(const std::vector< std::vector<cv::Point3f> > Qcam, const std::vector<cv::Point3f> Qobj, cv::Vec3f &axis, cv::Vec3f &point){`
228		310
229	`// number of frames (points on each arch)`	311	`// number of frames (points on each arch)`
230	`int l = Qcam.size();`	312	`int l = Qcam.size();`
231		313
232	`// number of points in each frame`	314	`// number of points in each frame`
233	`int mn = Qobj.size();`	315	`int mn = Qobj.size();`
234		316
235	`assert(mn == Qcam[0].size());`	317	`assert(mn == Qcam[0].size());`
236		318
237	`// construct matrix for axis determination`	319	`// construct matrix for axis determination`
238	`cv::Mat M(6, 6, CV_32F, cv::Scalar(0));`	320	`cv::Mat M(6, 6, CV_32F, cv::Scalar(0));`
239		321
240	`for(int k=0; k<l; k++){`	322	`for(int k=0; k<l; k++){`
241	`for(int idx=0; idx<mn; idx++){`	323	`for(int idx=0; idx<mn; idx++){`
242		324
243	`// float i = Qobj[idx].x+4;`	325	`// float i = Qobj[idx].x+4;`
244	`// float j = Qobj[idx].y+4;`	326	`// float j = Qobj[idx].y+4;`
245	`float i = Qobj[idx].x;`	327	`float i = Qobj[idx].x;`
246	`float j = Qobj[idx].y;`	328	`float j = Qobj[idx].y;`
247		329
248	`float x = Qcam[k][idx].x;`	330	`float x = Qcam[k][idx].x;`
249	`float y = Qcam[k][idx].y;`	331	`float y = Qcam[k][idx].y;`
250	`float z = Qcam[k][idx].z;`	332	`float z = Qcam[k][idx].z;`
251		333
252	`M += (cv::Mat_<float>(6,6) << xx, xy, xz, x, ix, j*x,`	334	`M += (cv::Mat_<float>(6,6) << xx, xy, xz, x, ix, j*x,`
253	`0, yy, yz, y, iy, jy,`	335	`0, yy, yz, y, iy, jy,`
254	`0, 0, zz, z, iz, j*z,`	336	`0, 0, zz, z, iz, j*z,`
255	`0, 0, 0, 1, i, j,`	337	`0, 0, 0, 1, i, j,`
256	`0, 0, 0, 0, ii, ij,`	338	`0, 0, 0, 0, ii, ij,`
257	`0, 0, 0, 0, 0, j*j);`	339	`0, 0, 0, 0, 0, j*j);`
258		340
259	`}`	341	`}`
260	`}`	342	`}`
261		343
262	`cv::completeSymm(M, false);`	344	`cv::completeSymm(M, false);`
263		345
264	`// solve for axis`	346	`// solve for axis`
265	`std::vector<float> lambda;`	347	`std::vector<float> lambda;`
266	`cv::Mat u;`	348	`cv::Mat u;`
267	`cv::eigen(M, lambda, u);`	349	`cv::eigen(M, lambda, u);`
268		350
269	`float minLambda = abs(lambda[0]);`	351	`float minLambda = abs(lambda[0]);`
270	`int idx = 0;`	352	`int idx = 0;`
271	`for(int i=1; i<lambda.size(); i++){`	353	`for(int i=1; i<lambda.size(); i++){`
272	`if(abs(lambda[i]) < minLambda){`	354	`if(abs(lambda[i]) < minLambda){`
273	`minLambda = lambda[i];`	355	`minLambda = lambda[i];`
274	`idx = i;`	356	`idx = i;`
275	`}`	357	`}`
276	`}`	358	`}`
277		359
278	`axis = u.row(idx).colRange(0, 3);`	360	`axis = u.row(idx).colRange(0, 3);`
279	`axis = cv::normalize(axis);`	361	`axis = cv::normalize(axis);`
280		362
281	`float nx = u.at<float>(idx, 0);`	363	`float nx = u.at<float>(idx, 0);`
282	`float ny = u.at<float>(idx, 1);`	364	`float ny = u.at<float>(idx, 1);`
283	`float nz = u.at<float>(idx, 2);`	365	`float nz = u.at<float>(idx, 2);`
284	`float d = u.at<float>(idx, 3);`	366	`float d = u.at<float>(idx, 3);`
285	`float dh = u.at<float>(idx, 4);`	367	`float dh = u.at<float>(idx, 4);`
286	`float dv = u.at<float>(idx, 5);`	368	`float dv = u.at<float>(idx, 5);`
287		369
288	`// // Paper version: c is initially eliminated`	370	`// // Paper version: c is initially eliminated`
289	`// cv::Mat A(l*mn, mn+2, CV_32F, cv::Scalar(0.0));`	371	`// cv::Mat A(l*mn, mn+2, CV_32F, cv::Scalar(0.0));`
290	`// cv::Mat bb(l*mn, 1, CV_32F);`	372	`// cv::Mat bb(l*mn, 1, CV_32F);`
291		373
292	`// for(int k=0; k<l; k++){`	374	`// for(int k=0; k<l; k++){`
293	`// for(int idx=0; idx<mn; idx++){`	375	`// for(int idx=0; idx<mn; idx++){`
294		376
295	`// float i = Qobj[idx].x;`	377	`// float i = Qobj[idx].x;`
296	`// float j = Qobj[idx].y;`	378	`// float j = Qobj[idx].y;`
297		379
298	`// float x = Qcam[k][idx].x;`	380	`// float x = Qcam[k][idx].x;`
299	`// float y = Qcam[k][idx].y;`	381	`// float y = Qcam[k][idx].y;`
300	`// float z = Qcam[k][idx].z;`	382	`// float z = Qcam[k][idx].z;`
301		383
302	`// float f = xx + yy + zz + (2xnx + 2yny + 2znz)(idh + jdv);`	384	`// float f = xx + yy + zz + (2xnx + 2yny + 2znz)(idh + jdv);`
303		385
304	`// int row = k*mn+idx;`	386	`// int row = k*mn+idx;`
305	`// A.at<float>(row, 0) = 2x - (2z*nx)/nz;`	387	`// A.at<float>(row, 0) = 2x - (2z*nx)/nz;`
306	`// A.at<float>(row, 1) = 2y - (2z*ny)/nz;`	388	`// A.at<float>(row, 1) = 2y - (2z*ny)/nz;`
307	`// A.at<float>(row, idx+2) = 1.0;`	389	`// A.at<float>(row, idx+2) = 1.0;`
308		390
309	`// bb.at<float>(row, 0) = f + (2zd)/nz;`	391	`// bb.at<float>(row, 0) = f + (2zd)/nz;`
310	`// }`	392	`// }`
311	`// }`	393	`// }`
312		394
313	`// // solve for point`	395	`// // solve for point`
314	`// cv::Mat abe;`	396	`// cv::Mat abe;`
315	`// cv::solve(A, bb, abe, cv::DECOMP_SVD);`	397	`// cv::solve(A, bb, abe, cv::DECOMP_SVD);`
316		398
317	`// float a = abe.at<float>(0, 0);`	399	`// float a = abe.at<float>(0, 0);`
318	`// float b = abe.at<float>(1, 0);`	400	`// float b = abe.at<float>(1, 0);`
319	`// float c = -(nxa+nyb+d)/nz;`	401	`// float c = -(nxa+nyb+d)/nz;`
320		402
321	`// Our version: solve simultanously for a,b,c`	403	`// Our version: solve simultanously for a,b,c`
322	`cv::Mat A(l*mn, mn+3, CV_32F, cv::Scalar(0.0));`	404	`cv::Mat A(l*mn, mn+3, CV_32F, cv::Scalar(0.0));`
323	`cv::Mat bb(l*mn, 1, CV_32F);`	405	`cv::Mat bb(l*mn, 1, CV_32F);`
324		406
325	`for(int k=0; k<l; k++){`	407	`for(int k=0; k<l; k++){`
326	`for(int idx=0; idx<mn; idx++){`	408	`for(int idx=0; idx<mn; idx++){`
327		409
328	`float i = Qobj[idx].x;`	410	`float i = Qobj[idx].x;`
329	`float j = Qobj[idx].y;`	411	`float j = Qobj[idx].y;`
330		412
331	`float x = Qcam[k][idx].x;`	413	`float x = Qcam[k][idx].x;`
332	`float y = Qcam[k][idx].y;`	414	`float y = Qcam[k][idx].y;`
333	`float z = Qcam[k][idx].z;`	415	`float z = Qcam[k][idx].z;`
334		416
335	`float f = xx + yy + zz + (2xnx + 2yny + 2znz)(idh + jdv);`	417	`float f = xx + yy + zz + (2xnx + 2yny + 2znz)(idh + jdv);`
336		418
337	`int row = k*mn+idx;`	419	`int row = k*mn+idx;`
338	`A.at<float>(row, 0) = 2*x;`	420	`A.at<float>(row, 0) = 2*x;`
339	`A.at<float>(row, 1) = 2*y;`	421	`A.at<float>(row, 1) = 2*y;`
340	`A.at<float>(row, 2) = 2*z;`	422	`A.at<float>(row, 2) = 2*z;`
341	`A.at<float>(row, idx+3) = 1.0;`	423	`A.at<float>(row, idx+3) = 1.0;`
342		424
343	`bb.at<float>(row, 0) = f;`	425	`bb.at<float>(row, 0) = f;`
344	`}`	426	`}`
345	`}`	427	`}`
346		428
347	`// solve for point`	429	`// solve for point`
348	`cv::Mat abe;`	430	`cv::Mat abe;`
349	`cv::solve(A, bb, abe, cv::DECOMP_SVD);`	431	`cv::solve(A, bb, abe, cv::DECOMP_SVD);`
350		432
351	`float a = abe.at<float>(0, 0);`	433	`float a = abe.at<float>(0, 0);`
352	`float b = abe.at<float>(1, 0);`	434	`float b = abe.at<float>(1, 0);`
353	`float c = abe.at<float>(2, 0);`	435	`float c = abe.at<float>(2, 0);`
354		436
355	`point[0] = a;`	437	`point[0] = a;`
356	`point[1] = b;`	438	`point[1] = b;`
357	`point[2] = c;`	439	`point[2] = c;`
358		440
359	`}`	441	`}`
360		442
361	`// Function to fit two sets of corresponding pose data.`	443	`// Function to fit two sets of corresponding pose data.`
362	`// Finds [Omega \| tau], to minimize \|\|[R_mark \| t_mark] - [Omega \| tau][R \| t]\|\|^2`	444	`// Finds [Omega \| tau], to minimize \|\|[R_mark \| t_mark] - [Omega \| tau][R \| t]\|\|^2`
363	`// Algorithm and notation according to Mili Shah, Comparing two sets of corresponding six degree of freedom data, CVIU 2011.`	445	`// Algorithm and notation according to Mili Shah, Comparing two sets of corresponding six degree of freedom data, CVIU 2011.`
364	`// DTU, 2013, Oline V. Olesen, Jakob Wilm`	446	`// DTU, 2013, Oline V. Olesen, Jakob Wilm`
365	`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){`	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){`
366		448
367	`int N = R.size();`	449	`int N = R.size();`
368	`assert(N == R_mark.size());`	450	`assert(N == R_mark.size());`
369	`assert(N == t.size());`	451	`assert(N == t.size());`
370	`assert(N == t_mark.size());`	452	`assert(N == t_mark.size());`
371		453
372	`// Mean translations`	454	`// Mean translations`
373	`cv::Vec3f t_mean;`	455	`cv::Vec3f t_mean;`
374	`cv::Vec3f t_mark_mean;`	456	`cv::Vec3f t_mark_mean;`
375	`for(int i=0; i<N; i++){`	457	`for(int i=0; i<N; i++){`
376	`t_mean += 1.0/N * t[i];`	458	`t_mean += 1.0/N * t[i];`
377	`t_mark_mean += 1.0/N * t_mark[i];`	459	`t_mark_mean += 1.0/N * t_mark[i];`
378	`}`	460	`}`
379		461
380	`// Data with mean adjusted translations`	462	`// Data with mean adjusted translations`
381	`cv::Mat X_bar(3, 4*N, CV_32F);`	463	`cv::Mat X_bar(3, 4*N, CV_32F);`
382	`cv::Mat X_mark_bar(3, 4*N, CV_32F);`	464	`cv::Mat X_mark_bar(3, 4*N, CV_32F);`
383	`for(int i=0; i<N; i++){`	465	`for(int i=0; i<N; i++){`
384	`cv::Mat(R[i]).copyTo(X_bar.colRange(i4,i4+3));`	466	`cv::Mat(R[i]).copyTo(X_bar.colRange(i4,i4+3));`
385	`cv::Mat(t[i] - t_mean).copyTo(X_bar.col(i*4+3));`	467	`cv::Mat(t[i] - t_mean).copyTo(X_bar.col(i*4+3));`
386	`cv::Mat(R_mark[i]).copyTo(X_mark_bar.colRange(i4,i4+3));`	468	`cv::Mat(R_mark[i]).copyTo(X_mark_bar.colRange(i4,i4+3));`
387	`cv::Mat(t_mark[i] - t_mark_mean).copyTo(X_mark_bar.col(i*4+3));`	469	`cv::Mat(t_mark[i] - t_mark_mean).copyTo(X_mark_bar.col(i*4+3));`
388	`}`	470	`}`
389	`//std::cout << X_bar << std::endl;`	471	`//std::cout << X_bar << std::endl;`
390	`// SVD`	472	`// SVD`
391	`cv::Mat W, U, VT;`	473	`cv::Mat W, U, VT;`
392	`cv::SVDecomp(X_bar*X_mark_bar.t(), W, U, VT);`	474	`cv::SVDecomp(X_bar*X_mark_bar.t(), W, U, VT);`
393		475
394	`cv::Matx33f D = cv::Matx33f::eye();`	476	`cv::Matx33f D = cv::Matx33f::eye();`
395	`if(cv::determinant(VT*U) < 0)`	477	`if(cv::determinant(VT*U) < 0)`
396	`D(3,3) = -1;`	478	`D(3,3) = -1;`
397		479
398	`// Best rotation`	480	`// Best rotation`
399	`Omega = cv::Matx33f(cv::Mat(VT.t()))Dcv::Matx33f(cv::Mat(U.t()));`	481	`Omega = cv::Matx33f(cv::Mat(VT.t()))Dcv::Matx33f(cv::Mat(U.t()));`
400		482
401	`// Best translation`	483	`// Best translation`
402	`tau = t_mark_mean - Omega*t_mean;`	484	`tau = t_mark_mean - Omega*t_mean;`
403		485
404	`}`	486	`}`
405		487
406	`// Forward distortion of points. The inverse of the undistortion in cv::initUndistortRectifyMap().`	488	`// Forward distortion of points. The inverse of the undistortion in cv::initUndistortRectifyMap().`
407	`// Inspired by Pascal Thomet, http://code.opencv.org/issues/1387#note-11`	489	`// Inspired by Pascal Thomet, http://code.opencv.org/issues/1387#note-11`
408	`// Convention for distortion parameters: http://www.vision.caltech.edu/bouguetj/calib_doc/htmls/parameters.html`	490	`// Convention for distortion parameters: http://www.vision.caltech.edu/bouguetj/calib_doc/htmls/parameters.html`
409	`void initDistortMap(const cv::Matx33f cameraMatrix, const cv::Vec<float, 5> distCoeffs, const cv::Size size, cv::Mat &map1, cv::Mat &map2){`	491	`void initDistortMap(const cv::Matx33f cameraMatrix, const cv::Vec<float, 5> distCoeffs, const cv::Size size, cv::Mat &map1, cv::Mat &map2){`
410		492
411	`float fx = cameraMatrix(0,0);`	493	`float fx = cameraMatrix(0,0);`
412	`float fy = cameraMatrix(1,1);`	494	`float fy = cameraMatrix(1,1);`
413	`float ux = cameraMatrix(0,2);`	495	`float ux = cameraMatrix(0,2);`
414	`float uy = cameraMatrix(1,2);`	496	`float uy = cameraMatrix(1,2);`
415		497
416	`float k1 = distCoeffs[0];`	498	`float k1 = distCoeffs[0];`
417	`float k2 = distCoeffs[1];`	499	`float k2 = distCoeffs[1];`
418	`float p1 = distCoeffs[2];`	500	`float p1 = distCoeffs[2];`

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