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


#include "cvtools.h"
 
#ifdef _WIN32
#include <cstdint>
#endif
 
#include <stdio.h>
 
namespace cvtools{
 
// Convert an BGR 3-channel image back into a Bayered image
void cvtColorBGRToBayerBG(const cv::Mat &imBGR, cv::Mat &imBayerBG){
 
    imBayerBG.create(imBGR.size(), CV_8UC1);
 
 
    for(int r=0; r<imBGR.rows; r++){
        for(int c=0; c<imBGR.cols; c++){
 
            bool evenRow = r % 2;
            bool evenCol = c % 2;
 
            if(evenRow & evenCol)
                imBayerBG.at<uchar>(r,c) = imBGR.at<cv::Vec3b>(r,c)[0];
            else if(!evenRow & !evenCol)
                imBayerBG.at<uchar>(r,c) = imBGR.at<cv::Vec3b>(r,c)[2];
            else
                imBayerBG.at<uchar>(r,c) = imBGR.at<cv::Vec3b>(r,c)[1];
 
        }
 
    }
 
 
}
 
 
// Removes matches not satisfying the epipolar constraint.
// F is the fundamental matrix.
// Works like cv::correctMatches(), except it removes matches with an error distance greater than maxD.
void removeIncorrectMatches(const cv::Mat F, const std::vector<cv::Point2f> &q0, const std::vector<cv::Point2f> &q1, const float maxD,
                                std::vector<cv::Point2f> q0Correct, std::vector<cv::Point2f> q1Correct){
 
    int n0 = (int)q0.size(), n1 = (int)q1.size();
    q0Correct.reserve(n0);
    q1Correct.reserve(n1);
 
    // Point to line distance
//    for( int i = 0; i < n1; i++ ){
//        cv::Vec3f p0 = cv::Vec3f(q0[i].x, q0[i].y, 1.0);
//        // Epipolar line defined by p0
//        cv::Vec3f l = F*p0;
//        l /= sqrt(l(0)*l(0) + l(1)*l(1));
//        for( int j = 0; j < n2; j++ ){
//            cv::Vec3f p1 = cv::Vec3f(q1[i].x, q1[i].y, 1.0);
//            // Signed distance to line
//            float d = l.dot(p1);
//            if(d < maxD){
//                q0Correct.push_back(q0[i]);
//                q1Correct.push_back(q1[i]);
//            }
//        }
//    }
 
    // Symmetric epipolar distance
    std::vector<cv::Point3f> l0, l1;
    cv::computeCorrespondEpilines(q0, 1, F, l0);
    cv::computeCorrespondEpilines(q1, 2, F, l1);
 
    for(int i = 0; i < n0; i++){
        cv::Vec3f p0 = cv::Vec3f(q0[i].x, q0[i].y, 1.0);
        for(int j = 0; j < n1; j++){
            cv::Vec3f p1 = cv::Vec3f(q1[j].x, q1[j].y, 1.0);
            float d01 = l0[i].dot(p1);
            float d10 = l1[j].dot(p0);
            float d = d01*d01 + d10*d10;
            if(d < maxD){
                q0Correct.push_back(q0[i]);
                q1Correct.push_back(q1[i]);
            }
        }
    }
 
//    // Sampson Error (H&Z, p. 287) (expensive...)
//    std::vector<cv::Point3f> p0, p1;
//    cv::convertPointsToHomogeneous(q0, p0);
//    cv::convertPointsToHomogeneous(q1, p1);
//    cv::Mat Fp0Mat = cv::Mat(F)*cv::Mat(p0).reshape(1).t();
//    cv::Mat FTp1Mat = cv::Mat(F.t())*cv::Mat(p1).reshape(1).t();
//    for( int i = 0; i < n1; i++ ){
//        cv::Vec3f Fp0 = Fp0Mat.col(i);
//        for( int j = 0; j < n2; j++ ){
//            cv::Vec3f FTp1 = FTp1Mat.col(j);
//            cv::Matx<float,1,1> p1TFp0 = cv::Matx31f(p1[j]).t()*F*cv::Matx31f(p0[i]);
//            float d = p1TFp0(0)*p1TFp0(0) / (Fp0(0)*Fp0(0) + Fp0(1)*Fp0(1) + FTp1(0)*FTp1(0) + FTp1(1)*FTp1(1));
//            if(d < maxD){
//                q0Correct.push_back(q0[i]);
//                q1Correct.push_back(q1[i]);
//            }
//        }
//    }
 
    return;
}
 
// 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 121	Rev 139
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	`// Convert an BGR 3-channel image back into a Bayered image`
-		12	`void cvtColorBGRToBayerBG(const cv::Mat &imBGR, cv::Mat &imBayerBG){`
-		13
-		14	`imBayerBG.create(imBGR.size(), CV_8UC1);`
-		15
-		16
-		17	`for(int r=0; r<imBGR.rows; r++){`
-		18	`for(int c=0; c<imBGR.cols; c++){`
-		19
-		20	`bool evenRow = r % 2;`
-		21	`bool evenCol = c % 2;`
-		22
-		23	`if(evenRow & evenCol)`
-		24	`imBayerBG.at<uchar>(r,c) = imBGR.at<cv::Vec3b>(r,c)[0];`
-		25	`else if(!evenRow & !evenCol)`
-		26	`imBayerBG.at<uchar>(r,c) = imBGR.at<cv::Vec3b>(r,c)[2];`
-		27	`else`
-		28	`imBayerBG.at<uchar>(r,c) = imBGR.at<cv::Vec3b>(r,c)[1];`
-		29
-		30	`}`
-		31
-		32	`}`
-		33
-		34
-		35	`}`
-		36
-		37
11	`// Removes matches not satisfying the epipolar constraint.`	38	`// Removes matches not satisfying the epipolar constraint.`
12	`// F is the fundamental matrix.`	39	`// F is the fundamental matrix.`
13	`// Works like cv::correctMatches(), except it removes matches with an error distance greater than maxD.`	40	`// Works like cv::correctMatches(), except it removes matches with an error distance greater than maxD.`
14	`void removeIncorrectMatches(const cv::Mat F, const std::vector<cv::Point2f> &q0, const std::vector<cv::Point2f> &q1, const float maxD,`	41	`void removeIncorrectMatches(const cv::Mat F, const std::vector<cv::Point2f> &q0, const std::vector<cv::Point2f> &q1, const float maxD,`
15	`std::vector<cv::Point2f> q0Correct, std::vector<cv::Point2f> q1Correct){`	42	`std::vector<cv::Point2f> q0Correct, std::vector<cv::Point2f> q1Correct){`
16		43
17	`int n0 = (int)q0.size(), n1 = (int)q1.size();`	44	`int n0 = (int)q0.size(), n1 = (int)q1.size();`
18	`q0Correct.reserve(n0);`	45	`q0Correct.reserve(n0);`
19	`q1Correct.reserve(n1);`	46	`q1Correct.reserve(n1);`
20		47
21	`// Point to line distance`	48	`// Point to line distance`
22	`// for( int i = 0; i < n1; i++ ){`	49	`// for( int i = 0; i < n1; i++ ){`
23	`// cv::Vec3f p0 = cv::Vec3f(q0[i].x, q0[i].y, 1.0);`	50	`// cv::Vec3f p0 = cv::Vec3f(q0[i].x, q0[i].y, 1.0);`
24	`// // Epipolar line defined by p0`	51	`// // Epipolar line defined by p0`
25	`// cv::Vec3f l = F*p0;`	52	`// cv::Vec3f l = F*p0;`
26	`// l /= sqrt(l(0)l(0) + l(1)l(1));`	53	`// l /= sqrt(l(0)l(0) + l(1)l(1));`
27	`// for( int j = 0; j < n2; j++ ){`	54	`// for( int j = 0; j < n2; j++ ){`
28	`// cv::Vec3f p1 = cv::Vec3f(q1[i].x, q1[i].y, 1.0);`	55	`// cv::Vec3f p1 = cv::Vec3f(q1[i].x, q1[i].y, 1.0);`
29	`// // Signed distance to line`	56	`// // Signed distance to line`
30	`// float d = l.dot(p1);`	57	`// float d = l.dot(p1);`
31	`// if(d < maxD){`	58	`// if(d < maxD){`
32	`// q0Correct.push_back(q0[i]);`	59	`// q0Correct.push_back(q0[i]);`
33	`// q1Correct.push_back(q1[i]);`	60	`// q1Correct.push_back(q1[i]);`
34	`// }`	61	`// }`
35	`// }`	62	`// }`
36	`// }`	63	`// }`
37		64
38	`// Symmetric epipolar distance`	65	`// Symmetric epipolar distance`
39	`std::vector<cv::Point3f> l0, l1;`	66	`std::vector<cv::Point3f> l0, l1;`
40	`cv::computeCorrespondEpilines(q0, 1, F, l0);`	67	`cv::computeCorrespondEpilines(q0, 1, F, l0);`
41	`cv::computeCorrespondEpilines(q1, 2, F, l1);`	68	`cv::computeCorrespondEpilines(q1, 2, F, l1);`
42		69
43	`for(int i = 0; i < n0; i++){`	70	`for(int i = 0; i < n0; i++){`
44	`cv::Vec3f p0 = cv::Vec3f(q0[i].x, q0[i].y, 1.0);`	71	`cv::Vec3f p0 = cv::Vec3f(q0[i].x, q0[i].y, 1.0);`
45	`for(int j = 0; j < n1; j++){`	72	`for(int j = 0; j < n1; j++){`
46	`cv::Vec3f p1 = cv::Vec3f(q1[j].x, q1[j].y, 1.0);`	73	`cv::Vec3f p1 = cv::Vec3f(q1[j].x, q1[j].y, 1.0);`
47	`float d01 = l0[i].dot(p1);`	74	`float d01 = l0[i].dot(p1);`
48	`float d10 = l1[j].dot(p0);`	75	`float d10 = l1[j].dot(p0);`
49	`float d = d01d01 + d10d10;`	76	`float d = d01d01 + d10d10;`
50	`if(d < maxD){`	77	`if(d < maxD){`
51	`q0Correct.push_back(q0[i]);`	78	`q0Correct.push_back(q0[i]);`
52	`q1Correct.push_back(q1[i]);`	79	`q1Correct.push_back(q1[i]);`
53	`}`	80	`}`
54	`}`	81	`}`
55	`}`	82	`}`
56		83
57	`// // Sampson Error (H&Z, p. 287) (expensive...)`	84	`// // Sampson Error (H&Z, p. 287) (expensive...)`
58	`// std::vector<cv::Point3f> p0, p1;`	85	`// std::vector<cv::Point3f> p0, p1;`
59	`// cv::convertPointsToHomogeneous(q0, p0);`	86	`// cv::convertPointsToHomogeneous(q0, p0);`
60	`// cv::convertPointsToHomogeneous(q1, p1);`	87	`// cv::convertPointsToHomogeneous(q1, p1);`
61	`// cv::Mat Fp0Mat = cv::Mat(F)*cv::Mat(p0).reshape(1).t();`	88	`// cv::Mat Fp0Mat = cv::Mat(F)*cv::Mat(p0).reshape(1).t();`
62	`// cv::Mat FTp1Mat = cv::Mat(F.t())*cv::Mat(p1).reshape(1).t();`	89	`// cv::Mat FTp1Mat = cv::Mat(F.t())*cv::Mat(p1).reshape(1).t();`
63	`// for( int i = 0; i < n1; i++ ){`	90	`// for( int i = 0; i < n1; i++ ){`
64	`// cv::Vec3f Fp0 = Fp0Mat.col(i);`	91	`// cv::Vec3f Fp0 = Fp0Mat.col(i);`
65	`// for( int j = 0; j < n2; j++ ){`	92	`// for( int j = 0; j < n2; j++ ){`
66	`// cv::Vec3f FTp1 = FTp1Mat.col(j);`	93	`// cv::Vec3f FTp1 = FTp1Mat.col(j);`
67	`// cv::Matx<float,1,1> p1TFp0 = cv::Matx31f(p1[j]).t()Fcv::Matx31f(p0[i]);`	94	`// cv::Matx<float,1,1> p1TFp0 = cv::Matx31f(p1[j]).t()Fcv::Matx31f(p0[i]);`
68	`// float d = p1TFp0(0)p1TFp0(0) / (Fp0(0)Fp0(0) + Fp0(1)Fp0(1) + FTp1(0)FTp1(0) + FTp1(1)*FTp1(1));`	95	`// float d = p1TFp0(0)p1TFp0(0) / (Fp0(0)Fp0(0) + Fp0(1)Fp0(1) + FTp1(0)FTp1(0) + FTp1(1)*FTp1(1));`
69	`// if(d < maxD){`	96	`// if(d < maxD){`
70	`// q0Correct.push_back(q0[i]);`	97	`// q0Correct.push_back(q0[i]);`
71	`// q1Correct.push_back(q1[i]);`	98	`// q1Correct.push_back(q1[i]);`
72	`// }`	99	`// }`
73	`// }`	100	`// }`
74	`// }`	101	`// }`
75		102
76	`return;`	103	`return;`
77	`}`	104	`}`
78		105
79	`// Lightly modified OpenCV function which accepts a line width argument`	106	`// Lightly modified OpenCV function which accepts a line width argument`
80	`void drawChessboardCorners(cv::InputOutputArray _image, cv::Size patternSize, cv::InputArray _corners, bool patternWasFound, int line_width){`	107	`void drawChessboardCorners(cv::InputOutputArray _image, cv::Size patternSize, cv::InputArray _corners, bool patternWasFound, int line_width){`
81	`cv::Mat corners = _corners.getMat();`	108	`cv::Mat corners = _corners.getMat();`
82	`if( corners.empty() )`	109	`if( corners.empty() )`
83	`return;`	110	`return;`
84	`cv::Mat image = _image.getMat(); CvMat c_image = _image.getMat();`	111	`cv::Mat image = _image.getMat(); CvMat c_image = _image.getMat();`
85	`int nelems = corners.checkVector(2, CV_32F, true);`	112	`int nelems = corners.checkVector(2, CV_32F, true);`
86	`CV_Assert(nelems >= 0);`	113	`CV_Assert(nelems >= 0);`
87	`cvDrawChessboardCorners( &c_image, patternSize, (CvPoint2D32f*)corners.data,`	114	`cvDrawChessboardCorners( &c_image, patternSize, (CvPoint2D32f*)corners.data,`
88	`nelems, patternWasFound, line_width);`	115	`nelems, patternWasFound, line_width);`
89	`}`	116	`}`
90		117
91	`void rshift(cv::Mat& I, unsigned int shift){`	118	`void rshift(cv::Mat& I, unsigned int shift){`
92		119
93	`int nRows = I.rows;`	120	`int nRows = I.rows;`
94	`int nCols = I.cols;`	121	`int nCols = I.cols;`
95		122
96	`if (I.isContinuous()){`	123	`if (I.isContinuous()){`
97	`nCols *= nRows;`	124	`nCols *= nRows;`
98	`nRows = 1;`	125	`nRows = 1;`
99	`}`	126	`}`
100		127
101	`int i,j;`	128	`int i,j;`
102	`unsigned short* p;`	129	`unsigned short* p;`
103	`for( i = 0; i < nRows; ++i){`	130	`for( i = 0; i < nRows; ++i){`
104	`p = I.ptr<unsigned short>(i);`	131	`p = I.ptr<unsigned short>(i);`
105	`for ( j = 0; j < nCols; ++j){`	132	`for ( j = 0; j < nCols; ++j){`
106	`p[j] = p[j]>>shift;`	133	`p[j] = p[j]>>shift;`
107	`}`	134	`}`
108	`}`	135	`}`
109	`}`	136	`}`
110		137
111	`void cvDrawChessboardCorners(CvArr* _image, CvSize pattern_size, CvPoint2D32f* corners, int count, int found, int line_width){`	138	`void cvDrawChessboardCorners(CvArr* _image, CvSize pattern_size, CvPoint2D32f* corners, int count, int found, int line_width){`
112	`const int shift = 0;`	139	`const int shift = 0;`
113	`const int radius = 12;`	140	`const int radius = 12;`
114	`const int r = radius*(1 << shift);`	141	`const int r = radius*(1 << shift);`
115	`int i;`	142	`int i;`
116	`CvMat stub, *image;`	143	`CvMat stub, *image;`
117	`double scale = 1;`	144	`double scale = 1;`
118	`int type, cn, line_type;`	145	`int type, cn, line_type;`
119		146
120	`image = cvGetMat( _image, &stub );`	147	`image = cvGetMat( _image, &stub );`
121		148
122	`type = CV_MAT_TYPE(image->type);`	149	`type = CV_MAT_TYPE(image->type);`
123	`cn = CV_MAT_CN(type);`	150	`cn = CV_MAT_CN(type);`
124	`if( cn != 1 && cn != 3 && cn != 4 )`	151	`if( cn != 1 && cn != 3 && cn != 4 )`
125	`CV_Error( CV_StsUnsupportedFormat, "Number of channels must be 1, 3 or 4" );`	152	`CV_Error( CV_StsUnsupportedFormat, "Number of channels must be 1, 3 or 4" );`
126		153
127	`switch( CV_MAT_DEPTH(image->type) )`	154	`switch( CV_MAT_DEPTH(image->type) )`
128	`{`	155	`{`
129	`case CV_8U:`	156	`case CV_8U:`
130	`scale = 1;`	157	`scale = 1;`
131	`break;`	158	`break;`
132	`case CV_16U:`	159	`case CV_16U:`
133	`scale = 256;`	160	`scale = 256;`
134	`break;`	161	`break;`
135	`case CV_32F:`	162	`case CV_32F:`
136	`scale = 1./255;`	163	`scale = 1./255;`
137	`break;`	164	`break;`
138	`default:`	165	`default:`
139	`CV_Error( CV_StsUnsupportedFormat,`	166	`CV_Error( CV_StsUnsupportedFormat,`
140	`"Only 8-bit, 16-bit or floating-point 32-bit images are supported" );`	167	`"Only 8-bit, 16-bit or floating-point 32-bit images are supported" );`
141	`}`	168	`}`
142		169
143	`line_type = type == CV_8UC1 \|\| type == CV_8UC3 ? CV_AA : 8;`	170	`line_type = type == CV_8UC1 \|\| type == CV_8UC3 ? CV_AA : 8;`
144		171
145	`if( !found )`	172	`if( !found )`
146	`{`	173	`{`
147	`CvScalar color = {{0,0,255}};`	174	`CvScalar color = {{0,0,255}};`
148	`if( cn == 1 )`	175	`if( cn == 1 )`
149	`color = cvScalarAll(200);`	176	`color = cvScalarAll(200);`
150	`color.val[0] *= scale;`	177	`color.val[0] *= scale;`
151	`color.val[1] *= scale;`	178	`color.val[1] *= scale;`
152	`color.val[2] *= scale;`	179	`color.val[2] *= scale;`
153	`color.val[3] *= scale;`	180	`color.val[3] *= scale;`
154		181
155	`for( i = 0; i < count; i++ )`	182	`for( i = 0; i < count; i++ )`
156	`{`	183	`{`
157	`CvPoint pt;`	184	`CvPoint pt;`
158	`pt.x = cvRound(corners[i].x*(1 << shift));`	185	`pt.x = cvRound(corners[i].x*(1 << shift));`
159	`pt.y = cvRound(corners[i].y*(1 << shift));`	186	`pt.y = cvRound(corners[i].y*(1 << shift));`
160	`cvLine( image, cvPoint( pt.x - r, pt.y - r ),`	187	`cvLine( image, cvPoint( pt.x - r, pt.y - r ),`
161	`cvPoint( pt.x + r, pt.y + r ), color, line_width, line_type, shift );`	188	`cvPoint( pt.x + r, pt.y + r ), color, line_width, line_type, shift );`
162	`cvLine( image, cvPoint( pt.x - r, pt.y + r),`	189	`cvLine( image, cvPoint( pt.x - r, pt.y + r),`
163	`cvPoint( pt.x + r, pt.y - r), color, line_width, line_type, shift );`	190	`cvPoint( pt.x + r, pt.y - r), color, line_width, line_type, shift );`
164	`cvCircle( image, pt, r+(1<<shift), color, line_width, line_type, shift );`	191	`cvCircle( image, pt, r+(1<<shift), color, line_width, line_type, shift );`
165	`}`	192	`}`
166	`}`	193	`}`
167	`else`	194	`else`
168	`{`	195	`{`
169	`int x, y;`	196	`int x, y;`
170	`CvPoint prev_pt = {0, 0};`	197	`CvPoint prev_pt = {0, 0};`
171	`const int line_max = 7;`	198	`const int line_max = 7;`
172	`static const CvScalar line_colors[line_max] =`	199	`static const CvScalar line_colors[line_max] =`
173	`{`	200	`{`
174	`{{0,0,255}},`	201	`{{0,0,255}},`
175	`{{0,128,255}},`	202	`{{0,128,255}},`
176	`{{0,200,200}},`	203	`{{0,200,200}},`
177	`{{0,255,0}},`	204	`{{0,255,0}},`
178	`{{200,200,0}},`	205	`{{200,200,0}},`
179	`{{255,0,0}},`	206	`{{255,0,0}},`
180	`{{255,0,255}}`	207	`{{255,0,255}}`
181	`};`	208	`};`
182		209
183	`for( y = 0, i = 0; y < pattern_size.height; y++ )`	210	`for( y = 0, i = 0; y < pattern_size.height; y++ )`
184	`{`	211	`{`
185	`CvScalar color = line_colors[y % line_max];`	212	`CvScalar color = line_colors[y % line_max];`
186	`if( cn == 1 )`	213	`if( cn == 1 )`
187	`color = cvScalarAll(200);`	214	`color = cvScalarAll(200);`
188	`color.val[0] *= scale;`	215	`color.val[0] *= scale;`
189	`color.val[1] *= scale;`	216	`color.val[1] *= scale;`
190	`color.val[2] *= scale;`	217	`color.val[2] *= scale;`
191	`color.val[3] *= scale;`	218	`color.val[3] *= scale;`
192		219
193	`for( x = 0; x < pattern_size.width; x++, i++ )`	220	`for( x = 0; x < pattern_size.width; x++, i++ )`
194	`{`	221	`{`
195	`CvPoint pt;`	222	`CvPoint pt;`
196	`pt.x = cvRound(corners[i].x*(1 << shift));`	223	`pt.x = cvRound(corners[i].x*(1 << shift));`
197	`pt.y = cvRound(corners[i].y*(1 << shift));`	224	`pt.y = cvRound(corners[i].y*(1 << shift));`
198		225
199	`if( i != 0 )`	226	`if( i != 0 )`
200	`cvLine( image, prev_pt, pt, color, 1, line_type, shift );`	227	`cvLine( image, prev_pt, pt, color, 1, line_type, shift );`
201		228
202	`cvLine( image, cvPoint(pt.x - r, pt.y - r),`	229	`cvLine( image, cvPoint(pt.x - r, pt.y - r),`
203	`cvPoint(pt.x + r, pt.y + r), color, line_width, line_type, shift );`	230	`cvPoint(pt.x + r, pt.y + r), color, line_width, line_type, shift );`
204	`cvLine( image, cvPoint(pt.x - r, pt.y + r),`	231	`cvLine( image, cvPoint(pt.x - r, pt.y + r),`
205	`cvPoint(pt.x + r, pt.y - r), color, line_width, line_type, shift );`	232	`cvPoint(pt.x + r, pt.y - r), color, line_width, line_type, shift );`
206	`cvCircle( image, pt, r+(1<<shift), color, line_width, line_type, shift );`	233	`cvCircle( image, pt, r+(1<<shift), color, line_width, line_type, shift );`
207	`prev_pt = pt;`	234	`prev_pt = pt;`
208	`}`	235	`}`
209	`}`	236	`}`
210	`}`	237	`}`
211	`}`	238	`}`
212		239
213	`// Returns the result of mod(mat(x,y), moduli) for each matrix element`	240	`// Returns the result of mod(mat(x,y), moduli) for each matrix element`
214	`cv::Mat modulo(const cv::Mat &mat, float n){`	241	`cv::Mat modulo(const cv::Mat &mat, float n){`
215		242
216	`cv::Mat ret(mat.rows, mat.cols, mat.type());`	243	`cv::Mat ret(mat.rows, mat.cols, mat.type());`
217		244
218	`for(int row=0; row<ret.rows; row++){`	245	`for(int row=0; row<ret.rows; row++){`
219	`for(int col=0; col<ret.cols; col++){`	246	`for(int col=0; col<ret.cols; col++){`
220	`float val = mat.at<float>(row, col);`	247	`float val = mat.at<float>(row, col);`
221	`// note: std::fmod calculates the remainder, not arithmetic modulo`	248	`// note: std::fmod calculates the remainder, not arithmetic modulo`
222	`ret.at<float>(row, col) = val - n * std::floor(val / n);`	249	`ret.at<float>(row, col) = val - n * std::floor(val / n);`
223	`}`	250	`}`
224	`}`	251	`}`
225		252
226	`return ret;`	253	`return ret;`
227	`}`	254	`}`
228		255
229	`// Convert a 3xN matrix to a vector of Point3fs.`	256	`// Convert a 3xN matrix to a vector of Point3fs.`
230	`void matToPoints3f(const cv::Mat &mat, std::vector<cv::Point3f> &points){`	257	`void matToPoints3f(const cv::Mat &mat, std::vector<cv::Point3f> &points){`
231		258
232	`unsigned int nPoints = mat.cols;`	259	`unsigned int nPoints = mat.cols;`
233	`points.resize(nPoints);`	260	`points.resize(nPoints);`
234		261
235	`for(unsigned int i=0; i<nPoints; i++)`	262	`for(unsigned int i=0; i<nPoints; i++)`
236	`points[i] = cv::Point3f(mat.at<float>(0, i), mat.at<float>(1, i), mat.at<float>(2, i));`	263	`points[i] = cv::Point3f(mat.at<float>(0, i), mat.at<float>(1, i), mat.at<float>(2, i));`
237	`}`	264	`}`
238		265
239	`// Convert a (Dim+1)xN matrix of homogenous points to a DimxN matrix of points in non-homogenous coordinates.`	266	`// Convert a (Dim+1)xN matrix of homogenous points to a DimxN matrix of points in non-homogenous coordinates.`
240	`void convertMatFromHomogeneous(cv::Mat &src, cv::Mat &dst){`	267	`void convertMatFromHomogeneous(cv::Mat &src, cv::Mat &dst){`
241	`unsigned int N = src.cols;`	268	`unsigned int N = src.cols;`
242	`unsigned int Dim = src.rows-1;`	269	`unsigned int Dim = src.rows-1;`
243	`dst.create(Dim, N, src.type());`	270	`dst.create(Dim, N, src.type());`
244	`for(unsigned int i=0; i<N; i++){`	271	`for(unsigned int i=0; i<N; i++){`
245	`for(unsigned int j=0; j<Dim; j++)`	272	`for(unsigned int j=0; j<Dim; j++)`
246	`dst.at<float>(j,i) = src.at<float>(j,i)/src.at<float>(Dim,i);`	273	`dst.at<float>(j,i) = src.at<float>(j,i)/src.at<float>(Dim,i);`
247	`}`	274	`}`
248		275
249	`}`	276	`}`
250		277
251	`// Function to solve the hand-eye (or eye-in-hand) calibration problem.`	278	`// Function to solve the hand-eye (or eye-in-hand) calibration problem.`
252	`// Finds [Omega \| tau], to minimize \|\|[R_mark \| t_mark][Omega \| tau] - [Omega \| tau][R \| t]\|\|^2`	279	`// Finds [Omega \| tau], to minimize \|\|[R_mark \| t_mark][Omega \| tau] - [Omega \| tau][R \| t]\|\|^2`
253	`// Algorithm according to Tsai, Lenz, A new technique for fully autonomous and efficient 3d robotics hand-eye calibration`	280	`// Algorithm according to Tsai, Lenz, A new technique for fully autonomous and efficient 3d robotics hand-eye calibration`
254	`// DTU, 2014, Jakob Wilm`	281	`// DTU, 2014, Jakob Wilm`
255	`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){`	282	`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){`
256		283
257	`int N = R.size();`	284	`int N = R.size();`
258	`assert(N == R_mark.size());`	285	`assert(N == R_mark.size());`
259	`assert(N == t.size());`	286	`assert(N == t.size());`
260	`assert(N == t_mark.size());`	287	`assert(N == t_mark.size());`
261		288
262	`// construct equations for rotation`	289	`// construct equations for rotation`
263	`cv::Mat A(3*N, 3, CV_32F);`	290	`cv::Mat A(3*N, 3, CV_32F);`
264	`cv::Mat b(3*N, 1, CV_32F);`	291	`cv::Mat b(3*N, 1, CV_32F);`
265	`for(int i=0; i<N; i++){`	292	`for(int i=0; i<N; i++){`
266	`// angle axis representations`	293	`// angle axis representations`
267	`cv::Vec3f rot;`	294	`cv::Vec3f rot;`
268	`cv::Vec3f rot_mark;`	295	`cv::Vec3f rot_mark;`
269	`cv::Rodrigues(R[i], rot);`	296	`cv::Rodrigues(R[i], rot);`
270	`cv::Rodrigues(R_mark[i], rot_mark);`	297	`cv::Rodrigues(R_mark[i], rot_mark);`
271		298
272	`cv::Vec3f P = 2.0sin(cv::norm(rot)/2.0)cv::normalize(rot);`	299	`cv::Vec3f P = 2.0sin(cv::norm(rot)/2.0)cv::normalize(rot);`
273	`//std::cout << "P: " << std::endl << P << std::endl;`	300	`//std::cout << "P: " << std::endl << P << std::endl;`
274	`cv::Vec3f P_mark = 2.0sin(cv::norm(rot_mark)/2.0)cv::normalize(rot_mark);`	301	`cv::Vec3f P_mark = 2.0sin(cv::norm(rot_mark)/2.0)cv::normalize(rot_mark);`
275	`//std::cout << "P_mark: " << std::endl << P_mark << std::endl;`	302	`//std::cout << "P_mark: " << std::endl << P_mark << std::endl;`
276	`cv::Vec3f sum = P+P_mark;`	303	`cv::Vec3f sum = P+P_mark;`
277	`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);`	304	`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);`
278	`//std::cout << "crossProduct: " << std::endl << crossProduct << std::endl;`	305	`//std::cout << "crossProduct: " << std::endl << crossProduct << std::endl;`
279	`crossProduct.copyTo(A.rowRange(i3, i3+3));`	306	`crossProduct.copyTo(A.rowRange(i3, i3+3));`
280		307
281	`cv::Mat(P-P_mark).copyTo(b.rowRange(i3, i3+3));`	308	`cv::Mat(P-P_mark).copyTo(b.rowRange(i3, i3+3));`
282	`}`	309	`}`
283		310
284	`// solve for rotation`	311	`// solve for rotation`
285	`cv::Vec3f P_prime;`	312	`cv::Vec3f P_prime;`
286	`cv::solve(A, b, P_prime, cv::DECOMP_SVD);`	313	`cv::solve(A, b, P_prime, cv::DECOMP_SVD);`
287	`cv::Vec3f P = 2.0P_prime/(cv::sqrt(1.0 + cv::norm(P_prime)cv::norm(P_prime)));`	314	`cv::Vec3f P = 2.0P_prime/(cv::sqrt(1.0 + cv::norm(P_prime)cv::norm(P_prime)));`
288	`float nP = cv::norm(P);`	315	`float nP = cv::norm(P);`
289	`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);`	316	`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);`
290	`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);`	317	`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);`
291	`Omega = cv::Matx33f(OmegaMat);`	318	`Omega = cv::Matx33f(OmegaMat);`
292		319
293	`// construct equations for translation`	320	`// construct equations for translation`
294	`A.setTo(0.0);`	321	`A.setTo(0.0);`
295	`b.setTo(0.0);`	322	`b.setTo(0.0);`
296	`for(int i=0; i<N; i++){`	323	`for(int i=0; i<N; i++){`
297		324
298	`cv::Mat diff = cv::Mat(R_mark[i]) - cv::Mat::eye(3, 3, CV_32F);`	325	`cv::Mat diff = cv::Mat(R_mark[i]) - cv::Mat::eye(3, 3, CV_32F);`
299	`diff.copyTo(A.rowRange(i3, i3+3));`	326	`diff.copyTo(A.rowRange(i3, i3+3));`
300		327
301	`cv::Mat diff_mark = cv::Mat(Omega*t[i] - t_mark[i]);`	328	`cv::Mat diff_mark = cv::Mat(Omega*t[i] - t_mark[i]);`
302	`diff_mark.copyTo(b.rowRange(i3, i3+3));`	329	`diff_mark.copyTo(b.rowRange(i3, i3+3));`
303	`}`	330	`}`
304		331
305	`// solve for translation`	332	`// solve for translation`
306	`cv::solve(A, b, tau, cv::DECOMP_SVD);`	333	`cv::solve(A, b, tau, cv::DECOMP_SVD);`
307		334
308	`cv::Mat err_tau = b - (A*cv::Mat(tau));`	335	`cv::Mat err_tau = b - (A*cv::Mat(tau));`
309	`std::cout << err_tau << std::endl;`	336	`std::cout << err_tau << std::endl;`
310	`}`	337	`}`
311		338
312	`// Function to solve for the rotation axis from sets of 3D point coordinates of flat pattern feature points`	339	`// Function to solve for the rotation axis from sets of 3D point coordinates of flat pattern feature points`
313	`// Algorithm according to Chen et al., Rotation axis calibration of a turntable using constrained global optimization, Optik 2014`	340	`// Algorithm according to Chen et al., Rotation axis calibration of a turntable using constrained global optimization, Optik 2014`
314	`// DTU, 2014, Jakob Wilm`	341	`// DTU, 2014, Jakob Wilm`
315	`void rotationAxisCalibration(const std::vector< std::vector<cv::Point3f> > Qcam, const std::vector<cv::Point3f> Qobj, cv::Vec3f &axis, cv::Vec3f &point){`	342	`void rotationAxisCalibration(const std::vector< std::vector<cv::Point3f> > Qcam, const std::vector<cv::Point3f> Qobj, cv::Vec3f &axis, cv::Vec3f &point){`
316		343
317	`// number of frames (points on each arch)`	344	`// number of frames (points on each arch)`
318	`int l = Qcam.size();`	345	`int l = Qcam.size();`
319		346
320	`// number of points in each frame`	347	`// number of points in each frame`
321	`int mn = Qobj.size();`	348	`int mn = Qobj.size();`
322		349
323	`assert(mn == Qcam[0].size());`	350	`assert(mn == Qcam[0].size());`
324		351
325	`// construct matrix for axis determination`	352	`// construct matrix for axis determination`
326	`cv::Mat M(6, 6, CV_32F, cv::Scalar(0));`	353	`cv::Mat M(6, 6, CV_32F, cv::Scalar(0));`
327		354
328	`for(int k=0; k<l; k++){`	355	`for(int k=0; k<l; k++){`
329	`for(int idx=0; idx<mn; idx++){`	356	`for(int idx=0; idx<mn; idx++){`
330		357
331	`// float i = Qobj[idx].x+4;`	358	`// float i = Qobj[idx].x+4;`
332	`// float j = Qobj[idx].y+4;`	359	`// float j = Qobj[idx].y+4;`
333	`float i = Qobj[idx].x;`	360	`float i = Qobj[idx].x;`
334	`float j = Qobj[idx].y;`	361	`float j = Qobj[idx].y;`
335		362
336	`float x = Qcam[k][idx].x;`	363	`float x = Qcam[k][idx].x;`
337	`float y = Qcam[k][idx].y;`	364	`float y = Qcam[k][idx].y;`
338	`float z = Qcam[k][idx].z;`	365	`float z = Qcam[k][idx].z;`
339		366
340	`M += (cv::Mat_<float>(6,6) << xx, xy, xz, x, ix, j*x,`	367	`M += (cv::Mat_<float>(6,6) << xx, xy, xz, x, ix, j*x,`
341	`0, yy, yz, y, iy, jy,`	368	`0, yy, yz, y, iy, jy,`
342	`0, 0, zz, z, iz, j*z,`	369	`0, 0, zz, z, iz, j*z,`
343	`0, 0, 0, 1, i, j,`	370	`0, 0, 0, 1, i, j,`
344	`0, 0, 0, 0, ii, ij,`	371	`0, 0, 0, 0, ii, ij,`
345	`0, 0, 0, 0, 0, j*j);`	372	`0, 0, 0, 0, 0, j*j);`
346		373
347	`}`	374	`}`
348	`}`	375	`}`
349		376
350	`cv::completeSymm(M, false);`	377	`cv::completeSymm(M, false);`
351		378
352	`// solve for axis`	379	`// solve for axis`
353	`std::vector<float> lambda;`	380	`std::vector<float> lambda;`
354	`cv::Mat u;`	381	`cv::Mat u;`
355	`cv::eigen(M, lambda, u);`	382	`cv::eigen(M, lambda, u);`
356		383
357	`float minLambda = abs(lambda[0]);`	384	`float minLambda = abs(lambda[0]);`
358	`int idx = 0;`	385	`int idx = 0;`
359	`for(int i=1; i<lambda.size(); i++){`	386	`for(int i=1; i<lambda.size(); i++){`
360	`if(abs(lambda[i]) < minLambda){`	387	`if(abs(lambda[i]) < minLambda){`
361	`minLambda = lambda[i];`	388	`minLambda = lambda[i];`
362	`idx = i;`	389	`idx = i;`
363	`}`	390	`}`
364	`}`	391	`}`
365		392
366	`axis = u.row(idx).colRange(0, 3);`	393	`axis = u.row(idx).colRange(0, 3);`
367	`axis = cv::normalize(axis);`	394	`axis = cv::normalize(axis);`
368		395
369	`float nx = u.at<float>(idx, 0);`	396	`float nx = u.at<float>(idx, 0);`
370	`float ny = u.at<float>(idx, 1);`	397	`float ny = u.at<float>(idx, 1);`
371	`float nz = u.at<float>(idx, 2);`	398	`float nz = u.at<float>(idx, 2);`
372	`float d = u.at<float>(idx, 3);`	399	`float d = u.at<float>(idx, 3);`
373	`float dh = u.at<float>(idx, 4);`	400	`float dh = u.at<float>(idx, 4);`
374	`float dv = u.at<float>(idx, 5);`	401	`float dv = u.at<float>(idx, 5);`
375		402
376	`// // Paper version: c is initially eliminated`	403	`// // Paper version: c is initially eliminated`
377	`// cv::Mat A(l*mn, mn+2, CV_32F, cv::Scalar(0.0));`	404	`// cv::Mat A(l*mn, mn+2, CV_32F, cv::Scalar(0.0));`
378	`// cv::Mat bb(l*mn, 1, CV_32F);`	405	`// cv::Mat bb(l*mn, 1, CV_32F);`
379		406
380	`// for(int k=0; k<l; k++){`	407	`// for(int k=0; k<l; k++){`
381	`// for(int idx=0; idx<mn; idx++){`	408	`// for(int idx=0; idx<mn; idx++){`
382		409
383	`// float i = Qobj[idx].x;`	410	`// float i = Qobj[idx].x;`
384	`// float j = Qobj[idx].y;`	411	`// float j = Qobj[idx].y;`
385		412
386	`// float x = Qcam[k][idx].x;`	413	`// float x = Qcam[k][idx].x;`
387	`// float y = Qcam[k][idx].y;`	414	`// float y = Qcam[k][idx].y;`
388	`// float z = Qcam[k][idx].z;`	415	`// float z = Qcam[k][idx].z;`
389		416
390	`// float f = xx + yy + zz + (2xnx + 2yny + 2znz)(idh + jdv);`	417	`// float f = xx + yy + zz + (2xnx + 2yny + 2znz)(idh + jdv);`
391		418
392	`// int row = k*mn+idx;`	419	`// int row = k*mn+idx;`
393	`// A.at<float>(row, 0) = 2x - (2z*nx)/nz;`	420	`// A.at<float>(row, 0) = 2x - (2z*nx)/nz;`
394	`// A.at<float>(row, 1) = 2y - (2z*ny)/nz;`	421	`// A.at<float>(row, 1) = 2y - (2z*ny)/nz;`
395	`// A.at<float>(row, idx+2) = 1.0;`	422	`// A.at<float>(row, idx+2) = 1.0;`
396		423
397	`// bb.at<float>(row, 0) = f + (2zd)/nz;`	424	`// bb.at<float>(row, 0) = f + (2zd)/nz;`
398	`// }`	425	`// }`
399	`// }`	426	`// }`
400		427
401	`// // solve for point`	428	`// // solve for point`
402	`// cv::Mat abe;`	429	`// cv::Mat abe;`
403	`// cv::solve(A, bb, abe, cv::DECOMP_SVD);`	430	`// cv::solve(A, bb, abe, cv::DECOMP_SVD);`
404		431
405	`// float a = abe.at<float>(0, 0);`	432	`// float a = abe.at<float>(0, 0);`
406	`// float b = abe.at<float>(1, 0);`	433	`// float b = abe.at<float>(1, 0);`
407	`// float c = -(nxa+nyb+d)/nz;`	434	`// float c = -(nxa+nyb+d)/nz;`
408		435
409	`// Our version: solve simultanously for a,b,c`	436	`// Our version: solve simultanously for a,b,c`
410	`cv::Mat A(l*mn, mn+3, CV_32F, cv::Scalar(0.0));`	437	`cv::Mat A(l*mn, mn+3, CV_32F, cv::Scalar(0.0));`
411	`cv::Mat bb(l*mn, 1, CV_32F);`	438	`cv::Mat bb(l*mn, 1, CV_32F);`
412		439
413	`for(int k=0; k<l; k++){`	440	`for(int k=0; k<l; k++){`
414	`for(int idx=0; idx<mn; idx++){`	441	`for(int idx=0; idx<mn; idx++){`
415		442
416	`float i = Qobj[idx].x;`	443	`float i = Qobj[idx].x;`
417	`float j = Qobj[idx].y;`	444	`float j = Qobj[idx].y;`
418		445
419	`float x = Qcam[k][idx].x;`	446	`float x = Qcam[k][idx].x;`
420	`float y = Qcam[k][idx].y;`	447	`float y = Qcam[k][idx].y;`
421	`float z = Qcam[k][idx].z;`	448	`float z = Qcam[k][idx].z;`
422		449
423	`float f = xx + yy + zz + (2xnx + 2yny + 2znz)(idh + jdv);`	450	`float f = xx + yy + zz + (2xnx + 2yny + 2znz)(idh + jdv);`
424		451
425	`int row = k*mn+idx;`	452	`int row = k*mn+idx;`
426	`A.at<float>(row, 0) = 2*x;`	453	`A.at<float>(row, 0) = 2*x;`
427	`A.at<float>(row, 1) = 2*y;`	454	`A.at<float>(row, 1) = 2*y;`
428	`A.at<float>(row, 2) = 2*z;`	455	`A.at<float>(row, 2) = 2*z;`
429	`A.at<float>(row, idx+3) = 1.0;`	456	`A.at<float>(row, idx+3) = 1.0;`
430		457
431	`bb.at<float>(row, 0) = f;`	458	`bb.at<float>(row, 0) = f;`
432	`}`	459	`}`
433	`}`	460	`}`
434		461
435	`// solve for point`	462	`// solve for point`
436	`cv::Mat abe;`	463	`cv::Mat abe;`
437	`cv::solve(A, bb, abe, cv::DECOMP_SVD);`	464	`cv::solve(A, bb, abe, cv::DECOMP_SVD);`
438		465
439	`float a = abe.at<float>(0, 0);`	466	`float a = abe.at<float>(0, 0);`
440	`float b = abe.at<float>(1, 0);`	467	`float b = abe.at<float>(1, 0);`
441	`float c = abe.at<float>(2, 0);`	468	`float c = abe.at<float>(2, 0);`
442		469
443	`point[0] = a;`	470	`point[0] = a;`
444	`point[1] = b;`	471	`point[1] = b;`
445	`point[2] = c;`	472	`point[2] = c;`
446		473
447	`}`	474	`}`
448		475
449	`// Function to fit two sets of corresponding pose data.`	476	`// Function to fit two sets of corresponding pose data.`
450	`// Finds [Omega \| tau], to minimize \|\|[R_mark \| t_mark] - [Omega \| tau][R \| t]\|\|^2`	477	`// Finds [Omega \| tau], to minimize \|\|[R_mark \| t_mark] - [Omega \| tau][R \| t]\|\|^2`
451	`// Algorithm and notation according to Mili Shah, Comparing two sets of corresponding six degree of freedom data, CVIU 2011.`	478	`// Algorithm and notation according to Mili Shah, Comparing two sets of corresponding six degree of freedom data, CVIU 2011.`
452	`// DTU, 2013, Oline V. Olesen, Jakob Wilm`	479	`// DTU, 2013, Oline V. Olesen, Jakob Wilm`
453	`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){`	480	`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){`
454		481
455	`int N = R.size();`	482	`int N = R.size();`
456	`assert(N == R_mark.size());`	483	`assert(N == R_mark.size());`
457	`assert(N == t.size());`	484	`assert(N == t.size());`
458	`assert(N == t_mark.size());`	485	`assert(N == t_mark.size());`
459		486
460	`// Mean translations`	487	`// Mean translations`
461	`cv::Vec3f t_mean;`	488	`cv::Vec3f t_mean;`
462	`cv::Vec3f t_mark_mean;`	489	`cv::Vec3f t_mark_mean;`
463	`for(int i=0; i<N; i++){`	490	`for(int i=0; i<N; i++){`
464	`t_mean += 1.0/N * t[i];`	491	`t_mean += 1.0/N * t[i];`
465	`t_mark_mean += 1.0/N * t_mark[i];`	492	`t_mark_mean += 1.0/N * t_mark[i];`
466	`}`	493	`}`
467		494
468	`// Data with mean adjusted translations`	495	`// Data with mean adjusted translations`
469	`cv::Mat X_bar(3, 4*N, CV_32F);`	496	`cv::Mat X_bar(3, 4*N, CV_32F);`
470	`cv::Mat X_mark_bar(3, 4*N, CV_32F);`	497	`cv::Mat X_mark_bar(3, 4*N, CV_32F);`
471	`for(int i=0; i<N; i++){`	498	`for(int i=0; i<N; i++){`
472	`cv::Mat(R[i]).copyTo(X_bar.colRange(i4,i4+3));`	499	`cv::Mat(R[i]).copyTo(X_bar.colRange(i4,i4+3));`
473	`cv::Mat(t[i] - t_mean).copyTo(X_bar.col(i*4+3));`	500	`cv::Mat(t[i] - t_mean).copyTo(X_bar.col(i*4+3));`

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