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


#include "cvtools.h"
 
#ifdef _WIN32
#include <cstdint>
#endif
 
#include <stdio.h>
 
namespace cvtools{
 
// 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 120	Rev 121
1	`#include "cvtools.h"`	1	`#include "cvtools.h"`
2		2
3	`#ifdef _WIN32`	3	`#ifdef _WIN32`
4	`#include <cstdint>`	4	`#include <cstdint>`
5	`#endif`	5	`#endif`
6		6
7	`#include <stdio.h>`	7	`#include <stdio.h>`
8		8
9	`namespace cvtools{`	9	`namespace cvtools{`
10		10
11	`// Create a mask for feature matching which disallows matches not satisfying the epipolar constraint.`	11	`// Removes matches not satisfying the epipolar constraint.`
12	`// Works like cv::windowedMatchingMask in conjunction with cv::BFMatcher::match().`	-
13	`// F is the fundamental matrix.`	12	`// F is the fundamental matrix.`
14	`// maxD is the maximum point to line distance permissible.`	13	`// Works like cv::correctMatches(), except it removes matches with an error distance greater than maxD.`
15	`cv::Mat epipolarMatchingMask(const cv::vector<cv::KeyPoint> &keypoints1, const cv::vector<cv::KeyPoint> &keypoints2, cv::Matx33f F, float maxD){`	14	`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){`
16		16
17	`if(keypoints1.empty() \|\| keypoints2.empty())`	17	`int n0 = (int)q0.size(), n1 = (int)q1.size();`
18	`return cv::Mat();`	18	`q0Correct.reserve(n0);`
19		-
20	`int n1 = (int)keypoints1.size(), n2 = (int)keypoints2.size();`	-
21	`cv::Mat mask(n1, n2, CV_8UC1);`	19	`q1Correct.reserve(n1);`
22		20
23	`// Point to line distance`	21	`// Point to line distance`
24	`// for( int i = 0; i < n1; i++ ){`	22	`// for( int i = 0; i < n1; i++ ){`
25	`// cv::Vec3f p1 = cv::Vec3f(keypoints1[i].pt.x, keypoints1[i].pt.y, 1.0);`	23	`// cv::Vec3f p0 = cv::Vec3f(q0[i].x, q0[i].y, 1.0);`
26	`// // Epipolar line defined by p1`	24	`// // Epipolar line defined by p0`
27	`// cv::Vec3f l = F*p1;`	25	`// cv::Vec3f l = F*p0;`
28	`// l /= sqrt(l(0)l(0) + l(1)l(1));`	26	`// l /= sqrt(l(0)l(0) + l(1)l(1));`
29	`// for( int j = 0; j < n2; j++ ){`	27	`// for( int j = 0; j < n2; j++ ){`
30	`// cv::Vec3f p2 = cv::Vec3f(keypoints2[j].pt.x, keypoints2[j].pt.y, 1.0);`	28	`// cv::Vec3f p1 = cv::Vec3f(q1[i].x, q1[i].y, 1.0);`
31	`// // Signed distance to line`	29	`// // Signed distance to line`
32	`// float d = l.dot(p2);`	30	`// float d = l.dot(p1);`
-		31	`// if(d < maxD){`
-		32	`// q0Correct.push_back(q0[i]);`
33	`// mask.at<uchar>(i, j) = fabs(d) < maxD;`	33	`// q1Correct.push_back(q1[i]);`
-		34	`// }`
34	`// }`	35	`// }`
35	`// }`	36	`// }`
36		37
37	`// Symmetric epipolar distance`	38	`// 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;`	39	`std::vector<cv::Point3f> l0, l1;`
42	`cv::computeCorrespondEpilines(q1, 1, F, l1);`	40	`cv::computeCorrespondEpilines(q0, 1, F, l0);`
43	`cv::computeCorrespondEpilines(q2, 2, F, l2);`	41	`cv::computeCorrespondEpilines(q1, 2, F, l1);`
44		42
45	`for( int i = 0; i < n1; i++ ){`	43	`for(int i = 0; i < n0; i++){`
46	`cv::Vec3f p1 = cv::Vec3f(q1[i].x, q1[i].y, 1.0);`	44	`cv::Vec3f p0 = cv::Vec3f(q0[i].x, q0[i].y, 1.0);`
47	`for( int j = 0; j < n2; j++ ){`	45	`for(int j = 0; j < n1; j++){`
48	`cv::Vec3f p2 = cv::Vec3f(q2[j].x, q2[j].y, 1.0);`	46	`cv::Vec3f p1 = cv::Vec3f(q1[j].x, q1[j].y, 1.0);`
49	`float d12 = l1[i].dot(p2);`	47	`float d01 = l0[i].dot(p1);`
50	`float d21 = l2[j].dot(p1);`	48	`float d10 = l1[j].dot(p0);`
51	`float d = d12d12 + d21d21;`	49	`float d = d01d01 + d10d10;`
52	`mask.at<uchar>(i, j) = d < maxD;`	50	`if(d < maxD){`
-		51	`q0Correct.push_back(q0[i]);`
-		52	`q1Correct.push_back(q1[i]);`
-		53	`}`
53	`}`	54	`}`
54	`}`	55	`}`
55		56
56	`// // Sampson Error (H&Z, p. 287) (expensive...)`	57	`// // Sampson Error (H&Z, p. 287) (expensive...)`
57	`// std::vector<cv::Point2f> q1, q2;`	58	`// std::vector<cv::Point3f> p0, p1;`
58	`// cvtools::keypointsToPoints(keypoints1, q1);`	-
59	`// cvtools::keypointsToPoints(keypoints2, q2);`	59	`// cv::convertPointsToHomogeneous(q0, p0);`
60	`// std::vector<cv::Point3f> p1, p2;`	-
61	`// cv::convertPointsToHomogeneous(q1, p1);`	60	`// cv::convertPointsToHomogeneous(q1, p1);`
62	`// cv::convertPointsToHomogeneous(q2, p2);`	-
63	`// cv::Mat Fp1Mat = cv::Mat(F)*cv::Mat(p1).reshape(1).t();`	61	`// cv::Mat Fp0Mat = cv::Mat(F)*cv::Mat(p0).reshape(1).t();`
64	`// cv::Mat FTp2Mat = cv::Mat(F.t())*cv::Mat(p2).reshape(1).t();`	62	`// cv::Mat FTp1Mat = cv::Mat(F.t())*cv::Mat(p1).reshape(1).t();`
65	`// for( int i = 0; i < n1; i++ ){`	63	`// for( int i = 0; i < n1; i++ ){`
66	`// cv::Vec3f Fp1 = Fp1Mat.col(i);`	64	`// cv::Vec3f Fp0 = Fp0Mat.col(i);`
67	`// for( int j = 0; j < n2; j++ ){`	65	`// for( int j = 0; j < n2; j++ ){`
68	`// cv::Vec3f FTp2 = FTp2Mat.col(j);`	66	`// cv::Vec3f FTp1 = FTp1Mat.col(j);`
69	`// cv::Matx<float,1,1> p2TFp1 = cv::Matx31f(p2[j]).t()Fcv::Matx31f(p1[i]);`	67	`// cv::Matx<float,1,1> p1TFp0 = cv::Matx31f(p1[j]).t()Fcv::Matx31f(p0[i]);`
70	`// float d = p2TFp1(0)p2TFp1(0) / (Fp1(0)Fp1(0) + Fp1(1)Fp1(1) + FTp2(0)FTp2(0) + FTp2(1)*FTp2(1));`	68	`// float d = p1TFp0(0)p1TFp0(0) / (Fp0(0)Fp0(0) + Fp0(1)Fp0(1) + FTp1(0)FTp1(0) + FTp1(1)*FTp1(1));`
71	`// mask.at<uchar>(i, j) = d < maxD;`	69	`// if(d < maxD){`
-		70	`// q0Correct.push_back(q0[i]);`
-		71	`// q1Correct.push_back(q1[i]);`
-		72	`// }`
72	`// }`	73	`// }`
73	`// }`	74	`// }`
74		75
75	`return mask;`	76	`return;`
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	`}`	77	`}`
92		78
93	`// Lightly modified OpenCV function which accepts a line width argument`	79	`// Lightly modified OpenCV function which accepts a line width argument`
94	`void drawChessboardCorners(cv::InputOutputArray _image, cv::Size patternSize, cv::InputArray _corners, bool patternWasFound, int line_width){`	80	`void drawChessboardCorners(cv::InputOutputArray _image, cv::Size patternSize, cv::InputArray _corners, bool patternWasFound, int line_width){`
95	`cv::Mat corners = _corners.getMat();`	81	`cv::Mat corners = _corners.getMat();`
96	`if( corners.empty() )`	82	`if( corners.empty() )`
97	`return;`	83	`return;`
98	`cv::Mat image = _image.getMat(); CvMat c_image = _image.getMat();`	84	`cv::Mat image = _image.getMat(); CvMat c_image = _image.getMat();`
99	`int nelems = corners.checkVector(2, CV_32F, true);`	85	`int nelems = corners.checkVector(2, CV_32F, true);`
100	`CV_Assert(nelems >= 0);`	86	`CV_Assert(nelems >= 0);`
101	`cvDrawChessboardCorners( &c_image, patternSize, (CvPoint2D32f*)corners.data,`	87	`cvDrawChessboardCorners( &c_image, patternSize, (CvPoint2D32f*)corners.data,`
102	`nelems, patternWasFound, line_width);`	88	`nelems, patternWasFound, line_width);`
103	`}`	89	`}`
104		90
105	`void rshift(cv::Mat& I, unsigned int shift){`	91	`void rshift(cv::Mat& I, unsigned int shift){`
106		92
107	`int nRows = I.rows;`	93	`int nRows = I.rows;`
108	`int nCols = I.cols;`	94	`int nCols = I.cols;`
109		95
110	`if (I.isContinuous()){`	96	`if (I.isContinuous()){`
111	`nCols *= nRows;`	97	`nCols *= nRows;`
112	`nRows = 1;`	98	`nRows = 1;`
113	`}`	99	`}`
114		100
115	`int i,j;`	101	`int i,j;`
116	`unsigned short* p;`	102	`unsigned short* p;`
117	`for( i = 0; i < nRows; ++i){`	103	`for( i = 0; i < nRows; ++i){`
118	`p = I.ptr<unsigned short>(i);`	104	`p = I.ptr<unsigned short>(i);`
119	`for ( j = 0; j < nCols; ++j){`	105	`for ( j = 0; j < nCols; ++j){`
120	`p[j] = p[j]>>shift;`	106	`p[j] = p[j]>>shift;`
121	`}`	107	`}`
122	`}`	108	`}`
123	`}`	109	`}`
124		110
125	`void cvDrawChessboardCorners(CvArr* _image, CvSize pattern_size, CvPoint2D32f* corners, int count, int found, int line_width){`	111	`void cvDrawChessboardCorners(CvArr* _image, CvSize pattern_size, CvPoint2D32f* corners, int count, int found, int line_width){`
126	`const int shift = 0;`	112	`const int shift = 0;`
127	`const int radius = 12;`	113	`const int radius = 12;`
128	`const int r = radius*(1 << shift);`	114	`const int r = radius*(1 << shift);`
129	`int i;`	115	`int i;`
130	`CvMat stub, *image;`	116	`CvMat stub, *image;`
131	`double scale = 1;`	117	`double scale = 1;`
132	`int type, cn, line_type;`	118	`int type, cn, line_type;`
133		119
134	`image = cvGetMat( _image, &stub );`	120	`image = cvGetMat( _image, &stub );`
135		121
136	`type = CV_MAT_TYPE(image->type);`	122	`type = CV_MAT_TYPE(image->type);`
137	`cn = CV_MAT_CN(type);`	123	`cn = CV_MAT_CN(type);`
138	`if( cn != 1 && cn != 3 && cn != 4 )`	124	`if( cn != 1 && cn != 3 && cn != 4 )`
139	`CV_Error( CV_StsUnsupportedFormat, "Number of channels must be 1, 3 or 4" );`	125	`CV_Error( CV_StsUnsupportedFormat, "Number of channels must be 1, 3 or 4" );`
140		126
141	`switch( CV_MAT_DEPTH(image->type) )`	127	`switch( CV_MAT_DEPTH(image->type) )`
142	`{`	128	`{`
143	`case CV_8U:`	129	`case CV_8U:`
144	`scale = 1;`	130	`scale = 1;`
145	`break;`	131	`break;`
146	`case CV_16U:`	132	`case CV_16U:`
147	`scale = 256;`	133	`scale = 256;`
148	`break;`	134	`break;`
149	`case CV_32F:`	135	`case CV_32F:`
150	`scale = 1./255;`	136	`scale = 1./255;`
151	`break;`	137	`break;`
152	`default:`	138	`default:`
153	`CV_Error( CV_StsUnsupportedFormat,`	139	`CV_Error( CV_StsUnsupportedFormat,`
154	`"Only 8-bit, 16-bit or floating-point 32-bit images are supported" );`	140	`"Only 8-bit, 16-bit or floating-point 32-bit images are supported" );`
155	`}`	141	`}`
156		142
157	`line_type = type == CV_8UC1 \|\| type == CV_8UC3 ? CV_AA : 8;`	143	`line_type = type == CV_8UC1 \|\| type == CV_8UC3 ? CV_AA : 8;`
158		144
159	`if( !found )`	145	`if( !found )`
160	`{`	146	`{`
161	`CvScalar color = {{0,0,255}};`	147	`CvScalar color = {{0,0,255}};`
162	`if( cn == 1 )`	148	`if( cn == 1 )`
163	`color = cvScalarAll(200);`	149	`color = cvScalarAll(200);`
164	`color.val[0] *= scale;`	150	`color.val[0] *= scale;`
165	`color.val[1] *= scale;`	151	`color.val[1] *= scale;`
166	`color.val[2] *= scale;`	152	`color.val[2] *= scale;`
167	`color.val[3] *= scale;`	153	`color.val[3] *= scale;`
168		154
169	`for( i = 0; i < count; i++ )`	155	`for( i = 0; i < count; i++ )`
170	`{`	156	`{`
171	`CvPoint pt;`	157	`CvPoint pt;`
172	`pt.x = cvRound(corners[i].x*(1 << shift));`	158	`pt.x = cvRound(corners[i].x*(1 << shift));`
173	`pt.y = cvRound(corners[i].y*(1 << shift));`	159	`pt.y = cvRound(corners[i].y*(1 << shift));`
174	`cvLine( image, cvPoint( pt.x - r, pt.y - r ),`	160	`cvLine( image, cvPoint( pt.x - r, pt.y - r ),`
175	`cvPoint( pt.x + r, pt.y + r ), color, line_width, line_type, shift );`	161	`cvPoint( pt.x + r, pt.y + r ), color, line_width, line_type, shift );`
176	`cvLine( image, cvPoint( pt.x - r, pt.y + r),`	162	`cvLine( image, cvPoint( pt.x - r, pt.y + r),`
177	`cvPoint( pt.x + r, pt.y - r), color, line_width, line_type, shift );`	163	`cvPoint( pt.x + r, pt.y - r), color, line_width, line_type, shift );`
178	`cvCircle( image, pt, r+(1<<shift), color, line_width, line_type, shift );`	164	`cvCircle( image, pt, r+(1<<shift), color, line_width, line_type, shift );`
179	`}`	165	`}`
180	`}`	166	`}`
181	`else`	167	`else`
182	`{`	168	`{`
183	`int x, y;`	169	`int x, y;`
184	`CvPoint prev_pt = {0, 0};`	170	`CvPoint prev_pt = {0, 0};`
185	`const int line_max = 7;`	171	`const int line_max = 7;`
186	`static const CvScalar line_colors[line_max] =`	172	`static const CvScalar line_colors[line_max] =`
187	`{`	173	`{`
188	`{{0,0,255}},`	174	`{{0,0,255}},`
189	`{{0,128,255}},`	175	`{{0,128,255}},`
190	`{{0,200,200}},`	176	`{{0,200,200}},`
191	`{{0,255,0}},`	177	`{{0,255,0}},`
192	`{{200,200,0}},`	178	`{{200,200,0}},`
193	`{{255,0,0}},`	179	`{{255,0,0}},`
194	`{{255,0,255}}`	180	`{{255,0,255}}`
195	`};`	181	`};`
196		182
197	`for( y = 0, i = 0; y < pattern_size.height; y++ )`	183	`for( y = 0, i = 0; y < pattern_size.height; y++ )`
198	`{`	184	`{`
199	`CvScalar color = line_colors[y % line_max];`	185	`CvScalar color = line_colors[y % line_max];`
200	`if( cn == 1 )`	186	`if( cn == 1 )`
201	`color = cvScalarAll(200);`	187	`color = cvScalarAll(200);`
202	`color.val[0] *= scale;`	188	`color.val[0] *= scale;`
203	`color.val[1] *= scale;`	189	`color.val[1] *= scale;`
204	`color.val[2] *= scale;`	190	`color.val[2] *= scale;`
205	`color.val[3] *= scale;`	191	`color.val[3] *= scale;`
206		192
207	`for( x = 0; x < pattern_size.width; x++, i++ )`	193	`for( x = 0; x < pattern_size.width; x++, i++ )`
208	`{`	194	`{`
209	`CvPoint pt;`	195	`CvPoint pt;`
210	`pt.x = cvRound(corners[i].x*(1 << shift));`	196	`pt.x = cvRound(corners[i].x*(1 << shift));`
211	`pt.y = cvRound(corners[i].y*(1 << shift));`	197	`pt.y = cvRound(corners[i].y*(1 << shift));`
212		198
213	`if( i != 0 )`	199	`if( i != 0 )`
214	`cvLine( image, prev_pt, pt, color, 1, line_type, shift );`	200	`cvLine( image, prev_pt, pt, color, 1, line_type, shift );`
215		201
216	`cvLine( image, cvPoint(pt.x - r, pt.y - r),`	202	`cvLine( image, cvPoint(pt.x - r, pt.y - r),`
217	`cvPoint(pt.x + r, pt.y + r), color, line_width, line_type, shift );`	203	`cvPoint(pt.x + r, pt.y + r), color, line_width, line_type, shift );`
218	`cvLine( image, cvPoint(pt.x - r, pt.y + r),`	204	`cvLine( image, cvPoint(pt.x - r, pt.y + r),`
219	`cvPoint(pt.x + r, pt.y - r), color, line_width, line_type, shift );`	205	`cvPoint(pt.x + r, pt.y - r), color, line_width, line_type, shift );`
220	`cvCircle( image, pt, r+(1<<shift), color, line_width, line_type, shift );`	206	`cvCircle( image, pt, r+(1<<shift), color, line_width, line_type, shift );`
221	`prev_pt = pt;`	207	`prev_pt = pt;`
222	`}`	208	`}`
223	`}`	209	`}`
224	`}`	210	`}`
225	`}`	211	`}`
226		212
227	`// Returns the result of mod(mat(x,y), moduli) for each matrix element`	213	`// Returns the result of mod(mat(x,y), moduli) for each matrix element`
228	`cv::Mat modulo(const cv::Mat &mat, float n){`	214	`cv::Mat modulo(const cv::Mat &mat, float n){`
229		215
230	`cv::Mat ret(mat.rows, mat.cols, mat.type());`	216	`cv::Mat ret(mat.rows, mat.cols, mat.type());`
231		217
232	`for(int row=0; row<ret.rows; row++){`	218	`for(int row=0; row<ret.rows; row++){`
233	`for(int col=0; col<ret.cols; col++){`	219	`for(int col=0; col<ret.cols; col++){`
234	`float val = mat.at<float>(row, col);`	220	`float val = mat.at<float>(row, col);`
235	`// note: std::fmod calculates the remainder, not arithmetic modulo`	221	`// note: std::fmod calculates the remainder, not arithmetic modulo`
236	`ret.at<float>(row, col) = val - n * std::floor(val / n);`	222	`ret.at<float>(row, col) = val - n * std::floor(val / n);`
237	`}`	223	`}`
238	`}`	224	`}`
239		225
240	`return ret;`	226	`return ret;`
241	`}`	227	`}`
242		228
243	`// Convert a 3xN matrix to a vector of Point3fs.`	229	`// Convert a 3xN matrix to a vector of Point3fs.`
244	`void matToPoints3f(const cv::Mat &mat, std::vector<cv::Point3f> &points){`	230	`void matToPoints3f(const cv::Mat &mat, std::vector<cv::Point3f> &points){`
245		231
246	`unsigned int nPoints = mat.cols;`	232	`unsigned int nPoints = mat.cols;`
247	`points.resize(nPoints);`	233	`points.resize(nPoints);`
248		234
249	`for(unsigned int i=0; i<nPoints; i++)`	235	`for(unsigned int i=0; i<nPoints; i++)`
250	`points[i] = cv::Point3f(mat.at<float>(0, i), mat.at<float>(1, i), mat.at<float>(2, i));`	236	`points[i] = cv::Point3f(mat.at<float>(0, i), mat.at<float>(1, i), mat.at<float>(2, i));`
251	`}`	237	`}`
252		238
253	`// Convert a (Dim+1)xN matrix of homogenous points to a DimxN matrix of points in non-homogenous coordinates.`	239	`// Convert a (Dim+1)xN matrix of homogenous points to a DimxN matrix of points in non-homogenous coordinates.`
254	`void convertMatFromHomogeneous(cv::Mat &src, cv::Mat &dst){`	240	`void convertMatFromHomogeneous(cv::Mat &src, cv::Mat &dst){`
255	`unsigned int N = src.cols;`	241	`unsigned int N = src.cols;`
256	`unsigned int Dim = src.rows-1;`	242	`unsigned int Dim = src.rows-1;`
257	`dst.create(Dim, N, src.type());`	243	`dst.create(Dim, N, src.type());`
258	`for(unsigned int i=0; i<N; i++){`	244	`for(unsigned int i=0; i<N; i++){`
259	`for(unsigned int j=0; j<Dim; j++)`	245	`for(unsigned int j=0; j<Dim; j++)`
260	`dst.at<float>(j,i) = src.at<float>(j,i)/src.at<float>(Dim,i);`	246	`dst.at<float>(j,i) = src.at<float>(j,i)/src.at<float>(Dim,i);`
261	`}`	247	`}`
262		248
263	`}`	249	`}`
264		250
265	`// Function to solve the hand-eye (or eye-in-hand) calibration problem.`	251	`// Function to solve the hand-eye (or eye-in-hand) calibration problem.`
266	`// Finds [Omega \| tau], to minimize \|\|[R_mark \| t_mark][Omega \| tau] - [Omega \| tau][R \| t]\|\|^2`	252	`// Finds [Omega \| tau], to minimize \|\|[R_mark \| t_mark][Omega \| tau] - [Omega \| tau][R \| t]\|\|^2`
267	`// Algorithm according to Tsai, Lenz, A new technique for fully autonomous and efficient 3d robotics hand-eye calibration`	253	`// Algorithm according to Tsai, Lenz, A new technique for fully autonomous and efficient 3d robotics hand-eye calibration`
268	`// DTU, 2014, Jakob Wilm`	254	`// DTU, 2014, Jakob Wilm`
269	`void handEyeCalibrationTsai(const std::vector<cv::Matx33f> R, const std::vector<cv::Vec3f> t, const std::vector<cv::Matx33f> R_mark, const std::vector<cv::Vec3f> t_mark, cv::Matx33f &Omega, cv::Vec3f &tau){`	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){`
270		256
271	`int N = R.size();`	257	`int N = R.size();`
272	`assert(N == R_mark.size());`	258	`assert(N == R_mark.size());`
273	`assert(N == t.size());`	259	`assert(N == t.size());`
274	`assert(N == t_mark.size());`	260	`assert(N == t_mark.size());`
275		261
276	`// construct equations for rotation`	262	`// construct equations for rotation`
277	`cv::Mat A(3*N, 3, CV_32F);`	263	`cv::Mat A(3*N, 3, CV_32F);`
278	`cv::Mat b(3*N, 1, CV_32F);`	264	`cv::Mat b(3*N, 1, CV_32F);`
279	`for(int i=0; i<N; i++){`	265	`for(int i=0; i<N; i++){`
280	`// angle axis representations`	266	`// angle axis representations`
281	`cv::Vec3f rot;`	267	`cv::Vec3f rot;`
282	`cv::Vec3f rot_mark;`	268	`cv::Vec3f rot_mark;`
283	`cv::Rodrigues(R[i], rot);`	269	`cv::Rodrigues(R[i], rot);`
284	`cv::Rodrigues(R_mark[i], rot_mark);`	270	`cv::Rodrigues(R_mark[i], rot_mark);`
285		271
286	`cv::Vec3f P = 2.0sin(cv::norm(rot)/2.0)cv::normalize(rot);`	272	`cv::Vec3f P = 2.0sin(cv::norm(rot)/2.0)cv::normalize(rot);`
287	`//std::cout << "P: " << std::endl << P << std::endl;`	273	`//std::cout << "P: " << std::endl << P << std::endl;`
288	`cv::Vec3f P_mark = 2.0sin(cv::norm(rot_mark)/2.0)cv::normalize(rot_mark);`	274	`cv::Vec3f P_mark = 2.0sin(cv::norm(rot_mark)/2.0)cv::normalize(rot_mark);`
289	`//std::cout << "P_mark: " << std::endl << P_mark << std::endl;`	275	`//std::cout << "P_mark: " << std::endl << P_mark << std::endl;`
290	`cv::Vec3f sum = P+P_mark;`	276	`cv::Vec3f sum = P+P_mark;`
291	`cv::Mat crossProduct = (cv::Mat_<float>(3,3) << 0.0, -sum(2), sum(1), sum(2), 0.0, -sum(0), -sum(1), sum(0), 0.0);`	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);`
292	`//std::cout << "crossProduct: " << std::endl << crossProduct << std::endl;`	278	`//std::cout << "crossProduct: " << std::endl << crossProduct << std::endl;`
293	`crossProduct.copyTo(A.rowRange(i3, i3+3));`	279	`crossProduct.copyTo(A.rowRange(i3, i3+3));`
294		280
295	`cv::Mat(P-P_mark).copyTo(b.rowRange(i3, i3+3));`	281	`cv::Mat(P-P_mark).copyTo(b.rowRange(i3, i3+3));`
296	`}`	282	`}`
297		283
298	`// solve for rotation`	284	`// solve for rotation`
299	`cv::Vec3f P_prime;`	285	`cv::Vec3f P_prime;`
300	`cv::solve(A, b, P_prime, cv::DECOMP_SVD);`	286	`cv::solve(A, b, P_prime, cv::DECOMP_SVD);`
301	`cv::Vec3f P = 2.0P_prime/(cv::sqrt(1.0 + cv::norm(P_prime)cv::norm(P_prime)));`	287	`cv::Vec3f P = 2.0P_prime/(cv::sqrt(1.0 + cv::norm(P_prime)cv::norm(P_prime)));`
302	`float nP = cv::norm(P);`	288	`float nP = cv::norm(P);`
303	`cv::Mat crossProduct = (cv::Mat_<float>(3,3) << 0.0, -P(2), P(1), P(2), 0.0, -P(0), -P(1), P(0), 0.0);`	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);`
304	`cv::Mat OmegaMat = (1.0-nPnP/2.0)cv::Mat::eye(3,3,CV_32F) + 0.5(cv::Mat(P)cv::Mat(P).t() + cv::sqrt(4.0 - nPnP)crossProduct);`	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);`
305	`Omega = cv::Matx33f(OmegaMat);`	291	`Omega = cv::Matx33f(OmegaMat);`
306		292
307	`// construct equations for translation`	293	`// construct equations for translation`
308	`A.setTo(0.0);`	294	`A.setTo(0.0);`
309	`b.setTo(0.0);`	295	`b.setTo(0.0);`
310	`for(int i=0; i<N; i++){`	296	`for(int i=0; i<N; i++){`
311		297
312	`cv::Mat diff = cv::Mat(R_mark[i]) - cv::Mat::eye(3, 3, CV_32F);`	298	`cv::Mat diff = cv::Mat(R_mark[i]) - cv::Mat::eye(3, 3, CV_32F);`
313	`diff.copyTo(A.rowRange(i3, i3+3));`	299	`diff.copyTo(A.rowRange(i3, i3+3));`
314		300
315	`cv::Mat diff_mark = cv::Mat(Omega*t[i] - t_mark[i]);`	301	`cv::Mat diff_mark = cv::Mat(Omega*t[i] - t_mark[i]);`
316	`diff_mark.copyTo(b.rowRange(i3, i3+3));`	302	`diff_mark.copyTo(b.rowRange(i3, i3+3));`
317	`}`	303	`}`
318		304
319	`// solve for translation`	305	`// solve for translation`
320	`cv::solve(A, b, tau, cv::DECOMP_SVD);`	306	`cv::solve(A, b, tau, cv::DECOMP_SVD);`
321		307
322	`cv::Mat err_tau = b - (A*cv::Mat(tau));`	308	`cv::Mat err_tau = b - (A*cv::Mat(tau));`
323	`std::cout << err_tau << std::endl;`	309	`std::cout << err_tau << std::endl;`
324	`}`	310	`}`
325		311
326	`// Function to solve for the rotation axis from sets of 3D point coordinates of flat pattern feature points`	312	`// Function to solve for the rotation axis from sets of 3D point coordinates of flat pattern feature points`
327	`// Algorithm according to Chen et al., Rotation axis calibration of a turntable using constrained global optimization, Optik 2014`	313	`// Algorithm according to Chen et al., Rotation axis calibration of a turntable using constrained global optimization, Optik 2014`
328	`// DTU, 2014, Jakob Wilm`	314	`// DTU, 2014, Jakob Wilm`
329	`void rotationAxisCalibration(const std::vector< std::vector<cv::Point3f> > Qcam, const std::vector<cv::Point3f> Qobj, cv::Vec3f &axis, cv::Vec3f &point){`	315	`void rotationAxisCalibration(const std::vector< std::vector<cv::Point3f> > Qcam, const std::vector<cv::Point3f> Qobj, cv::Vec3f &axis, cv::Vec3f &point){`
330		316
331	`// number of frames (points on each arch)`	317	`// number of frames (points on each arch)`
332	`int l = Qcam.size();`	318	`int l = Qcam.size();`
333		319
334	`// number of points in each frame`	320	`// number of points in each frame`
335	`int mn = Qobj.size();`	321	`int mn = Qobj.size();`
336		322
337	`assert(mn == Qcam[0].size());`	323	`assert(mn == Qcam[0].size());`
338		324
339	`// construct matrix for axis determination`	325	`// construct matrix for axis determination`
340	`cv::Mat M(6, 6, CV_32F, cv::Scalar(0));`	326	`cv::Mat M(6, 6, CV_32F, cv::Scalar(0));`
341		327
342	`for(int k=0; k<l; k++){`	328	`for(int k=0; k<l; k++){`
343	`for(int idx=0; idx<mn; idx++){`	329	`for(int idx=0; idx<mn; idx++){`
344		330
345	`// float i = Qobj[idx].x+4;`	331	`// float i = Qobj[idx].x+4;`
346	`// float j = Qobj[idx].y+4;`	332	`// float j = Qobj[idx].y+4;`
347	`float i = Qobj[idx].x;`	333	`float i = Qobj[idx].x;`
348	`float j = Qobj[idx].y;`	334	`float j = Qobj[idx].y;`
349		335
350	`float x = Qcam[k][idx].x;`	336	`float x = Qcam[k][idx].x;`
351	`float y = Qcam[k][idx].y;`	337	`float y = Qcam[k][idx].y;`
352	`float z = Qcam[k][idx].z;`	338	`float z = Qcam[k][idx].z;`
353		339
354	`M += (cv::Mat_<float>(6,6) << xx, xy, xz, x, ix, j*x,`	340	`M += (cv::Mat_<float>(6,6) << xx, xy, xz, x, ix, j*x,`
355	`0, yy, yz, y, iy, jy,`	341	`0, yy, yz, y, iy, jy,`
356	`0, 0, zz, z, iz, j*z,`	342	`0, 0, zz, z, iz, j*z,`
357	`0, 0, 0, 1, i, j,`	343	`0, 0, 0, 1, i, j,`
358	`0, 0, 0, 0, ii, ij,`	344	`0, 0, 0, 0, ii, ij,`
359	`0, 0, 0, 0, 0, j*j);`	345	`0, 0, 0, 0, 0, j*j);`
360		346
361	`}`	347	`}`
362	`}`	348	`}`
363		349
364	`cv::completeSymm(M, false);`	350	`cv::completeSymm(M, false);`
365		351
366	`// solve for axis`	352	`// solve for axis`
367	`std::vector<float> lambda;`	353	`std::vector<float> lambda;`
368	`cv::Mat u;`	354	`cv::Mat u;`
369	`cv::eigen(M, lambda, u);`	355	`cv::eigen(M, lambda, u);`
370		356
371	`float minLambda = abs(lambda[0]);`	357	`float minLambda = abs(lambda[0]);`
372	`int idx = 0;`	358	`int idx = 0;`
373	`for(int i=1; i<lambda.size(); i++){`	359	`for(int i=1; i<lambda.size(); i++){`
374	`if(abs(lambda[i]) < minLambda){`	360	`if(abs(lambda[i]) < minLambda){`
375	`minLambda = lambda[i];`	361	`minLambda = lambda[i];`
376	`idx = i;`	362	`idx = i;`
377	`}`	363	`}`
378	`}`	364	`}`
379		365
380	`axis = u.row(idx).colRange(0, 3);`	366	`axis = u.row(idx).colRange(0, 3);`
381	`axis = cv::normalize(axis);`	367	`axis = cv::normalize(axis);`
382		368
383	`float nx = u.at<float>(idx, 0);`	369	`float nx = u.at<float>(idx, 0);`
384	`float ny = u.at<float>(idx, 1);`	370	`float ny = u.at<float>(idx, 1);`
385	`float nz = u.at<float>(idx, 2);`	371	`float nz = u.at<float>(idx, 2);`
386	`float d = u.at<float>(idx, 3);`	372	`float d = u.at<float>(idx, 3);`
387	`float dh = u.at<float>(idx, 4);`	373	`float dh = u.at<float>(idx, 4);`
388	`float dv = u.at<float>(idx, 5);`	374	`float dv = u.at<float>(idx, 5);`
389		375
390	`// // Paper version: c is initially eliminated`	376	`// // Paper version: c is initially eliminated`
391	`// cv::Mat A(l*mn, mn+2, CV_32F, cv::Scalar(0.0));`	377	`// cv::Mat A(l*mn, mn+2, CV_32F, cv::Scalar(0.0));`
392	`// cv::Mat bb(l*mn, 1, CV_32F);`	378	`// cv::Mat bb(l*mn, 1, CV_32F);`
393		379
394	`// for(int k=0; k<l; k++){`	380	`// for(int k=0; k<l; k++){`
395	`// for(int idx=0; idx<mn; idx++){`	381	`// for(int idx=0; idx<mn; idx++){`
396		382
397	`// float i = Qobj[idx].x;`	383	`// float i = Qobj[idx].x;`
398	`// float j = Qobj[idx].y;`	384	`// float j = Qobj[idx].y;`
399		385
400	`// float x = Qcam[k][idx].x;`	386	`// float x = Qcam[k][idx].x;`
401	`// float y = Qcam[k][idx].y;`	387	`// float y = Qcam[k][idx].y;`
402	`// float z = Qcam[k][idx].z;`	388	`// float z = Qcam[k][idx].z;`
403		389
404	`// float f = xx + yy + zz + (2xnx + 2yny + 2znz)(idh + jdv);`	390	`// float f = xx + yy + zz + (2xnx + 2yny + 2znz)(idh + jdv);`
405		391
406	`// int row = k*mn+idx;`	392	`// int row = k*mn+idx;`
407	`// A.at<float>(row, 0) = 2x - (2z*nx)/nz;`	393	`// A.at<float>(row, 0) = 2x - (2z*nx)/nz;`
408	`// A.at<float>(row, 1) = 2y - (2z*ny)/nz;`	394	`// A.at<float>(row, 1) = 2y - (2z*ny)/nz;`
409	`// A.at<float>(row, idx+2) = 1.0;`	395	`// A.at<float>(row, idx+2) = 1.0;`
410		396
411	`// bb.at<float>(row, 0) = f + (2zd)/nz;`	397	`// bb.at<float>(row, 0) = f + (2zd)/nz;`
412	`// }`	398	`// }`
413	`// }`	399	`// }`
414		400
415	`// // solve for point`	401	`// // solve for point`
416	`// cv::Mat abe;`	402	`// cv::Mat abe;`
417	`// cv::solve(A, bb, abe, cv::DECOMP_SVD);`	403	`// cv::solve(A, bb, abe, cv::DECOMP_SVD);`
418		404
419	`// float a = abe.at<float>(0, 0);`	405	`// float a = abe.at<float>(0, 0);`
420	`// float b = abe.at<float>(1, 0);`	406	`// float b = abe.at<float>(1, 0);`
421	`// float c = -(nxa+nyb+d)/nz;`	407	`// float c = -(nxa+nyb+d)/nz;`
422		408
423	`// Our version: solve simultanously for a,b,c`	409	`// Our version: solve simultanously for a,b,c`
424	`cv::Mat A(l*mn, mn+3, CV_32F, cv::Scalar(0.0));`	410	`cv::Mat A(l*mn, mn+3, CV_32F, cv::Scalar(0.0));`
425	`cv::Mat bb(l*mn, 1, CV_32F);`	411	`cv::Mat bb(l*mn, 1, CV_32F);`
426		412
427	`for(int k=0; k<l; k++){`	413	`for(int k=0; k<l; k++){`
428	`for(int idx=0; idx<mn; idx++){`	414	`for(int idx=0; idx<mn; idx++){`
429		415
430	`float i = Qobj[idx].x;`	416	`float i = Qobj[idx].x;`
431	`float j = Qobj[idx].y;`	417	`float j = Qobj[idx].y;`
432		418
433	`float x = Qcam[k][idx].x;`	419	`float x = Qcam[k][idx].x;`
434	`float y = Qcam[k][idx].y;`	420	`float y = Qcam[k][idx].y;`
435	`float z = Qcam[k][idx].z;`	421	`float z = Qcam[k][idx].z;`
436		422
437	`float f = xx + yy + zz + (2xnx + 2yny + 2znz)(idh + jdv);`	423	`float f = xx + yy + zz + (2xnx + 2yny + 2znz)(idh + jdv);`
438		424
439	`int row = k*mn+idx;`	425	`int row = k*mn+idx;`
440	`A.at<float>(row, 0) = 2*x;`	426	`A.at<float>(row, 0) = 2*x;`
441	`A.at<float>(row, 1) = 2*y;`	427	`A.at<float>(row, 1) = 2*y;`
442	`A.at<float>(row, 2) = 2*z;`	428	`A.at<float>(row, 2) = 2*z;`
443	`A.at<float>(row, idx+3) = 1.0;`	429	`A.at<float>(row, idx+3) = 1.0;`
444		430
445	`bb.at<float>(row, 0) = f;`	431	`bb.at<float>(row, 0) = f;`
446	`}`	432	`}`
447	`}`	433	`}`
448		434
449	`// solve for point`	435	`// solve for point`
450	`cv::Mat abe;`	436	`cv::Mat abe;`
451	`cv::solve(A, bb, abe, cv::DECOMP_SVD);`	437	`cv::solve(A, bb, abe, cv::DECOMP_SVD);`
452		438
453	`float a = abe.at<float>(0, 0);`	439	`float a = abe.at<float>(0, 0);`
454	`float b = abe.at<float>(1, 0);`	440	`float b = abe.at<float>(1, 0);`
455	`float c = abe.at<float>(2, 0);`	441	`float c = abe.at<float>(2, 0);`
456		442
457	`point[0] = a;`	443	`point[0] = a;`
458	`point[1] = b;`	444	`point[1] = b;`
459	`point[2] = c;`	445	`point[2] = c;`
460		446
461	`}`	447	`}`
462		448
463	`// Function to fit two sets of corresponding pose data.`	449	`// Function to fit two sets of corresponding pose data.`
464	`// Finds [Omega \| tau], to minimize \|\|[R_mark \| t_mark] - [Omega \| tau][R \| t]\|\|^2`	450	`// Finds [Omega \| tau], to minimize \|\|[R_mark \| t_mark] - [Omega \| tau][R \| t]\|\|^2`
465	`// Algorithm and notation according to Mili Shah, Comparing two sets of corresponding six degree of freedom data, CVIU 2011.`	451	`// Algorithm and notation according to Mili Shah, Comparing two sets of corresponding six degree of freedom data, CVIU 2011.`
466	`// DTU, 2013, Oline V. Olesen, Jakob Wilm`	452	`// DTU, 2013, Oline V. Olesen, Jakob Wilm`
467	`void fitSixDofData(const std::vector<cv::Matx33f> R, const std::vector<cv::Vec3f> t, const std::vector<cv::Matx33f> R_mark, const std::vector<cv::Vec3f> t_mark, cv::Matx33f &Omega, cv::Vec3f &tau){`	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){`
468		454
469	`int N = R.size();`	455	`int N = R.size();`
470	`assert(N == R_mark.size());`	456	`assert(N == R_mark.size());`
471	`assert(N == t.size());`	457	`assert(N == t.size());`
472	`assert(N == t_mark.size());`	458	`assert(N == t_mark.size());`
473		459
474	`// Mean translations`	460	`// Mean translations`
475	`cv::Vec3f t_mean;`	461	`cv::Vec3f t_mean;`
476	`cv::Vec3f t_mark_mean;`	462	`cv::Vec3f t_mark_mean;`
477	`for(int i=0; i<N; i++){`	463	`for(int i=0; i<N; i++){`
478	`t_mean += 1.0/N * t[i];`	464	`t_mean += 1.0/N * t[i];`
479	`t_mark_mean += 1.0/N * t_mark[i];`	465	`t_mark_mean += 1.0/N * t_mark[i];`
480	`}`	466	`}`
481		467
482	`// Data with mean adjusted translations`	468	`// Data with mean adjusted translations`
483	`cv::Mat X_bar(3, 4*N, CV_32F);`	469	`cv::Mat X_bar(3, 4*N, CV_32F);`
484	`cv::Mat X_mark_bar(3, 4*N, CV_32F);`	470	`cv::Mat X_mark_bar(3, 4*N, CV_32F);`
485	`for(int i=0; i<N; i++){`	471	`for(int i=0; i<N; i++){`
486	`cv::Mat(R[i]).copyTo(X_bar.colRange(i4,i4+3));`	472	`cv::Mat(R[i]).copyTo(X_bar.colRange(i4,i4+3));`
487	`cv::Mat(t[i] - t_mean).copyTo(X_bar.col(i*4+3));`	473	`cv::Mat(t[i] - t_mean).copyTo(X_bar.col(i*4+3));`
488	`cv::Mat(R_mark[i]).copyTo(X_mark_bar.colRange(i4,i4+3));`	474	`cv::Mat(R_mark[i]).copyTo(X_mark_bar.colRange(i4,i4+3));`
489	`cv::Mat(t_mark[i] - t_mark_mean).copyTo(X_mark_bar.col(i*4+3));`	475	`cv::Mat(t_mark[i] - t_mark_mean).copyTo(X_mark_bar.col(i*4+3));`
490	`}`	476	`}`

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