Question in initUndistortRectifyMap source code

C++
,
1

anyone here to help me figure out it in // HERE?
why it be this way?
anyone help?

void cv::initUndistortRectifyMap( InputArray _cameraMatrix, InputArray _distCoeffs,
                              InputArray _matR, InputArray _newCameraMatrix,
                              Size size, int m1type, OutputArray _map1, OutputArray _map2 )
{
    Mat cameraMatrix = _cameraMatrix.getMat(), distCoeffs = _distCoeffs.getMat();
    Mat matR = _matR.getMat(), newCameraMatrix = _newCameraMatrix.getMat();

    if( m1type <= 0 )
        m1type = CV_16SC2;
    CV_Assert( m1type == CV_16SC2 || m1type == CV_32FC1 || m1type == CV_32FC2 );
    _map1.create( size, m1type );
    Mat map1 = _map1.getMat(), map2;
    if( m1type != CV_32FC2 )
    {
        _map2.create( size, m1type == CV_16SC2 ? CV_16UC1 : CV_32FC1 );
        map2 = _map2.getMat();
    }
    else
        _map2.release();

    Mat_<double> R = Mat_<double>::eye(3, 3);
    Mat_<double> A = Mat_<double>(cameraMatrix), Ar;

    if( !newCameraMatrix.empty() )
        Ar = Mat_<double>(newCameraMatrix);
    else
        Ar = getDefaultNewCameraMatrix( A, size, true );

    if( !matR.empty() )
        R = Mat_<double>(matR);

    if( !distCoeffs.empty() )
        distCoeffs = Mat_<double>(distCoeffs);
    else
    {
        distCoeffs.create(14, 1, CV_64F);
        distCoeffs = 0.;
    }

    CV_Assert( A.size() == Size(3,3) && A.size() == R.size() );
    CV_Assert( Ar.size() == Size(3,3) || Ar.size() == Size(4, 3));
    Mat_<double> iR = (Ar.colRange(0,3)*R).inv(DECOMP_LU);*//HERE*
    const double* ir = &iR(0,0);

    double u0 = A(0, 2),  v0 = A(1, 2);
    double fx = A(0, 0),  fy = A(1, 1);

    CV_Assert( distCoeffs.size() == Size(1, 4) || distCoeffs.size() == Size(4, 1) ||
               distCoeffs.size() == Size(1, 5) || distCoeffs.size() == Size(5, 1) ||
               distCoeffs.size() == Size(1, 8) || distCoeffs.size() == Size(8, 1) ||
               distCoeffs.size() == Size(1, 12) || distCoeffs.size() == Size(12, 1) ||
               distCoeffs.size() == Size(1, 14) || distCoeffs.size() == Size(14, 1));

    if( distCoeffs.rows != 1 && !distCoeffs.isContinuous() )
        distCoeffs = distCoeffs.t();

    const double* const distPtr = distCoeffs.ptr<double>();
    double k1 = distPtr[0];
    double k2 = distPtr[1];
    double p1 = distPtr[2];
    double p2 = distPtr[3];
    double k3 = distCoeffs.cols + distCoeffs.rows - 1 >= 5 ? distPtr[4] : 0.;
    double k4 = distCoeffs.cols + distCoeffs.rows - 1 >= 8 ? distPtr[5] : 0.;
    double k5 = distCoeffs.cols + distCoeffs.rows - 1 >= 8 ? distPtr[6] : 0.;
    double k6 = distCoeffs.cols + distCoeffs.rows - 1 >= 8 ? distPtr[7] : 0.;
    double s1 = distCoeffs.cols + distCoeffs.rows - 1 >= 12 ? distPtr[8] : 0.;
    double s2 = distCoeffs.cols + distCoeffs.rows - 1 >= 12 ? distPtr[9] : 0.;
    double s3 = distCoeffs.cols + distCoeffs.rows - 1 >= 12 ? distPtr[10] : 0.;
    double s4 = distCoeffs.cols + distCoeffs.rows - 1 >= 12 ? distPtr[11] : 0.;
    double tauX = distCoeffs.cols + distCoeffs.rows - 1 >= 14 ? distPtr[12] : 0.;
    double tauY = distCoeffs.cols + distCoeffs.rows - 1 >= 14 ? distPtr[13] : 0.;

    // Matrix for trapezoidal distortion of tilted image sensor
    cv::Matx33d matTilt = cv::Matx33d::eye();
    cv::detail::computeTiltProjectionMatrix(tauX, tauY, &matTilt);

    for( int i = 0; i < size.height; i++ )
    {
        float* m1f = map1.ptr<float>(i);
        float* m2f = map2.empty() ? 0 : map2.ptr<float>(i);
        short* m1 = (short*)m1f;
        ushort* m2 = (ushort*)m2f;
        double _x = i*ir[1] + ir[2], _y = i*ir[4] + ir[5], _w = i*ir[7] + ir[8]; *// HERE*

        for( int j = 0; j < size.width; j++, _x += ir[0], _y += ir[3], _w += ir[6] ) *// HERE*
        {
            double w = 1./_w, x = _x*w, y = _y*w;
            double x2 = x*x, y2 = y*y;
            double r2 = x2 + y2, _2xy = 2*x*y;
            double kr = (1 + ((k3*r2 + k2)*r2 + k1)*r2)/(1 + ((k6*r2 + k5)*r2 + k4)*r2);
            double xd = (x*kr + p1*_2xy + p2*(r2 + 2*x2) + s1*r2+s2*r2*r2);
            double yd = (y*kr + p1*(r2 + 2*y2) + p2*_2xy + s3*r2+s4*r2*r2);
            cv::Vec3d vecTilt = matTilt*cv::Vec3d(xd, yd, 1);
            double invProj = vecTilt(2) ? 1./vecTilt(2) : 1;
            double u = fx*invProj*vecTilt(0) + u0;
            double v = fy*invProj*vecTilt(1) + v0;
            if( m1type == CV_16SC2 )
            {
                int iu = saturate_cast<int>(u*INTER_TAB_SIZE);
                int iv = saturate_cast<int>(v*INTER_TAB_SIZE);
                m1[j*2] = (short)(iu >> INTER_BITS);
                m1[j*2+1] = (short)(iv >> INTER_BITS);
                m2[j] = (ushort)((iv & (INTER_TAB_SIZE-1))*INTER_TAB_SIZE + (iu & (INTER_TAB_SIZE-1)));
            }
            else if( m1type == CV_32FC1 )
            {
                m1f[j] = (float)u;
                m2f[j] = (float)v;
            }
            else
            {
                m1f[j*2] = (float)u;
                m1f[j*2+1] = (float)v;
            }
        }
    }
}
2

that looks like a micro-optimization of a matrix-vector product where repeated multiplication, by an increasing y, is replaced by repeated additions instead.

3

could u plz show it in formula？

Mat_ iR = (Ar.colRange(0,3)R).inv(DECOMP_LU);//HERE*

iR is like
[ r11 r12 r13
r21 r22 r23
r31 r32 r33]
and in
[ir[0] ir[1] ir[2]
ir[3] ir[4] ir[5]
ir[6] ir[7] ir[8]]
then i cannot understand :frowning:

4

iR is a constant 3x3 matrix.

i is a row index, so it’s something vertical, “y”.
j is a column index, so it’s something horizontal, “x”.

generally, they calculate:

\begin{pmatrix} x \\ y \\ w \end{pmatrix} = \begin{pmatrix} \texttt{ir[0]} & \texttt{ir[1]} & \texttt{ir[2]} \\ \texttt{ir[3]} & \texttt{ir[4]} & \texttt{ir[5]} \\ \texttt{ir[6]} & \texttt{ir[7]} & \texttt{ir[8]} \\ \end{pmatrix} \cdot \begin{pmatrix} j \\ i \\ 1 \end{pmatrix}

before the inner loop, they calculate with j = 0. you can see how the matrix multiplication simplifies to what you see before the loop.

in the inner loop, instead of increasing j by 1 (!) and recalculating entirely, they just add the contributions, which are 1*ir[0], 1*ir[3], 1*ir[6].

(j+1) * ir[0] == (j * ir[0]) + ir[0]

1 Like
5

sure,I get it:)
thank you!