Multiplying SVD components of a matrix in OpenCV

Question

I applied SVD to a CV_32FC1 cvMat and modified some values in the 'u' component. Now I am trying to multiply the 'u, 'w' and 'vt' components to get a single matrix A. But OpenCV fails to multiply the matrices with the following error.

OpenCV Error: Assertion failed (type == B.type() && (type == CV_32FC1 || type == CV_64FC1 || type == CV_32FC2 || type == CV_64FC2)) in gemm, file /build/buildd/opencv-2.1.0/src/cxcore/cxmatmul.cpp, line 687
terminate called after throwing an instance of 'cv::Exception'
  what():  /build/buildd/opencv-2.1.0/src/cxcore/cxmatmul.cpp:687: error: (-215) type == B.type() && (type == CV_32FC1 || type == CV_64FC1 || type == CV_32FC2 || type == CV_64FC2) in function gemm

When I inspected the types of the matrices in the SVD object, they seem to have type = 20, which doesn't match any of the default matrix types.

#include <iostream>
#include <stdio.h>
#include "cv.h"
#include "highgui.h"
#include "constants.h"

const unsigned int MAX = 10000;

using namespace cv;
using namespace std;

int NO_FRAMES;

Mat resize_image(Mat &src, Mat img)
{
    Mat dst;
    resize(src, dst, Size(img.rows, img.cols));
    return dst;
}

bool check_exit()
{
     return (waitKey(27) > 0)?true:false;
}

int main(int argc, char ** argv)
{
    Mat rgb[MAX];
    Mat ycbcr[MAX];
    Mat wm_rgb[MAX];
    SVD svd[MAX];
    namedWindow("watermark",1);
    namedWindow("RGB", 2);
    namedWindow("YCBCR",3);
    namedWindow("u",4);
    namedWindow("w",5);
    namedWindow("vt",6);
    if (argc < 3)
    {
        cout<<"Video file required! (Supported formats: avi, mp4, mpeg)\n";
        return 1;
    }

    VideoCapture capture(argv[1]);
    Mat watermark = imread(argv[2]);
    if(!capture.isOpened())
    {
        cout<<"Unable to open the video file!\n";
        return 1;
    }

    int i=0;
        capture >> rgb[i];

    while(!rgb[i].empty())
    {
        imshow("RGB", rgb[i]);
        cvtColor(rgb[i], ycbcr[i], CV_RGB2YCrCb);
        imshow("YCBCR", ycbcr[i]);
        i++;
        capture >> rgb[i];

        if(check_exit())
            exit(0);
    }

    NO_FRAMES = i;

    watermark = resize_image(watermark, ycbcr[0]);
    VideoWriter writer("output.avi", CV_FOURCC('d', 'i', 'v', 'x'), 24.0, cvSize(ycbcr[0].cols, ycbcr[0].rows),  true);
    for(int i = 0; i < NO_FRAMES - 1; i++)
    {
        Mat dst(ycbcr[i].rows, ycbcr[i].cols, CV_32FC1);
        ycbcr[i].convertTo(dst, CV_32S); 
        SVD temp(dst, 5);
        imshow("u", temp.u);
        imshow("w", temp.w);
        imshow("vt", temp.vt);
        svd[i] = temp;

        if(check_exit())
            exit(0);
    }


    int j = 0, k = 0;
    for (i = 0; i < NO_FRAMES; i++)
    {
        for (int p = 0; p < svd[i].u.rows; p++)
        {
            for(int q = 0; q < svd[i].u.cols; q++)
            {

                if (p == q)
                {
                    if (j >= watermark.rows)
                    {
                        goto x;
                    }
                    if (k >= watermark.cols)
                    {
                        k = 0;
                        j++;
                    }
                    svd[i].u.at<float>(p, q) = watermark.at<float>(j,k);
                    k++;
                }
            }
        }
    }


x:  for (i = 0; i < NO_FRAMES; i++)
    {
        Mat A(rgb[0].rows, rgb[0].cols, CV_32FC1);

                //Here
                A = svd[i].u * svd[i].w * svd[i].vt;
        Mat B(A.rows, A.cols, CV_32FC1);
        cvtColor(A, B, CV_YCrCb2RGB);
        writer << B;
    }

    capture.release();
    return 0;
}

Answer 1

The error appears in the matrix multiplication operation (gemm()) although the error may have propagated to the next line where you are trying to create the new matrix B with ill-formed matrix A. Note that the SVD algorithm in OpenCV produces outputs of the form below: For a matrix A(mxn), SVD produces the following three matrices:

w – calculated singular values (min(m,n) x 1)

u – calculated left singular vectors (mxm)

vt – transposed matrix of right singular values (nxn)

Here the singular values are stored in a compact column vector of dimensions (min(m,n) x 1) and not as the actual mathematical equivalent which is a diagonal matrix of dimensions (min(m,n), min(m,n)) .

Therefore if you want to reconstruct the matrix from the individual SVD components you'll have to first bring the vector 'w' into a diagonal matrix form. You can do this using OpenCV's diag() method:

A = svd[i].u * Mat::diag(svd[i].w) * svd[i].vt;

Answer 2

I also encountered this now, thought I should write here, In my case while computing SVD, my size was like 2 * (#imagePixels), Thus one of the U or Vt matrix became huge which cannot be allocated on heap, thus this exception std::bad_alloc came, as in my case Vt size will be imagePixels * imagePixels which is huge.

May this is also happening in your case.

Leaving this here so that next person encountering this should have a look on the Matrix size also.