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Singular Value Decomposition (SVD) with opencv

asked 2018-09-10 05:05:28 -0600

Digital Design gravatar image

updated 2018-09-10 05:27:36 -0600

berak gravatar image

Hi, I am using SVD for my algorithm and the decomposition is done by this instruction:

const int N= 16;
Mat x= (Mat_<double>(N, N)<< 23, 24, 24, 23, 22.5, 21.5, 20, 20, 19, 20, 22, 23,    23, 23.5, 24, 25.5,
        23.5, 24, 23, 21, 21, 22, 21, 20, 18.5, 18, 19, 20, 20.5, 23, 24, 24,
        24, 24, 22, 21, 21.5, 21.5, 21, 20, 19.5, 20, 21, 21, 22, 23, 24, 24,
        24.5, 24, 23, 23, 23, 21, 20, 20, 20, 22, 22, 22, 23, 23, 24, 24,
        24, 24, 24, 24, 24, 22, 20, 20, 20, 21, 21, 21, 21, 22, 24, 24,
        24, 24.5, 25, 24.5, 24, 22, 20, 21, 21, 21, 22, 22, 22, 23, 24, 24,
        24, 24.5, 25, 24.5, 24, 22, 20, 22, 23, 23, 24, 24, 23, 22, 22.5, 23,
        24.5, 24.5, 24, 24, 23, 22, 22, 23, 24.5, 24.5, 23, 21.5, 21, 21, 22.5, 22.5,
        23.5, 24.5, 25.5, 25, 23.5, 24.5, 26, 25.5, 24, 25, 22.5, 20.5, 20.5, 21, 21, 20.5,
        24.5, 25.5, 26, 25.5, 24.5, 25, 25.5, 25, 24, 24, 22, 20.5, 20.5, 19.5, 18.5, 19.5,
        25.5, 25.5, 26, 26, 25, 25, 25, 25, 23.5, 24, 22, 20, 20, 19.5, 18.5, 21,
        24, 24, 24, 24, 24, 24.5,   23, 22.5, 24, 24.5, 23, 20.5, 20, 20, 20.5, 22.5,
        24, 24, 24, 24, 24, 24, 23, 22.5, 24, 23.5, 23, 21.5, 20, 19.5, 22, 24,
        22.5, 23, 22.5, 22, 23, 23, 22, 21.5, 23, 22, 22, 22, 20, 20.5, 23, 24,
        22.5, 21.5, 21.5, 22, 23, 24, 22.5, 20, 21, 20.5, 20.5, 22, 22, 23, 23.5, 23.5,
        22.5, 21, 21, 21, 21, 23, 21.5, 20, 20, 20.5, 20.5, 22, 24, 24, 23.5, 23.5);
Mat Sigma= Mat::zeros(N, N, CV_64FC1);
Mat S, U, VT, x_hat, err;  
int minLoc[2], maxLoc[2];
double minVal, maxVal;
SVDecomp(x, S, U, VT, cv::SVD::FULL_UV);
/*Please note that S is a column vector and S should be a square diagonal matrix, Assigning the components of the S    to the diagonal components of Sigma*/
x_hat= U * Sigma* VT;
cout<< "U * Sigma* VT= "<< endl<< x_hat<< endl;
absdiff(x, x_hat, err);

And the error is really huge!!! (Terminal output)

Reconstruction err: MIN= 0.00135955, MAX= 2.99473, sum= [176.076, 0, 0, 0]

Which is shit! The whole process is done very straight forward with matlab. What's wrong with opencv SVD? Why does the operation loon irreversible?!!!! Your advices are highly appreciated.

minMaxIdx(err, &minVal, &maxVal, minLoc, maxLoc);
cout<< "Reconstruction err: MIN= "<< minVal<< ", MAX= "<< maxVal<< ", sum= "<< ...
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answered 2018-09-10 08:14:09 -0600

LBerger gravatar image

updated 2018-09-10 08:14:40 -0600

Try this :

     SVDecomp(x, S, U, VT, cv::SVD::FULL_UV);
     /*Please note that S is a column vector and S should be a square diagonal matrix, Assigning the components of the S    to the diagonal components of Sigma*/
     for (int i = 0; i < VT.rows; i++)
         VT.row(i) = VT.row(i) * S.at<double>(i, 0);
     x_hat = U * VT;
     cout << "U * Sigma* VT= " << endl << x_hat << endl;
     absdiff(x, x_hat, err);
     minMaxIdx(err, &minVal, &maxVal, minLoc, maxLoc);
     cout << "Reconstruction err: MIN= " << minVal << ", MAX= " << maxVal << ", sum= " << sum(err) << endl;

and it is not Sigma.at<double>(i1, i1) but S.at<double>(i1,0); results are

U * Sigma* VT=
[23, 24.00000000000001, 23.99999999999999, 23.00000000000001, 22.5, 21.49999999999999, 20.00000000000002, 19.99999999999999, 19, 20, 21.99999999999999, 23, 23, 23.5, 24, 25.5;
 23.50000000000001, 24.00000000000003, 22.99999999999999, 21.00000000000001, 21, 21.99999999999999, 21.00000000000001, 20, 18.5, 18, 18.99999999999999, 20, 20.50000000000001, 23, 24, 24;
 24.00000000000002, 24.00000000000002, 22, 21.00000000000003, 21.5, 21.5, 21.00000000000001, 20, 19.5, 20.00000000000001, 21.00000000000001, 21, 22.00000000000001, 23.00000000000001, 24, 24;
 24.49999999999999, 24, 22.99999999999998, 23.00000000000001, 22.99999999999998, 20.99999999999999, 20.00000000000001, 19.99999999999998, 20, 22, 21.99999999999999, 21.99999999999999, 23, 23, 23.99999999999999, 24;
 24.00000000000001, 24.00000000000002, 24, 24.00000000000001, 24, 22, 20.00000000000002, 20, 20.00000000000001, 21.00000000000001, 21.00000000000001, 21, 21.00000000000001, 22.00000000000001, 24.00000000000001, 24.00000000000001;
 23.99999999999999, 24.5, 24.99999999999998, 24.50000000000001, 23.99999999999998, 21.99999999999999, 20, 20.99999999999999, 21, 21, 21.99999999999999, 22, 22.00000000000001, 22.99999999999999, 24, 24;
 23.99999999999999, 24.5, 24.99999999999998, 24.50000000000001, 23.99999999999999, 21.99999999999999, 20.00000000000002, 21.99999999999999, 23.00000000000001, 23, 24, 23.99999999999999, 23.00000000000001, 22, 22.5, 23;
 24.5, 24.5, 24, 24.00000000000001, 22.99999999999999, 22, 22.00000000000002, 22.99999999999999, 24.5, 24.50000000000001, 23, 21.49999999999999, 21.00000000000001, 21.00000000000001, 22.5, 22.5;
 23.5, 24.5, 25.49999999999998, 25, 23.49999999999999, 24.49999999999999, 26.00000000000001, 25.49999999999999, 24, 25, 22.5, 20.5, 20.5, 21, 21, 20.50000000000001;
 24.5, 25.50000000000002, 25.99999999999999, 25.5, 24.5, 24.99999999999998, 25.5, 24.99999999999999, 24, 24, 21.99999999999998, 20.49999999999999, 20.49999999999999, 19.5, 18.49999999999999, 19.5;
 25.49999999999999, 25.49999999999999, 25.99999999999998, 25.99999999999999, 24.99999999999998, 24.99999999999998, 25, 24.99999999999998, 23.49999999999999, 24, 22, 20, 20.00000000000001, 19.50000000000001, 18.5, 21;
 24, 24, 23.99999999999998, 24.00000000000001, 23.99999999999998, 24.49999999999999, 23, 22.49999999999999, 24, 24.50000000000001, 23, 20.49999999999999, 20.00000000000001, 20.00000000000001, 20.5, 22.5;
 24.00000000000002, 24.00000000000003, 24.00000000000001, 24.00000000000003, 24, 24, 23.00000000000003, 22.5, 24.00000000000002, 23.50000000000001, 23.00000000000001, 21.50000000000002, 20.00000000000003, 19.50000000000003, 22.00000000000002, 24.00000000000002;
 22.5, 23.00000000000001, 22.49999999999998, 22, 22.99999999999999, 22.99999999999999, 22.00000000000001, 21.49999999999999, 23.00000000000001, 22.00000000000001, 22.00000000000001, 22, 20.00000000000001, 20.50000000000001, 23.00000000000001 ...
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Comments

Many thanks for your answer. It works!! Just out of curiosity, why do you multiply each line of VT by corresponding singular value: for (int i = 0; i < VT.rows; i++) VT.row(i) = VT.row(i) * S.at<double>(i, 0); The second question is that I am processing a very huge matrix and I use pointers to access the elements efficiently. Is there a faster way to modify the whole row of VT? Thanks a lot

Digital Design gravatar imageDigital Design ( 2018-09-10 08:28:14 -0600 )edit

because image description

"a very huge matrix "? iteraive method are better. About pointer it's here=efficient way you should use opencv with lapack support

LBerger gravatar imageLBerger ( 2018-09-10 13:50:47 -0600 )edit

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Asked: 2018-09-10 05:05:28 -0600

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Last updated: Sep 10 '18