Calculating covariance matrix with OpenCV

1
votes

I am trying to use opencv's cv::calcCovarMatrix in order to get covariance matrix. I have created a dummy testcase:

A = [1 2; 3 4] // matlab style 
B = [1 0; 5 8]

If I run this with matlab, I get:

>> cov(A,B)
ans =
1.6667    4.3333
4.3333   13.6667

Which seems ok according to my calculation, but when I use cv::calcCovarMatrix, I am not able to obtain the same result:

cv::Mat covar, mean;
cv::Mat A = (cv::Mat_<float>(2,2) << 1, 2, 3, 4);
cv::Mat B = (cv::Mat_<float>(2,2) << 1, 0, 5, 8);
cv::Mat x[2] = {A, B};
cv::calcCovarMatrix(x, 2, covar, mean, CV_COVAR_SCRAMBLED );
std::cout << covar << std::endl; 
// gives [6, -6;
//        -6, 6]

What am I missing?

3
c++matlabopencvcovariance
opencv is working on rows, matlab on cols, so add CV_COVAR_COLS to your flag – berak
According to opencv doc, the CV_COVAR_COLS is meant to use only with different prototype of calling cv::calcCovarMatrix, and after looking into the source code of the function, the mentioned flag is just removed. – dohnto
if you're using opencv3.0, cv::COVAR_COLS – berak
also in opencv you need to scale cov matrix after cov=cov/(nsamples-1). – mrgloom

3 Answers

1
votes

It is just a flag that is missing. Try:

cv::calcCovarMatrix(x, 2, covar, mean, cv::COVAR_ROWS | cv::COVAR_SCRAMBLED );

COVAR_ROWS mean : all the input vectors are stored as rows of the samples matrix. (from opencv 3.0 doc)

1
votes

I had the same problem two days ago, and I have no idea why the problem occurs, but I've written a code that works for all the samples I tested in OpenCV and MATLAB.

void matlab_covar(Mat A,Mat B)
{
   Mat covar,mean;
   if(A.rows!=1) // check if A and B has one row don't reshape them 
   {
       A=A.reshape(1,A.rows*A.cols).t(); //reshape A to be one row
       B=B.reshape(1,A.rows*A.cols).t(); //rehsape B to be one row
   }
   vconcat(A,B,A);          //vertical attaching
   cv::calcCovarMatrix(A,covar, mean,CV_COVAR_COLS|CV_COVAR_NORMAL);
   Mat Matlab_covar = covar/(A.cols-1);  //scaling
   cout<<Matlab_covar<<endl;
}

I tested some examples to show that this code works properly (but I'm not sure why it works)

example-1

in MATLAB

>> A = [1 2; 3 4];
>> B = [1 0; 5 8];
>> cov(A,B)

ans =

1.6667    4.3333
4.3333   13.6667

In Opencv

    cv::Mat A = (cv::Mat_<double>(2,2) << 1,2,3,4);
    cv::Mat B = (cv::Mat_<double>(2,2) << 1,0,5,8);
    matlab_covar(A,B);   //the function i write

output

[1.666666666666667, 4.333333333333333;
 4.333333333333333, 13.66666666666667]

example-2

MATLAB

>> A = [3 3 3;2 2 2];
>> B = [1 2 3;3 2 1];
>> cov(A,B)

ans =

0.3000         0
     0    0.8000

OpenCV

[0.3, 0;
 0, 0.8]

Example-3

Matlab

 >> a=rand(3,1)

 a =

 0.8147
 0.9058
 0.1270

 >> b=rand(3,1)

 b =

 0.9134
 0.6324
 0.0975

 >> cov(a,b)

 ans =

 0.1813    0.1587
 0.1587    0.1718

OpenCV

    cv::Mat A = (cv::Mat_<double>(3,1) << 0.8147,0.9058,0.1270);
    cv::Mat B = (cv::Mat_<double>(3,1) << 0.9134,0.6324,0.0975);
    matlab_covar(A,B);

    [0.1812933233333333, 0.1586792416666666;
     0.1586792416666666, 0.1717953033333333]
-1
votes

I used the following command:

calcCovarMatrix(Z.t(), cov, mu, CV_COVAR_ROWS | CV_COVAR_SCRAMBLED |CV_COVAR_NORMAL);

After dividing cov by (nsamples-1), this covariance matches with the MATLAB calculation result.