Does opencv Sobel operator compute correlation?

Question

Does opencv Sobel operator compute correlation, not the convolution? I know that the filter2D function computes correlation and i just found out (based from the results of the code)that the Sobel operator also computes correlation. Is this expected? AM i missing something here?

Mat sobelx, dest1,dest2;
Sobel(src, sobelx, src.depth(),1,0,3);
imshow("Sobel filtered in x dir" ,sobelx);
Mat kern = (Mat_<float>(3,3)<<-1,0,1,-1,0,1,-1,0,1);
filter2D(src,dest1,src.type(),kern);
imshow("Sobel in x-dir using corr ", dest1);
/* dest1 equals sobelx  */
flip(kern,kern, -1);//flip the kernel in x and y direction for convolution
filter2D(src,dest2,src.type(),kern);
imshow("Sobel in x-dir using conv ",dest2,);

Answer 1

Here is the test that i wrote and the output tells the truth. cv::Sobel computes correlation and not convolution. I have used the following kernel which is the same as used by cv::Sobel

kern = [-1, 0, 1;
        -2, 0, 2;
        -1, 0, 1]

The results show that the output of sobelx and filter2d(correlation) is same.

void test_sobel(){
cv::RNG(0);
cv::Mat src(4,4, CV_8U);
cv::randu(src, 0, 256);
cv::Mat sobelx, dest_corr,dest_conv;
cv::Sobel(src, sobelx, CV_32F,1,0,3);
// sobel uses a 3x3 filter shown as below
Mat kern = (Mat_<float>(3,3)<<-1,0,1,-2,0,2,-1,0,1);
// filter2D computes correlation
cv::filter2D(src,dest_corr,CV_32F,kern);

//flip the kernel in x and y direction for convolution
cv::Mat kern_conv;
cv::flip(kern,kern_conv, -1);
cv::filter2D(src,dest_conv,CV_32F,kern_conv);

std::cout << "kern = \n" << kern<< std::endl;
std::cout << "kern_conv = \n" << kern_conv<< std::endl;
std::cout << "src = \n" << src << std::endl;
std::cout << "sobelx = \n" << sobelx<< std::endl;
std::cout << "dest_corr = \n" << dest_corr<< std::endl;
std::cout << "dest_conv =\n" << dest_conv << std::endl;
cv::Mat diff1 = sobelx - dest_corr;
cv::Mat diff2 = sobelx - dest_conv;
std::cout << "sobelx - dest_corr = " << cv::sum( diff1 )[0] << std::endl;
std::cout << "sobelx - dest_conv = " << cv::sum( diff2 )[0] << std::endl;
}

Output:

kern = 
[-1, 0, 1;
 -2, 0, 2;
-1, 0, 1]
kern_conv = 
[1, 0, -1;
 2, 0, -2;
 1, 0, -1]
src = 
[246, 156, 192,   7;
 165, 166,   2, 179;
 231, 212, 171, 230;
  93, 138, 123,  80]
sobelx = 
[0, -434, -272, 0;
 0, -440, -105, 0;
 0, -253, -9, 0;
 0, -60, -80, 0]
dest_corr = 
[0, -434, -272, 0;
 0, -440, -105, 0;
 0, -253, -9, 0;
 0, -60, -80, 0]
dest_conv =
[0, 434, 272, 0;
 0, 440, 105, 0;
 0, 253, 9, 0;
 0, 60, 80, 0]
sobelx - dest_corr = 0
sobelx - dest_conv = -3306