difference between convolution and correlation?

asked 2012-12-14 06:18:59 -0500

mrgloom gravatar image

This document points that convolution and correlation very related operations. (also here)

here I found the code of convolution.

void convolveDFT(const Mat& A, const Mat& B, Mat& C)
    // reallocate the output array if needed
    C.create(abs(A.rows - B.rows)+1, abs(A.cols - B.cols)+1, A.type());
    Size dftSize;
    // compute the size of DFT transform
    dftSize.width = getOptimalDFTSize(A.cols + B.cols - 1);
    dftSize.height = getOptimalDFTSize(A.rows + B.rows - 1);

    // allocate temporary buffers and initialize them with 0's
    Mat tempA(dftSize, A.type(), Scalar::all(0));
    Mat tempB(dftSize, B.type(), Scalar::all(0));

    // copy A and B to the top-left corners of tempA and tempB, respectively
    Mat roiA(tempA, Rect(0,0,A.cols,A.rows));
    Mat roiB(tempB, Rect(0,0,B.cols,B.rows));

    // now transform the padded A & B in-place;
    // use "nonzeroRows" hint for faster processing
    dft(tempA, tempA, 0, A.rows);
    dft(tempB, tempB, 0, B.rows);

    // multiply the spectrums;
    // the function handles packed spectrum representations well
    mulSpectrums(tempA, tempB, tempA);

    // transform the product back from the frequency domain.
    // Even though all the result rows will be non-zero,
    // we need only the first C.rows of them, and thus we
    // pass nonzeroRows == C.rows
    dft(tempA, tempA, DFT_INVERSE + DFT_SCALE, C.rows);

    // now copy the result back to C.
    tempA(Rect(0, 0, C.cols, C.rows)).copyTo(C);

    // all the temporary buffers will be deallocated automatically

so how correlation code looks like? maybe I misleaded in terminology? also how to compute correlation and convolution in spatial domain(not in freqency domain with dft(fft))?

another question why opencv matchtemplate use block-wise cross correlation why it doesn't use phase correlation?

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