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I know that Sobel is a filter for edge detection and we should use convolution to find edges, but is there any difference if we use correlation instead of convolution? I think Sobel tries to find a pixel which has different values from its surrounding pixels, and the difference between correlation and convolution is just flipping the filter, I think, there should be no difference.

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You're correct, convolution is the same as correlation except that 2D Sobel filter kernel is rotated for 180 degrees.

Generally speaking for spatial filtering using correlation or convolution is a matter of personal/domain preferences/convention.

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