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A Sobel operation is a matrix convolution
If you mean clock edge detection, then you're indeed correct. It has nothing to do with it. But when it comes to video edge detection, then it's a technique that is regularly used...I wonder then what does a sobel operator has to do with edge detection
Sounds irrelevant, doesn't it?...
Convolution van be set up to do all sorts of filters.
Consider the following 1x3 matrix: (-1 0 1). If you convolve this along a line (a video perhaps) you would have a basic edge detector, because solid blocks of intensity would cancel itself out, but when you hit a luma change, the output would have a magnitude greater or lower than 1 (giving you the gradient).