Usually the filters for detecting edges have the sum of all the values in the filter matrix equal to 0. For example: [-1 -2 -1, 0 0 0, 1 2 1].
Why is it so ?
Answer
An edge detection filter is, by definition, a high-pass filter. It is looking for quick changes (i.e. high frequencies), not slow trends. Thus, a good edge detection filter will have a response of 0 at DC. A FIR filter whose taps sum to 0 has a response of 0 at DC.
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