Is there a need to (re-)normalize the weights so that the output pixel stays on a desired magnitude?
Assume the Gaussian kernel is a constant, but f(x) can suppress any pixel in the support region, based on the data, chances are we can only collect a small subset of weighted pixels, resulting in a very small magnitude of output?
@zf. Your intuition is correct. Weights will be normalized so that they sum to one. I left it out for simplicity.