I am trying to understand is it possible to say what variance I'll have if apply convolution to image. In my case I have matrix(image) and I am applying Gaussian Blur(with known parameters $\sigma_X = 1$, $\sigma_Y = 1$). Then I can easily calculate a variance of any row or column from matrix before and after convolution. So I did. But is there any way to say what variance I get after convolution process known variance before, $\sigma_X$ and $\sigma_Y$.
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$\begingroup$ Not really, because unless the image is white noise, columns will be associated with their neighbors and rows will be associated with their neighbors: and the degree of this association, as measured by their correlation coefficients, is a necessary part of the answer. $\endgroup$– whuber ♦Commented Aug 14, 2023 at 20:48
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