How to calculate the autocorrelation function width parameter for each image pixel?

Question

Mathematics

There is a non-stationary process in the image.
Using a sliding window, it is necessary to find for each pixel (except for the boundary ones) a value proportional to the width of the two-dimensional autocorrelation function of this window.
In the literature, such a parameter as the second moment (second degree spread) of the ACF for the analysis of textural features was found, but the calculation methods proposed there are considered too long.