Repeated Gaussian Blur in Image Processing
gaussian, image, image-processing, matlab, python
Solution
Successively applying multiple gaussian blurs to an image has the same effect as applying a single, larger gaussian blur, whose radius is the square root of the sum of the squares of the blur radii that were actually applied. In your case, `s2 = sqrt(n*s1^2)`, and the blur radii is approximated as `3*si` where `i = 1, 2`, which means pixels at a distance of more than 3si are small enough to be considered effectively zero during the blurring process.
Problem
I have two questions relating to repeated Gaussian blur. What happens when we repeatedly apply gaussian blur to an image keeping the sigma and the radius same ? And is it possible that after `n` iterations of repeatedly applying gaussian blur (`sigma = s1`) the image becomes the same as it would be on applying gaussian blur ( of `sigma = s2; s1 < s2` ) 1 time on the original image. And if so what is the general formula for deriving that `n` number of times we have to apply gaussian blur with `s1`, given `s1` and `s2` (`s1 < s2`).