Repeated Gaussian Blur in Image Processing
Date: 2023-02-25 15:24:02
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
).
Answer:
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.