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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).
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What is Gaussian blurring? Named after mathematician Carl Friedrich Gauss (rhymes with “grouse”), Gaussian (“gow-see-an”) blur is the application of a mathematical function to an image in order to blur it. “It's like laying a translucent material like vellum on top of the image,” says photographer Kenton Waltz.
Four types of blur are considered: defocus, rectangular, motion and Gaussian ones.
Gaussian Blur in Photoshop is a type of low pass filter which cuts out unevenness and smoothens pixel values in a photograph. In simple terms, if you want to reduce noise in an image, add an artistic blur effect to it, or intend to create depth in it by blurring the background, this feature can help.
If you remember the exact radius of the Gaussian blur, and you processed and saved the images in a 16 bit or greater format then you can remove the blur by inverse filtering in Matlab.
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.
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