[Solved]: median filter one after the other

Problem Detail: 

Operate on an image by performing Median Filtering in a 3x3 window.
Operate on the resulting image by performing, again, Median Filtering in a 3x3 window.
Can the resulting image be obtained from a single Median filtering?

my initial thought is that it can be done with the right mask. maybe a median next to a median. but i'm not sure.

Asked By : Gilad

Answered By : Yuval Filmus

The value a pixel gets after applying the median filter only depends on points in the $3\times 3$ window centered at it. So applying the media filter twice, any pixel depends only on points in the $5\times 5$ window centered at it. So you could in principle do it in one go, using a larger window and a more complicated function. How complicated - I'll let you to find out.

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Question Source : http://cs.stackexchange.com/questions/9336