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Generalized Kuwahara Filter from GPU Pro 1

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I'm trying to understand something about the Generalized Kuwahara Filter discussed on page 251 of "GPU Pro 1." 

 

On page 252, he defines the "weighted mean" at a point (x0, y0).  My questions are:

 

1. Is (x0,y0) the point being filtered?  I'm assuming the shift w_k(x-x0, y-y0) is used to center the weight function about the point (x0, y0).

 

2. Multiplying the image by this weight when computing the mean gives bias to pixels in the sector subregion.  Is that just a side effect when building the smooth weight functions?  When computing the subregion mean, I don't see why some pixels should be given more weight than others. 

 

3. Why compute the "weighted variance" in the subregion?  Why not just the variance, and use that to define the subregion weight?

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