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This set of images highlights what we want to do. Our initial texture can be
thought of having "regions" in which we want the filtering to take place.
I show these as constant color regions with black boundaries
on the image on the
left. If we don't filter at all, we get the pixelated result we saw earlier,
which is the result shown in the image in the middle. If we properly
filter inside these
regions, we can get the image shown on the right. Note how the sharp
edges are still preserved, but the pixelation is gone.
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