Well, it turns out that these images don't look so good with
the algorithm we have talked about so far. Here I show two
examples of natural textures
that were taken from real photographs. You can see that for
these two examples we get
the sharp boundaries we were looking for, but the interior regions
of the textures are severely pixelated. This is because we
are currently performing
something similar to the nearest neighbor lookup I talked about
earlier. The only difference is that we are looking
up the texture samples in a
deformed texture rather than a regular texture with square cells.
In order to avoid these artifacts, we really need to perform filtering in the interior of these regions. The filter must respect the discontinuities and not interpolate across the indicated boundaries.