Slide 21 of 42
Now here, we're sampling everywhere on a grid, with no respect to the
original boundary, and at even a coarser resolution than before. But
still, the same curves are being traced out as before. This works,
because of the original assumptions of material uniformity and
isotropic blurring. And, we should have good coverage of these curves
for at last two reasons- the boundaries of real objects tend to assume
a variety of positions and orientations relative to the sampling grid,
and, because real measurement devices necessarily band limit, there is
always going to be some blurring of the boundary, so there will be
intermediate values to fill out these curves. I should note however,
that we have found it sometimes helps to blur
the volume a little bit as a pre-process to increase the coherence
of these scatterplot curves.
