Slide 29 of 42
So lets see how it works on some synthetic datasets first. Here's a
slice of a volume with two concentric spheres, and here are the
scatterplots. From the cross-section or the scatterplots, you can see
that there are really just two boundaries- from black to gray, and
from gray to white. And here is the position function, which was
automatically calculated from the histogram volume for this dataset.
Because there were two boundaries, there are two curves here, and they
have precisely the expected shape.
