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So what are our goals in looking at this kind of data? Basically, we
would like to visualize it in a way that shows the three-dimensional
structure and shape of the anisotropic regions, especially the white
matter fiber tracts. This has a number of useful applications- obviously
to improve our understanding of neuroanatomy, but also for the sake
of surgical planning and cognitive science. The challenge is that the
tensor contains a great deal of information- it has six degrees of
freedom. If you have one tensor, you can use an ellipsoid, but what
about a full three-dimensional field of them? There's a trade-off between
showing enough of the information so you're conveying a good sense of
what's going on, versus overloading the information with so much information
that its either a visually cluttered opaque block, or is so dense that
its unintelligible.