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Abstract:
Crease surfaces are two-dimensional manifolds along which a scalar
field assumes a local maximum (ridge) or a local minimum (valley) in
a constrained space. Unlike isosurfaces, they are able to capture
extremal structures in the data. Creases have a long tradition in
image processing and computer vision, and have recently become a
popular tool for visualization. When extracting crease surfaces,
degeneracies of the Hessian (i.e., lines along which two eigenvalues
are equal), have so far been ignored. We show that these loci,
however, have two important consequences for the topology of crease
surfaces: First, creases are bounded not only by a side constraint
on eigenvalue sign, but also by Hessian degeneracies. Second, crease
surfaces are not in general orientable. We describe an efficient
algorithm for the extraction of crease surfaces which takes these
insights into account and demonstrate that it produces more accurate
results than previous approaches. Finally, we show that DT-MRI
streamsurfaces, which were previously used for the analysis of
planar regions in diffusion tensor MRI data, are mathematically
ill-defined. As an example application of our method, creases in a
measure of planarity are presented as a viable substitute.
