Polygonizing extremal surfaces with manifold guarantees
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
Lagrangian coherent structures with guaranteed material separation
EuroVis'11 Proceedings of the 13th Eurographics / IEEE - VGTC conference on Visualization
Fast extraction of high-quality crease surfaces for visual analysis
EuroVis'11 Proceedings of the 13th Eurographics / IEEE - VGTC conference on Visualization
| Hi-index | 0.00 |
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 diffusion tensor magnetic resonance imaging (DT-MRI) stream surfaces, 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.