In this thesis I discuss the application of two topological structures to scientific visualization. The first is the contour tree, a structure that represents the connectivity of the level sets of a function. I describe methods to compute the contour tree from piecewise-quadratic functions, and I develop a volume rendering framework that uses the contour tree to apply individual transfer functions to topologically distinct regions of the dataset. The second structure I consider is the separating surface of a multiphase 3D segmentation, i.e., a segmentation containing many more than two regions. Specifically, I consider the problem of constructing this separating surface given a series of 2D cross-sections. Two methods are described: A numerical method that operates on a voxel grid and produces smooth triangulated surface using a nearly-minimal number of triangles, and a topological method that operates only on the combinatorial structure of the segmentation and produces a cell complex that connects prescribed regions in adjacent cross-sections. For both the contour tree and the separating surface, properties of the described methods and algorithms are proved, implementation details are discussed, and experimental results are presented.
|Commitee:||Amena, Nina, Hamann, Bernd, Joy, Kenneth I.|
|School:||University of California, Davis|
|School Location:||United States -- California|
|Source:||DAI-B 70/08, Dissertation Abstracts International|
|Keywords:||Contour trees, Materials science, Morse theory, Multiphase segmentations, Scientific visualization, Topology|
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