Dissertation/Thesis Abstract

Contour trees and cross-sections of multiphase segmentations
by Dillard, Scott Edward, Ph.D., University of California, Davis, 2009, 143; 3369925
Abstract (Summary)

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.

Indexing (document details)
Advisor: Hamann, Bernd
Commitee: Amena, Nina, Hamann, Bernd, Joy, Kenneth I.
School: University of California, Davis
Department: Computer Science
School Location: United States -- California
Source: DAI-B 70/08, Dissertation Abstracts International
Subjects: Computer science
Keywords: Contour trees, Materials science, Morse theory, Multiphase segmentations, Scientific visualization, Topology
Publication Number: 3369925
ISBN: 9781109326321
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