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MPI-INF D4 Publications :: Thesis :: Günther, David

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Thesis - Doctoral dissertation | @PhdThesis | Doktorarbeit

Author(s)*:Günther, David
BibTeX citekey*:guenther12phd

Title, School
Title*:Topological Analysis of Discrete Scalar Data
School:Universität des Saarlandes
Type of Thesis*:Doctoral dissertation

Note, Abstract, Copyright
LaTeX Abstract:This thesis presents a novel computational framework that allows for a robust extraction and quantification of the Morse-Smale complex of a scalar field given on a 2- or 3-dimensional manifold. The proposed framework is based on Forman's discrete Morse theory, which guarantees the topological consistency of the computed complex. Using a graph theoretical formulation of this theory, we present an algorithmic library that computes the Morse-Smale complex combinatorially with an optimal complexity of

$O(n^2)$ and efficiently creates a multi-level representation of it. We explore the discrete nature of this complex, and relate it to the smooth counterpart. It is often necessary to estimate the feature strength of the individual components of the Morse-Smale complex -- the critical points and separatrices. To do so, we propose a novel output-sensitive strategy to compute the persistence of the critical points. We also extend this wellfounded concept to separatrices by introducing a novel measure of feature strength called separatrix persistence. We evaluate the applicability of our methods in a wide variety of application areas ranging from computer graphics to planetary science to computer and electron tomography.

Keywords:Discrete Morse Theory, Algorithms, Feature Extraction, Combinatorial Topology
Download Access Level:Public
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Referees, Status, Dates
1. Referee:Tino Weinkauf, Hans-Peter Seidel
2. Referee:Eugene Zhang, Olga Sorkine
Supervisor:Tino Weinkauf
Date Kolloquium:18 December 2012
Chair Kolloquium:Christian Theobaldt

MPG Unit:Max-Planck-Institut für Informatik
MPG Subunit:Computer Graphics Group
MPG Subsubunit:Feature-Based Data Analysis For Computer Graphics and Visualization
Audience:experts only
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BibTeX Entry:
AUTHOR = {G{\"u}nther, David},
TITLE = {Topological Analysis of Discrete Scalar Data},
SCHOOL = {Universit{\"a}t des Saarlandes},
YEAR = {2012},
TYPE = {Doctoral dissertation}
PAGES = {153},
MONTH = {December},

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