Computing and Comprehending Topology: Persistence and Hierarchical Morse Complexes
Zomorodian, Afra Joze
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https://hdl.handle.net/2142/81590
Description
Title
Computing and Comprehending Topology: Persistence and Hierarchical Morse Complexes
Author(s)
Zomorodian, Afra Joze
Issue Date
2001
Doctoral Committee Chair(s)
Edelsbrunner, Herbert
Department of Study
Computer Science
Discipline
Computer Science
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Computer Science
Language
eng
Abstract
The thesis also gives algorithms for computing the theoretically defined measures or structures in each case. Using persistence, we may distinguish between topological noise and features of a space. This differentiation enables us to simplify a space topologically. To denoise two-dimensional density functions, we first construct Morse complexes over their underlying space. Applying persistence, we create a hierarchy of progressively coarser Morse complexes. The thesis describes implementations of the algorithms and presents experimental evidence of their feasibility on a variety of data.
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