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Title:Computing and Comprehending Topology: Persistence and Hierarchical Morse Complexes
Author(s):Zomorodian, Afra Joze
Doctoral Committee Chair(s):Edelsbrunner, Herbert
Department / Program:Computer Science
Discipline:Computer Science
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Computer Science
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.
Issue Date:2001
Type:Text
Language:English
Description:168 p.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2001.
URI:http://hdl.handle.net/2142/81590
Other Identifier(s):(MiAaPQ)AAI3023247
Date Available in IDEALS:2015-09-25
Date Deposited:2001


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