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University of Illinois at Urbana-Champaign
Computing and Comprehending Topology: Persistence and Hierarchical Morse Complexes
Abstract
dc:descriptionThe 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.
Degree
thesis:*- Name thesis:degree_name
- Ph.D.
- Level thesis:degree_level
- Dissertation
- Discipline thesis:degree_discipline
- Computer Science
- Grantor
- University of Illinois at Urbana-Champaign
- Year dc:date
- 2015
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Zomorodian, Afra Joze
- Contributors dc:contributor
-
- Edelsbrunner, Herbert
Subjects
dc:subject × 1Rights
- Language dc:language
- eng
Identifiers
dc:identifier.*- Identifier
- (MiAaPQ)AAI3023247
- OAI identifier oai:identifier
- oai:www.ideals.illinois.edu:2142/81590