Inferring local homology from sampled stratified spaces Conference Paper

Author(s): Bendich, Paul; Cohen-Steiner, David; Edelsbrunner, Herbert; Harer, John; Morozov, Dmitriy
Title: Inferring local homology from sampled stratified spaces
Abstract: We study the reconstruction of a stratified space from a possibly noisy point sample. Specifically, we use the vineyard of the distance function restricted to a I-parameter family of neighborhoods of a point to assess the local homology of the stratified space at that point. We prove the correctness of this assessment under the assumption of a sufficiently dense sample. We also give an algorithm that constructs the vineyard and makes the local assessment in time at most cubic in the size of the Delaunay triangulation of the point sample.
Keywords: Algorithms; Simplicial complexes; Persistence; topological data analysis; local homology; stratified spaces; power diagrams; Delaunay triangulations
Conference Title: FOCS: Foundations of Computer Science
Conference Dates: Oclober 20-23, 2007
Conference Location: Providence, RI
Publisher: IEEE  
Date Published: 2007-01-01
Start Page: 536
End Page: 546
DOI: 10.1109/FOCS.2007.33
Open access: no
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