Homology and robustness of level and interlevel sets Journal Article


Author(s): Bendich, Paul; Edelsbrunner, Herbert; Morozov, Dmitriy; Patel, Amit
Article Title: Homology and robustness of level and interlevel sets
Affiliation IST Austria
Abstract: Given a continuous function f:X-R on a topological space, we consider the preimages of intervals and their homology groups and show how to read the ranks of these groups from the extended persistence diagram of f. In addition, we quantify the robustness of the homology classes under perturbations of f using well groups, and we show how to read the ranks of these groups from the same extended persistence diagram. The special case X=R3 has ramifications in the fields of medical imaging and scientific visualization.
Journal Title: Homology, Homotopy and Applications
Volume: 15
Issue 1
ISSN: 1532-0073
Publisher: International Press  
Date Published: 2013-01-01
Start Page: 51
End Page: 72
Sponsor: This research is partially supported by the National Science Foundation (NSF) under grant DBI-0820624 and the Defense Advanced Research Projects Agency (DARPA) under grants HR0011-05-1-0057 and HR0011-09-0065.
URL:
DOI: 10.4310/HHA.2013.v15.n1.a3
Open access: yes (repository)
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