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2013 Homology and robustness of level and interlevel sets
Paul Bendich, Herbert Edelsbrunner, Dmitriy Morozov, Amit Patel
Homology Homotopy Appl. 15(1): 51-72 (2013).

Abstract

Given a continuous function $f\colon \mathbb{X} \to \mathbb{R}$ 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 $\mathbb{X} = \mathbb{R}^3$ has ramifications in the fields of medical imaging and scientific visualization.

Citation

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Paul Bendich. Herbert Edelsbrunner. Dmitriy Morozov. Amit Patel. "Homology and robustness of level and interlevel sets." Homology Homotopy Appl. 15 (1) 51 - 72, 2013.

Information

Published: 2013
First available in Project Euclid: 8 November 2013

zbMATH: 1266.55004
MathSciNet: MR3031814

Subjects:
Primary: 55 , 68

Keywords: homology , levelset , Persistence , perturbation , robustness , well group , zigzag

Rights: Copyright © 2013 International Press of Boston

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Vol.15 • No. 1 • 2013
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