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arXiv · 1102.3389

Homology and Robustness of Level and Interlevel Sets

Paul Bendich·Herbert Edelsbrunner·Dmitriy Morozov·Amit Patel
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Abstract

Given a function $f: \Xspace \to \Rspace$ 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 $\Xspace = \Rspace^3$ has ramifications in the fields of medical imaging and scientific visualization.

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Paul Bendich, Herbert Edelsbrunner, Dmitriy Morozov, Amit Patel. 2011-02-16. Homology and Robustness of Level and Interlevel Sets. https://arxiv.org/abs/1102.3389

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