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Homology and Robustness of Level and Interlevel Sets

# Homology and Robustness of Level and Interlevel Sets,Computing Research Repository,Paul Bendich,Herbert Edelsbrunner,Dmitriy Morozov,Amit K. Patel

Homology and Robustness of Level and Interlevel Sets
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.
Journal: Computing Research Repository - CORR , vol. abs/1102.3, 2011
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