Geodesic
Homology and robustness of level and interlevel sets
Homology, homotopy, and applications, Tome 15 (2013) no. 1, pp. 51-72.

Voir la notice de l'article provenant de la source International Press of Boston

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.
DOI : 10.4310/HHA.2013.v15.n1.a3
Classification : 55-xx, 68-xx
Keywords: zigzag, levelset, homology, perturbation, well group, robustness 
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Paul Bendich; Herbert Edelsbrunner; Dmitriy Morozov; Amit Patel. Homology and robustness of level and interlevel sets. Homology, homotopy, and applications, Tome 15 (2013) no. 1, pp. 51-72. doi : 10.4310/HHA.2013.v15.n1.a3. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2013.v15.n1.a3/

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