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Publications [#303523] of Paul L Bendich

Papers Published

  1. Bendich, P; Edelsbrunner, H; Morozov, D; Patel, A, Homology and Robustness of Level and Interlevel Sets (February, 2011) [1102.3389v1]
    (last updated on 2017/12/15)

    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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