Homology and robustness of level and interlevel sets


Journal Article

Given a continuous function f: X → 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 X = ℝ3 has ramifications in the fields of medical imaging and scientific visualization. © 2013, International Press.

Full Text

Duke Authors

Cited Authors

  • Bendich, P; Edelsbrunner, H; Morozov, D; Patel, A

Published Date

  • April 23, 2013

Published In

Volume / Issue

  • 15 / 1

Start / End Page

  • 51 - 72

Electronic International Standard Serial Number (EISSN)

  • 1532-0081

International Standard Serial Number (ISSN)

  • 1532-0073

Digital Object Identifier (DOI)

  • 10.4310/HHA.2013.v15.n1.a3

Citation Source

  • Scopus