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The Robustness of Level Sets

  • Paul Bendich
  • Herbert Edelsbrunner
  • Dmitriy Morozov
  • Amit Patel
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6346)

Abstract

We define the robustness of a level set homology class of a function \(f: {\mathbb X} \to {\mathbb R}\) as the magnitude of a perturbation necessary to kill the class. Casting this notion into a group theoretic framework, we compute the robustness for each class, using a connection to extended persistent homology. The special case \({\mathbb X} = {\mathbb R}^3\) has ramifications in medical imaging and scientific visualization.

Keywords

Topological spaces continuous functions level sets perturbations homology extended persistence well groups well diagrams robustness 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Paul Bendich
    • 1
    • 2
    • 3
  • Herbert Edelsbrunner
    • 1
    • 2
    • 3
    • 5
  • Dmitriy Morozov
    • 4
  • Amit Patel
    • 1
    • 2
  1. 1.IST Austria (Institute of Science and Technology Austria)KlosterneuburgAustria
  2. 2.Dept. Comput. Sci.Duke Univ.Durham
  3. 3.Dept. MathematicsDuke Univ.Durham
  4. 4.Depts. Comput. Sci. and Math.Stanford Univ.Stanford
  5. 5.Geomagic, Research Triangle Park

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