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Discrete & Computational Geometry

, Volume 37, Issue 1, pp 103–120 | Cite as

Stability of Persistence Diagrams

  • David Cohen-Steiner
  • Herbert Edelsbrunner
  • John Harer
Article

Abstract

The persistence diagram of a real-valued function on a topological space is a multiset of points in the extended plane. We prove that under mild assumptions on the function, the persistence diagram is stable: small changes in the function imply only small changes in the diagram. We apply this result to estimating the homology of sets in a metric space and to comparing and classifying geometric shapes.

Keywords

Topological Space Simplicial Complex Homology Group Hausdorff Distance Rigid Motion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer 2006

Authors and Affiliations

  1. 1.INRIA, 2004 Route des Lucioles, BP 93, 06904Sophia-AntipolisFrance
  2. 2.Department of Computer Science, Duke University, Durham, NC 27708 and GeomagicResearch Triangle Park, NC 27709USA
  3. 3.Department of Mathematics, Duke UniversityDurham, NC 27708USA

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