Stability of Persistence Diagrams (original) (raw)

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.

Article PDF

Similar content being viewed by others

Author information

Authors and Affiliations

  1. INRIA, 2004 Route des Lucioles, BP 93, 06904, Sophia-Antipolis, France
    David Cohen-Steiner
  2. Department of Computer Science, Duke University, Durham, NC 27708 and Geomagic, Research Triangle Park, NC 27709, USA
    Herbert Edelsbrunner
  3. Department of Mathematics, Duke University, Durham, NC 27708, USA
    John Harer

Authors

  1. David Cohen-Steiner
    You can also search for this author inPubMed Google Scholar
  2. Herbert Edelsbrunner
    You can also search for this author inPubMed Google Scholar
  3. John Harer
    You can also search for this author inPubMed Google Scholar

Corresponding authors

Correspondence toDavid Cohen-Steiner, Herbert Edelsbrunner or John Harer.

Rights and permissions

About this article

Cite this article

Cohen-Steiner, D., Edelsbrunner, H. & Harer, J. Stability of Persistence Diagrams.Discrete Comput Geom 37, 103–120 (2007). https://doi.org/10.1007/s00454-006-1276-5

Download citation

Keywords