Discrete & Computational Geometry

, Volume 37, Issue 1, pp 103–120

Stability of Persistence Diagrams


DOI: 10.1007/s00454-006-1276-5

Cite this article as:
Cohen-Steiner, D., Edelsbrunner, H. & Harer, J. Discrete Comput Geom (2007) 37: 103. doi:10.1007/s00454-006-1276-5


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.

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