Discrete & Computational Geometry

, Volume 37, Issue 1, pp 103–120

Stability of Persistence Diagrams


    • INRIA, 2004 Route des Lucioles, BP 93, 06904
    • Department of Computer Science, Duke University, Durham, NC 27708 and Geomagic
    • Department of Mathematics, Duke University

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.

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© Springer 2006