European Congress of Mathematics
Kraków, 2 – 7 July, 2012

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pp: 31–50

DOI: 10.4171/120-1/3

Persistent Homology: Theory and Practice

Herbert Edelsbrunner[1] and Dmitriy Morozov[2]

(1) Institute of Science and Technology Austria, Klosterneuburg, Austria
(2) Lawrence National Laboratory, Berkeley, USA

Persistent homology is a recent grandchild of homology that has found use in science and engineering as well as in mathematics. This paper surveys the method as well as the applications, neglecting completeness in favor of highlighting ideas and directions.

Keywords: Algebraic topology, homology groups, distance, stability, algorithms, scale, shape analysis, topology repair, high-dimensional data