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We consider the setting of Reeb graphs of piecewise linear functions and study distances between them that are stable, meaning that functions which are similar in the supremum norm ought to have similar Reeb graphs.
Sur les points singuliers d’une forme de Pfaff complétement intégrable ou d’une fonction numérique
Georges Reeb · 1946
Earlier work this paper cites.
Constructing a Reeb graph automatically from cross sections
Yoshihisa Shinagawa and Tosiyasu L. Kunii · 1991
Earlier work this paper cites.
Brick’s Quasi Simple Filtrations and 3-Manifolds
John R. Stallings · 1993
Earlier work this paper cites.
Topology matching for fully automatic similarity estimation of 3D shapes
Masaki Hilaga, Yoshihisa Shinagawa, Taku Kohmura, and Tosiyasu L. Kunii · 2001
Earlier work this paper cites.
Topological Methods for the Analysis of High Dimensional Data Sets and 3D Object Recognition
Gurjeet Singh, Facundo Memoli, and Gunnar Carlsson · 2007
Earlier work this paper cites.
Category Theory
Steve Awodey · 2010
Cited alongside, same era.
Natural Pseudo-Distance and optimal matching between reduced size functions
Michele d’Amico, Patrizio Frosini, and Claudia Landi · 2010
Cited alongside, same era.
Reeb graphs of curves are stable under function perturbations
Barbara Di Fabio and Claudia Landi · 2012
Cited alongside, same era.
Measuring distance between Reeb graphs
Ulrich Bauer, Xiaoyin Ge, and Yusu Wang · 2014
Cited alongside, same era.
Strong equivalence of the interleaving and functional distortion metrics for Reeb graphs
Ulrich Bauer, Elizabeth Munch, and Yusu Wang · 2015
Cited alongside, same era.
The theory of the interleaving distance on multidimensional persistence modules
Michael Lesnick · 2015
Later among the works it cites.
An Edit Distance for Reeb Graphs
Ulrich Bauer, Barbara Di Fabio, and Claudia Landi · 2016
Later among the works it cites.
Categorified Reeb graphs
Vin de Silva, Elizabeth Munch, and Amit Patel · 2016
Later among the works it cites.
The edit distance for Reeb graphs of surfaces
Barbara Di Fabio and Claudia Landi · 2016
Later among the works it cites.
A distance between filtered spaces via tripods
Facundo Memoli · 2017
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