Reeb graphs of surfaces are stable under function perturbations

Di Fabio, Barbara ; Landi, Claudia (2014) Reeb graphs of surfaces are stable under function perturbations. [Preprint]
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Abstract

Reeb graphs are combinatorial signatures that capture shape properties from the perspective of a chosen function. One of the most important questions is whether Reeb graphs are robust against function perturbations that may occur because of noise and approximation errors in the data acquisition process. In this work we tackle the problem of stability providing an editing distance between Reeb graphs of orientable surfaces in terms of the cost necessary to transform one graph into another by edit operations. Our main result is that changes in the functions, measured by the maximum norm, imply not greater changes in this distance, yielding the stability property under function perturbations.

Abstract
Document type
Preprint
Creators
CreatorsAffiliationORCID
Di Fabio, Barbara
Landi, Claudia
Keywords
shape similarity, editing distance, Morse function, natural stratification
Subjects
DOI
Deposit date
21 Feb 2014 09:13
Last modified
10 Nov 2014 08:27
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