We consider the problem of assessing the similarity of 3D shapes using Reeb graphs from the standpoint of robustness under perturbations. For this purpose, 3D objects are viewed as spaces endowed with real-valued functions, while the similarity between the resulting Reeb graphs is addressed through a graph edit distance. The cases of smooth functions on manifolds and piecewise linear functions on polyhedra stand out as the most interesting ones. The main contribution of this paper is the introduction of a general edit distance suitable for comparing Reeb graphs in these settings. This edit distance promises to be useful for applications in 3D object retrieval because of its stability properties in the presence of noise.

An Edit Distance for Reeb Graphs / Bauer, Ulrich; Di Fabio, Barbara; Landi, Claudia. - ELETTRONICO. - (2016), pp. 27-34. ((Intervento presentato al convegno 9th Eurographics Workshop on 3D Object Retrieval, 3DOR 2016 tenutosi a Lisbona, Portogallo nel 7-8 Maggio 2016 [10.2312/3dor.20161084].

An Edit Distance for Reeb Graphs

DI FABIO, Barbara;LANDI, Claudia
2016

Abstract

We consider the problem of assessing the similarity of 3D shapes using Reeb graphs from the standpoint of robustness under perturbations. For this purpose, 3D objects are viewed as spaces endowed with real-valued functions, while the similarity between the resulting Reeb graphs is addressed through a graph edit distance. The cases of smooth functions on manifolds and piecewise linear functions on polyhedra stand out as the most interesting ones. The main contribution of this paper is the introduction of a general edit distance suitable for comparing Reeb graphs in these settings. This edit distance promises to be useful for applications in 3D object retrieval because of its stability properties in the presence of noise.
9th Eurographics Workshop on 3D Object Retrieval, 3DOR 2016
Lisbona, Portogallo
7-8 Maggio 2016
27
34
Bauer, Ulrich; Di Fabio, Barbara; Landi, Claudia
An Edit Distance for Reeb Graphs / Bauer, Ulrich; Di Fabio, Barbara; Landi, Claudia. - ELETTRONICO. - (2016), pp. 27-34. ((Intervento presentato al convegno 9th Eurographics Workshop on 3D Object Retrieval, 3DOR 2016 tenutosi a Lisbona, Portogallo nel 7-8 Maggio 2016 [10.2312/3dor.20161084].
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11380/1101194
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