Bauer, Ulrich ; Di Fabio, Barbara ; Landi, Claudia
(2016)
An edit distance for Reeb graphs.
[Preprint]
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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.
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.
Document type
Preprint
Creators
Subjects
DOI
Deposit date
29 Feb 2016 09:48
Last modified
29 Feb 2016 09:48
URI
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Document type
Preprint
Creators
Subjects
DOI
Deposit date
29 Feb 2016 09:48
Last modified
29 Feb 2016 09:48
URI
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