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Communication Dans Un Congrès Année : 2014

Gromov-Hausdorff Approximation of Filament Structure Using Reeb-type Graph

Frédéric Chazal

Résumé

In many real-world applications data appear to be sampled around 1-dimensional filamentary structures that can be seen as topological metric graphs. In this paper we address the metric reconstruction problem of such filamentary structures from data sampled around them. We prove that they can be approximated, with respect to the Gromov-Hausdorff distance by well-chosen Reeb graphs (and some of their variants) and we provide an efficient and easy to implement algorithm to compute such approximations in almost linear time. We illustrate the performances of our algorithm on a few data sets.
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Dates et versions

hal-01073070 , version 1 (08-10-2014)

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Frédéric Chazal, Jian Sun. Gromov-Hausdorff Approximation of Filament Structure Using Reeb-type Graph. SOCG 2014 - 30th ACM Annual Symposium on Computational Geometry, Jun 2014, Kyoto, Japan. pp.491-500, ⟨10.1145/2582112.2582129⟩. ⟨hal-01073070⟩
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