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Gromov-Hausdorff Approximation of Metric Spaces with Linear Structure

Frédéric Chazal 1 Jian Sun 2
1 GEOMETRICA - Geometric computing
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
Abstract : In many real-world applications data come as discrete metric spaces sampled around 1-dimensional filamentary structures that can be seen as 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 synthetic and real data sets.
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Contributor : Frédéric Chazal Connect in order to contact the contributor
Submitted on : Monday, May 6, 2013 - 11:02:36 AM
Last modification on : Tuesday, June 1, 2021 - 2:34:10 PM
Long-term archiving on: : Tuesday, April 4, 2017 - 5:21:31 AM


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  • HAL Id : hal-00820599, version 1
  • ARXIV : 1305.1172



Frédéric Chazal, Jian Sun. Gromov-Hausdorff Approximation of Metric Spaces with Linear Structure. 2013. ⟨hal-00820599⟩



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