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In many real-world applications data come as discrete metric spaces sampledaround 1-dimensional filamentary structures that can be seen as metric graphs.In this paper we address the metric reconstruction problem of such filamentarystructures from data sampled around them. We prove that they can beapproximated, with respect to the Gromov-Hausdorff distance by well-chosen Reebgraphs (and some of their variants) and we provide an efficient and easy toimplement algorithm to compute such approximations in almost linear time. Weillustrate the performances of our algorithm on a few synthetic and real datasets.

Gromov-Hausdorff Approximation of Metric Spaces with Linear Structure