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