Metric graph reconstruction from noisy data

Mridul Aanjaneya (1) , Frédéric Chazal (2) , Daniel Chen (1) , Marc Glisse (2) , Leonidas J. Guibas (1) , Dmitriy Morozov (3)

1 Computer Science Department [Stanford]
2 GEOMETRICA - Geometric computing
3 LBNL - Lawrence Berkeley National Laboratory [Berkeley]

Many real-world data sets can be viewed of as noisy samples of special types of metric spaces called metric graphs. Building on the notions of correspondence and Gromov-Hausdorff distance in metric geometry, we describe a model for such data sets as an approximation of an underlying metric graph. We present a novel algorithm that takes as an input such a data set, and outputs the underlying metric graph with guarantees. We also implement the algorithm, and evaluate its performance on a variety of real world data sets.

Domaines: Géométrie algorithmique [cs.CG]

Mridul Aanjaneya, Frédéric Chazal, Daniel Chen, Marc Glisse, Leonidas J. Guibas, et al.. Metric graph reconstruction from noisy data. 27th Annual Symposium on Computational Geometry, 2011, Paris, France. pp.37-46, ⟨10.1145/1998196.1998203⟩. ⟨inria-00630774⟩