Metric Graph Reconstruction from Noisy Data

Mridul Aanjaneya, Frédéric Chazal, Daniel Chen, Marc Glisse, Leonidas Guibas, Dmitriy Morozov.
IJCGA: International Journal of Computational Geometry and Applications, pages 305-325, 2012.
SoCG'11: Proceedings of the Annual Symposium on Computational Geometry, pages 37-46, 2011.
DOI: 10.1142/S0218195912600072
Many real-world data sets can be viewed of as noisy samples of special types of metric spaces called metric graphs [16]. 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.
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