Gromov-Hausdorff Stable Signatures for Shapes using Persistence

Frédéric Chazal 1, * David Cohen-Steiner 1 Leonidas J. Guibas 2 Facundo Mémoli 3 Steve Oudot 1
* Corresponding author
1 GEOMETRICA - Geometric computing
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
Abstract : We introduce a family of signatures for finite metric spaces, possibly endowed with real valued functions, based on the persistence diagrams of suitable filtrations built on top of these spaces. We prove the stability of our signatures under Gromov-Hausdorff perturbations of the spaces. We also extend these results to metric spaces equipped with measures. Our signatures are well-suited for the study of unstructured point cloud data, which we illustrate through an application in shape classification.
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Frédéric Chazal, David Cohen-Steiner, Leonidas J. Guibas, Facundo Mémoli, Steve Oudot. Gromov-Hausdorff Stable Signatures for Shapes using Persistence. Computer Graphics Forum, Wiley, 2009, 28 (5), pp.1393-1403. ⟨10.1111/j.1467-8659.2009.01516.x⟩. ⟨hal-00772413⟩



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