Gromov-Hausdorff Stable Signatures for Shapes using Persistence |
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Authors: | Fré dé ric Chazal, David Cohen-Steiner,Leonidas J. Guibas, Facundo Mé moli,Steve Y. Oudot |
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Affiliation: | INRIA Saclay;INRIA Sophia;Stanford University, Dept. Computer Science;Stanford University, Dept. Mathematics |
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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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Keywords: | I.3.5 [Computer Graphics]: Computational Geometry and Object Modelling— |
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