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Journal Articles Computer Graphics Forum Year : 2009

Gromov-Hausdorff Stable Signatures for Shapes using Persistence

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Frédéric Chazal
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David Cohen-Steiner
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Leonidas J. Guibas
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Facundo Mémoli
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Steve Oudot
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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.

Dates and versions

hal-00772413 , version 1 (10-01-2013)

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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, 2009, 28 (5), pp.1393-1403. ⟨10.1111/j.1467-8659.2009.01516.x⟩. ⟨hal-00772413⟩

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