Gromov-hausdorff stable signatures for shapes using persistence

Frédéric Chazal; David Cohen-SteineR.; Leonidas J. Guibas; Facundo Mémoli; Steve Y. Oudot

doi:10.1111/j.1467-8659.2009.01516.x

Gromov-hausdorff stable signatures for shapes using persistence

Frédéric Chazal
, David Cohen-SteineR.
, Leonidas J. Guibas
, Facundo Mémoli
, Steve Y. Oudot

INRIA
INRIA
Stanford University
Stanford University

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	1393-1403
Number of pages	11
Journal	Computer Graphics Forum
Volume	28
Issue number	5
DOIs	https://doi.org/10.1111/j.1467-8659.2009.01516.x
Publication status	Published - 1 Jan 2009
Externally published	Yes

Keywords

Computational Geometry and Object Modelling
I.3.5 [Computer Graphics]

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10.1111/j.1467-8659.2009.01516.x

Cite this

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AU - Oudot, Steve Y.

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AB - 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.

KW - Computational Geometry and Object Modelling

KW - I.3.5 [Computer Graphics]

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Gromov-hausdorff stable signatures for shapes using persistence

Abstract

Keywords

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