Gromov-Hausdorff Stable Signatures for Shapes using Persistence
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Date
2009
Journal Title
Journal ISSN
Volume Title
Publisher
The Eurographics Association and Blackwell Publishing Ltd
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.
Description
@article{10.1111:j.1467-8659.2009.01516.x,
journal = {Computer Graphics Forum},
title = {{Gromov-Hausdorff Stable Signatures for Shapes using Persistence}},
author = {Chazal, Frederic and Cohen-Steiner, David and Guibas, Leonidas J. and Memoli, Facundo and Oudot, Steve Y.},
year = {2009},
publisher = {The Eurographics Association and Blackwell Publishing Ltd},
ISSN = {1467-8659},
DOI = {10.1111/j.1467-8659.2009.01516.x}
}