# Gromov‐Hausdorff Stable Signatures for Shapes using Persistence

@article{Chazal2009GromovHausdorffSS, title={Gromov‐Hausdorff Stable Signatures for Shapes using Persistence}, author={Fr{\'e}d{\'e}ric Chazal and David Cohen-Steiner and Leonidas J. Guibas and Facundo M{\'e}moli and Steve Oudot}, journal={Computer Graphics Forum}, year={2009}, volume={28} }

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…

## 231 Citations

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