F. Chazal, D. Cohen-Steiner, L. J. Guibas, F. Mémoli, S. Y. Oudot. Gromov-Hausdorff Stable Signatures for Shapes using Persistence. Computer Graphics Forum (proc. SGP 2009), pages 1393-1403.
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.
, author = "F. Chazal and D. Cohen-Steiner and L. J. Guibas and
F. M'emoli and S. Y. Oudot"
, title = "Gromov-Hausdorff Stable Signatures for Shapes using
, journal = "Computer Graphics Forum (proc. SGP 2009)"
, pages = "1393--1403"
, year = 2009