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