Gromov-Hausdorff stable signatures for shapes using persistence
Date
2009
Authors
Chazal, Frederic
Cohen-Steiner, David
Guibas, Leonidas J.
Memoli, Facundo
Oudot, Steve Y.
Editors
Advisors
Journal Title
Journal ISSN
Volume Title
Type:
Journal article
Citation
Computer Graphics Forum, 2009; 28(5):1393-1403
Statement of Responsibility
Frédéric Chazal, David Cohen-Steiner, Leonidas J. Guibas, Facundon Mémoli and Steve Y. Oudot
Conference Name
Eurographics Symposium on Geometry Processing (2009 : Berlin)
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.
School/Discipline
School of Computer Science
Dissertation Note
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Description
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Rights
© 2009 The Author(s) Journal compilation © 2009 The Eurographics Association and Blackwell Publishing Ltd.