Persistence Barcodes for Shapes

Carlssony, Gunnar; Zomorodian, Afra; Collins, Anne; Guibas, Leonidas

Persistence Barcodes for Shapes

Files

127-138.pdf (476.39 KB)

Date

2004

Authors

Carlssony, Gunnar
Zomorodian, Afra
Collins, Anne
Guibas, Leonidas

Publisher

The Eurographics Association

Abstract

In this paper, we initiate a study of shape description and classification via the application of persistent homology to two tangential constructions on geometric objects. Our techniques combine the differentiating power of geometry with the classifying power of topology. The homology of our first construction, the tangent complex, can distinguish between topologically identical shapes with different "sharp" features, such as corners. To capture "soft" curvature-dependent features, we define a second complex, the filtered tangent complex, obtained by parametrizing a family of increasing subcomplexes of the tangent complex. Applying persistent homology, we obtain a shape descriptor, called a barcode, that is a finite union of intervals. We define a metric over the space of such intervals, arriving at a continuous invariant that reflects the geometric properties of shapes. We illustrate the power of our methods through a number of detailed studies of parametrized families of mathematical shapes.

        @inproceedings{:10.2312/SGP/SGP04/127-138
,
booktitle = {Symposium on Geometry Processing
},
editor = {Roberto Scopigno and Denis Zorin
},
title = {{Persistence Barcodes for Shapes
}},
author = {Carlssony, Gunnar and 
Zomorodian, Afra and 
Collins, Anne and 
Guibas, Leonidas
},
year = {2004
},
publisher = {The Eurographics Association
},
ISSN = {1727-8384
},
ISBN = {3-905673-13-4
},
DOI = {/10.2312/SGP/SGP04/127-138
}
}