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2004

Persistence Barcodes for Shapes

10 years 6 months ago
Persistence Barcodes for Shapes
In this paper, we initiate a study of shape description and classification via the application of persistent homology to 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" curvaturedependent features, we define a second complex, the filtered tangent complex, obtained by parameterizing 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 familie...
Gunnar Carlsson, Afra Zomorodian, Anne D. Collins,
Added 30 Sep 2010
Updated 30 Sep 2010
Type Conference
Year 2004
Where SGP
Authors Gunnar Carlsson, Afra Zomorodian, Anne D. Collins, Leonidas J. Guibas
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