PERSISTENCE BARCODES FOR SHAPES.

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Bibliographic Details
Title:	PERSISTENCE BARCODES FOR SHAPES.
Authors:	CARLSSON, GUNNAR¹ gunnar@math.stanford.edu, ZOMORODIAN, AFRA² afra@cs.stanford.edu, COLLINS, ANNE³ collins@centre.edu, GUIBAS, LEONIDAS J.² guibas@cs.stanford.edu
Source:	International Journal of Shape Modeling. Dec2005, Vol. 11 Issue 2, p149-187. 39p. 20 Diagrams, 2 Charts.
Subjects:	Geometric shapes, Tangential coordinates, Homology theory, Topology, Geometry, Interval analysis
Abstract:	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" curvature-dependent 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 parameterized families of mathematical shapes. [ABSTRACT FROM AUTHOR]
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Database:	Engineering Source

Description
Abstract:	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" curvature-dependent 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 parameterized families of mathematical shapes. [ABSTRACT FROM AUTHOR]
ISSN:	02186543
DOI:	10.1142/S0218654305000761