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Shape analysis of elastic curves in Euclidean spaces

Srivastava, A.; Klassen, E.; Joshi, S.H.; Jermyn, I.H.

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Authors

A. Srivastava

E. Klassen

S.H. Joshi



Abstract

This paper introduces a square-root velocity (SRV) representation for analyzing shapes of curves in euclidean spaces under an elastic metric. In this SRV representation, the elastic metric simplifies to the IL2 metric, the reparameterization group acts by isometries, and the space of unit length curves becomes the unit sphere. The shape space of closed curves is the quotient space of (a submanifold of) the unit sphere, modulo rotation, and reparameterization groups, and we find geodesics in that space using a path straightening approach. These geodesics and geodesic distances provide a framework for optimally matching, deforming, and comparing shapes. These ideas are demonstrated using: 1) shape analysis of cylindrical helices for studying protein structure, 2) shape analysis of facial curves for recognizing faces, 3) a wrapped probability distribution for capturing shapes of planar closed curves, and 4) parallel transport of deformations for predicting shapes from novel poses.

Citation

Srivastava, A., Klassen, E., Joshi, S., & Jermyn, I. (2011). Shape analysis of elastic curves in Euclidean spaces. IEEE Transactions on Pattern Analysis and Machine Intelligence, 33(7), 1415-1428. https://doi.org/10.1109/tpami.2010.184

Journal Article Type Article
Publication Date Jul 1, 2011
Deposit Date Aug 12, 2011
Publicly Available Date Mar 29, 2024
Journal IEEE Transactions on Pattern Analysis and Machine Intelligence
Print ISSN 0162-8828
Publisher Institute of Electrical and Electronics Engineers
Peer Reviewed Peer Reviewed
Volume 33
Issue 7
Pages 1415-1428
DOI https://doi.org/10.1109/tpami.2010.184

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