Shape analysis of elastic curves in Euclidean spaces

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

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: Aug 26, 2015
• Journal: IEEE Transactions on Pattern Analysis and Machine Intelligence
• Print ISSN: 0162-8828
• Electronic ISSN: 1939-3539
• 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
• Public URL: https://durham-repository.worktribe.com/output/1537659