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Shape analysis of elastic curves in Euclidean spaces.

Srivastava, A. and Klassen, E. and Joshi, S.H. and Jermyn, I.H. (2011) 'Shape analysis of elastic curves in Euclidean spaces.', IEEE transactions on pattern analysis and machine intelligence., 33 (7). pp. 1415-1428.


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.

Item Type:Article
Full text:(AM) Accepted Manuscript
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Publisher statement:© 2011 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Date accepted:No date available
Date deposited:26 August 2015
Date of first online publication:July 2011
Date first made open access:No date available

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