UCLA Brain Mapping Center

Publications

Shape Analysis of Elastic Curves in Euclidean Spaces.

Srivastava A; Klassen E; Joshi SH; Jermyn IH;
IEEE transactions on pattern analysis and machine intelligence. 2010-Sep-30;
 
This paper introduces a square-root velocity (SRV) representation for analyzing shapes of curves in Euclidean spaces using an elastic metric. Under this SRV representation the elastic metric simplifies to the L2 metric, the re-parameterization group acts by isometries, and the space of unit length curves becomes the unit sphere. The shape space of closed curves is quotient space of (a submanifold of) the unit sphere, modulo rotation and re-parameterization groups, and one finds 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: (i) Shape analysis of cylindrical helices for studying protein structures, (ii) Shape analysis of facial curves for face recognition, (iii) A wrapped probability distribution to capture shapes of planar closed curves, and (iv) Parallel transport of deformations for predicting shapes from novel poses.
 
PMID: 20921581    doi: 10.1109/TPAMI.2010.184
 

BMAP Author