A Novel Representation for Riemannian Analysis of Elastic Curves in Rn

Abstract

We propose a novel representation of continuous, closed curves in Rⁿ that is quite efficient for analyzing their shapes. We combine the strengths of two important ideas-elastic shape metric and path-straightening methods - in shape analysis and present a fast algorithm for finding geodesies in shape spaces. The elastic metric allows for optimal matching of features while path-straightening provides geodesies between curves. Efficiency results from the fact that the elastic metric becomes the simple L² metric in the proposed representation. We present step-by-step algorithms for computing geodesies in this framework, and demonstrate them with 2-D as well as 3-D examples.