title: A Novel Representation for Riemannian Analysis of Elastic Curves in ℝ
abstract: We propose a novel representation of continuous, closed curves in ℝ(n) 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 geodesics in shape spaces. The elastic metric allows for optimal matching of features while path-straightening provides geodesics between curves. Efficiency results from the fact that the elastic metric becomes the simple (2) metric in the proposed representation. We present step-by-step algorithms for computing geodesics in this framework, and demonstrate them with 2-D as well as 3-D examples.
authors.affiliation: Department of Electrical Engineering, Florida State University, Tallahassee, FL.
authors.forename: Shantanu H
authors.initials: SH
authors.lastname: Joshi
authors.forename: Eric
authors.initials: E
authors.lastname: Klassen
authors.forename: Anuj
authors.initials: A
authors.lastname: Srivastava
authors.forename: Ian
authors.initials: I
authors.lastname: Jermyn