Removing shape-preserving transformations in square-root elastic (SRE) framework for shape analysis of curves

Authors:
Shantanu H. Joshi;Eric Klassen;Anuj Srivastava;Ian Jermyn
Affiliations:
Dept. of Electrical Engineering, Florida State University, Tallahassee, FL;Dept. of Mathematics, Florida State University, Tallahassee, FL;Dept. of Statistics, Florida State University, Tallahassee, FL;INRIA Sophia Antipolis, Cedex, France
Venue:
EMMCVPR'07 Proceedings of the 6th international conference on Energy minimization methods in computer vision and pattern recognition
Year:
2007

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Abstract

This paper illustrates and extends an efficient framework, called the square-root-elastic (SRE) framework, for studying shapes of closed curves, that was first introduced in [2]. This framework combines the strengths of two important ideas - elastic shape metric and path-straightening methods - for finding geodesics in shape spaces of curves. The elastic metric allows for optimal matching of features between curves while path-straightening ensures that the algorithm results in geodesic paths. This paper extends this framework by removing two important shape preserving transformations: rotations and re-parameterizations, by forming quotient spaces and constructing geodesics on these quotient spaces. These ideas are demonstrated using experiments involving 2D and 3D curves.