On Shape of Plane Elastic Curves

Authors:
Washington Mio;Anuj Srivastava;Shantanu Joshi
Affiliations:
Department of Mathematics, Florida State University, Tallahassee 32306-4510;Department of Statistics, Florida State University, Tallahassee 32306-4330;Department of Electrical and Computer Engineering, Florida State University, Tallahassee 32310-6046
Venue:
International Journal of Computer Vision
Year:
2007

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Abstract

We study shapes of planar arcs and closed contours modeled on elastic curves obtained by bending, stretching or compressing line segments non-uniformly along their extensions. Shapes are represented as elements of a quotient space of curves obtained by identifying those that differ by shape-preserving transformations. The elastic properties of the curves are encoded in Riemannian metrics on these spaces. Geodesics in shape spaces are used to quantify shape divergence and to develop morphing techniques. The shape spaces and metrics constructed are novel and offer an environment for the study of shape statistics. Elasticity leads to shape correspondences and deformations that are more natural and intuitive than those obtained in several existing models. Applications of shape geodesics to the definition and calculation of mean shapes and to the development of shape clustering techniques are also investigated.