Elastic-string models for representation and analysis of planar shapes

Authors:
Washington Mio;Anuj Srivastava
Affiliations:
Department of Mathematics, Florida State University, Tallahassee, FL;Department of Statistics, Florida State University, Tallahassee, FL
Venue:
CVPR'04 Proceedings of the 2004 IEEE computer society conference on Computer vision and pattern recognition
Year:
2004

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Abstract

We develop a new framework for the quantitative analysis of shapes of planar curves. Shapes are modeled on elastic strings that can be bent, stretched or compressed at different rates along the curve. Shapes are treated as elements of a space obtained as the quotient of an infinite-dimensional Riemannian manifold of elastic curves by the action of a reparameterization group. The Riemannian metric encodes the elastic properties of the string and has the property that reparameterizations act by isometries. Geodesics in shape space are used to quantify shape dissimilarities, interpolate and extrapolate shapes, and align shapes according to their elastic properties. The shape spaces and metrics constructed offer a novel environment for the study of shape statistics and for the investigation and simulation of shape dynamics.