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Analysis of planar shapes using geodesic paths on shape spaces.

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1
Department of Mathematics, Florida State University, Tallahassee, FL 32306, USA. klassen@math.fsu.edu

Abstract

For analyzing shapes of planar, closed curves, we propose differential geometric representations of curves using their direction functions and curvature functions. Shapes are represented as elements of infinite-dimensional spaces and their pairwise differences are quantified using the lengths of geodesics connecting them on these spaces. We use a Fourier basis to represent tangents to the shape spaces and then use a gradient-based shooting method to solve for the tangent that connects any two shapes via a geodesic. Using the Surrey fish database, we demonstrate some applications of this approach: 1) interpolation and extrapolations of shape changes, 2) clustering of objects according to their shapes, 3) statistics on shape spaces, and 4) Bayesian extraction of shapes in low-quality images.

PMID:
15376883
DOI:
10.1109/TPAMI.2004.1262333
[Indexed for MEDLINE]
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