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<p><b>Abstract</b>—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.</p>
Shape metrics, geodesic paths, shape statistics, intrinsic mean shapes, shape-based clustering, shape interpolation.
Washington Mio, Eric Klassen, Shantanu H. Joshi, Anuj Srivastava, "Analysis of Planar Shapes Using Geodesic Paths on Shape Spaces", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 26, no. , pp. 372-383, March 2004, doi:10.1109/TPAMI.2004.1262333
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