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Analysis of Planar Shapes Using Geodesic Paths on Shape Spaces
March 2004 (vol. 26 no. 3)
pp. 372-383
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.
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Index Terms:
Shape metrics, geodesic paths, shape statistics, intrinsic mean shapes, shape-based clustering, shape interpolation.
Citation:
Eric Klassen, Anuj Srivastava, Washington Mio, Shantanu H. Joshi, "Analysis of Planar Shapes Using Geodesic Paths on Shape Spaces," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 26, no. 3, pp. 372-383, Mar. 2004, doi:10.1109/TPAMI.2004.1262333
