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Analysis of planar shapes using geodesic paths on shape spaces

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4 Author(s)
Klassen, E. ; Dept. of Math., Florida State Univ., Tallahassee, FL, USA ; Srivastava, A. ; Mio, W. ; Joshi, S.H.

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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Pattern Analysis and Machine Intelligence, IEEE Transactions on  (Volume:26 ,  Issue: 3 )