Geometric Analysis of Constrained Curves

Part of Advances in Neural Information Processing Systems 16 (NIPS 2003)

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Anuj Srivastava, Washington Mio, Xiuwen Liu, Eric Klassen


We present a geometric approach to statistical shape analysis of closed curves in images. The basic idea is to specify a space of closed curves satisfying given constraints, and exploit the differential geometry of this space to solve optimization and inference problems. We demonstrate this approach by: (i) defining and computing statistics of observed shapes, (ii) defining and learning a parametric probability model on shape space, and (iii) designing a binary hypothesis test on this space.