Document Zbl 1338.49088

Huang, Wen; Gallivan, Kyle A.; Srivastava, Anuj; Absil, Pierre-Antoine

Riemannian optimization for registration of curves in elastic shape analysis. (English) Zbl 1338.49088

J. Math. Imaging Vis. 54, No. 3, 320-343 (2016).

Summary: In elastic shape analysis, a representation of a shape is invariant to translation, scaling, rotation, and reparameterization, and important problems such as computing the distance and geodesic between two curves, the mean of a set of curves, and other statistical analyses require finding a best rotation and reparameterization between two curves. In this paper, we focus on this key subproblem and study different tools for optimizations on the joint group of rotations and reparameterizations. We develop and analyze a novel Riemannian optimization approach and evaluate its use in shape distance computation and classification using two public datasets. Experiments show significant advantages in computational time and reliability in performance compared to the current state-of-the-art method. A brief version of this paper can be found in [W. Huang et al., “Riemannian optimization for elastic shape analysis”, in: Proceedings of the 21st International Symposium on Mathematical Theory of Networks and Systems (2014)].

Cited in 14 Documents

MSC:

49Q10	Optimization of shapes other than minimal surfaces
49L20	Dynamic programming in optimal control and differential games
49M15	Newton-type methods
90C39	Dynamic programming
90C53	Methods of quasi-Newton type

Keywords:

elastic shape analysis; Riemannian optimization; square-root velocity function; elastic closed curves; dynamic programming; Riemannian quasi-Newton method

Software:

Flavia

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Full Text: DOI

References:

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