Riemannian Optimization for Registration of Curves in Elastic Shape Analysis

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 rot...

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Bibliographic Details
Published in:Journal of mathematical imaging and vision 2016-03, Vol.54 (3), p.320-343
Main Authors: Huang, Wen, Gallivan, Kyle A., Srivastava, Anuj, Absil, Pierre-Antoine
Format: Article
Language:English
Subjects:
Applications of Mathematics
Computer Science
Image Processing and Computer Vision
Mathematical Methods in Physics
Signal,Image and Speech Processing
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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 Huang et al. (Proceedings of the 21st International Symposium on Mathematical Theory of Networks and Systems 2014 ).
ISSN:0924-9907
1573-7683
DOI:10.1007/s10851-015-0606-8