Paper ID sheet UCL-INMA-2014.07


Riemannian optimization for elastic shape analysis

Wen Huang, K. A. Gallivan, Anuj Srivastava, P.-A. Absil
In elastic shape analysis, a representation of a shape is invariant to translation, scaling, rotation and re-parameterization 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 re-parameterization 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 re-parameterizations. In this conference paper, we give a first account of a novel Riemannian optimization approach and evaluate its use in computing the distance between two curves and classification using two public data sets. Experiments show significant advantages in computational time and reliability in performance compared to the current state-of-the-art method. Further information will become available in a forthcoming full version of this conference paper.
Key words
Elastic shape; Square root velocity function; Elastic closed curves; Dynamic programming; Riemannian optimization; Riemannian quasi-Newton
accepted for publication in the proceedings of MTNS 2014