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 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 data sets. Experiments show significant advantages in computational time and reliability in performance compared to the current state-of-the-art method