A Riemannian Approach for Computing Geodesics in Elastic Shape Analysis
Yaqing You, Wen Huang, Kyle A. Gallivan, P.-A. Absil
In the framework of elastic shape analysis, a shape is invariant to scaling, translation, rotation and reparameterization. Since this framework does not yield a closed form of geodesic between two shapes, iterative methods have been proposed. In particular, path straightening methods have been proposed and used for computing a geodesic that is invariant to curve scaling and translation. Path straightening can then be exploited within a coordinate-descent algorithm that computes the best rotation and reparameterization of the end point curves. In this paper, we propose a Riemannian quasi-Newton method to compute a geodesic invariant to scaling, translation, rotation and reparameterization and show that it is more efficient than the coordinate-descent/path-straightening approach.