Abstract—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 geodesic between two shapes, iterative methods are used. 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.