Computing the geodesic interpolating spline

We examine non-rigid image registration by knotpoint matching. We consider registering two images, each with a set of knotpoints marked, where one of the images is to be registered to the other by a nonlinear warp so that the knotpoints on the template image are exactly aligned with the corresponding knotpoints on the reference image. We explore two approaches for computing the registration by the Geodesic Interpolating Spline. First, we describe a method which exploits the structure of the problem in order to permit efficient optimization and second, we outline an approach using the framework of classical mechanics