Conformal Wasserstein distance: II. computational aspects and extensions

Abstract

This paper is a companion paper to [Lipman and Daubechies 2011]. We provide numerical procedures and algorithms for computing the alignment of and distance between two disk type surfaces. We provide a convergence analysis of the discrete approximation to the arising mass-transportation problems. We furthermore generalize the framework to support sphere-type surfaces, and prove a result connecting this distance to local geodesic distortion. Lastly, we provide numerical experiments on several surfaces' datasets and compare to state of the art method.