Conformal Wasserstein Distance: II. Computational Aspects and Extensions
  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. 
Yaron Lipman, Jesus Puente, Ingrid Daubechies
math.NA