Computational study demonstrates efficient alignment algorithms for disk- and sphere-type surfaces, suggesting improved accuracy over state-of-the-art geometric methods.
This paper is a companion paper to [Yaron Lipman and Ingrid Daubechies, Conformal Wasserstein distances: Comparing surfaces in polynomial time , Adv. in Math. (ELS), 227 (2011), no. 3, 1047–1077, (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. Finally, we perform numerical experiments on several surface datasets and compare them to state-of-the-art methods.
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Lipman et al. (2012) studied this question.
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