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Conformal Wasserstein distance: II. computational aspects and extensions

Authors: Y. Lipman, J. Puente and I. Daubechies
Journal: Math. Comp. 82 (2013), 331-381
MSC (2010): Primary 65D18
Published electronically: July 16, 2012
MathSciNet review: 2983027
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Abstract | References | Similar Articles | Additional Information

Abstract: 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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Additional Information

Y. Lipman
Affiliation: Department of Mathematics and Computer Science, Weizmann Institute of Science, Rehovot, 76100 Israel

J. Puente
Affiliation: Department of Mathematics, Princeton University, Princeton, New Jersey

I. Daubechies
Affiliation: Department of Mathematics, Duke University, Durham, North Carolina

Received by editor(s): May 4, 2010
Received by editor(s) in revised form: October 10, 2010
Published electronically: July 16, 2012
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.