Conformal Wasserstein distance: II. Computational aspects and extensions

Journal Article (Journal Article)

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. © 2012 American Mathematical Society.

Full Text

Duke Authors

Cited Authors

  • Lipman, Y; Puente, J; Daubechies, I

Published Date

  • January 17, 2013

Published In

Volume / Issue

  • 82 / 281

Start / End Page

  • 331 - 381

International Standard Serial Number (ISSN)

  • 0025-5718

Digital Object Identifier (DOI)

  • 10.1090/S0025-5718-2012-02569-5

Citation Source

  • Scopus