Conformal Wasserstein distance: II. Computational aspects and extensions

Yaron Lipman, J. Puente, I. Daubechies

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)331-381
Number of pages51
JournalMathematics of Computation
Volume82
Issue number281
DOIs
StatePublished - 2013

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics
  • Algebra and Number Theory

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