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Conformal Wasserstein distance: II. Computational aspects and extensions

Publication ,  Journal Article
Lipman, Y; Puente, J; Daubechies, I
Published in: Mathematics of Computation
January 17, 2013

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.

Duke Scholars

Published In

Mathematics of Computation

DOI

ISSN

0025-5718

Publication Date

January 17, 2013

Volume

82

Issue

281

Start / End Page

331 / 381

Related Subject Headings

  • Numerical & Computational Mathematics
  • 4903 Numerical and computational mathematics
  • 4901 Applied mathematics
  • 0802 Computation Theory and Mathematics
  • 0103 Numerical and Computational Mathematics
  • 0102 Applied Mathematics
 

Citation

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Lipman, Y., Puente, J., & Daubechies, I. (2013). Conformal Wasserstein distance: II. Computational aspects and extensions. Mathematics of Computation, 82(281), 331–381. https://doi.org/10.1090/S0025-5718-2012-02569-5
Lipman, Y., J. Puente, and I. Daubechies. “Conformal Wasserstein distance: II. Computational aspects and extensions.” Mathematics of Computation 82, no. 281 (January 17, 2013): 331–81. https://doi.org/10.1090/S0025-5718-2012-02569-5.
Lipman Y, Puente J, Daubechies I. Conformal Wasserstein distance: II. Computational aspects and extensions. Mathematics of Computation. 2013 Jan 17;82(281):331–81.
Lipman, Y., et al. “Conformal Wasserstein distance: II. Computational aspects and extensions.” Mathematics of Computation, vol. 82, no. 281, Jan. 2013, pp. 331–81. Scopus, doi:10.1090/S0025-5718-2012-02569-5.
Lipman Y, Puente J, Daubechies I. Conformal Wasserstein distance: II. Computational aspects and extensions. Mathematics of Computation. 2013 Jan 17;82(281):331–381.
Journal cover image

Published In

Mathematics of Computation

DOI

ISSN

0025-5718

Publication Date

January 17, 2013

Volume

82

Issue

281

Start / End Page

331 / 381

Related Subject Headings

  • Numerical & Computational Mathematics
  • 4903 Numerical and computational mathematics
  • 4901 Applied mathematics
  • 0802 Computation Theory and Mathematics
  • 0103 Numerical and Computational Mathematics
  • 0102 Applied Mathematics