Conformal Wasserstein distances: Comparing surfaces in polynomial time

Published

Journal Article

We present a constructive approach to surface comparison realizable by a polynomial-time algorithm. We determine the "similarity" of two given surfaces by solving a mass-transportation problem between their conformal densities. This mass transportation problem differs from the standard case in that we require the solution to be invariant under global Möbius transformations. We present in detail the case where the surfaces to compare are disk-like; we also sketch how the approach can be generalized to other types of surfaces. © 2011 Elsevier Inc.

Full Text

Duke Authors

Cited Authors

  • Lipman, Y; Daubechies, I

Published Date

  • June 20, 2011

Published In

Volume / Issue

  • 227 / 3

Start / End Page

  • 1047 - 1077

Electronic International Standard Serial Number (EISSN)

  • 1090-2082

International Standard Serial Number (ISSN)

  • 0001-8708

Digital Object Identifier (DOI)

  • 10.1016/j.aim.2011.01.020

Citation Source

  • Scopus