Dynamical optimal transport on discrete surfaces

Hugo Lavenant, Sebastian Claici, Edward Chien, Justin Solomon

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

13 Scopus citations

Abstract

We propose a technique for interpolating between probability distributions on discrete surfaces, based on the theory of optimal transport. Unlike previous attempts that use linear programming, our method is based on a dynamical formulation of quadratic optimal transport proposed for flat domains by Benamou and Brenier [2000], adapted to discrete surfaces. Our structure-preserving construction yields a Riemannian metric on the (finite-dimensional) space of probability distributions on a discrete surface, which translates the so-called Otto calculus to discrete language. From a practical perspective, our technique provides a smooth interpolation between distributions on discrete surfaces with less diffusion than state-of-the-art algorithms involving entropic regularization. Beyond interpolation, we show how our discrete notion of optimal transport extends to other tasks, such as distribution-valued Dirichlet problems and time integration of gradient flows.

Original languageEnglish
Title of host publicationSIGGRAPH Asia 2018 Technical Papers, SIGGRAPH Asia 2018
PublisherAssociation for Computing Machinery, Inc
ISBN (Electronic)9781450360081
DOIs
StatePublished - 4 Dec 2018
Externally publishedYes
EventSIGGRAPH Asia 2018 Technical Papers - International Conference on Computer Graphics and Interactive Techniques, SIGGRAPH Asia 2018 - Tokyo, Japan
Duration: 4 Dec 20187 Dec 2018

Publication series

NameSIGGRAPH Asia 2018 Technical Papers, SIGGRAPH Asia 2018

Conference

ConferenceSIGGRAPH Asia 2018 Technical Papers - International Conference on Computer Graphics and Interactive Techniques, SIGGRAPH Asia 2018
Country/TerritoryJapan
CityTokyo
Period4/12/187/12/18

Bibliographical note

Publisher Copyright:
© 2018 Copyright held by the owner/author(s). Publication rights licensed to ACM.

Keywords

  • Discrete Differential Geometry
  • Optimal Transport
  • Wasserstein Distance

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