Dynamical optimal transport on discrete surfaces
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.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Dec 04, 2018
- Source ID
- 10.1145/3272127.3275064
Entities
People
- Edward Chien
- Hugo Lavenant
- Justin Solomon
- Sebastian Claici
Organizations
- Army Research Office
- Massachusetts Institute of Technology
- University of Paris-Sud