期刊
SIGGRAPH ASIA'18: SIGGRAPH ASIA 2018 TECHNICAL PAPERS
卷 -, 期 -, 页码 -出版社
ASSOC COMPUTING MACHINERY
DOI: 10.1145/3272127.3275064
关键词
Optimal Transport; Wasserstein Distance; Discrete Differential Geometry
资金
- Army Research Office [W911NF-12-R-0011]
- National Science Foundation [IIS-1838071]
- MIT Research Support Committee
- Amazon Research Award
- MIT-IBM Watson Al Laboratory
- Skoltech-MI Next Generation ProgramT
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.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据