NDLI: Convolutional wasserstein distances: efficient optimal transportation on geometric domains

Content Provider	ACM Digital Library
Author	Solomon, Justin Cuturi, Marco Nguyen, Andy Butscher, Adrian Du, Tao Peyré, Gabriel De goes, Fernando Guibas, Leonidas
Copyright Year	2015
Description	Author Affiliation: Kyoto University(Autodesk, Inc. (Butscher, Adrian; Pixar animation studios (de goes, Fernando); Cnrs & univ. paris-dauphine (peyr, Gabriel); Guibas, Leonidas); Du, Tao; Nguyen, Andy; Stanford university (solomon, Justin; Cuturi, Marco))
Abstract	This paper introduces a new class of algorithms for optimization problems involving optimal transportation over geometric domains. Our main contribution is to show that optimal transportation can be made tractable over large domains used in graphics, such as images and triangle meshes, improving performance by orders of magnitude compared to previous work. To this end, we approximate optimal transportation distances using entropic regularization. The resulting objective contains a geodesic distance-based kernel that can be approximated with the heat kernel. This approach leads to simple iterative numerical schemes with linear convergence, in which each iteration only requires Gaussian convolution or the solution of a sparse, pre-factored linear system. We demonstrate the versatility and efficiency of our method on tasks including reflectance interpolation, color transfer, and geometry processing.
Starting Page	1
Ending Page	11
Page Count	11
File Format	PDF
ISSN	07300301
e-ISSN	15577368
DOI	10.1145/2766963
Volume Number	34
Issue Number	4
Journal	ACM Transactions on Graphics (TOG)
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2015-07-27
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Displacement interpolation Entropy Optimal transportation Wasserstein distances
Content Type	Text
Resource Type	Article
Subject	Computer Graphics and Computer-Aided Design

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