Solomon, Justin, Fernando de Goes, Gabriel Peyré, Marco Cuturi, Adrian Butscher, Andy Nguyen, Tao Du, and Leonidas Guibas. "Convolutional Wasserstein Distances: Efficient Optimal Transportation on Geometric Domains." SIGGRAPH 2015, Los Angeles.
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 result-
ing objective contains a geodesic distance-based kernel that can
be approximated with the heat kernel. This approach leads to sim-
ple 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 versa-
tility and efficiency of our method on tasks including reflectance
interpolation, color transfer, and geometry processing.