Instant Transport Maps on 2D Grids
Language
en
Article de revue
This item was published in
ACM Transactions on Graphics. 2018-11, vol. 37, n° 6, p. 13
Association for Computing Machinery
English Abstract
In this paper, we introduce a novel and extremely fast algorithm to compute continuous transport maps between 2D probability densities discretized on uniform grids. The core of our method is a novel iterative solver computing ...Read more >
In this paper, we introduce a novel and extremely fast algorithm to compute continuous transport maps between 2D probability densities discretized on uniform grids. The core of our method is a novel iterative solver computing the L 2 optimal transport map from a grid to the uniform density in the 2D Euclidean plane. A transport map between arbitrary densities is then recovered through numerical inversion and composition. In this case, the resulting map is only approximately optimal, but it is continuous and density preserving. Our solver is derivative-free, and it converges in a few cheap iterations. We demonstrate interactive performance in various applications such as adaptive sampling, feature sensitive remeshing, and caustic design.Read less <
English Keywords
Optimal Transport
Nonlinear solver
Re-meshing
Sampling
ANR Project
Représentation et manipulation de formes extrement détaillées - ANR-14-CE24-0004
Origin
Hal imported