NADER, Georges; GUENNEBAUD, Gael

doi:10.1145/3272127.3275091

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NADER, Georges
Melting the frontiers between Light, Shape and Matter [MANAO]

GUENNEBAUD, Gael
Melting the frontiers between Light, Shape and Matter [MANAO]

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Article de revue

Ce document a été publié dans

ACM Transactions on Graphics. 2018-11, vol. 37, n° 6, p. 13

Association for Computing Machinery

Résumé en anglais

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.< Réduire

Mots clés en anglais

Optimal Transport

Nonlinear solver

Re-meshing

Sampling

URI

https://oskar-bordeaux.fr/handle/20.500.12278/181788

DOI

http://dx.doi.org/10.1145/3272127.3275091

Project ANR

Représentation et manipulation de formes extrement détaillées - ANR-14-CE24-0004

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Importé de hal

Unités de recherche

Laboratoire Photonique, Numérique et Nanosciences (LP2N) - UMR 5298