A geometric view of optimal transportation and generative model

DOI10.1016/j.cagd.2018.10.005zbMath1430.49050arXiv1710.05488OpenAlexW2963875852MaRDI QIDQ669014

Li Cui, Xianfeng David Gu, Kehua Su, Na Lei, Shing Tung Yau

Publication date: 20 March 2019

Published in: Computer Aided Geometric Design (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1710.05488

zbMATH Keywords

Wasserstein distanceoptimal mass transportationMonge-AmpereGAN

Mathematics Subject Classification ID

Optimal transportation (49Q22)

Related Items (8)

The singularity set of optimal transportation maps ⋮ Convergence Analysis of Volumetric Stretch Energy Minimization and Its Associated Optimal Mass Transport ⋮ Ellipsoidal conformal and area-/volume-preserving parameterizations and associated optimal mass transportations ⋮ A Scalable Deep Learning Approach for Solving High-Dimensional Dynamic Optimal Transport ⋮ Multi-projection of unequal dimension optimal transport theory for generative adversary networks ⋮ Discrete Lie flow: a measure controllable parameterization method ⋮ Projected gradient method combined with homotopy techniques for volume-measure-preserving optimal mass transportation problems ⋮ The Singularity Set of Optimal Transportation Maps

Uses Software

• CycleGAN
• pix2pix
• Wasserstein GAN
• DeLiGAN
• AdaGAN

Cites Work

• Variational principles for Minkowski type problems, discrete optimal transport, and discrete Monge-Ampère equations
• A discrete uniformization theorem for polyhedral surfaces
• Polar factorization and monotone rearrangement of vector‐valued functions
• Semidual Regularized Optimal Transport
• Convex Polyhedra
• From Knothe's Rearrangement to Brenier's Optimal Transport Map
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