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• W4387355890 abstract "We propose a volumetric formulation for computing the Optimal Transport problem defined on surfaces in $mathbb{R}^3$, found in disciplines like optics, computer graphics, and computational methodologies. Instead of directly tackling the original problem on the surface, we define a new Optimal Transport problem on a thin tubular region, $T_{epsilon}$, adjacent to the surface. This extension offers enhanced flexibility and simplicity for numerical discretization on Cartesian grids. The Optimal Transport mapping and potential function computed on $T_{epsilon}$ are consistent with the original problem on surfaces. We demonstrate that, with the proposed volumetric approach, it is possible to use simple and straightforward numerical methods to solve Optimal Transport for $Gamma = mathbb{S}^2$." @default.
• W4387355890 created "2023-10-05" @default.
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• W4387355890 date "2023-10-02" @default.
• W4387355890 modified "2023-10-06" @default.
• W4387355890 title "A Volumetric Approach to Monge's Optimal Transport on Surfaces" @default.
• W4387355890 doi "https://doi.org/10.48550/arxiv.2310.01745" @default.
• W4387355890 hasPublicationYear "2023" @default.
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