Talk:Semidiscrete Optimal Transport: Difference between revisions

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==Introduction==
* Cite the source of your image on Voronoi cells.
* ``and the other one is ABSOLUTELY continuous with respect to Lebesgue measure''


==Formulation==
* In your first equation, swap the roles of phi and psi, so you don't have to replace psi with phi later on.
* Explain that nu is replaced with nu = sum of Diracs at locations y_j with weights b_j. Explain that phi_j = phi(y_j)
==Voronoi cells to find weights==
* The weights b_j are given. The goal of the algorithm is to find which REGIONS V_\phi(j) in the support of the source measure \mu are sent to each y_j. These regions are determined by the function phi. You want to find a function phi so that b_j = \int_{V_\phi(j)} f(x) dx.
==Finding the weights==
* As above, the goal is to find phi. The weights are given.
* Cite Merigot for the fact that the energy E(\phi) is concave.
* You may consider either clarifying or removing the last sentence of this section.
==Algorithm discussion==
* This is a very nice summary. Consider adding some references.

Latest revision as of 04:07, 12 June 2020

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