Talk:Semidiscrete Optimal Transport

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.