Talk:Semidiscrete Optimal Transport: Difference between revisions

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==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==
==Voronoi cells to find weights==

Revision as of 04:05, 12 June 2020

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.
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