Limits of density-constrained optimal transport

Interpolation between Images by Constrained Optimal Transport

In this paper, the recently proposed technique of constrained optimal transport is used to interpolate between images under specified constraints. The intensity values in both images are considered as mass distributions, and a flow of minimum kinetic energy is computed to transport the initial distribution to the final one, while satisfying specified constraints on the intermediate mass as well...

Insights into capacity-constrained optimal transport.

A variant of the classical optimal transportation problem is the following: among all joint measures with fixed marginals and that are dominated by a given density, find the optimal one. Existence and uniqueness of solutions to this variant were established by Korman and McCann. In the present article, we expose an unexpected symmetry leading to explicit examples in two and more dimensions. The...

Dual measures for capacity constrained optimal transport∗

This note addresses the transport of one probability density f ∈ L1(Rm) onto another one g ∈ L1(Rn) so as to optimize a cost function c ∈ L1(Rm+n) while respecting the capacity constraints 0 ≤ h ≤ h̄ ∈ L∞(Rm+n). If f, g and h̄ are continuous, compactly supported, and bounded away from zero on their supports, and if the problem remains feasible when h̄ is replaced by h̄ − for some > 0, we characteri...

Dual potentials for capacity constrained optimal transport

Optimal transportation with capacity constraints, a variant of the well-known optimal transportation problem, is concerned with transporting one probability density f ∈ L1(Rm) onto another one g ∈ L1(Rn) so as to optimize a cost function c ∈ L1(Rm+n) while respecting the capacity constraints 0 ≤ h ≤ h̄ ∈ L∞(Rm+n). A linear programming duality theorem for this problem was first established by Lev...

Diffeomorphic Density Matching by Optimal Information Transport