  Recently, Papadakis et al. proposed an efficient primal-dual algorithm for
solving the dynamic optimal transport problem with quadratic ground cost and
measures having densities with respect to the Lebesgue measure. It is based on
the fluid mechanics formulation by Benamou and Brenier and proximal splitting
schemes. In this paper we extend the framework to color image processing. We
show how the transportation problem for RGB color images can be tackled by
prescribing periodic boundary conditions in the color dimension. This requires
the solution of a 4D Poisson equation with mixed Neumann and periodic boundary
conditions in each iteration step of the algorithm. This 4D Poisson equation
can be efficiently handled by fast Fourier and Cosine transforms. Furthermore,
we sketch how the same idea can be used in a modified way to transport periodic
1D data such as the histogram of cyclic hue components of images. We discuss
the existence and uniqueness of a minimizer of the associated energy
functional. Numerical examples illustrate the meaningfulness of our approach.
