  We propose two models for the interpolation between RGB images based on the
dynamic optimal transport model of Benamou and Brenier [8]. While the
application of dynamic optimal transport and its extensions to unbalanced
transform were examined for gray-values images in various papers, this is the
first attempt to generalize the idea to color images. The nontrivial task to
incorporate color into the model is tackled by considering RGB images as
three-dimensional arrays, where the transport in the RGB direction is performed
in a periodic way. Following the approach of Papadakis et al. [35] for
gray-value images we propose two discrete variational models, a constrained and
a penalized one which can also handle unbalanced transport. We show that a
minimizer of our discrete model exists, but it is not unique for some special
initial/final images. For minimizing the resulting functionals we apply a
primal-dual algorithm. One step of this algorithm requires the solution of a
four-dimensional discretized Poisson equation with various boundary conditions
in each dimension. For instance, for the penalized approach we have
simultaneously zero, mirror and periodic boundary conditions. The solution can
be computed efficiently using fast Sin-I, Cos-II and Fourier transforms.
Numerical examples demonstrate the meaningfulness of our model.
