  The diffeomorphic registration framework enables to define an optimal
matching function between two probability measures with respect to a
data-fidelity loss function. The non convexity of the optimization problem
renders the choice of this loss function crucial to avoid poor local minima.
Recent work showed experimentally the efficiency of entropy-regularized optimal
transportation costs, as they are computationally fast and differentiable while
having few minima. Following this approach, we provide in this paper a new
framework based on Sinkhorn divergences, unbiased entropic optimal
transportation costs, and prove the statistical consistency with rate of the
empirical optimal deformations.
