Diffeomorphic Registration Using Sinkhorn Divergences*

The diffeomorphic registration framework enables one to define an optimal matching function be-tween two probability measures with respect to a data-fidelity loss function. The nonconvexity of the optimization problem renders the choice of this loss function crucial to avoid poor local minima. Re-cent work showed experimentally the efficiency of entropy-regularized optimal transportation costs, as they are computationally fast and differentiable while having few minima. Following this ap-proach, 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.