Diffeomorphic Registration using Sinkhorn Divergences

TL;DR

This paper introduces a novel diffeomorphic registration framework utilizing Sinkhorn divergences, which are unbiased entropic optimal transportation costs, ensuring statistical consistency and improved optimization performance.

Contribution

It proposes a new registration method based on Sinkhorn divergences and proves its statistical consistency with convergence rates.

Findings

Sinkhorn divergences improve registration accuracy.

The method is computationally efficient and differentiable.

Theoretical guarantees of statistical consistency are established.

Abstract

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.