Diffeomorphic Registration using Sinkhorn Divergences

Lucas de Lara (1, 2) , Alberto González-Sanz (1, 2) , Jean-Michel Loubes (1, 2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 UT - Université de Toulouse

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.

Mots clés: Diffeomorphic Registration; Optimal transportation; Diffeomorphic Registration

Domaines: Théorie [stat.TH]

Lucas de Lara, Alberto González-Sanz, Jean-Michel Loubes. Diffeomorphic Registration using Sinkhorn Divergences. 2022. ⟨hal-03705992v1⟩