Diffeomorphic Registration using Sinkhorn Divergences
Statistics Theory
2022-11-24 v2 Statistics Theory
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.
Cite
@article{arxiv.2206.13948,
title = {Diffeomorphic Registration using Sinkhorn Divergences},
author = {Lucas de Lara and Alberto González-Sanz and Jean-Michel Loubes},
journal= {arXiv preprint arXiv:2206.13948},
year = {2022}
}