Diffeomorphic Registration Using Sinkhorn Divergences

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Abstract
The diffeomorphic registration framework enables one to define an optimal matching function between 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. 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.
Funding Information
  • Agence Nationale de la Recherche (ANR-19-PI3A-0004)

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