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.
翻译:diffeorphic 注册框架能够界定数据-忠诚损失功能两个概率计量之间的最佳匹配功能。 由于优化问题不精确,因此选择这一损失功能对于避免当地微量损失十分关键。最近的工作实验性地显示,在计算速度和可变性的同时,微量运输成本是快速和可变的,因此,微量的注册框架能够界定最佳匹配功能。遵循这一方法,我们在本文件中提供了一个基于辛克霍恩差异的新框架,公正的微量最佳运输成本,并证明统计与实验性最佳变形率的一致。