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表明,在计算速度和可变性同时几乎没有微量的情况下,对英特罗比-正规化最佳运输成本的效率进行了快速和可变的计算。遵循这一方法,我们在本文件中提供了基于辛克霍恩差异的新框架、公正的英特罗地最佳运输成本,并证明统计与经验最佳变形率的一致。