中文摘要：

近年来,非线性图像配准各种方法的数值分析已经十分成熟;但是大多数工作都没有考虑理论上的收敛性分析.本文对非线性图像配准极小问题进行了理论上的分析证明.我们得到了极小问题正则解的存在性、稳定性及收敛性,证明了在正则化算子和正则参数分别满足一定的条件下,极小问题的正则解收敛到我们所关心的问题的解.这一理论上的证明过程及结果将对非线性图像配准的正则化算子的选取提供十分重要的依据.

英文摘要：

The numerical methods for nonlinear image registration have been extensively studied during the recent years. However, most of these researches does not consider the convergence analysis. In this paper, we focus on the theoretical analysis about the minimization problem of nonlinear registration. Specifically, we obtain the existence, stability and convergence of the regularized solutions under some conditions of the regularization operator and the regularization parameter. These theoretical results will provide some important information for the selection of regularization operators in nonlinear image registration.