基于多尺度方法的多模态微分同胚图像配准

摘要/Abstract

摘要：

多模态图像配准在遥感、临床医学等领域有着极其广泛的应用. 在过去几十年, 人们提出了许多有关多模态图像配准的模型. 关于此问题, 存在两大挑战: (1) 物理网格重叠现象存在; (2) 相似性度量极小/极大化问题不适定. 针对这两个困难, 该文提出了一种基于瑞利度量的多尺度微分同胚图像配准方法, 该方法避免了估计联合概率密度函数, 且在没有网格重叠及先验正则项的前提下, 得到了能量泛函的一个光滑极小值点. 此外, 该文证明了所提模型的解的存在性及多尺度方法的收敛性, 并通过数值实验验证了所提算法在单模态和多模态图像配准中的有效性.

关键词: 多模态, 微分同胚, 多尺度, 图像配准, 瑞利度量

Abstract:

Multi-modality image registration is widely used in remote sensing, clinical medicine and other fields. Many models for multi-modality image registration have been proposed in the past few decades. Concerning this problem, there are two major challenges: (1) the existence of physical mesh folding; (2) the ill-posedness of similarity measure minimization/maximization problem. In order to address those problems, a multi-scale approach for diffeomorphic image registration based on Rényi's statistical dependence measure is proposed, which can avoid estimating joint probability density function, and obtain a smooth minimizer of the energy functional without mesh folding and prior regularization. In addition, the existence of solution for the proposed model and the convergence of the multi-scale approach are proved. And numerical experiments are performed to show the efficiency of the proposed algorithm in the monomodality image registration and multi-modality image registration.

Key words: Multi-modality, Diffeomorphic, Multi-scale, Image registration, Rényi's statistical dependence measure

中图分类号:

TP391

丁自娟,韩欢. 基于多尺度方法的多模态微分同胚图像配准[J]. 数学物理学报, 2023, 43(5): 1620-1640.

Ding Zijuan,Han Huan. Multi-Scale Approach for Diffeomorphic Multi-Modality Image Registration[J]. Acta mathematica scientia,Series A, 2023, 43(5): 1620-1640.

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