基于拟共形理论的分数阶多尺度微分同胚图像配准

数学物理学报 ›› 2024, Vol. 44 ›› Issue (6): 1665-1688.

基于拟共形理论的分数阶多尺度微分同胚图像配准

王慧楠(),韩欢^*()

武汉理工大学数学系武汉 430070

收稿日期:2023-10-18 修回日期:2024-04-30 出版日期:2024-12-26 发布日期:2024-11-22
通讯作者: ^*韩欢, Email: hanhuan11@whut.edu.cn
作者简介:王慧楠, Email: whn@whut.edu.cn
基金资助:
国家自然科学基金(11901443);湖北省自然科学基金(2022CFB379)

Multi-Scale Approach for Diffeomorphic Image Registration with Fractional-Order Regularization Based on Quasiconformal Theory

Wang Huinan(),Han Huan^*()

Department of Mathematics, Wuhan University of Technology, Wuhan 430070

Received:2023-10-18 Revised:2024-04-30 Online:2024-12-26 Published:2024-11-22
Supported by:
National Natural Science Foundation of China(11901443);Natural Science Foundation of Hubei Province of China(2022CFB379)

摘要/Abstract

摘要：

图像配准领域存在着两大挑战: (1) 网格重叠现象; (2) 贪婪配准问题不适定. 针对这两大挑战, 该文提出了一个基于拟共形理论的多尺度分数阶微分同胚图像配准模型, 该模型在无网格重叠及先验正则项的前提下, 得到了相似性度量泛函的一个光滑极小值点. 此外, 该文证明了所提模型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能有效避免网格重叠并得到较好的配准结果.

关键词: 微分同胚, 多尺度, 拟共形理论, 分数阶, 图像配准

Abstract:

Two significant challenges relating to image registration include the issue of mesh folding and the unresolved problem of greedy registration. To tackle these challenges, a multi-scale approach for diffeomorphic image registration model with fractional-order regularization based on quasiconformal theory is proposed in this paper. It employs fractional-order differential to achieve a smooth energy functional minima without mesh folding and a priori regular terms. Furthermore, the existence of solution for the proposed model and the convergence of the multi-scale approach are proved. And numerical tests are performed to demonstrate that the proposed algorithm effectively eliminates mesh folding and generates superior registration results.

Key words: Diffeomorphic, Multi-scale, Quasiconformal theory, Fractional-order regularization, Image registration

中图分类号:

TP391

王慧楠, 韩欢. 基于拟共形理论的分数阶多尺度微分同胚图像配准[J]. 数学物理学报, 2024, 44(6): 1665-1688.

Wang Huinan, Han Huan. Multi-Scale Approach for Diffeomorphic Image Registration with Fractional-Order Regularization Based on Quasiconformal Theory[J]. Acta mathematica scientia,Series A, 2024, 44(6): 1665-1688.

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