摘要： 由于人体器官的形态变化复杂且多样，可变形三维医学图像配准面临诸多挑战。尽管已有多种先进的配准模型被提出，但卷积神经网络的感受野大小受限且卷积核大小固定，导致其在特征提取过程中对全局上下文信息的感知和捕捉能力仍显不足。针对这一问题，在可变形三维医学图像配准方法中引入频率域信息，构建了一种基于空频双域的可变形三维医学图像配准网络（Spatial-Frequency Deformable Registration Network, SFDR-Net），通过空频双域和动态门控融合相结合的方法增强不同尺度特征的表征能力和协同作用。首先，考虑到傅里叶变换能够有效提取高低频信息的同时对形变较为敏感，将其引入可变形三维医学图像配准，并提出了一种高效的空频双域Transformer模块(Space-Frequency Dual-Domain Transformer Block, SFTB)，通过频率域快速傅里叶变换（Fast Fourier Transform, FFT）提取紧凑的全局结构信息，并与空间域多尺度卷积结合，通过不同粒度特征的相互作用精准估计大范围形变；其次，采用动态门控融合模块（Dynamic Gating Fusion Module, DGFM），对多个尺度的空间-频率优化特征进行融合增强，并有选择地将其引入下一阶段形变估计中，避免由于远距离特征信息的退化导致形变估计的不准确。实验结果表明，SFDR-Net在Mindboggle-101、OASIS和IXI数据集上的平均Dice分数分别为64.33%、81.89%和79.81%，与其他先进网络相比平均提升了5.20%、2.75%和2.34%，更具备有效交互整体特征与细节信息的能力，能够自适应地平衡不同尺度形变特征，实现各种形变场景下更精确的配准。

Abstract: Deformable 3D medical image registration faces many challenges due to the complex and diverse morphological changes of human organs. Although various advanced registration models have demonstrated promising results, the limitation of the convolutional neural network’s fixed receptive field and kernel size restricts its ability to capture global contextual information during feature extraction. To address this issue, frequency domain information is incorporated into deformable 3D medical image registration, resulting in the Spatial-Frequency Deformable Registration Network (SFDR-Net). This network synergistically combines spatial and frequency domains with a dynamic gating mechanism to enhance the representation and interaction of multi-scale features. Specifically, given that the Fourier transform is sensitive to deformations while extracting high- and low-frequency information, it is integrated into deformable 3D medical image registration, leading to the development of an efficient Space-Frequency Dual-Domain Transformer Block (SFTB).The SFTB leverages the Fast Fourier Transform (FFT) to extract compact global structural information, which is then combined with multi-scale convolutions in the spatial domain to precisely estimate extensive deformations through the interaction of features at different granularities. Furthermore, a Dynamic Gating Fusion Module (DGFM) is employed to fuse and enhance multi-scale spatial-frequency optimized features, selectively incorporating them into subsequent deformation estimation stages to avert inaccuracies arising from the degradation of long-range feature information. SFDR-Net achieved average Dice scores of 64.33%, 81.89%, and 79.81% on the Mindboggle-101, OASIS, and IXI datasets, respectively, representing average improvements of 5.2%, 2.75%, and 2.34% compared to other state-of-the-art networks. This highlights its superior capability to integrate overall features with fine details and adaptively balance multi-scale deformation features for more precise registration across various deformation scenarios.