Coronary microvascular disease constitutes a substantial risk to human
health. Employing computer-aided analysis and diagnostic systems, medical
professionals can intervene early in disease progression, with 3D vessel
segmentation serving as a crucial component. Nevertheless, conventional U-Net
architectures tend to yield incoherent and imprecise segmentation outcomes,
particularly for small vessel structures. While models with attention
mechanisms, such as Transformers and large convolutional kernels, demonstrate
superior performance, their extensive computational demands during training and
inference lead to increased time complexity. In this study, we leverage Fourier
domain learning as a substitute for multi-scale convolutional kernels in 3D
hierarchical segmentation models, which can reduce computational expenses while
preserving global receptive fields within the network. Furthermore, a
zero-parameter frequency domain fusion method is designed to improve the skip
connections in U-Net architecture. Experimental results on a public dataset and
an in-house dataset indicate that our novel Fourier transformation-based
network achieves remarkable dice performance (84.37\% on ASACA500 and 80.32\%
on ImageCAS) in tubular vessel segmentation tasks and substantially reduces
computational requirements without compromising global receptive fields.

冠状微血管疾病的风险对人类健康构成了重大威胁。通过计算机辅助分析和诊断系统，医学专业人员可以在疾病进展的早期进行干预，而 3D 血管分割作为关键组成部分。我们利用傅立叶域学习作为 3D 分层分割模型中多尺度卷积核的替代方法，既可以降低计算负荷，又能保持网络内的全局感受野。此外，设计了一个零参数频域融合方法来改进 U-Net 架构中的跳过连接。在一个公共数据集和一个内部数据集上的实验结果表明，我们的新颖傅立叶变换基于网络在管状血管分割任务中取得了显著的骰子性能（ASACA500 上达到 84.37％，ImageCAS 上达到 80.32％），同时还大大减少了计算需求，而不损害全局感受野。