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.

翻译：冠状动脉微血管疾病对人类健康构成重大威胁。借助计算机辅助分析与诊断系统，医疗专业人员可在疾病发展早期进行干预，其中三维血管分割是关键环节。然而，传统U-Net架构往往产生不连贯且不精确的分割结果，尤其是针对细小血管结构。尽管采用注意力机制的模型（如Transformer和大卷积核）表现出更优性能，但其在训练和推理过程中巨大的计算需求导致时间复杂度增加。在本研究中，我们利用傅里叶域学习替代三维分层分割模型中的多尺度卷积核，该方案可在保持网络全局感受野的同时降低计算开销。此外，我们设计了一种零参数频域融合方法，用于改进U-Net架构中的跳跃连接。在公开数据集和内部数据集上的实验结果表明，基于傅里叶变换的新型网络在管状血管分割任务中取得了卓越的Dice性能（ASACA500数据集84.37%，ImageCAS数据集80.32%），并在不牺牲全局感受野的前提下大幅降低了计算需求。