  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.
