Leveraging Frequency Domain Learning in 3D Vessel Segmentation

TL;DR

This paper tackles 3D coronary vessel segmentation from CT angiography, where standard CNNs struggle to accurately segment tiny tubular vessels and to capture global context. It introduces a frequency-domain learning framework, replacing traditional multi-scale convolutions with 3D Discrete Fourier Transform (DFT) based operations to preserve global receptive fields while reducing computational cost, and adds a zero-parameter Fourier Fusion Decoder to merge encoder and decoder features. The proposed Hierarchical Fourier Segmentation Network (Fseg) demonstrates strong Dice scores on public and in-house datasets (e.g., 84.37% on ASACA500 and 80.32% on ImageCAS) and offers favorable efficiency compared with attention-based models. By leveraging FFT-based processing and frequency-domain feature fusion, the approach enables efficient, globally informed 3D vessel segmentation with potential impact for automated CAD workflows in coronary microvascular disease detection and planning.

Abstract

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.

Figures (4)

• Figure 1: Hierarchical Fourier Segmentation(Fseg) Network Overview
• Figure 2: Convolution vs DFT-IDFT. $\textbf{I}_p$(or $\textbf{K}_p$) means image(or kernel) with padding, and $\odot$ means Hadamard product. The third figure denotes vanilla linear convolution result, while the latter two figures denote multiply in the frequency domain with(or without) padding respectively. A significant visual shift can be found when comparing the 3rd column with the 4th column.
• Figure 3: Fourier Fusion Decoder
• Figure 4: Comparison of segmentation results using some recent methods. A dashed box is an enlargement of a solid box for better comparison. The blue arrows indicate areas of poor segmentation.