RSF-Conv: Rotation-and-Scale Equivariant Fourier Parameterized Convolution for Retinal Vessel Segmentation

Retinal vessel segmentation is of great clinical significance for the diagnosis of many eye-related diseases, but it is still a formidable challenge due to the intricate vascular morphology. With the skillful characterization of the translation symmetry existing in retinal vessels, convolutional neural networks (CNNs) have achieved great success in retinal vessel segmentation. However, the rotation-and-scale symmetry, as a more widespread image prior in retinal vessels, fails to be characterized by CNNs. Therefore, we propose a rotation-and-scale equivariant Fourier parameterized convolution (RSF-Conv) specifically for retinal vessel segmentation and provide the corresponding equivariance analysis. As a general module, RSF-Conv can be integrated into existing networks in a plug-and-play manner while significantly reducing the number of parameters. For instance, we replace the traditional convolution filters in U-Net, Iter-Net, DE-DCGCN-EE, and FR-UNet, with RSF-Convs, and faithfully conduct comprehensive experiments. RSF-Conv-enhanced methods not only have slight advantages under in-domain evaluation but also, more importantly, outperform all comparison methods by a significant margin under out-of-domain evaluation. It indicates that the remarkable generalization of RSF-Conv holds greater practical clinical significance for the prevalent cross-device and cross-hospital challenges in clinical practice. To comprehensively demonstrate the effectiveness of RSF-Conv, we also apply RSF-Conv + U-Net and RSF-Conv + Iter-Net to retinal artery/vein classification and achieve promising performance as well, indicating its clinical application potential. The code is available at https://github.com/szhc0gk/RSF-Conv.