With translation equivariance, convolution neural networks (CNNs) have
achieved great success in retinal vessel segmentation. However, some other
symmetries of the vascular morphology are not characterized by CNNs, such as
rotation and scale symmetries. To embed more equivariance into CNNs and achieve
the accuracy requirement for retinal vessel segmentation, we construct a novel
convolution operator (FRS-Conv), which is Fourier parameterized and equivariant
to rotation and scaling. Specifically, we first adopt a new parameterization
scheme, which enables convolutional filters to arbitrarily perform
transformations with high accuracy. Secondly, we derive the formulations for
the rotation and scale equivariant convolution mapping. Finally, we construct
FRS-Conv following the proposed formulations and replace the traditional
convolution filters in U-Net and Iter-Net with FRS-Conv (FRS-Nets). We
faithfully reproduce all compared methods and conduct comprehensive experiments
on three public datasets under both in-dataset and cross-dataset settings. With
merely 13.9% parameters of corresponding baselines, FRS-Nets have achieved
state-of-the-art performance and significantly outperform all compared methods.
It demonstrates the remarkable accuracy, generalization, and clinical
application potential of FRS-Nets.

通过构建傅立叶参数化的 FR-Conv（旋转和缩放等变）卷积操作符，来在卷积神经网络中嵌入更多的等变性，用于视网膜血管分割，实现对精确度的要求，并在公共数据集上进行全面实验验证，结果表明 FRS-Nets 在参数量约为基线模型的 13.9% 的情况下，取得了最先进的性能，并且明显优于所有对比方法，展示了 FRS-Nets 的显著准确性、泛化性和临床应用潜力。