FRS-Nets: Fourier Parameterized Rotation and Scale Equivariant Networks
  for Retinal Vessel Segmentation
Zihong Sun Qi Xie Deyu Meng
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.