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

arXiv: https://arxiv.org/abs/2309.15638 · HTML: https://mlsanity.com/paper/2309.15638/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 59 references that are in the map.
- First posted on arXiv 27 Sep 2023.

## Builds on (most cited first, 28 of 28)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Masked-attention Mask Transformer for Universal Image Segmentation](https://mlsanity.com/paper/2112.01527/) (2021)
- [Swin-Unet: Unet-like Pure Transformer for Medical Image Segmentation](https://mlsanity.com/paper/2105.05537/) (2021)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [UNet++: Redesigning Skip Connections to Exploit Multiscale Features in Image Segmentation](https://mlsanity.com/paper/1912.05074/) (2019)
- [General E(2)-Equivariant Steerable CNNs](https://mlsanity.com/paper/1911.08251/) (2019)
- [CE-Net: Context Encoder Network for 2D Medical Image Segmentation](https://mlsanity.com/paper/1903.02740/) (2019)
- [Learning Steerable Filters for Rotation Equivariant CNNs](https://mlsanity.com/paper/1711.07289/) (2017)
- [Transformation Consistent Self-ensembling Model for Semi-supervised Medical Image Segmentation](https://mlsanity.com/paper/1903.00348/) (2019)
- [Deep Scale-spaces: Equivariance Over Scale](https://mlsanity.com/paper/1905.11697/) (2019)
- [Scale-Equivariant Steerable Networks](https://mlsanity.com/paper/1910.11093/) (2019)
- [IterNet: Retinal Image Segmentation Utilizing Structural Redundancy in Vessel Networks](https://mlsanity.com/paper/1912.05763/) (2019)
- [Scale-Invariant Convolutional Neural Networks](https://mlsanity.com/paper/1411.6369/) (2014)
- [FANet: A Feedback Attention Network for Improved Biomedical Image Segmentation](https://mlsanity.com/paper/2103.17235/) (2021)
- [DISCO: accurate Discrete Scale Convolutions](https://mlsanity.com/paper/2106.02733/) (2021)
- [PDO-eConvs: Partial Differential Operator Based Equivariant Convolutions](https://mlsanity.com/paper/2007.10408/) (2020)
- [HexaConv](https://mlsanity.com/paper/1803.02108/) (2018)
- [Fourier Series Expansion Based Filter Parametrization for Equivariant Convolutions](https://mlsanity.com/paper/2107.14519/) (2021)
- [RV-GAN: Segmenting Retinal Vascular Structure in Fundus Photographs using a Novel Multi-scale Generative Adversarial Network](https://mlsanity.com/paper/2101.00535/) (2021)
- [Study Group Learning: Improving Retinal Vessel Segmentation Trained with Noisy Labels](https://mlsanity.com/paper/2103.03451/) (2021)
- [Deep Retinal Image Segmentation with Regularization Under Geometric Priors](https://mlsanity.com/paper/1909.09175/) (2019)
- [Multi-Task Neural Networks with Spatial Activation for Retinal Vessel Segmentation and Artery/Vein Classification](https://mlsanity.com/paper/2007.09337/) (2020)
- [Local Intensity Order Transformation for Robust Curvilinear Object Segmentation](https://mlsanity.com/paper/2202.12587/) (2022)
- [Genetic U-Net: Automatically Designed Deep Networks for Retinal Vessel Segmentation Using a Genetic Algorithm](https://mlsanity.com/paper/2010.15560/) (2020)
- [Exploring The Limits Of Data Augmentation For Retinal Vessel Segmentation](https://mlsanity.com/paper/2105.09365/) (2021)
- [TR-GAN: Topology Ranking GAN with Triplet Loss for Retinal Artery/Vein Classification](https://mlsanity.com/paper/2007.14852/) (2020)
- [RVD: A Handheld Device-Based Fundus Video Dataset for Retinal Vessel Segmentation](https://mlsanity.com/paper/2307.06577/) (2023)

## Built on by (most cited first, 5 of 5)

- [RPCANet++: Deep Interpretable Robust PCA for Sparse Object Segmentation](https://mlsanity.com/paper/2508.04190/) (2025)
- [A Refreshed Similarity-based Upsampler for Direct High-Ratio Feature Upsampling](https://mlsanity.com/paper/2407.02283/) (2024)
- [DUN-SRE: Deep Unrolling Network with Spatiotemporal Rotation Equivariance for Dynamic MRI Reconstruction](https://mlsanity.com/paper/2506.10309/) (2025)
- [Widest-Path Reachability Fields for Connectivity-Preserving Slender Structure Segmentation](https://mlsanity.com/paper/2607.07123/) (2026)
- [Effective Receptive Field Ordering Matters for Infrared Small Target Detection](https://mlsanity.com/paper/2607.23994/) (2026)

## Abstract (arXiv)

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 and Iter-Net with RSF-Convs, and faithfully conduct comprehensive experiments. RSF-Conv+U-Net and RSF-Conv+Iter-Net not only have slight advantages under in-domain evaluation, but more importantly, outperform all comparison methods by a significant margin under out-of-domain evaluation. It indicates the remarkable generalization of RSF-Conv, which 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.