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Improved Vessel Segmentation with Symmetric Rotation-Equivariant U-Net

Jiazhen Zhang, Yuexi Du, Nicha C. Dvornek, John A. Onofrey

TL;DR

This work addresses the lack of rotation and reflection equivariance in standard CNN-based vessel segmentation by introducing SRE-Conv, a centrally symmetric kernel design that enforces rotation-equivariant features with far fewer parameters. Integrated into a U-Net backbone as SRE U-Net, the method achieves superior Dice and AUC on rotated DRIVE fundus images while using a fraction of the parameters compared to baselines and SoTA methods. The study demonstrates robust performance under angular perturbations and provides ablation evidence that carefully chosen kernel sizes enhance local detail preservation. The approach offers practical impact for medical image segmentation where orientation varies across scans and could be extended to other architectures and tasks.

Abstract

Automated segmentation plays a pivotal role in medical image analysis and computer-assisted interventions. Despite the promising performance of existing methods based on convolutional neural networks (CNNs), they neglect useful equivariant properties for images, such as rotational and reflection equivariance. This limitation can decrease performance and lead to inconsistent predictions, especially in applications like vessel segmentation where explicit orientation is absent. While existing equivariant learning approaches attempt to mitigate these issues, they substantially increase learning cost, model size, or both. To overcome these challenges, we propose a novel application of an efficient symmetric rotation-equivariant (SRE) convolutional (SRE-Conv) kernel implementation to the U-Net architecture, to learn rotation and reflection-equivariant features, while also reducing the model size dramatically. We validate the effectiveness of our method through improved segmentation performance on retina vessel fundus imaging. Our proposed SRE U-Net not only significantly surpasses standard U-Net in handling rotated images, but also outperforms existing equivariant learning methods and does so with a reduced number of trainable parameters and smaller memory cost. The code is available at https://github.com/OnofreyLab/sre_conv_segm_isbi2025.

Improved Vessel Segmentation with Symmetric Rotation-Equivariant U-Net

TL;DR

This work addresses the lack of rotation and reflection equivariance in standard CNN-based vessel segmentation by introducing SRE-Conv, a centrally symmetric kernel design that enforces rotation-equivariant features with far fewer parameters. Integrated into a U-Net backbone as SRE U-Net, the method achieves superior Dice and AUC on rotated DRIVE fundus images while using a fraction of the parameters compared to baselines and SoTA methods. The study demonstrates robust performance under angular perturbations and provides ablation evidence that carefully chosen kernel sizes enhance local detail preservation. The approach offers practical impact for medical image segmentation where orientation varies across scans and could be extended to other architectures and tasks.

Abstract

Automated segmentation plays a pivotal role in medical image analysis and computer-assisted interventions. Despite the promising performance of existing methods based on convolutional neural networks (CNNs), they neglect useful equivariant properties for images, such as rotational and reflection equivariance. This limitation can decrease performance and lead to inconsistent predictions, especially in applications like vessel segmentation where explicit orientation is absent. While existing equivariant learning approaches attempt to mitigate these issues, they substantially increase learning cost, model size, or both. To overcome these challenges, we propose a novel application of an efficient symmetric rotation-equivariant (SRE) convolutional (SRE-Conv) kernel implementation to the U-Net architecture, to learn rotation and reflection-equivariant features, while also reducing the model size dramatically. We validate the effectiveness of our method through improved segmentation performance on retina vessel fundus imaging. Our proposed SRE U-Net not only significantly surpasses standard U-Net in handling rotated images, but also outperforms existing equivariant learning methods and does so with a reduced number of trainable parameters and smaller memory cost. The code is available at https://github.com/OnofreyLab/sre_conv_segm_isbi2025.
Paper Structure (10 sections, 1 equation, 3 figures, 2 tables)

This paper contains 10 sections, 1 equation, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Methods
  3. Symmetric Rotation-Equivariant (SRE) Convolution
  4. Network Architecture
  5. Experiments and Results
  6. Experimental Setup
  7. Quantitative Evaluation
  8. Qualitative Evaluation
  9. Ablation Studies
  10. Discussion and Conclusion

Figures (3)

  • Figure 1: Symmetric Rotation-Equivariant (SRE) U-Net. Compared to standard U-Net, SRE U-Net utilizes a parameter-efficient symmetric kernel to enable rotational equivariance. Difference image maps between the output of the original and rotated (90°) images illustrate SRE U-Net's equivariant property by maintaining consistent feature response after rotation on a 2D fundus image.
  • Figure 2: Performance Across Rotation Degree. We plot Dice and AUC across each rotation degree to visualize the influence of small rotation on the model's performance.
  • Figure 3: Qualitative Results. An example fundus image is rotated and fed into the models and the outputs are rotated back to compare with the output from the original image. Difference maps visualize the difference in the predictions under different rotational conditions and we quantitatively summarize this error using Mean Squared Error (MSE). Our proposed method shows consistent results due to its rotational equivariance property.