# Sample Efficient Semantic Segmentation using Rotation Equivariant Convolutional Networks

arXiv: https://arxiv.org/abs/1807.00583 · HTML: https://mlsanity.com/paper/1807.00583/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jul 2018.

## Built on by (most cited first, 11 of 11)

- [Equivariance versus Augmentation for Spherical Images](https://mlsanity.com/paper/2202.03990/) (2022)
- [Exploiting Redundancy: Separable Group Convolutional Networks on Lie Groups](https://mlsanity.com/paper/2110.13059/) (2021)
- [Rotation-Scale Equivariant Steerable Filters](https://mlsanity.com/paper/2304.04600/) (2023)
- [Self-Supervised Learning for Image Segmentation: A Comprehensive Survey](https://mlsanity.com/paper/2505.13584/) (2025)
- [Leveraging SO(3)-steerable convolutions for pose-robust semantic segmentation in 3D medical data](https://mlsanity.com/paper/2303.00351/) (2023)
- [EcoFlow: Efficient Convolutional Dataflows for Low-Power Neural Network Accelerators](https://mlsanity.com/paper/2202.02310/) (2022)
- [Improved Vessel Segmentation with Symmetric Rotation-Equivariant U-Net](https://mlsanity.com/paper/2501.14592/) (2025)
- [GMR-Conv: An Efficient Rotation and Reflection Equivariant Convolution Kernel Using Gaussian Mixture Rings](https://mlsanity.com/paper/2504.02819/) (2025)
- [Scale-Translation Equivariant Network for Oceanic Internal Solitary Wave Localization](https://mlsanity.com/paper/2406.13060/) (2024)
- [On the effectiveness of Rotation-Equivariance in U-Net: A Benchmark for Image Segmentation](https://mlsanity.com/paper/2412.09182/) (2024)
- [Equivariant Imaging Biomarkers for Robust Unsupervised Segmentation of Histopathology](https://mlsanity.com/paper/2505.05689/) (2025)

## Abstract (arXiv)

We propose a semantic segmentation model that exploits rotation and reflection symmetries. We demonstrate significant gains in sample efficiency due to increased weight sharing, as well as improvements in robustness to symmetry transformations. The group equivariant CNN framework is extended for segmentation by introducing a new equivariant (G->Z2)-convolution that transforms feature maps on a group to planar feature maps. Also, equivariant transposed convolution is formulated for up-sampling in an encoder-decoder network. To demonstrate improvements in sample efficiency we evaluate on multiple data regimes of a rotation-equivariant segmentation task: cancer metastases detection in histopathology images. We further show the effectiveness of exploiting more symmetries by varying the size of the group.