# Roto-Translation Equivariant Convolutional Networks: Application to Histopathology Image Analysis

arXiv: https://arxiv.org/abs/2002.08725 · HTML: https://mlsanity.com/paper/2002.08725/

## Key facts

- Cited by 32 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Feb 2020.

## Built on by (most cited first, 30 of 32)

- [Mitosis domain generalization in histopathology images -- The MIDOG challenge](https://mlsanity.com/paper/2204.03742/) (2022)
- [Geometric Algebra Transformer](https://mlsanity.com/paper/2305.18415/) (2023)
- [CPP-Net: Context-aware Polygon Proposal Network for Nucleus Segmentation](https://mlsanity.com/paper/2102.06867/) (2021)
- [Domain Generalization in Computational Pathology: Survey and Guidelines](https://mlsanity.com/paper/2310.19656/) (2023)
- [Beyond Euclid: An Illustrated Guide to Modern Machine Learning with Geometric, Topological, and Algebraic Structures](https://mlsanity.com/paper/2407.09468/) (2024)
- [Generalization capabilities of translationally equivariant neural networks](https://mlsanity.com/paper/2103.14686/) (2021)
- [Scale-invariant scale-channel networks: Deep networks that generalise to previously unseen scales](https://mlsanity.com/paper/2106.06418/) (2021)
- [Almost Equivariance via Lie Algebra Convolutions](https://mlsanity.com/paper/2310.13164/) (2023)
- [SE(3)-Equivariant and Noise-Invariant 3D Rigid Motion Tracking in Brain MRI](https://mlsanity.com/paper/2312.13534/) (2023)
- [Equivariant Wavelets: Fast Rotation and Translation Invariant Wavelet Scattering Transforms](https://mlsanity.com/paper/2104.11244/) (2021)
- [Rotation Invariance and Extensive Data Augmentation: a strategy for the Mitosis Domain Generalization (MIDOG) Challenge](https://mlsanity.com/paper/2109.00823/) (2021)
- [Advanced deep-reinforcement-learning methods for flow control: group-invariant and positional-encoding networks improve learning speed and quality](https://mlsanity.com/paper/2407.17822/) (2024)
- [Learning Symmetries via Weight-Sharing with Doubly Stochastic Tensors](https://mlsanity.com/paper/2412.04594/) (2024)
- [Using and Abusing Equivariance](https://mlsanity.com/paper/2308.11316/) (2023)
- [Learning Invariant Representations for Equivariant Neural Networks Using Orthogonal Moments](https://mlsanity.com/paper/2209.10944/) (2022)
- [Fine-Grained Hard Negative Mining: Generalizing Mitosis Detection with a Fifth of the MIDOG 2022 Dataset](https://mlsanity.com/paper/2301.01079/) (2023)
- [Structure Preserving Diffusion Models](https://mlsanity.com/paper/2402.19369/) (2024)
- [On Universality of Deep Equivariant Networks](https://mlsanity.com/paper/2510.15814/) (2025)
- [Learning to Transform for Generalizable Instance-wise Invariance](https://mlsanity.com/paper/2309.16672/) (2023)
- [Few-shot Shape Recognition by Learning Deep Shape-aware Features](https://mlsanity.com/paper/2312.01315/) (2023)
- [Current Symmetry Group Equivariant Convolution Frameworks for Representation Learning](https://mlsanity.com/paper/2409.07327/) (2024)
- [Achieving Rotation-Invariant Convolution via Non-Learnable Orientation Alignment Operators](https://mlsanity.com/paper/2404.11309/) (2024)
- [Occlusion-Invariant Rotation-Equivariant Semi-Supervised Depth Based Cross-View Gait Pose Estimation](https://mlsanity.com/paper/2109.01397/) (2021)
- [Reconstructing group wavelet transform from feature maps with a reproducing kernel iteration](https://mlsanity.com/paper/2110.00600/) (2021)
- [Permutation Equivariant Neural Networks for Symmetric Tensors](https://mlsanity.com/paper/2503.11276/) (2025)
- [DUN-SRE: Deep Unrolling Network with Spatiotemporal Rotation Equivariance for Dynamic MRI Reconstruction](https://mlsanity.com/paper/2506.10309/) (2025)
- [Sequential Hard Mining: a data-centric approach for Mitosis Detection](https://mlsanity.com/paper/2509.02588/) (2025)
- [Equi-ViT: Rotational Equivariant Vision Transformer for Robust Histopathology Analysis](https://mlsanity.com/paper/2601.09130/) (2026)
- [The geometry of invariant learning: an information-theoretic analysis of data augmentation and generalization](https://mlsanity.com/paper/2602.14423/) (2026)
- [Accurate Shift Invariant Convolutional Neural Networks Using Gaussian-Hermite Moments](https://mlsanity.com/paper/2603.17098/) (2026)

## Abstract (arXiv)

Rotation-invariance is a desired property of machine-learning models for medical image analysis and in particular for computational pathology applications. We propose a framework to encode the geometric structure of the special Euclidean motion group SE(2) in convolutional networks to yield translation and rotation equivariance via the introduction of SE(2)-group convolution layers. This structure enables models to learn feature representations with a discretized orientation dimension that guarantees that their outputs are invariant under a discrete set of rotations. Conventional approaches for rotation invariance rely mostly on data augmentation, but this does not guarantee the robustness of the output when the input is rotated. At that, trained conventional CNNs may require test-time rotation augmentation to reach their full capability. This study is focused on histopathology image analysis applications for which it is desirable that the arbitrary global orientation information of the imaged tissues is not captured by the machine learning models. The proposed framework is evaluated on three different histopathology image analysis tasks (mitosis detection, nuclei segmentation and tumor classification). We present a comparative analysis for each problem and show that consistent increase of performances can be achieved when using the proposed framework.