# Scale-Equivariant UNet for Histopathology Image Segmentation

arXiv: https://arxiv.org/abs/2304.04595 · HTML: https://mlsanity.com/paper/2304.04595/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 24 references that are in the map.
- First posted on arXiv 10 Apr 2023.

## Builds on (most cited first, 17 of 17)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Rich feature hierarchies for accurate object detection and semantic segmentation](https://mlsanity.com/paper/1311.2524/) (2013)
- [Super-Convergence: Very Fast Training of Neural Networks Using Large Learning Rates](https://mlsanity.com/paper/1708.07120/) (2017)
- [Deep Scale-spaces: Equivariance Over Scale](https://mlsanity.com/paper/1905.11697/) (2019)
- [Scale-Equivariant Steerable Networks](https://mlsanity.com/paper/1910.11093/) (2019)
- [B-Spline CNNs on Lie Groups](https://mlsanity.com/paper/1909.12057/) (2019)
- [Scale-Invariant Convolutional Neural Networks](https://mlsanity.com/paper/1411.6369/) (2014)
- [DISCO: accurate Discrete Scale Convolutions](https://mlsanity.com/paper/2106.02733/) (2021)
- [Pushing the Boundaries of Boundary Detection using Deep Learning](https://mlsanity.com/paper/1511.07386/) (2015)
- [Locally Scale-Invariant Convolutional Neural Networks](https://mlsanity.com/paper/1412.5104/) (2014)
- [Signet Ring Cell Detection With a Semi-supervised Learning Framework](https://mlsanity.com/paper/1907.03954/) (2019)
- [Resolution learning in deep convolutional networks using scale-space theory](https://mlsanity.com/paper/2106.03412/) (2021)
- [Scale-covariant and scale-invariant Gaussian derivative networks](https://mlsanity.com/paper/2011.14759/) (2020)
- [Scale equivariance in CNNs with vector fields](https://mlsanity.com/paper/1807.11783/) (2018)
- [Scaling-Translation-Equivariant Networks with Decomposed Convolutional Filters](https://mlsanity.com/paper/1909.11193/) (2019)

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

- [Equivariant Adaptation of Large Pretrained Models](https://mlsanity.com/paper/2310.01647/) (2023)
- [Graph Neural PDE Solvers with Conservation and Similarity-Equivariance](https://mlsanity.com/paper/2405.16183/) (2024)
- [Scale-Equivariant Deep Learning for 3D Data](https://mlsanity.com/paper/2304.05864/) (2023)
- [HyperSpace: Hypernetworks for spacing-adaptive image segmentation](https://mlsanity.com/paper/2407.03681/) (2024)
- [Unified theory for joint covariance properties under geometric image transformations for spatio-temporal receptive fields according to the generalized Gaussian derivative model for visual receptive fields](https://mlsanity.com/paper/2311.10543/) (2023)
- [Riesz feature representation: scale equivariant scattering network for classification tasks](https://mlsanity.com/paper/2307.08467/) (2023)
- [Approximation properties relative to continuous scale space for hybrid discretizations of Gaussian derivative operators](https://mlsanity.com/paper/2405.05095/) (2024)
- [Scale generalisation properties of extended scale-covariant and scale-invariant Gaussian derivative networks on image datasets with spatial scaling variations](https://mlsanity.com/paper/2409.11140/) (2024)
- [Modelling and analysis of the 8 filters from the "master key filters hypothesis" for depthwise-separable deep networks in relation to idealized receptive fields based on scale-space theory](https://mlsanity.com/paper/2509.12746/) (2025)
- [Hybrid Lie semi-group and cascade structures for the generalized Gaussian derivative model for visual receptive fields](https://mlsanity.com/paper/2509.15748/) (2025)
- [Scale-invariant Gaussian derivative residual networks](https://mlsanity.com/paper/2603.02843/) (2026)

## Abstract (arXiv)

Digital histopathology slides are scanned and viewed under different magnifications and stored as images at different resolutions. Convolutional Neural Networks (CNNs) trained on such images at a given scale fail to generalise to those at different scales. This inability is often addressed by augmenting training data with re-scaled images, allowing a model with sufficient capacity to learn the requisite patterns. Alternatively, designing CNN filters to be scale-equivariant frees up model capacity to learn discriminative features. In this paper, we propose the Scale-Equivariant UNet (SEUNet) for image segmentation by building on scale-space theory. The SEUNet contains groups of filters that are linear combinations of Gaussian basis filters, whose scale parameters are trainable but constrained to span disjoint scales through the layers of the network. Extensive experiments on a nuclei segmentation dataset and a tissue type segmentation dataset demonstrate that our method outperforms other approaches, with much fewer trainable parameters.