# Rotation-Scale Equivariant Steerable Filters

arXiv: https://arxiv.org/abs/2304.04600 · HTML: https://mlsanity.com/paper/2304.04600/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 31 references that are in the map.
- First posted on arXiv 10 Apr 2023.

## Builds on (most cited first, 20 of 20)

- [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)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [General E(2)-Equivariant Steerable CNNs](https://mlsanity.com/paper/1911.08251/) (2019)
- [Rotation Equivariant CNNs for Digital Pathology](https://mlsanity.com/paper/1806.03962/) (2018)
- [Harmonic Networks: Deep Translation and Rotation Equivariance](https://mlsanity.com/paper/1612.04642/) (2016)
- [Gland Segmentation in Colon Histology Images: The GlaS Challenge Contest](https://mlsanity.com/paper/1603.00275/) (2016)
- [Learning Steerable Filters for Rotation Equivariant CNNs](https://mlsanity.com/paper/1711.07289/) (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)
- [Roto-Translation Covariant Convolutional Networks for Medical Image Analysis](https://mlsanity.com/paper/1804.03393/) (2018)
- [DISCO: accurate Discrete Scale Convolutions](https://mlsanity.com/paper/2106.02733/) (2021)
- [Dense Steerable Filter CNNs for Exploiting Rotational Symmetry in Histology Images](https://mlsanity.com/paper/2004.03037/) (2020)
- [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)
- [Scaling-Translation-Equivariant Networks with Decomposed Convolutional Filters](https://mlsanity.com/paper/1909.11193/) (2019)
- [RotDCF: Decomposition of Convolutional Filters for Rotation-Equivariant Deep Networks](https://mlsanity.com/paper/1805.06846/) (2018)
- [Sample Efficient Semantic Segmentation using Rotation Equivariant Convolutional Networks](https://mlsanity.com/paper/1807.00583/) (2018)
- [Deformation Robust Roto-Scale-Translation Equivariant CNNs](https://mlsanity.com/paper/2111.10978/) (2021)

## Built on by (most cited first, 3 of 3)

- [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)
- [Current Symmetry Group Equivariant Convolution Frameworks for Representation Learning](https://mlsanity.com/paper/2409.07327/) (2024)
- [Robust Canonicalization through Bootstrapped Data Re-Alignment](https://mlsanity.com/paper/2510.08178/) (2025)

## Abstract (arXiv)

Incorporating either rotation equivariance or scale equivariance into CNNs has proved to be effective in improving models' generalization performance. However, jointly integrating rotation and scale equivariance into CNNs has not been widely explored. Digital histology imaging of biopsy tissue can be captured at arbitrary orientation and magnification and stored at different resolutions, resulting in cells appearing in different scales. When conventional CNNs are applied to histopathology image analysis, the generalization performance of models is limited because 1) a part of the parameters of filters are trained to fit rotation transformation, thus decreasing the capability of learning other discriminative features; 2) fixed-size filters trained on images at a given scale fail to generalize to those at different scales. To deal with these issues, we propose the Rotation-Scale Equivariant Steerable Filter (RSESF), which incorporates steerable filters and scale-space theory. The RSESF contains copies of filters that are linear combinations of Gaussian filters, whose direction is controlled by directional derivatives and whose scale parameters are trainable but constrained to span disjoint scales in successive layers of the network. Extensive experiments on two gland segmentation datasets demonstrate that our method outperforms other approaches, with much fewer trainable parameters and fewer GPU resources required. The source code is available at: https://github.com/ynulonger/RSESF.