# Affine steerers for structured keypoint description

arXiv: https://arxiv.org/abs/2408.14186 · HTML: https://mlsanity.com/paper/2408.14186/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 68 of its 91 references that are in the map.
- First posted on arXiv 26 Aug 2024.

## Builds on (most cited first, 30 of 68)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [SuperGlue: Learning Feature Matching with Graph Neural Networks](https://mlsanity.com/paper/1911.11763/) (2019)
- [SuperPoint: Self-Supervised Interest Point Detection and Description](https://mlsanity.com/paper/1712.07629/) (2017)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [LoFTR: Detector-Free Local Feature Matching with Transformers](https://mlsanity.com/paper/2104.00680/) (2021)
- [MegaDepth: Learning Single-View Depth Prediction from Internet Photos](https://mlsanity.com/paper/1804.00607/) (2018)
- [LightGlue: Local Feature Matching at Light Speed](https://mlsanity.com/paper/2306.13643/) (2023)
- [General E(2)-Equivariant Steerable CNNs](https://mlsanity.com/paper/1911.08251/) (2019)
- [DISK: Learning local features with policy gradient](https://mlsanity.com/paper/2006.13566/) (2020)
- [LIFT: Learned Invariant Feature Transform](https://mlsanity.com/paper/1603.09114/) (2016)
- [RoMa: Robust Dense Feature Matching](https://mlsanity.com/paper/2305.15404/) (2023)
- [HPatches: A benchmark and evaluation of handcrafted and learned local descriptors](https://mlsanity.com/paper/1704.05939/) (2017)
- [Understanding image representations by measuring their equivariance and equivalence](https://mlsanity.com/paper/1411.5908/) (2014)
- [Working hard to know your neighbor's margins: Local descriptor learning loss](https://mlsanity.com/paper/1705.10872/) (2017)
- [ReDet: A Rotation-equivariant Detector for Aerial Object Detection](https://mlsanity.com/paper/2103.07733/) (2021)
- [DKM: Dense Kernelized Feature Matching for Geometry Estimation](https://mlsanity.com/paper/2202.00667/) (2022)
- [GLU-Net: Global-Local Universal Network for Dense Flow and Correspondences](https://mlsanity.com/paper/1912.05524/) (2019)
- [SOSNet: Second Order Similarity Regularization for Local Descriptor Learning](https://mlsanity.com/paper/1904.05019/) (2019)
- [MatchFormer: Interleaving Attention in Transformers for Feature Matching](https://mlsanity.com/paper/2203.09645/) (2022)
- [ALIKED: A Lighter Keypoint and Descriptor Extraction Network via Deformable Transformation](https://mlsanity.com/paper/2304.03608/) (2023)
- [Key.Net: Keypoint Detection by Handcrafted and Learned CNN Filters](https://mlsanity.com/paper/1904.00889/) (2019)
- [Learning Accurate Dense Correspondences and When to Trust Them](https://mlsanity.com/paper/2101.01710/) (2021)
- [XFeat: Accelerated Features for Lightweight Image Matching](https://mlsanity.com/paper/2404.19174/) (2024)
- [Learning to Match Features with Seeded Graph Matching Network](https://mlsanity.com/paper/2108.08771/) (2021)
- [PDC-Net+: Enhanced Probabilistic Dense Correspondence Network](https://mlsanity.com/paper/2109.13912/) (2021)

## Built on by (most cited first, 6 of 6)

- [DaD: Distilled Reinforcement Learning for Diverse Keypoint Detection](https://mlsanity.com/paper/2503.07347/) (2025)
- [Deep Learning Reforms Image Matching: A Survey and Outlook](https://mlsanity.com/paper/2506.04619/) (2025)
- [To Match or Not to Match: Revisiting Image Matching for Reliable Visual Place Recognition](https://mlsanity.com/paper/2504.06116/) (2025)
- [Who Handles Orientation? Investigating Invariance in Feature Matching](https://mlsanity.com/paper/2604.11809/) (2026)
- [CrossFeat: Bridging Imaging Modalities in Feature Descriptor Space](https://mlsanity.com/paper/2609.00272/) (2026)
- [RoES: Rotational Equivariant Selective-frequency Fusion for Multimodal Images](https://mlsanity.com/paper/2609.12497/) (2026)

## Abstract (arXiv)

We propose a way to train deep learning based keypoint descriptors that makes them approximately equivariant for locally affine transformations of the image plane. The main idea is to use the representation theory of GL(2) to generalize the recently introduced concept of steerers from rotations to affine transformations. Affine steerers give high control over how keypoint descriptions transform under image transformations. We demonstrate the potential of using this control for image matching. Finally, we propose a way to finetune keypoint descriptors with a set of steerers on upright images and obtain state-of-the-art results on several standard benchmarks. Code will be published at github.com/georg-bn/affine-steerers.