# Learning Rotation-Equivariant Features for Visual Correspondence

arXiv: https://arxiv.org/abs/2303.15472 · HTML: https://mlsanity.com/paper/2303.15472/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- Builds on 44 of its 74 references that are in the map.
- First posted on arXiv 25 Mar 2023.

## Builds on (most cited first, 30 of 44)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [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)
- [ORB-SLAM: a Versatile and Accurate Monocular SLAM System](https://mlsanity.com/paper/1502.00956/) (2015)
- [LoFTR: Detector-Free Local Feature Matching with Transformers](https://mlsanity.com/paper/2104.00680/) (2021)
- [General E(2)-Equivariant Steerable CNNs](https://mlsanity.com/paper/1911.08251/) (2019)
- [D2-Net: A Trainable CNN for Joint Detection and Description of Local Features](https://mlsanity.com/paper/1905.03561/) (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)
- [Steerable CNNs](https://mlsanity.com/paper/1612.08498/) (2016)
- [Harmonic Networks: Deep Translation and Rotation Equivariance](https://mlsanity.com/paper/1612.04642/) (2016)
- [HPatches: A benchmark and evaluation of handcrafted and learned local descriptors](https://mlsanity.com/paper/1704.05939/) (2017)
- [A General Theory of Equivariant CNNs on Homogeneous Spaces](https://mlsanity.com/paper/1811.02017/) (2018)
- [Image Matching across Wide Baselines: From Paper to Practice](https://mlsanity.com/paper/2003.01587/) (2020)
- [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)
- [Learning Steerable Filters for Rotation Equivariant CNNs](https://mlsanity.com/paper/1711.07289/) (2017)
- [LF-Net: Learning Local Features from Images](https://mlsanity.com/paper/1805.09662/) (2018)
- [SOSNet: Second Order Similarity Regularization for Local Descriptor Learning](https://mlsanity.com/paper/1904.05019/) (2019)
- [ASLFeat: Learning Local Features of Accurate Shape and Localization](https://mlsanity.com/paper/2003.10071/) (2020)
- [Hypercolumns for Object Segmentation and Fine-grained Localization](https://mlsanity.com/paper/1411.5752/) (2014)
- [Rotation equivariant vector field networks](https://mlsanity.com/paper/1612.09346/) (2016)
- [Oriented Response Networks](https://mlsanity.com/paper/1701.01833/) (2017)
- [Repeatability Is Not Enough: Learning Affine Regions via Discriminability](https://mlsanity.com/paper/1711.06704/) (2017)
- [Hyperpixel Flow: Semantic Correspondence with Multi-layer Neural Features](https://mlsanity.com/paper/1908.06537/) (2019)

## Built on by (most cited first, 23 of 23)

- [6DGS: 6D Pose Estimation from a Single Image and a 3D Gaussian Splatting Model](https://mlsanity.com/paper/2407.15484/) (2024)
- [Local Feature Matching Using Deep Learning: A Survey](https://mlsanity.com/paper/2401.17592/) (2024)
- [Steerers: A framework for rotation equivariant keypoint descriptors](https://mlsanity.com/paper/2312.02152/) (2023)
- [Weakly-supervised Camera Localization by Ground-to-satellite Image Registration](https://mlsanity.com/paper/2409.06471/) (2024)
- [Learning to Make Keypoints Sub-Pixel Accurate](https://mlsanity.com/paper/2407.11668/) (2024)
- [Learning Intra-view and Cross-view Geometric Knowledge for Stereo Matching](https://mlsanity.com/paper/2402.19270/) (2024)
- [Flopping for FLOPs: Leveraging equivariance for computational efficiency](https://mlsanity.com/paper/2502.05169/) (2025)
- [FRED: Towards a Full Rotation-Equivariance in Aerial Image Object Detection](https://mlsanity.com/paper/2401.06159/) (2023)
- [Deep Learning Reforms Image Matching: A Survey and Outlook](https://mlsanity.com/paper/2506.04619/) (2025)
- [Affine steerers for structured keypoint description](https://mlsanity.com/paper/2408.14186/) (2024)
- [RIDE: Self-Supervised Learning of Rotation-Equivariant Keypoint Detection and Invariant Description for Endoscopy](https://mlsanity.com/paper/2309.09563/) (2023)
- [Leveraging Semantic Cues from Foundation Vision Models for Enhanced Local Feature Correspondence](https://mlsanity.com/paper/2410.09533/) (2024)
- [Open-Pose 3D Zero-Shot Learning: Benchmark and Challenges](https://mlsanity.com/paper/2312.07039/) (2023)
- [Rigid Single-Slice-in-Volume registration via rotation-equivariant 2D/3D feature matching](https://mlsanity.com/paper/2410.18683/) (2024)
- [3D Equivariant Pose Regression via Direct Wigner-D Harmonics Prediction](https://mlsanity.com/paper/2411.00543/) (2024)
- [RotBench: Evaluating Multimodal Large Language Models on Identifying Image Rotation](https://mlsanity.com/paper/2508.13968/) (2025)
- [SplatPose: Geometry-Aware 6-DoF Pose Estimation from Single RGB Image via 3D Gaussian Splatting](https://mlsanity.com/paper/2503.05174/) (2025)
- [Who Handles Orientation? Investigating Invariance in Feature Matching](https://mlsanity.com/paper/2604.11809/) (2026)
- [REMM:Rotation-Equivariant Framework for End-to-End Multimodal Image Matching](https://mlsanity.com/paper/2407.11637/) (2024)
- [Cross-Modality Feature Fusion Based on Structured State Space Duality for Multimodal Image Registration Network](https://mlsanity.com/paper/2606.03341/) (2026)
- [REDI-Match: Rotation-Equivariant Distillation for Efficient and Robust Dense Matching](https://mlsanity.com/paper/2606.24330/) (2026)
- [Robust structure from motion for aerial-ground images via detector-free feature matching and multi-view track refinement](https://mlsanity.com/paper/2608.15251/) (2026)
- [RoES: Rotational Equivariant Selective-frequency Fusion for Multimodal Images](https://mlsanity.com/paper/2609.12497/) (2026)

## Abstract (arXiv)

Extracting discriminative local features that are invariant to imaging variations is an integral part of establishing correspondences between images. In this work, we introduce a self-supervised learning framework to extract discriminative rotation-invariant descriptors using group-equivariant CNNs. Thanks to employing group-equivariant CNNs, our method effectively learns to obtain rotation-equivariant features and their orientations explicitly, without having to perform sophisticated data augmentations. The resultant features and their orientations are further processed by group aligning, a novel invariant mapping technique that shifts the group-equivariant features by their orientations along the group dimension. Our group aligning technique achieves rotation-invariance without any collapse of the group dimension and thus eschews loss of discriminability. The proposed method is trained end-to-end in a self-supervised manner, where we use an orientation alignment loss for the orientation estimation and a contrastive descriptor loss for robust local descriptors to geometric/photometric variations. Our method demonstrates state-of-the-art matching accuracy among existing rotation-invariant descriptors under varying rotation and also shows competitive results when transferred to the task of keypoint matching and camera pose estimation.