# Leveraging Equivariant Features for Absolute Pose Regression

arXiv: https://arxiv.org/abs/2204.02163 · HTML: https://mlsanity.com/paper/2204.02163/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 65 references that are in the map.
- First posted on arXiv 5 Apr 2022.

## Builds on (most cited first, 30 of 32)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [PoseCNN: A Convolutional Neural Network for 6D Object Pose Estimation in Cluttered Scenes](https://mlsanity.com/paper/1711.00199/) (2017)
- [Spherical CNNs](https://mlsanity.com/paper/1801.10130/) (2018)
- [General E(2)-Equivariant Steerable CNNs](https://mlsanity.com/paper/1911.08251/) (2019)
- [Steerable CNNs](https://mlsanity.com/paper/1612.08498/) (2016)
- [A General Theory of Equivariant CNNs on Homogeneous Spaces](https://mlsanity.com/paper/1811.02017/) (2018)
- [Geometric Loss Functions for Camera Pose Regression with Deep Learning](https://mlsanity.com/paper/1704.00390/) (2017)
- [Pix2Pose: Pixel-Wise Coordinate Regression of Objects for 6D Pose Estimation](https://mlsanity.com/paper/1908.07433/) (2019)
- [T-LESS: An RGB-D Dataset for 6D Pose Estimation of Texture-less Objects](https://mlsanity.com/paper/1701.05498/) (2017)
- [ReDet: A Rotation-equivariant Detector for Aerial Object Detection](https://mlsanity.com/paper/2103.07733/) (2021)
- [Understanding the Limitations of CNN-based Absolute Camera Pose Regression](https://mlsanity.com/paper/1903.07504/) (2019)
- [Geometry-Aware Learning of Maps for Camera Localization](https://mlsanity.com/paper/1712.03342/) (2017)
- [EPOS: Estimating 6D Pose of Objects with Symmetries](https://mlsanity.com/paper/2004.00605/) (2020)
- [GDRNPP: A Geometry-guided and Fully Learning-based Object Pose Estimator](https://mlsanity.com/paper/2102.12145/) (2021)
- [On Translation Invariance in CNNs: Convolutional Layers can Exploit Absolute Spatial Location](https://mlsanity.com/paper/2003.07064/) (2020)
- [Image-based localization using LSTMs for structured feature correlation](https://mlsanity.com/paper/1611.07890/) (2016)
- [Modelling Uncertainty in Deep Learning for Camera Relocalization](https://mlsanity.com/paper/1509.05909/) (2015)
- [Learning Multi-Scene Absolute Pose Regression with Transformers](https://mlsanity.com/paper/2103.11468/) (2021)
- [Segmentation-driven 6D Object Pose Estimation](https://mlsanity.com/paper/1812.02541/) (2018)
- [AtLoc: Attention Guided Camera Localization](https://mlsanity.com/paper/1909.03557/) (2019)
- [Equivariant Point Network for 3D Point Cloud Analysis](https://mlsanity.com/paper/2103.14147/) (2021)
- [Image-based Localization using Hourglass Networks](https://mlsanity.com/paper/1703.07971/) (2017)
- [Deep Roto-Translation Scattering for Object Classification](https://mlsanity.com/paper/1412.8659/) (2014)
- [Survey on Deep Neural Networks in Speech and Vision Systems](https://mlsanity.com/paper/1908.07656/) (2019)
- [Position, Padding and Predictions: A Deeper Look at Position Information in CNNs](https://mlsanity.com/paper/2101.12322/) (2021)
- [Rotation Equivariant Siamese Networks for Tracking](https://mlsanity.com/paper/2012.13078/) (2020)

## Built on by (most cited first, 17 of 17)

- [Neural Refinement for Absolute Pose Regression with Feature Synthesis](https://mlsanity.com/paper/2303.10087/) (2023)
- [A Survey on Deep Learning-Based Monocular Spacecraft Pose Estimation: Current State, Limitations and Prospects](https://mlsanity.com/paper/2305.07348/) (2023)
- [Graph-CoVis: GNN-based Multi-view Panorama Global Pose Estimation](https://mlsanity.com/paper/2304.13201/) (2023)
- [Loss it right: Euclidean and Riemannian Metrics in Learning-based Visual Odometry](https://mlsanity.com/paper/2401.05396/) (2023)
- [Self-Supervised Learning for Place Representation Generalization across Appearance Changes](https://mlsanity.com/paper/2303.02370/) (2023)
- [Monocular visual simultaneous localization and mapping: (r)evolution from geometry to deep learning-based pipelines](https://mlsanity.com/paper/2503.02955/) (2025)
- [FastPose-ViT: A Vision Transformer for Real-Time Spacecraft Pose Estimation](https://mlsanity.com/paper/2512.09792/) (2025)
- [Fast and Lightweight Scene Regressor for Camera Relocalization](https://mlsanity.com/paper/2212.01830/) (2022)
- [Densely Connected G-invariant Deep Neural Networks with Signed Permutation Representations](https://mlsanity.com/paper/2303.04614/) (2023)
- [Conditional Variational Autoencoders for Probabilistic Pose Regression](https://mlsanity.com/paper/2410.04989/) (2024)
- [NaVIP: An Image-Centric Indoor Navigation Solution for Visually Impaired People](https://mlsanity.com/paper/2410.18109/) (2024)
- [Activating Self-Attention for Multi-Scene Absolute Pose Regression](https://mlsanity.com/paper/2411.01443/) (2024)
- [Impact of Disentanglement on Pruning Neural Networks](https://mlsanity.com/paper/2307.09994/) (2023)
- [Robust Visual Localization via Semantic-Guided Multi-Scale Transformer](https://mlsanity.com/paper/2506.08526/) (2025)
- [ThermalLoc: A Vision Transformer-Based Approach for Robust Thermal Camera Relocalization in Large-Scale Environments](https://mlsanity.com/paper/2506.18268/) (2025)
- [Equivariant symmetry-aware head pose estimation for fetal MRI](https://mlsanity.com/paper/2512.04890/) (2025)
- [Cross-Modal RGB-D Fusion Transformer for 6D Pose Estimation of Non-Cooperative Spacecraft with Stereo-Derived Depth](https://mlsanity.com/paper/2605.08592/) (2026)

## Abstract (arXiv)

While end-to-end approaches have achieved state-of-the-art performance in many perception tasks, they are not yet able to compete with 3D geometry-based methods in pose estimation. Moreover, absolute pose regression has been shown to be more related to image retrieval. As a result, we hypothesize that the statistical features learned by classical Convolutional Neural Networks do not carry enough geometric information to reliably solve this inherently geometric task. In this paper, we demonstrate how a translation and rotation equivariant Convolutional Neural Network directly induces representations of camera motions into the feature space. We then show that this geometric property allows for implicitly augmenting the training data under a whole group of image plane-preserving transformations. Therefore, we argue that directly learning equivariant features is preferable than learning data-intensive intermediate representations. Comprehensive experimental validation demonstrates that our lightweight model outperforms existing ones on standard datasets.