# RING#: PR-by-PE Global Localization with Roto-translation Equivariant Gram Learning

arXiv: https://arxiv.org/abs/2409.00206 · HTML: https://mlsanity.com/paper/2409.00206/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 56 of its 99 references that are in the map.
- First posted on arXiv 30 Aug 2024.

## Builds on (most cited first, 30 of 56)

- [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)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [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)
- [BEVFormer: Learning Bird's-Eye-View Representation from Multi-Camera Images via Spatiotemporal Transformers](https://mlsanity.com/paper/2203.17270/) (2022)
- [Lift, Splat, Shoot: Encoding Images From Arbitrary Camera Rigs by Implicitly Unprojecting to 3D](https://mlsanity.com/paper/2008.05711/) (2020)
- [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)
- [NetVLAD: CNN architecture for weakly supervised place recognition](https://mlsanity.com/paper/1511.07247/) (2015)
- [BEVDet: High-performance Multi-camera 3D Object Detection in Bird-Eye-View](https://mlsanity.com/paper/2112.11790/) (2021)
- [DETR3D: 3D Object Detection from Multi-view Images via 3D-to-2D Queries](https://mlsanity.com/paper/2110.06922/) (2021)
- [BEVDepth: Acquisition of Reliable Depth for Multi-view 3D Object Detection](https://mlsanity.com/paper/2206.10092/) (2022)
- [From Coarse to Fine: Robust Hierarchical Localization at Large Scale](https://mlsanity.com/paper/1812.03506/) (2018)
- [PETR: Position Embedding Transformation for Multi-View 3D Object Detection](https://mlsanity.com/paper/2203.05625/) (2022)
- [Fine-tuning CNN Image Retrieval with No Human Annotation](https://mlsanity.com/paper/1711.02512/) (2017)
- [General E(2)-Equivariant Steerable CNNs](https://mlsanity.com/paper/1911.08251/) (2019)
- [BEVFormer v2: Adapting Modern Image Backbones to Bird's-Eye-View Recognition via Perspective Supervision](https://mlsanity.com/paper/2211.10439/) (2022)
- [Patch-NetVLAD: Multi-Scale Fusion of Locally-Global Descriptors for Place Recognition](https://mlsanity.com/paper/2103.01486/) (2021)
- [PointNetVLAD: Deep Point Cloud Based Retrieval for Large-Scale Place Recognition](https://mlsanity.com/paper/1804.03492/) (2018)
- [COTR: Correspondence Transformer for Matching Across Images](https://mlsanity.com/paper/2103.14167/) (2021)
- [AnyLoc: Towards Universal Visual Place Recognition](https://mlsanity.com/paper/2308.00688/) (2023)
- [MixVPR: Feature Mixing for Visual Place Recognition](https://mlsanity.com/paper/2303.02190/) (2023)
- [The Oxford Radar RobotCar Dataset: A Radar Extension to the Oxford RobotCar Dataset](https://mlsanity.com/paper/1909.01300/) (2019)
- [MatchFormer: Interleaving Attention in Transformers for Feature Matching](https://mlsanity.com/paper/2203.09645/) (2022)
- [MinkLoc3D: Point Cloud Based Large-Scale Place Recognition](https://mlsanity.com/paper/2011.04530/) (2020)
- [Self-supervising Fine-grained Region Similarities for Large-scale Image Localization](https://mlsanity.com/paper/2006.03926/) (2020)
- [TransVPR: Transformer-based place recognition with multi-level attention aggregation](https://mlsanity.com/paper/2201.02001/) (2022)

## Built on by (most cited first, 5 of 5)

- [VGGT-MPR: VGGT-Enhanced Multimodal Place Recognition in Autonomous Driving Environments](https://mlsanity.com/paper/2602.19735/) (2026)
- [VLM-Loc: Localization in Point Cloud Maps via Vision-Language Models](https://mlsanity.com/paper/2603.09826/) (2026)
- [BEVDiffLoc: End-to-End LiDAR Global Localization in BEV View based on Diffusion Model](https://mlsanity.com/paper/2503.11372/) (2025)
- [UniMPR: A Unified Framework for Multimodal Place Recognition with Heterogeneous Sensor Configurations](https://mlsanity.com/paper/2512.18279/) (2025)
- [RoSe-SLAM: Robust Semantic-Aware Gaussian Splatting SLAM from Dynamic Monocular Videos](https://mlsanity.com/paper/2608.29003/) (2026)

## Abstract (arXiv)

Global localization using onboard perception sensors, such as cameras and LiDARs, is crucial in autonomous driving and robotics applications when GPS signals are unreliable. Most approaches achieve global localization by sequential place recognition (PR) and pose estimation (PE). Some methods train separate models for each task, while others employ a single model with dual heads, trained jointly with separate task-specific losses. However, the accuracy of localization heavily depends on the success of place recognition, which often fails in scenarios with significant changes in viewpoint or environmental appearance. Consequently, this renders the final pose estimation of localization ineffective. To address this, we introduce a new paradigm, PR-by-PE localization, which bypasses the need for separate place recognition by directly deriving it from pose estimation. We propose RING#, an end-to-end PR-by-PE localization network that operates in the bird's-eye-view (BEV) space, compatible with both vision and LiDAR sensors. RING# incorporates a novel design that learns two equivariant representations from BEV features, enabling globally convergent and computationally efficient pose estimation. Comprehensive experiments on the NCLT and Oxford datasets show that RING# outperforms state-of-the-art methods in both vision and LiDAR modalities, validating the effectiveness of the proposed approach. The code will be publicly released.