# RING++: Roto-translation Invariant Gram for Global Localization on a Sparse Scan Map

arXiv: https://arxiv.org/abs/2210.05984 · HTML: https://mlsanity.com/paper/2210.05984/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 78 references that are in the map.
- First posted on arXiv 12 Oct 2022.

## Builds on (most cited first, 27 of 27)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [VoxelNet: End-to-End Learning for Point Cloud Based 3D Object Detection](https://mlsanity.com/paper/1711.06396/) (2017)
- [NetVLAD: CNN architecture for weakly supervised place recognition](https://mlsanity.com/paper/1511.07247/) (2015)
- [Open3D: A Modern Library for 3D Data Processing](https://mlsanity.com/paper/1801.09847/) (2018)
- [Fine-tuning CNN Image Retrieval with No Human Annotation](https://mlsanity.com/paper/1711.02512/) (2017)
- [PointNetVLAD: Deep Point Cloud Based Retrieval for Large-Scale Place Recognition](https://mlsanity.com/paper/1804.03492/) (2018)
- [FAST-LIO2: Fast Direct LiDAR-inertial Odometry](https://mlsanity.com/paper/2107.06829/) (2021)
- [The Oxford Radar RobotCar Dataset: A Radar Extension to the Oxford RobotCar Dataset](https://mlsanity.com/paper/1909.01300/) (2019)
- [MinkLoc3D: Point Cloud Based Large-Scale Place Recognition](https://mlsanity.com/paper/2011.04530/) (2020)
- [OverlapNet: Loop Closing for LiDAR-based SLAM](https://mlsanity.com/paper/2105.11344/) (2021)
- [Scan Context++: Structural Place Recognition Robust to Rotation and Lateral Variations in Urban Environments](https://mlsanity.com/paper/2109.13494/) (2021)
- [LCDNet: Deep Loop Closure Detection and Point Cloud Registration for LiDAR SLAM](https://mlsanity.com/paper/2103.05056/) (2021)
- [MinkLoc++: Lidar and Monocular Image Fusion for Place Recognition](https://mlsanity.com/paper/2104.05327/) (2021)
- [LiDAR Iris for Loop-Closure Detection](https://mlsanity.com/paper/1912.03825/) (2019)
- [Locus: LiDAR-based Place Recognition using Spatiotemporal Higher-Order Pooling](https://mlsanity.com/paper/2011.14497/) (2020)
- [AdaFusion: Visual-LiDAR Fusion with Adaptive Weights for Place Recognition](https://mlsanity.com/paper/2111.11739/) (2021)
- [DiSCO: Differentiable Scan Context with Orientation](https://mlsanity.com/paper/2010.10949/) (2020)
- [EgoNN: Egocentric Neural Network for Point Cloud Based 6DoF Relocalization at the City Scale](https://mlsanity.com/paper/2110.12486/) (2021)
- [SSC: Semantic Scan Context for Large-Scale Place Recognition](https://mlsanity.com/paper/2107.00382/) (2021)
- [PCAM: Product of Cross-Attention Matrices for Rigid Registration of Point Clouds](https://mlsanity.com/paper/2110.01269/) (2021)
- [LocNet: Global localization in 3D point clouds for mobile vehicles](https://mlsanity.com/paper/1712.02165/) (2017)
- [CORAL: Colored structural representation for bi-modal place recognition](https://mlsanity.com/paper/2011.10934/) (2020)
- [MinkLoc3D-SI: 3D LiDAR place recognition with sparse convolutions, spherical coordinates, and intensity](https://mlsanity.com/paper/2112.06539/) (2021)
- [One RING to Rule Them All: Radon Sinogram for Place Recognition, Orientation and Translation Estimation](https://mlsanity.com/paper/2204.07992/) (2022)
- [Translation Invariant Global Estimation of Heading Angle Using Sinogram of LiDAR Point Cloud](https://mlsanity.com/paper/2203.00924/) (2022)

## Built on by (most cited first, 29 of 29)

- [General Place Recognition Survey: Towards Real-World Autonomy](https://mlsanity.com/paper/2405.04812/) (2024)
- [G3Reg: Pyramid Graph-based Global Registration using Gaussian Ellipsoid Model](https://mlsanity.com/paper/2308.11573/) (2023)
- [GOReloc: Graph-based Object-Level Relocalization for Visual SLAM](https://mlsanity.com/paper/2408.07917/) (2024)
- [GSPR: Multimodal Place Recognition Using 3D Gaussian Splatting for Autonomous Driving](https://mlsanity.com/paper/2410.00299/) (2024)
- [ForestLPR: LiDAR Place Recognition in Forests Attentioning Multiple BEV Density Images](https://mlsanity.com/paper/2503.04475/) (2025)
- [RING#: PR-by-PE Global Localization with Roto-translation Equivariant Gram Learning](https://mlsanity.com/paper/2409.00206/) (2024)
- [LiDAR-VGGT: Cross-Modal Coarse-to-Fine Fusion for Globally Consistent and Metric-Scale Dense Mapping](https://mlsanity.com/paper/2511.01186/) (2025)
- [Leveraging BEV Representation for 360-degree Visual Place Recognition](https://mlsanity.com/paper/2305.13814/) (2023)
- [HOTFLoc++: End-to-End Hierarchical LiDAR Place Recognition, Re-Ranking, and 6-DoF Metric Localisation in Forests](https://mlsanity.com/paper/2511.09170/) (2025)
- [A Minimal Subset Approach for Informed Keyframe Sampling in Large-Scale SLAM](https://mlsanity.com/paper/2501.01791/) (2025)
- [Polar Perspectives: Evaluating 2-D LiDAR Projections for Robust Place Recognition with Visual Foundation Models](https://mlsanity.com/paper/2512.02897/) (2025)
- [VNI-Net: Vector Neurons-based Rotation-Invariant Descriptor for LiDAR Place Recognition](https://mlsanity.com/paper/2308.12870/) (2023)
- [TreeLoc: 6-DoF LiDAR Global Localization in Forests via Inter-Tree Geometric Matching](https://mlsanity.com/paper/2602.01501/) (2026)
- [PROBE: Probabilistic Occupancy BEV Encoding with Analytical Translation Robustness for 3D Place Recognition](https://mlsanity.com/paper/2603.05965/) (2026)
- [LEADER: Learning Reliable Local-to-Global Correspondences for LiDAR Relocalization](https://mlsanity.com/paper/2604.11355/) (2026)
- [The City that Never Settles: Simulation-based LiDAR Dataset for Long-Term Place Recognition Under Extreme Structural Changes](https://mlsanity.com/paper/2505.05076/) (2025)
- [Multi-Representation Geometric Hierarchy Fusion: An Implicit-Submap Driven Framework for Resilient 3D Place Recognition](https://mlsanity.com/paper/2506.14243/) (2025)
- [A Pseudo Global Fusion Paradigm-Based Cross-View Network for LiDAR-Based Place Recognition](https://mlsanity.com/paper/2508.08917/) (2025)
- [GMOR: A Lightweight Robust Point Cloud Registration Framework via Geometric Maximum Overlapping](https://mlsanity.com/paper/2508.17427/) (2025)
- [DCReg: Decoupled Characterization for Efficient Degenerate LiDAR Registration](https://mlsanity.com/paper/2509.06285/) (2025)
- [Gaussian Semantic Field for One-shot LiDAR Global Localization](https://mlsanity.com/paper/2510.12101/) (2025)
- [Calibrated Keyframe-Segment Selection for Descriptor-Agnostic LiDAR Loop Closure in Repetitive Environments](https://mlsanity.com/paper/2512.09447/) (2025)
- [From Single Scan to Sequential Consistency: A New Paradigm for LIDAR Relocalization](https://mlsanity.com/paper/2602.03198/) (2026)
- [MAG-VLAQ: Multi-modal Aerial-Ground Query Aggregation for Cross-View Place Recognition](https://mlsanity.com/paper/2605.09418/) (2026)
- [PROBE-X: Learning-Free Cross-FOV Place Recognition](https://mlsanity.com/paper/2607.06782/) (2026)
- [InLiER: Learning-Free Heterogeneous LiDAR Place Recognition via Intermediate Mixed-Radix Structural Keypoint Tokenization](https://mlsanity.com/paper/2607.16862/) (2026)
- [DTIF: Robust Loop Closure Detection via Delaunay Triangle Topology in Complex Forests](https://mlsanity.com/paper/2607.21138/) (2026)
- [UpDown-SC: Gravity-Canonicalized Dual-Envelope Scan Context for Indoor LiDAR Place Recognition](https://mlsanity.com/paper/2609.29118/) (2026)
- [Temporal-Aware Fusion for Robust Outdoor LiDAR Localization](https://mlsanity.com/paper/2609.36432/) (2026)

## Abstract (arXiv)

Global localization plays a critical role in many robot applications. LiDAR-based global localization draws the community's focus with its robustness against illumination and seasonal changes. To further improve the localization under large viewpoint differences, we propose RING++ which has roto-translation invariant representation for place recognition, and global convergence for both rotation and translation estimation. With the theoretical guarantee, RING++ is able to address the large viewpoint difference using a lightweight map with sparse scans. In addition, we derive sufficient conditions of feature extractors for the representation preserving the roto-translation invariance, making RING++ a framework applicable to generic multi-channel features. To the best of our knowledge, this is the first learning-free framework to address all subtasks of global localization in the sparse scan map. Validations on real-world datasets show that our approach demonstrates better performance than state-of-the-art learning-free methods, and competitive performance with learning-based methods. Finally, we integrate RING++ into a multi-robot/session SLAM system, performing its effectiveness in collaborative applications.