QuadricsReg: Large-Scale Point Cloud Registration
using Semantic Quadric Primitives

Ji Wu, Huai Yu, Shu Han, Xi-Meng Cai, Ming-Feng Wang, Wen Yang, Gui-Song Xia
CAPTAIN Robotics Group, Wuhan University

Paper arXiv Code

Global point cloud registration using QuadricsReg. The raw point clouds are collected by a UGV, a UAV, and a handheld platform equipped with different LiDAR sensors in a roof garden. Despite challenges of massive data, structural diversity, and wide viewpoint variations, QuadricsReg effectively aligns point clouds in overlapping regions and enables cross-platform mapping.

Abstract

Designing an effective and scalable scene primitive representation is fundamental for large-scale point cloud registration. Existing studies that predominantly rely on dense point clouds or single-type geometric primitives struggle to scale to scenes characterized by massive data volume, structural diversity, and wide viewpoint variations. To address these, this paper introduces QuadricsReg, a novel point cloud registration framework based on quadric primitives for large-scale environments. We compactly model diverse scene structures within a unified semantic quadric formulation, achieving high compression while preserving geometric richness and discriminability. This representation enables efficient quadric matching initialization via intrinsic similarity and robust correspondence pruning by maximizing geometric consistency in a multi-level graph, ensuring reliable associations even under large viewpoint variations. Furthermore, we design a factor graph based on degeneracy-aware quadric residual to estimate the transformation, ensuring accurate alignment in heterogeneous scenes. We evaluate QuadricsReg on 5 public datasets, where its exceptional registration performance with low overhead demonstrates strong scalability for large-scale scenarios. With a compact representation of ~29.5 KB/scan on KITTI, nearly 100% registration success rate is achieved for point cloud pairs within 10 m. Real-world testing on the self-collected dataset further validates its robustness and generalization ability across different LiDAR sensors and robot platforms.

Scene Representation by Quadrics

Compared to points, lines, and planes, quadrics offer a more expressive and compact scene representation. With only 10 parameters, a single quadric can model 17 common shape types (e.g., planes, cylinders, ellipsoids, cones), capturing richer geometric structures while maintaining high compression. This makes quadrics particularly suited for large-scale registration where both efficiency and discriminability are critical.

Comparison of Different Representations

Quadric Representation of Pantheon in Italy

Quadric Representation of LiDAR Point Clouds

Registration by QuadricsReg

Benefiting from the compact, expressive, and discriminative quadric representation, QuadricsReg establishes robust correspondences via semantic-geometric consistency and estimates accurate transformations through degeneracy-aware factor-graph optimization, achieving exceptional performance across 5 public datasets and 5 LiDAR types, with real-world validation on heterogeneous platforms (UGV, UAV, handheld) in diverse environments.

Overview of Registration Results

Previous Next

Registration of LiDAR Point Clouds

Real-World Applications

QuadricsReg supports practical applications including loop closure detection and multi-session map merging across heterogeneous platforms (UGV, UAV, handheld) equipped with different LiDAR sensors, enabling efficient long-term operation in large-scale environments.

Overview of the Self-Collected Hetero-Reg Dataset

Loop Closure

Multi-session Mapping

References

1. Quatro++: Robust global registration exploiting ground segmentation for loop closing in LiDAR SLAM [paper]
   Lim, Hyungtae and Kim, Beomsoo and Kim, Daebeom and Mason Lee, Eungchang and Myung, Hyun
   The International Journal of Robotics Research, 2024.
2. G3Reg: Pyramid Graph-Based Global Registration Using Gaussian Ellipsoid Model [paper]
   Qiao, Zhijian and Yu, Zehuan and Jiang, Binqian and Yin, Huan and Shen, Shaojie
   IEEE Transactions on Automation Science and Engineering, 2024.
3. QuadricsNet: Learning Concise Representation for Geometric Primitives in Point Clouds [paper]
   Wu, Ji and Yu, Huai and Yang, Wen and Xia, Gui-Song
   IEEE International Conference on Robotics and Automation (ICRA), 2024.
4. Unified Representation of Geometric Primitives for Graph-SLAM Optimization Using Decomposed Quadrics [paper]
   Zhen, Weikun and Yu, Huai and Hu, Yaoyu and Scherer, Sebastian
   International Conference on Robotics and Automation (ICRA), 2022.
5. TEASER: Fast and Certifiable Point Cloud Registration [paper]
   Yang, Heng and Shi, Jingnan and Carlone, Luca
   IEEE Transactions on Robotics, 2021.
6. LIO-SAM: Tightly-coupled Lidar Inertial Odometry via Smoothing and Mapping [paper]
   Shan, Tixiao and Englot, Brendan and Meyers, Drew and Wang, Wei and Ratti, Carlo and Rus Daniela
   IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2020.

BibTeX

@ARTICLE{wu2026quadricsreg,
  author  = {Ji Wu and Huai Yu and Shu Han and Xi-Meng Cai and Ming-Feng Wang and Wen Yang and Gui-Song Xia},
  title   = {QuadricsReg: Large-Scale Point Cloud Registration using Semantic Quadric Primitives},
  journal = {IEEE Transactions on Robotics},
  year    = {2026},
  volume  = {42},
  number  = {},
  pages   = {1961-1981}
}

@INPROCEEDINGS{wu2024quadricsnet,
  author    = {Wu, Ji and Yu, Huai and Yang, Wen and Xia, Gui-Song},
  booktitle = {IEEE International Conference on Robotics and Automation (ICRA)},
  title     = {QuadricsNet: Learning Concise Representation for Geometric Primitives in Point Clouds},
  year      = {2024},
  pages     = {4060-4066}
}