# Quadric Representations for LiDAR Odometry, Mapping and Localization

arXiv: https://arxiv.org/abs/2304.14190 · HTML: https://mlsanity.com/paper/2304.14190/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 49 references that are in the map.
- First posted on arXiv 27 Apr 2023.

## Builds on (most cited first, 20 of 20)

- [ORB-SLAM: a Versatile and Accurate Monocular SLAM System](https://mlsanity.com/paper/1502.00956/) (2015)
- [ORB-SLAM3: An Accurate Open-Source Library for Visual, Visual-Inertial and Multi-Map SLAM](https://mlsanity.com/paper/2007.11898/) (2020)
- [ORB-SLAM2: an Open-Source SLAM System for Monocular, Stereo and RGB-D Cameras](https://mlsanity.com/paper/1610.06475/) (2016)
- [VINS-Mono: A Robust and Versatile Monocular Visual-Inertial State Estimator](https://mlsanity.com/paper/1708.03852/) (2017)
- [LIO-SAM: Tightly-coupled Lidar Inertial Odometry via Smoothing and Mapping](https://mlsanity.com/paper/2007.00258/) (2020)
- [SpinNet: Learning a General Surface Descriptor for 3D Point Cloud Registration](https://mlsanity.com/paper/2011.12149/) (2020)
- [LO-Net: Deep Real-time Lidar Odometry](https://mlsanity.com/paper/1904.08242/) (2019)
- [F-LOAM: Fast LiDAR Odometry And Mapping](https://mlsanity.com/paper/2107.00822/) (2021)
- [IMLS-SLAM: scan-to-model matching based on 3D data](https://mlsanity.com/paper/1802.08633/) (2018)
- [CT-ICP: Real-time Elastic LiDAR Odometry with Loop Closure](https://mlsanity.com/paper/2109.12979/) (2021)
- [Rotational Projection Statistics for 3D Local Surface Description and Object Recognition](https://mlsanity.com/paper/1304.3192/) (2013)
- [Direct LiDAR Odometry: Fast Localization with Dense Point Clouds](https://mlsanity.com/paper/2110.00605/) (2021)
- [BALM: Bundle Adjustment for Lidar Mapping](https://mlsanity.com/paper/2010.08215/) (2020)
- [MULLS: Versatile LiDAR SLAM via Multi-metric Linear Least Square](https://mlsanity.com/paper/2102.03771/) (2021)
- [Range Image-based LiDAR Localization for Autonomous Vehicles](https://mlsanity.com/paper/2105.12121/) (2021)
- [LodoNet: A Deep Neural Network with 2D Keypoint Matchingfor 3D LiDAR Odometry Estimation](https://mlsanity.com/paper/2009.00164/) (2020)
- [UrbanLoco: A Full Sensor Suite Dataset for Mapping and Localization in Urban Scenes](https://mlsanity.com/paper/1912.09513/) (2019)
- [Globally Consistent 3D LiDAR Mapping with GPU-accelerated GICP Matching Cost Factors](https://mlsanity.com/paper/2109.07073/) (2021)
- [Efficient LiDAR Odometry for Autonomous Driving](https://mlsanity.com/paper/2104.10879/) (2021)
- [CURL: Continuous, Ultra-compact Representation for LiDAR](https://mlsanity.com/paper/2205.06059/) (2022)

## Built on by (most cited first, 9 of 9)

- [Q-SLAM: Quadric Representations for Monocular SLAM](https://mlsanity.com/paper/2403.08125/) (2024)
- [ProtoDepth: Unsupervised Continual Depth Completion with Prototypes](https://mlsanity.com/paper/2503.12745/) (2025)
- [Extending Foundational Monocular Depth Estimators to Fisheye Cameras with Calibration Tokens](https://mlsanity.com/paper/2508.04928/) (2025)
- [Radar-Guided Polynomial Fitting for Metric Depth Estimation](https://mlsanity.com/paper/2503.17182/) (2025)
- [ETA: Energy-based Test-time Adaptation for Depth Completion](https://mlsanity.com/paper/2508.05989/) (2025)
- [SHOW3D: Capturing Scenes of 3D Hands and Objects in the Wild](https://mlsanity.com/paper/2603.28760/) (2026)
- [QuadricsReg: Large-Scale Point Cloud Registration using Quadric Primitives](https://mlsanity.com/paper/2412.02998/) (2024)
- [Ego-Exo 3D Hand Tracking in the Wild with a Mobile Multi-Camera Rig](https://mlsanity.com/paper/2510.02601/) (2025)
- [A Real-Time Multi-Model Parametric Representation of Point Clouds](https://mlsanity.com/paper/2509.14773/) (2025)

## Abstract (arXiv)

Current LiDAR odometry, mapping and localization methods leverage point-wise representations of 3D scenes and achieve high accuracy in autonomous driving tasks. However, the space-inefficiency of methods that use point-wise representations limits their development and usage in practical applications. In particular, scan-submap matching and global map representation methods are restricted by the inefficiency of nearest neighbor searching (NNS) for large-volume point clouds. To improve space-time efficiency, we propose a novel method of describing scenes using quadric surfaces, which are far more compact representations of 3D objects than conventional point clouds. In contrast to point cloud-based methods, our quadric representation-based method decomposes a 3D scene into a collection of sparse quadric patches, which improves storage efficiency and avoids the slow point-wise NNS process. Our method first segments a given point cloud into patches and fits each of them to a quadric implicit function. Each function is then coupled with other geometric descriptors of the patch, such as its center position and covariance matrix. Collectively, these patch representations fully describe a 3D scene, which can be used in place of the original point cloud and employed in LiDAR odometry, mapping and localization algorithms. We further design a novel incremental growing method for quadric representations, which eliminates the need to repeatedly re-fit quadric surfaces from the original point cloud. Extensive odometry, mapping and localization experiments on large-volume point clouds in the KITTI and UrbanLoco datasets demonstrate that our method maintains low latency and memory utility while achieving competitive, and even superior, accuracy.