# Simultaneous Localisation and Mapping with Quadric Surfaces

arXiv: https://arxiv.org/abs/2203.08040 · HTML: https://mlsanity.com/paper/2203.08040/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 40 references that are in the map.
- First posted on arXiv 15 Mar 2022.

## Builds on (most cited first, 8 of 8)

- [ORB-SLAM2: an Open-Source SLAM System for Monocular, Stereo and RGB-D Cameras](https://mlsanity.com/paper/1610.06475/) (2016)
- [Direct Sparse Odometry](https://mlsanity.com/paper/1607.02565/) (2016)
- [QuadricSLAM: Dual Quadrics from Object Detections as Landmarks in Object-oriented SLAM](https://mlsanity.com/paper/1804.04011/) (2018)
- [NodeSLAM: Neural Object Descriptors for Multi-View Shape Reconstruction](https://mlsanity.com/paper/2004.04485/) (2020)
- [PL-SLAM: a Stereo SLAM System through the Combination of Points and Line Segments](https://mlsanity.com/paper/1705.09479/) (2017)
- [Structure Aware SLAM using Quadrics and Planes](https://mlsanity.com/paper/1804.09111/) (2018)
- [Real-Time Monocular Object-Model Aware Sparse SLAM](https://mlsanity.com/paper/1809.09149/) (2018)
- [Unified Representation of Geometric Primitives for Graph-SLAM Optimization Using Decomposed Quadrics](https://mlsanity.com/paper/2108.08957/) (2021)

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

- [6DGS: 6D Pose Estimation from a Single Image and a 3D Gaussian Splatting Model](https://mlsanity.com/paper/2407.15484/) (2024)
- [SuperPrimitive: Scene Reconstruction at a Primitive Level](https://mlsanity.com/paper/2312.05889/) (2023)
- [TextSLAM: Visual SLAM with Semantic Planar Text Features](https://mlsanity.com/paper/2305.10029/) (2023)
- [Temporally Consistent Object 6D Pose Estimation for Robot Control](https://mlsanity.com/paper/2605.02708/) (2026)
- [Stable and Scalable Bundle Adjustment of Holistic 3D Structures](https://mlsanity.com/paper/2609.04026/) (2026)

## Abstract (arXiv)

There are many possibilities for how to represent the map in simultaneous localisation and mapping (SLAM). While sparse, keypoint-based SLAM systems have achieved impressive levels of accuracy and robustness, their maps may not be suitable for many robotic tasks. Dense SLAM systems are capable of producing dense reconstructions, but can be computationally expensive and, like sparse systems, lack higher-level information about the structure of a scene. Human-made environments contain a lot of structure, and we seek to take advantage of this by enabling the use of quadric surfaces as features in SLAM systems. We introduce a minimal representation for quadric surfaces and show how this can be included in a least-squares formulation. We also show how our representation can be easily extended to include additional constraints on quadrics such as those found in quadrics of revolution. Finally, we introduce a proof-of-concept SLAM system using our representation, and provide some experimental results using an RGB-D dataset.