# Unified Representation of Geometric Primitives for Graph-SLAM Optimization Using Decomposed Quadrics

arXiv: https://arxiv.org/abs/2108.08957 · HTML: https://mlsanity.com/paper/2108.08957/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 32 references that are in the map.
- First posted on arXiv 20 Aug 2021.

## Builds on (most cited first, 6 of 6)

- [CubeSLAM: Monocular 3D Object SLAM](https://mlsanity.com/paper/1806.00557/) (2018)
- [QuadricSLAM: Dual Quadrics from Object Detections as Landmarks in Object-oriented SLAM](https://mlsanity.com/paper/1804.04011/) (2018)
- [Semantic Visual Localization](https://mlsanity.com/paper/1712.05773/) (2017)
- [X-View: Graph-Based Semantic Multi-View Localization](https://mlsanity.com/paper/1709.09905/) (2017)
- [Super Odometry: IMU-centric LiDAR-Visual-Inertial Estimator for Challenging Environments](https://mlsanity.com/paper/2104.14938/) (2021)
- [Robust Visual SLAM with Point and Line Features](https://mlsanity.com/paper/1711.08654/) (2017)

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

- [Simultaneous Localisation and Mapping with Quadric Surfaces](https://mlsanity.com/paper/2203.08040/) (2022)
- [Monocular visual simultaneous localization and mapping: (r)evolution from geometry to deep learning-based pipelines](https://mlsanity.com/paper/2503.02955/) (2025)
- [QuadricsNet: Learning Concise Representation for Geometric Primitives in Point Clouds](https://mlsanity.com/paper/2309.14211/) (2023)
- [Object-based SLAM utilizing unambiguous pose parameters considering general symmetry types](https://mlsanity.com/paper/2303.07872/) (2023)
- [QuadricsReg: Large-Scale Point Cloud Registration using Quadric Primitives](https://mlsanity.com/paper/2412.02998/) (2024)

## Abstract (arXiv)

In Simultaneous Localization And Mapping (SLAM) problems, high-level landmarks have the potential to build compact and informative maps compared to traditional point-based landmarks. In this work, we focus on the parameterization of frequently used geometric primitives including points, lines, planes, ellipsoids, cylinders, and cones. We first present a unified representation based on quadrics, leading to a consistent and concise formulation. Then we further study a decomposed model of quadrics that discloses the symmetric and degenerated properties of a primitive. Based on the decomposition, we develop geometrically meaningful quadrics factors in the settings of a graph-SLAM problem. Then in simulation experiments, it is shown that the decomposed formulation has better efficiency and robustness to observation noises than baseline parameterizations. Finally, in real-world experiments, the proposed back-end framework is demonstrated to be capable of building compact and regularized maps.