# Convex Hull-based Algebraic Constraint for Visual Quadric SLAM

arXiv: https://arxiv.org/abs/2503.01254 · HTML: https://mlsanity.com/paper/2503.01254/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 34 references that are in the map.
- First posted on arXiv 3 Mar 2025.

## Builds on (most cited first, 16 of 16)

- [Segment Anything](https://mlsanity.com/paper/2304.02643/) (2023)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [ORB-SLAM2: an Open-Source SLAM System for Monocular, Stereo and RGB-D Cameras](https://mlsanity.com/paper/1610.06475/) (2016)
- [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)
- [DSP-SLAM: Object Oriented SLAM with Deep Shape Priors](https://mlsanity.com/paper/2108.09481/) (2021)
- [EAO-SLAM: Monocular Semi-Dense Object SLAM Based on Ensemble Data Association](https://mlsanity.com/paper/2004.12730/) (2020)
- [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)
- [OA-SLAM: Leveraging Objects for Camera Relocalization in Visual SLAM](https://mlsanity.com/paper/2209.08338/) (2022)
- [An Object SLAM Framework for Association, Mapping, and High-Level Tasks](https://mlsanity.com/paper/2305.07299/) (2023)
- [GOReloc: Graph-based Object-Level Relocalization for Visual SLAM](https://mlsanity.com/paper/2408.07917/) (2024)
- [VOOM: Robust Visual Object Odometry and Mapping using Hierarchical Landmarks](https://mlsanity.com/paper/2402.13609/) (2024)
- [Object SLAM-Based Active Mapping and Robotic Grasping](https://mlsanity.com/paper/2012.01788/) (2020)
- [Dual Quadrics from Object Detection BoundingBoxes as Landmark Representations in SLAM](https://mlsanity.com/paper/1708.00965/) (2017)
- [Scale Estimation with Dual Quadrics for Monocular Object SLAM](https://mlsanity.com/paper/2202.04816/) (2022)

## Abstract (arXiv)

Using Quadrics as the object representation has the benefits of both generality and closed-form projection derivation between image and world spaces. Although numerous constraints have been proposed for dual quadric reconstruction, we found that many of them are imprecise and provide minimal improvements to localization.After scrutinizing the existing constraints, we introduce a concise yet more precise convex hull-based algebraic constraint for object landmarks, which is applied to object reconstruction, frontend pose estimation, and backend bundle adjustment.This constraint is designed to fully leverage precise semantic segmentation, effectively mitigating mismatches between complex-shaped object contours and dual quadrics.Experiments on public datasets demonstrate that our approach is applicable to both monocular and RGB-D SLAM and achieves improved object mapping and localization than existing quadric SLAM methods. The implementation of our method is available at https://github.com/tiev-tongji/convexhull-based-algebraic-constraint.