Convex Hull-based Algebraic Constraint for Visual Quadric SLAM

TL;DR

This work addresses the fragility of localization in quadric-based SLAM by introducing a convex hull-based algebraic constraint that exploits precise instance segmentation to align dual quadrics with complex object contours. The method integrates this constraint into object reconstruction, frontend pose estimation, and bundle adjustment, achieving enhanced localization and mapping in both monocular and RGB-D SLAM. Empirical results on public datasets demonstrate superior performance over state-of-the-art quadric-SLAM methods, with ablations showing clear advantages of hull-based constraints over bbox, conic, and contour primitives. The approach offers practical gains for robust object-aware SLAM and foundational improvements for downstream semantic scene understanding.

Abstract

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.

Figures (5)

• Figure 1: The Proposed Convex Hull-based Algebraic Constraint between Dual Quadric and Camera Pose.
• Figure 2: Comparison of Conic Fitting from Contour and Convex Hull.
• Figure 3: The proposed object SLAM system framework
• Figure 4: Qualitative comparison of mapping results on the TUM RGB-D dataset. The first column represents the fr3-office sequence, and the second column represents the fr3-teddy sequence.
• Figure 5: The qualitative results of semantic mapping. From left to right, columns are results on sequence TUM fr1_desk, fr2_desk, fr3_desk and ICL NUIM office-traj2 respectively. (a) The 2-D projection of reconstructed quadrics on the image. (b) The object map built by our object SLAM.