GlobalPointer: Large-Scale Plane Adjustment with Bi-Convex Relaxation

TL;DR

GlobalPointer tackles large-scale plane adjustment in multi-view LiDAR by decoupling joint pose and plane estimation using Bi-Convex Relaxation, which alternates convex SDP subproblems for poses and planes. It introduces two variants: GlobalPointer (point-to-plane) and GlobalPointer++ (plane-to-plane), achieving linear time complexity in the numbers of planes $n$ and poses $m$ and showing robustness to poor initialization with empirical convergence to near-global optima. Extensive synthetic and real-data experiments demonstrate competitive accuracy with significantly reduced computation compared to state-of-the-art methods, and ablation highlights the importance of plane–pose overlap and normal-direction calibration. The approach provides practical scalability for large-scale LiDAR plane adjustment with open-source code available for reproducibility.

Abstract

Plane adjustment (PA) is crucial for many 3D applications, involving simultaneous pose estimation and plane recovery. Despite recent advancements, it remains a challenging problem in the realm of multi-view point cloud registration. Current state-of-the-art methods can achieve globally optimal convergence only with good initialization. Furthermore, their high time complexity renders them impractical for large-scale problems. To address these challenges, we first exploit a novel optimization strategy termed \textit{Bi-Convex Relaxation}, which decouples the original problem into two simpler sub-problems, reformulates each sub-problem using a convex relaxation technique, and alternately solves each one until the original problem converges. Building on this strategy, we propose two algorithmic variants for solving the plane adjustment problem, namely \textit{GlobalPointer} and \textit{GlobalPointer++}, based on point-to-plane and plane-to-plane errors, respectively. Extensive experiments on both synthetic and real datasets demonstrate that our method can perform large-scale plane adjustment with linear time complexity, larger convergence region, and robustness to poor initialization, while achieving similar accuracy as prior methods. The code is available at https://github.com/wu-cvgl/GlobalPointer.

Figures (22)

• Figure 1: Visualization of plane adjustment problem and convergence process. (a) The plane adjustment problem involves simultaneous pose estimation and plane reconstruction based on the assigned plane labels of each LiDAR point. As illustrated, the LiDAR poses and the 3D planes are tightly coupled with each other. (b) This example demonstrates the convergence process of our method starting from random initialization. Despite the poses and planes being randomly initialized, our approach achieves a global minimum within a few optimization iterations. For visualization purposes, points associated with the same plane are colored identically.
• Figure 2: Visualization of different point cloud error definitions.
• Figure 3: Illustration of the proposed Bi-Convex Relaxation. Three blue circles represent plane1, plane2, and plane3. Two yellow circles denote the LiDAR pose1 and LiDAR pose2. The connection edges denote the observation relationships. Fixing the planes leads to pose-only optimization (left), while fixing the LiDAR poses in plane-only optimization (right). Each sub-problem is then reformulated as SDP, which can be solved with globally optimal guarantees. Using these techniques, the plane adjustment algorithm alternately solves each sub-problem until the convergence of the original problem.
• Figure 4: Total optimization time analysis with increasing poses and planes.
• Figure 5: Accuracy comparisons on the synthetic dataset under varying point cloud noise levels and pose initialization noise levels. The $y$ axis represents the total point-to-plane error $e_{total}$ in the log10 scale.