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 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 GlobalPointer and 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.
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 planeonly 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.
Total optimization time analysis with increasing poses and planes.
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 in the log10 scale.
Relative time complexity comparisons. The x axis represents the number of planes and the y axis represents the number of poses. The color bar on the right side of each subplot indicates the mapping relationship between the multiplier of runtime growth and the colors.
Accuracy comparisons on the real dataset under varying pose initialization noise levels. The y axis represents the total point-to-plane error in the log10 scale.
@article{Liao2024GlobalPointer,
author = {Liao, Bangyan and Zhao, Zhenjun and Chen, Lu and Li, Haoang and Cremers, Daniel and Liu, Peidong},
title = {GlobalPointer: Large-Scale Plane Adjustment with Bi-Convex Relaxation},
journal = {European Conference on Computer Vision (ECCV)},
year = {2024},
}