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

TL;DR

This paper introduces GlobalPointer, a novel large-scale plane adjustment method using bi-convex relaxation, which achieves linear time complexity, robustness to poor initialization, and high accuracy in multi-view point cloud registration.

Contribution

The paper proposes a bi-convex relaxation optimization strategy and two algorithms, GlobalPointer and GlobalPointer++, for efficient large-scale plane adjustment.

Findings

Achieves linear time complexity for large-scale problems

Demonstrates robustness to poor initialization

Maintains high accuracy comparable to prior methods

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.