  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.
