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

Plane adjustment (PA) is important for many 3D applications, which involves simultaneous pose estimation and plane recovery. While significant progress has been made recently, it is still a challenging problem in the realm of multi-view point cloud registration. The successful convergence of current state-of-the-art methods heavily depends on good initialization. Furthermore, the time complexity renders existing approaches impractical for large-scale problems. To address these challenges, we exploit a novel optimization strategy termed Bi-Convex Relaxation for large scale plane adjustment to improve its efficiency, convergence region and scalability. In particular, we decouple the original complex problem into two simpler sub-problems, which are then reformulated using convex relaxation. Subsequently, we can alternately solve these two sub-problems until convergence. On top of this novel optimization strategy, we propose two variants of the algorithm, namely GlobalPointer and GlobalPointer++, based on point-to-plane and plane-to-plane error, respectively. Extensive experiments on both synthetic and real datasets demonstrate that our method is able to perform large-scale plane adjustment with linear time complexity, larger convergence basin, and poor initialization, while achieving similar accuracy as prior methods. We will release our code to the public for further study.