Minimax Registration for Point Cloud Alignment

Abstract

The alignment, or rigid registration, of three-dimensional (3D) point clouds plays an important role in many applications, such as robotics and computer vision. Recently, with the improvement in high precision and automated 3D scanners, the registration algorithm has become critical in a manufacturing setting for tolerance analysis, quality inspection, or reverse engineering purposes. Most of the currently developed registration algorithms focus on aligning the point clouds by minimizing the average squared deviations. However, in manufacturing practices, especially those involving the assembly of multiple parts, an envelope principle is widely used, which is based on minimax criteria. Our present work models the registration as a minimization problem of the maximum deviation between two point clouds, which can be recast as a second-order cone program. Variants for both pairwise and multiple point clouds registrations are discussed. We compared the performance of the proposed algorithm with other well-known registration algorithms, such as iterative closest point and partial Procrustes registration, on a variety of simulation studies and scanned data. Case studies in both additive manufacturing and reverse engineering applications are presented to demonstrate the usage of the proposed method.