Minimax Registration for Point Cloud Alignment

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 high precision automated 3D scanners, registration algorithm has become critical a manufacturing setting for tolerance analysis, quality inspection, reverse engineering purposes. Most currently developed algorithms focus on aligning by minimizing average squared deviations. However, practices, especially those involving assembly multiple parts, envelope principle is widely used, which based minimax criteria. Our present work models minimization problem maximum deviation between two clouds, can be recast second-order cone program. Variants both pairwise registrations are discussed. We compared performance proposed other well-known algorithms, iterative closest partial Procrustes variety simulation studies scanned data. Case additive applications presented to demonstrate usage method.