Axis-Constrained Fine Registration for Industrial Inspection Using a Closed-Form Quaternion Solver

Industrial dimensional inspection relies on accurate registration between scanned point clouds and nominal CAD models to evaluate geometric deviations with respect to engineering datums. Conventional fine registration methods, such as the Iterative Closest Point (ICP) algorithm, minimize global alignment error but may modify datum features that should remain fixed during inspection, leading to misleading defect localization and dimensional measurements. This work presents a constrained fine-registration method that preserves prescribed geometric constraints while aligning measured point clouds to their reference geometry. The constrained alignment is obtained through a closed-form quaternion formulation, replacing the iterative optimization typically required for constrained rigid alignment within the ICP framework. Experimental results show that the proposed method preserves the inspection reference frame while localizing geometric deviations to defective regions. The resulting formulation provides an efficient registration procedure for precision dimensional inspection. Future work includes extending the range of supported constraints and reducing sensitivity to initialization.