A Hybrid Vision and Optimization Strategy for Accurate 3D Laser Projection Calibration

A galvanometer-based laser 3D projection system requires accurate mapping between galvanometer control signals and workpiece coordinates to ensure reliable on-part marking. This study presents a calibration and verification pipeline that uses a color camera and a depth sensor to reconstruct 3D target points and estimate the extrinsic parameters between the projector and the workpiece. Laser spot centers are localized in color images, and corresponding depth values are acquired after color–depth alignment. The resulting 3D points are back-projected and transformed into the workpiece coordinate frame. A hybrid solver is employed: the Whale Optimization Algorithm (WOA) provides a global initial estimate, followed by Levenberg–Marquardt (LM) refinement to enhance convergence stability under noisy and small-sample conditions. Experimental validation on an independent 13-point set demonstrates sub-millimeter accuracy, with a mean error of approximately 0.37 mm and a maximum error of 0.87 mm. A further rectangular contour projection test confirms consistent performance, yielding a mean error of 0.434 mm and a maximum error of 0.879 mm, with all errors remaining below 1 mm.