A Geometric-Constraint-Based Extrinsic Calibration Method for Multi-Camera Line-Laser 3D Measurement of Shaft-like Parts

Multi-view line laser measurement systems require accurate calibration among sensors to reconstruct shaft geometries from multiple views. To address the limitations of conventional Iterative Closest Point (ICP)-based registration methods, a multi-camera calibration method based on a hexagonal prism calibration artifact is proposed. The geometric constraints of the artifact are utilized to construct local coordinate systems and estimate the rigid transformations among cameras. A fine registration model based on opposite-side distance residual compensation is further introduced to improve calibration accuracy. A three-camera line laser measurement system was established to validate the proposed method. Experimental results show that the proposed method achieves a system root mean square error (RMSE) of 0.2413 mm after calibration, while repeated calibration experiments yield a standard deviation below 0.0009 mm. In comparison, classical Iterative Closest Point (ICP) and Voxelized Generalized ICP (VGICP) achieve system RMSE values of 0.2651 mm and 0.2656 mm, respectively, on the same 20 mm evaluation point clouds. The proposed method estimates the calibration transformation from only a single cross-sectional profile (684 points per camera) with a computational time of approximately 0.056 s, while also exhibiting low sensitivity to initialization conditions and point cloud sparsity. Validation experiments on different shaft components achieve system RMSE values of 0.2400 mm and 0.2735 mm, respectively. The proposed method provides a simple, robust, and accurate calibration solution for multi-camera line laser measurement systems and is suitable for shaft measurement and three-dimensional reconstruction applications.