Abstract: Most current research on computer vision-based weld seam extraction primarily focuses on planar butt welds and fillet welds, while there is limited research on complex surface weld seams. In this paper, a welding trajectory extraction method for nozzle welds on pressure vessel heads, specifically for holes with circular or elliptical paths, was proposed. Firstly, the point clouds were preprocessed to improve the quality and reliability of the data. Then, the inner contour of the point cloud was extracted by establishing a complex coordinate system at the centroid of the point cloud, serving as the initial boundary. In the point cloud registration stage, the ICP registration method was adopted. A nonlinear optimization problem was constructed and solved by taking the three coordinate axis rotation angles and the radius for circular holes of the template point cloud (major and minor axes for elliptical holes) as design variables and the registration error as the objective function. The results indicate that the proposed algorithm can be applied to the welding of complex surfaces, realizes automatic guidance for welding robots, and meets the requirements of welding accuracy and efficiency, verifying the feasibility of the algorithm.