A Dual-Cuboid Constraint Method with Marching Cubes-Based Contour Extraction for Verticality Inspection of Square Tower Structures

Verticality inspection of square tower structures is of great significance for ensuring structural operational safety, extending service life, and optimizing maintenance strategies. However, conventional verticality inspection methods still exhibit deficiencies in point cloud noise suppression, removal of internal redundant points, and stable geometric feature extraction, which often lead to fluctuations in axis fitting results and fail to meet the requirements of non-contact, high-precision, and holistic perception-based verticality inspection for square tower structures. To address the above issues, this paper proposes a Dual-Cuboid Constraint Method with Marching Cubes-Based Contour Extraction for Verticality Inspection of Square Tower Structures. First, raw point cloud data of the surface of square tower structures were acquired through terrestrial LiDAR multi-station scanning. After preprocessing, including point cloud registration, coordinate system unification, redundancy removal, and denoising, high-precision effective point cloud data were obtained in a unified station-centered spatial coordinate system. Subsequently, the initial body center point coordinates and principal axis directions of the standard segment point clouds were determined using the principal axis projection method. Based on these results, a dual-cuboid constraint frame was constructed, and the shell point clouds of the standard segments were extracted through outer-frame enclosure and inner-frame exclusion. The principal axis projection method was then applied again to calculate the body center point coordinates of the shell point cloud for each standard segment. The central axis of the body center point set was subsequently fitted using the least squares method to determine the unit direction vector of the structural central axis. Finally, within the station-centered spatial coordinate system, vector operations were performed between the unit direction vector and the x-axis and z-axis, respectively, to calculate the tilt attitude parameters of the square tower structure, including the azimuth angle of inclination, the inclination angle, and the verticality. The detection results obtained from different schemes were then comparatively evaluated using the relative error metric. Field validation was conducted on a tower crane at a construction site in Beijing. Four dual-cuboid constraint frame schemes with dimensional errors of 20 mm, 40 mm, 60 mm, and 80 mm were designed. Furthermore, based on the experimental process of the method presented in this paper, an unconstrained solution was established as a comparison experiment, and it was compared with the two reference experiments based on the Marching Square algorithm and the RANSAC algorithm. The results indicated that the tower-body verticality values obtained using the four dual-cuboid constraint frame schemes with different dimensional errors were 3.48‰, 3.63‰, 3.60‰, and 3.82‰, respectively, with a mean value of 3.63‰ and a range of only 0.34‰. The verticality results obtained from the four constrained schemes were generally consistent and showed good agreement with those obtained from 3.03‰ and 3.14‰, and reasonable proximity to the result obtained from 2.82‰, respectively. The results further suggest that the proposed dual-cuboid constraint frame contributes to improving the stability of point cloud feature extraction and central axis fitting, and yields generally consistent detection results across different dimensional error parameters, indicating that the method exhibits robustness to variations in the constraint-frame dimensions within the tested parameter ranges.