Extraction of tunnel center line and cross-sections on fractional calculus, 3D invariant moments and best-fit ellipse

Abstract In order to measure and analyze the tunnel 3D deformation accurately, effectively and conveniently, we use the 3D point clouds instead of Total station data. A 63.6 m long tunnel was scanned twice by using a Leica C10 laser scanner (max scanning range is 300 m), for each of the scans, to obtain the accurate data and to avoid to having tunnel bending part, we divide the tunnel into five sections for the measurements, and for each measurement, the data is scanned in one station. Since the original data includes some noise, to remove noise in the point clouds, we study a new Fractional calculus template for data smoothing. After that, we propose a new method to extract the tunnel central axis based on the 3D invariant moments, and then the tunnel posture is rotated to make the central axis parallel to the reference direction, which is rotational invariant and repeatable. Based on the central axis in each section, the cross-sections are detected, and the elliptic features of a cross-section are calculated for analyzing the tunnel convergence. To make cross-section measurement rotational invariant, we apply the zeroth, the first and the second moments to obtain major and minor axes through the cross-section center. The experiment results demonstrate that this method can meet the accuracy requirements, and it can be with an accuracy of 2 mm for cross-section measurement. It is useful for tunnel engineering applications both in the tunnel 3D point cloud analysis and 3D information extraction.

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