Abstract
The terrestrial laser scanning technology is increasingly applied in the deformation monitoring of tunnel structures. However, outliers and data gaps in the terrestrial laser scanning point cloud data have a deteriorating effect on the model reconstruction. A traditional remedy is to delete the outliers in advance of the approximation, which could be time- and labor-consuming for large-scale structures. This research focuses on an outlier-resistant and intelligent method for B-spline approximation with a rank (R)-based estimator, and applies to tunnel measurements. The control points of the B-spline model are estimated specifically by means of the R-estimator based on Wilcoxon scores. A comparative study is carried out on rank-based and ordinary least squares methods, where the Hausdorff distance is adopted to analyze quantitatively for the different settings of control point number of B-spline approximation. It is concluded that the proposed method for tunnel profile modeling is robust against outliers and data gaps, computationally convenient, and it does not need to determine extra tuning constants.
Highlights
A variety of research has been carried out in the engineering field to recognize and reconstruct threedimensional (3D) objects.[1]
We propose a robust solution of such problems based on the rank methods
Outliers and data gaps of point cloud data generally lead to imprecision of the fitted B-spline model
Summary
A variety of research has been carried out in the engineering field to recognize and reconstruct threedimensional (3D) objects.[1]. The control point positions are obtained mostly through least squares (LS) estimation.[29] Some researchers determined the optimal number of control points, which was usually a model selection problem, by means of the Akaike Information Criterion, the Bayesian Information Criterion, or statistical learning theory.[30] The quality of the control point positions estimated was evaluated by the average estimated standard deviation, which focused on the quality of estimation procedure regarding datasets instead of the real shape of the object.[31] Minimizing energy function has recently been adopted to adjust control points which could be applied in smoothing and gap filling.[32] Xu et al.[33] employed an adaptive robust estimator based on Student’s t-distribution to fit a B-spline curve to measurement data This estimator involves the degree of freedom of the t-distribution as a parameter or tuning constant, which is adapted to the data given according to the outlier characteristics. The comparative results are presented in section ‘‘Results.’’ we draw the conclusion of the article in the final section
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