Model Selection for Parametric Surfaces Approximating 3D Point Clouds for Deformation Analysis

Abstract

Deformation monitoring of structures is a common application and one of the major tasks of engineering surveying. Terrestrial laser scanning (TLS) has become a popular method for detecting deformations due to high precision and spatial resolution in capturing a number of three-dimensional point clouds. Surface-based methodology plays a prominent role in rigorous deformation analysis. Consequently, it is of great importance to select an appropriate regression model that reflects the geometrical features of each state or epoch. This paper aims at providing the practitioner some guidance in this regard. Different from standard model selection procedures for surface models based on information criteria, we adopted the hypothesis tests from D.R. Cox and Q.H. Vuong to discriminate statistically between parametric models. The methodology was instantiated in two numerical examples by discriminating between widely used polynomial and B-spline surfaces as models of given TLS point clouds. According to the test decisions, the B-spline surface model showed a slight advantage when both surface types had few parameters in the first example, while it performed significantly better for larger numbers of parameters. Within B-spline surface models, the optimal one for the specific segment was fixed by Vuong's test whose result was quite consistent with the judgment of widely used Bayesian information criterion. The numerical instabilities of B-spline models due to data gap were clearly reflected by the model selection tests, which rejected inadequate B-spline models in another numerical example.

Finite Element Analysis based on A Parametric Model by Approximating Point Clouds

“…The aim is to research weak situations and positions in this deformed structure by combining TLS with the FE computation. The TLS equipment (FARO Focus S 350) and laser tracker equipment (FARO Laser Tracker Xi) were used here to obtain the 3D point clouds [46,[61][62][63]. The systematic distance error of this type TLS is ±1 mm.…”

“…They form the so-called control polygon in the calculation. Interested readers can refer to [12,13,63] for more details regarding the B-spline parameter calculation.…”

“…Ground-based sides of each feature are ignored. Other sides obtain reasonable numbers of controlled points as is shown in Table 1, which are referred to in detail in [12,63]. The extracted B-spline feature curves are then applied as the trimming and projection boundaries to the B-spline surfaces.…”

An Iterative Method Based on the Marginalized Particle Filter for Nonlinear B-Spline Data Approximation and Trajectory Optimization

“…B-spline functions, curves, and surfaces are widely used for approximation [1][2][3] and for defining the trajectories of vehicles [4,5], robots [6,7] and industrial machines [8]. Furthermore, they are common in computer graphics [9,10] and signal processing for filter design and signal representation [11][12][13][14][15].…”

Framework for 3D Point Cloud Modelling Aimed at Road Sight Distance Estimations

“…These models ought to be not only realistic and updated enough so as to perform visual inspections, but also must hold sufficient accuracy to perform robust evaluations, measurements and calculations. For these reasons, the use of LiDAR-derived models has been of great use in the field of civil engineering, with applications as wide as the inspection of existing infrastructure [4], road information inventory [5], road safety [6], among others.…”