TY - JOUR

T1 - Model Selection for Parametric Surfaces Approximating 3D Point Clouds for Deformation Analysis

AU - Zhao, Xin

AU - Kargoll, Boris

AU - Omidalizarandi, Mohammad

AU - Xu, Xiangyang

AU - Alkhatib, Hamza

N1 - Acknowledgments: The publication of this article was funded by the Open Access fund of Leibniz Universität Hannover.

PY - 2018/4

Y1 - 2018/4

N2 - 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.

AB - 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.

KW - B-spline

KW - Gauss-Markov model

KW - Polynomial

KW - Simulation-based Cox's test

KW - Surface modeling

KW - Terrestrial laser scanning

KW - Vuong's test

UR - http://www.scopus.com/inward/record.url?scp=85045967144&partnerID=8YFLogxK

U2 - 10.3390/rs10040634

DO - 10.3390/rs10040634

M3 - Article

AN - SCOPUS:85045967144

VL - 10

JO - Remote Sensing

JF - Remote Sensing

SN - 2072-4292

IS - 4

M1 - 634

ER -