The choice of an appropriate metric is mandatory to perform deformation analysis between two point clouds (PC)—the distance has to be trustworthy and, simultaneously, robust against measurement noise, which may be correlated and heteroscedastic. The Hausdorff distance (HD) or its averaged derivation (AHD) are widely used to compute local distances between two PC and are implemented in nearly all commercial software. Unfortunately, they are affected by measurement noise, particularly when correlations are present. In this contribution, we focus on terrestrial laser scanner (TLS) observations and assess the impact of neglecting correlations on the distance computation when a mathematical approximation is performed. The results of the simulations are extended to real observations from a bridge under load. Highly accurate laser tracker (LT) measurements were available for this experiment: they allow the comparison of the HD and AHD between two raw PC or between their mathematical approximations regarding reference values. Based on these results, we determine which distance is better suited in the case of heteroscedastic and correlated TLS observations for local deformation analysis. Finally, we set up a novel bootstrap testing procedure for this distance when the PC are approximated with B-spline surfaces.

Today, short- and long-term structural health monitoring of bridge infrastructures and their safe, reliable and cost-effective maintenance have received considerable attention. For this purpose, image-assisted total station (here, Leica Nova MS50 MultiStation) as a modern geodetic measurement system can be utilized for accurate displacement and vibration analysis. The Leica MS50 measurements comprise horizontal angles, vertical angles and distance measurements in addition to the captured images or video streams with practical sampling frequency of 10 Hz using an embedded on-axis telescope camera. Experiments were performed for two case studies under (1) a controlled laboratory environment and (2) a real-world situation observing a footbridge structure using a telescope camera of the Leica MS50. Furthermore, two highly accurate reference measurement systems, namely, a laser tracker Leica AT960-LR and a portable shaker vibration calibrator 9210D in addition to the known natural frequencies of the footbridge structure calculated from the finite element model analysis are used for validation. The feasibility of an optimal passive target pattern and its accurate as well as reliable detection at different epochs of time were investigated as a preliminary step. Subsequently, the vertical angular conversion factor of the telescope camera of the Leica MS50 was calibrated, which allows for an accurate conversion of the derived displacements from the pixel unit to the metric unit. A linear regression model in terms of a sum of sinusoids and an autoregressive model of the coloured measurement noise were employed and solved by means of a generalized expectation maximization algorithm to estimate amplitudes and frequencies with high accuracy. The results show the feasibility of the Leica MS50 for the accurate displacement and vibration analysis of the bridge structure for frequencies less than 5 Hz.

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.