Influence of the simplified stochastic model of TLS measurements on geometry-based deformation analysis

Abstract

Abstract Terrestrial laser scanners (TLS) are powerful instruments that can be employed for deformation monitoring due to their high precision and spatial resolution in capturing 3D point clouds. Deformation detections from scatter point clouds can be based on different comparison methods, among which the geometry-based method is one of the most popular. Compared with approximating surfaces with predetermined geometric primitives, such as plane or sphere, the B-splines surface approximation offers a great flexibility and can be used to fit nearly every object scanned with TLS. However, a variance-covariance matrix (VCM) of the observations involved in approximating the scattered points to B-spline surfaces impact the results of a congruency test, which is the uniformly most powerful invariant (UMPI) test for discriminating between the null hypothesis of zero deformation and its alternative hypotheses. Consequently, simplified stochastic models may weaken the UMPI property. Based on Monte Carlo simulations, the impact of the heteroscedasticity and mathematical correlations often neglected in B-splines approximation are investigated. These correlations are specific in approximating TLS measurements when the raw measurements are transformed into Cartesian coordinates. The rates of rejecting the null hypothesis in a congruency test is employed to reflect the impact of unspecified VCMs on the power of the congruency test. The rejection rates are not sensitive to the simplification of the stochastic models, in the larger deformation area with higher point accuracy, while they are obviously influenced in the smaller deformation area with unfavourable geometries, i. e. larger uncertainties. A threshold ratio of estimated differences to the relative standard deviation highlights whereas the results of congruency test are reliable when using simplified VCMs. It is concluded that the simplification of the stochastic model has a significant impact on the power of the congruency test, especially in the smaller deformation area with larger uncertainties.