Gaussian process based multi-scale modelling for precision measurement of complex surfaces

Uncertainty-guided intelligent sampling strategy for high-efficiency surface measurement via free-knot B-spline regression modelling

“…Our experiments show that FKBSmodelling-based adaptive sampling has comparable or higher performance to some state-of-the-art sampling solutions with nonparametric models, e.g. Gaussian process regression or kriging [36,41], and with less computational cost. In the following, the proposed solution is described mathematically in part 2 with step-by-step illustrations.…”

“…Adaptive sampling can redirect sampling effort in real time in response to prior observed topography values [13]. Adaptive sampling has been investigated for some time and many methods have been developed [11,25,26,[30][31][32][33][34][35][36][37][38][39][40][41]. Most of the developed methods of adaptive sampling follow a common pipeline, as shown in Figure 3, i.e.…”

“…Then, a real surface can be approximated by the surrogate model (the real model is usually unknown) without, or with limited, reconstruction error. Recently, a Gaussian process modelling (as a generalised kriging [37,38])-based intelligent sampling has drawn wide attentions [35,36,41] for their high-degree for modelling flexibility. However, these non-parametric modelling methods are designed for lowdynamic-range (LDR) homogeneous surfaces or near-homogeneous surfaces, e.g.…”

“…Testing points or candidate points * ∈ are the positions to be predicted in model reconstruction. In previous research work [11,36,38], a dense and uniform position set with a fixed size is constructed for NBP selection. This solution is not optimal and for large datasets, it is time-consuming as well, especially in areal measurement.…”

“…Within the iterative strategy above, stopping criteria are a critical factor to the performance of adaptive sampling. Some commonly applicable criteria have been used in previous research, such as the predefined sample size [37,38], predefined maximum reconstruction error [11,30,37,60] and uncertainty [35][36][37][38]. With combined use of these stopping criteria, adaptive sampling can be effectively applied.…”