LR B-splines to approximate bathymetry datasets: An improved statistical criterion to judge the goodness of fit

Abstract

• We introduce Locally Refined B-splines to approximate scattered point clouds. • The local approximation is performed iteratively when the error exceeds a certain threshold. • We investigate the choice of the refinement method with statistical criterion. • We apply our method to fit a small and a large bathymetry dataset. The task of representing remotely sensed scattered point clouds with mathematical surfaces is ubiquitous to reduce a high number of observations to a compact description with as few coefficients as possible. To reach that goal, locally refined B-splines provide a simple framework to perform surface approximation by allowing an iterative local refinement. Different setups exist (bidegree of the splines, tolerance, refinement strategies) and the choice is often made heuristically, depending on the applications and observations at hand. In this article, we introduce a statistical information criterion based on the t-distribution to judge the goodness of fit of the surface approximation for remote sensing data with outliers. We use a real bathymetry dataset and illustrate how concepts from model selection can be used to select the most adequate refinement strategy of the LR B-splines.