Using Structural Risk Minimization to Determine the Optimal Complexity of B-Spline Surfaces for Modelling Correlated Point Cloud Data

Abstract

The increased use of areal measurement techniques in engineering geodesy requires the development of adequate areal analysis strategies. Usually, such analysis strategies include a modelling of the data in order to reduce the amount of data while preserving as much information as possible. Free form surfaces like B-splines have been proven to be an appropriate tool to model point clouds. The complexity of those surfaces is among other model parameters determined by the number of control points. The selection of the appropriate number of control points constitutes a model selection task, which is typically solved under consideration of parsimony by trial-and-error procedures. In Harmening and Neuner (J Appl Geod 10(3):139–157, 2016; 11(1):43–52, 2017) a model selection approach based on structural risk minimization was developed for this specific problem. However, neither this strategy, nor standard model selection methods take correlations into account. For this reason, the performance of the developed model selection approach on correlated data sets is investigated and the respective results are compared to those provided by a standard model selection method, the Bayesian Information Criterion.