On the Use of Lr B-Splines to Fit Optimally a Point Cloud: a Statistical Investigation using Information Criteria for Model Selection
Abstract. The task of approximating point clouds with mathematical surfaces is ubiquitous to reduce a high number of observations to a more compact description. LR B-splines provide a framework that allows iterative local refinement of the mesh of knotline segments. The lack of local refinement associated with non-uniform tensor product B-splines is avoided in an elegant way. However, the challenge of representing noisy, scattered and parametrized point clouds with as few control points as possible and by avoiding overfitting, as efficiently as possible remains an unsolved problem. Information criteria provide a promising way to identify an optimal refinement strategy: They are based on the computation of a statistical function called the likelihood of a model, which is defined as an approximation with a given threshold, method or iteration step. A minimum of the Information Criterion is searched, which gives an estimation of the quality of each model relative to each of the other models. The statistical distribution of the approximation error must be chosen with care to avoid a bias in the likelihood computation. We will show how the Akaike Information Criterion using the student distribution can be used within the context of adaptive refinement with LR B-splines to help decide the most optimal approximation strategy. We will investigate different refinement options, and make use of real bathymetry data to illustrate our method.
- Research Council of Norway (RCN) / 270922
- Gottfried Wilhelm Leibniz Universität Hannover
- SINTEF Digital / Mathematics and Cybernetics
SIAM Conference on Geometric and Physical Modeling
27.09.2021 - 29.09.2021
Society for Industrial and Applied Mathematics