LR B-Splines for Representation of Terrain and Seabed: Data Fusion, Outliers, and Voids

AbstractPerforming surface approximation of geospatial point clouds with locally refined (LR) B-splines comes with several challenges: (i) Point clouds have varying data density, (ii) outliers should be eliminated without deleting features, (iii) voids, also called holes, or data gaps should be treated specifically to avoid the drop of the approximated surface in domains without points. These factors tend to be even more challenging when point clouds acquired from different sensors having different noise characteristics are fused together. The data set becomes non-uniform and the fusing process itself involves a risk of an increased noise level. In this chapter, we provide some tools to answer those specific challenges. We will use terrain and seabed data and show didactically how to perform adaptive surface approximation with local refinement and to select customized parameters. We will further address the problem of choosing an appropriate tolerance for performing an adaptive fitting, and discuss the refinement strategies within the context of LR B-splines. The latter is shown to provide a promising framework for surface fitting of heterogeneous point clouds from various sources.