Optimal Surface Fitting of Point Clouds Using Local Refinement

1. Front Matter

   Pages i-xix

   PDF

2. Introduction

   • Gaël Kermarrec, Vibeke Skytt, Tor Dokken

   Pages 1-12Open Access

3. Locally Refined B-Splines

   • Gaël Kermarrec, Vibeke Skytt, Tor Dokken

   Pages 13-21Open Access

4. Adaptive Surface Fitting with Local Refinement: LR B-Spline Surfaces

   • Gaël Kermarrec, Vibeke Skytt, Tor Dokken

   Pages 23-39Open Access

5. A Statistical Criterion to Judge the Goodness of Fit of LR B-Splines Surface Approximation

   • Gaël Kermarrec, Vibeke Skytt, Tor Dokken

   Pages 41-56Open Access

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

   • Gaël Kermarrec, Vibeke Skytt, Tor Dokken

   Pages 57-80Open Access

7. LR B-Spline Surfaces and Volumes for Deformation Analysis of Terrain Data

   • Gaël Kermarrec, Vibeke Skytt, Tor Dokken

   Pages 81-107Open Access

8. Conclusion

   • Gaël Kermarrec, Vibeke Skytt, Tor Dokken

   Pages 109-111Open Access

This open access book provides insights into the novel Locally Refined B-spline (LR B-spline) surface format, which is suited for representing terrain and seabed data in a compact way. It provides an alternative to the well know raster and triangulated surface representations. An LR B-spline surface has an overall smooth behavior and allows the modeling of local details with only a limited growth in data volume. In regions where many data points belong to the same smooth area, LR B-splines allow a very lean representation of the shape by locally adapting the resolution of the spline space to the size and local shape variations of the region. The iterative method can be modified to improve the accuracy in particular domains of a point cloud. The use of statistical information criterion can help determining the optimal threshold, the number of iterations to perform as well as some parameters of the underlying mathematical functions (degree of the splines, parameter representation). The resulting surfaces are well suited for analysis and computing secondary information such as contour curves and minimum and maximum points. Also deformation analysis are potential applications of fitting point clouds with LR B-splines.

• Open Access
• Surface Modeling
• Optimum Point Cloud Approximation
• Akaike Information Criterion
• LR B-Splines
• Contour Curves Determination
• Deformation Analysis
• Bathymetry data

• Institute for meteorology and climatology, Leibniz University Hanover, Hannover, Germany

  Gaël Kermarrec

• Mathematics and Cybernetics, SINTEF Digital, Oslo, Norway

  Vibeke Skytt, Tor Dokken