Analytical Method for High-Precision Seabed Surface Modelling Combining B-Spline Functions and Fourier Series

Abstract High-accuracy seabed surface modelling provides multi-source high-precision fundamental geographic datasets for marine visual computing, seabed topography detection, marine biology, marine engineering and other fields. Proposed in this paper is a high-precision seabed surface model, which combines B-spline functions and Fourier-series, referred to as the Spline-Fourier-series (S-FS) method. Firstly, the mathematical relationship between the B-spline functions and Fourier-series in the modelling process is explored in depth, deducing the non-recursive basis functions of the Spline-Fourier-series model and the specific representation of the two dimensional Spline-Fourier-series model. Furthermore, using a publicly available Large-area bathymetric dataset, extensive experiments are conducted for comparisons with traditional methods (nearest-neighbor, bilinear, bicubic) and traditional Fourier-series, which generally shows the S-FS method has higher accuracy, better convergence and stronger robustness. Finally, based on its mathematically theoretical model, three characteristics (dimensionality reduction, multi-resolution expression and multi-scale visualization) of the S-FS method for constructing high-precision seabed surface are analyzed visually and deeply. Compared with B-spline function, the basic functions of the S-FS method inherit its prioritized compactly-supported performance and do not need to be recursively calculated anymore, thereby further showing its feasibility and extensibility in the field of high-precision seabed surface modelling.