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 $p^{th}$ Spline-Fourier-series model and the specific representation of the two dimensional $p^{th}$ 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.

Keywords:

• B-spline functions
• dimensionality reduction
• Fourier series
• high-precision seabed surface modelling
• multi-scale visualization
• multi-resolution
• non-recursive calculation

Acknowledgments

The authors sincerely acknowledge the anonymous reviewers and editors for their valuable insights and comments to further improve the quality of the manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

Data availability statement

The data that supports the findings of this study is available in General Bathymetric Chart of the Oceans (GEBCO) 2020 Grid (doi:10.5285/a29c5465-b138-234d-e053-6c86abc040b9) and National Oceanic and Atmospheric Administration (NOAA) data collections.

Additional information

Funding

This work was supported by the [National Natural Science Foundation of China #1] under Grant [number 41971416, 41974005]; [National Science Foundation for Outstanding Young Scholars #2] under Grant [number 42122025]; [Natural Science Foundation for Distinguished Young Scholars of Hubei Province of China #3] under Grant [number 2019CFA086].