Analytical Method for High-Precision Seabed Surface Modelling Combining B-Spline Functions and Fourier Series. Issue 5 (16th August 2022)

• Record Type: Journal Article
• Authors: Zhang, Ruichen; Zhai, Guojun; Bian, Shaofeng; Li, Houpu; Ji, Bing
• Is Part Of: Marine geodesy. Volume 45:Issue 5(2022)
• Page Start: 519
• Page End: 556
• Publication Date: 2022-08-16
• Subjects: B-spline functions -- dimensionality reduction -- Fourier series -- high-precision seabed surface modelling -- multi-scale visualization -- multi-resolution -- non-recursive calculation; Marine geodesy -- Periodicals; Hydrographic surveying -- Periodicals; 526.99
• DOI: 10.1080/01490419.2022.2091695
• Languages: English
• ISSNs: 0149-0419

Abstract

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 t h Spline-Fourier-series model and the specific representation of the two dimensional p t h 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.