Analytical Method for High-Precision Seabed Surface Modelling Combining B-Spline Functions and Fourier Series
Analytical Method for High-Precision Seabed Surface Modelling Combining B-Spline Functions and Fourier Series
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DOI：
10.1080/01490419.2022.2091695
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发表时间：
2022-06
期刊：
影响因子：
1.6
通讯作者：
Ruichen Zhang;Guojun Zhai;S. Bian;Houpu Li;B. Ji
中科院分区：
文献类型：
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作者：
Ruichen Zhang;Guojun Zhai;S. Bian;Houpu Li;B. Ji
摘要高精度海底表面建模为海洋视觉计算、海底地形探测、海洋生物、海洋工程等领域提供了多源高精度基础地理数据集。提出了一种将B样条函数与傅里叶级数相结合的高精度海底表面模型，简称S-FS方法。首先，深入探讨了建模过程中B样条函数与傅里叶级数之间的数学关系，推导出了样条傅里叶级数模型的非递归基函数和二维样条傅里叶级数模型的具体表示。利用公开的大面积测深数据集，与传统方法（最近邻法、双线性法、双三次法）和传统傅里叶级数法进行了大量的对比实验，结果表明S-FS方法具有精度高、收敛性好、鲁棒性强等优点。最后，基于S-FS方法的数学理论模型，对S-FS方法构建高精度海底曲面的三大特点（降维、多分辨率表达和多尺度可视化）进行了直观深入的分析。与B样条函数相比，S-FS方法的基本函数继承了B样条函数优先紧支的特性，无需再进行递归计算，进一步显示了其在高精度海底曲面建模领域的可行性和可扩展性。
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.