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### 局部最优形态参数的RBF分块地形插值方法与实验

1. 1. 南京师范大学 虚拟地理环境教育部重点实验室,南京 210023
2. 云南师范大学旅游与地理科学学院,昆明 650500
• 收稿日期:2014-04-22 修回日期:2014-05-20 出版日期:2015-03-10 发布日期:2015-03-10
• 通讯作者: 盛业华 E-mail:lvhaiyang368@163.com;shengyehua@njnu.edu.cn
• 作者简介:

作者简介：吕海洋(1989-),男,博士生,研究方向为空间数据插值方法、地形建模。E-mail:lvhaiyang368@163.com

• 基金资助:
国家自然科学基金项目(41271383)

### A Hierarchical RBF Interpolation Method Based on Local Optimal Shape Parameters

LV Haiyang1(), SHENG Yehua1,*(), DUAN Ping1, ZHANG Siyang1, LI Jia2

1. 1. Key Laboratory of Virtual Geographical Environment, Ministry of Education, Nanjing Normal University, Nanjing 210023, China
2. College of Tourism and Geographical Sciences, Yunnan Normal University, Kunming 650500, China
• Received:2014-04-22 Revised:2014-05-20 Online:2015-03-10 Published:2015-03-10
• Contact: SHENG Yehua E-mail:lvhaiyang368@163.com;shengyehua@njnu.edu.cn
• About author:

*The author: SHEN Jingwei, E-mail:jingweigis@163.com

Abstract:

As an accurate spatial interpolation method for data in arbitrary dimensions, Radial Basis Function (referred RBF), was particularly suitable for Digital Elevation Model (referred DEM) interpolation with respect to complex terrain that no assumption is needed for the experiment data. But the interpolation model would become difficult to solve when the number of points, whose elevation is already known, used to construct RBF interpolation model is too large. This is due to the reason that the inversed RBF interpolation matrix would become too huge or too slow to be solved. To address this issue, the hierarchical RBF interpolation method based on local optimal shape parameters, was proposed in this paper and the DEM was interpolated and reconstructed in the experiment. The interpolation procedure was described as follows: first, set the minimum point number in the tree node sub-regions of the study area and define the overlap rate between the adjacent child node sub-regions. Then, construct the regional binary tree recursively from top to bottom, that means the study area was firstly divided from a complete area into two small overlapped regions, and each region could be taken as the child nodes of the binary tree. Second, use the Leave One Out Cross Validation (referred LOOCV) method to calculate the optimal shape parameters in the leaf node regions of the binary tree. As the point distributions in each sub-region are different from each other, as well as the elevation properties, it would lead to different optimal shape parameters. Next, establish the optimal RBF interpolation model, i.e. calculate the linear combination coefficients for each RBF node in the interpolation model with the optimal shape parameter. Third, calculate the elevations of the unknown points in the leaf node regions and get the elevation values using the weighted average method according to the principle of Partition of Unity. The weight of the unknown point in the child node sub-region is calculated using the distance to the center point of the sub-region. Solve the interpolation problem from the bottom to the top recursively to get the final elevation values of the unknown points. Experiments was carried out by using the DEM in some area of Yunnan Province, and the results showed that RBF hierarchical interpolation method with local optimal shape parameters had good stability and high accuracy when DEM was reconstructed from random distributed spatial elevation points, thus it can be taken as an reliable interpolation method.