| 基于RASM的紧支撑径向基函数自适应并行地形插值方法 |
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| 引用本文： | 吕海洋,盛业华,李佳,段平,张思阳.基于RASM的紧支撑径向基函数自适应并行地形插值方法[J].武汉大学学报(信息科学版),2017,42(9):1316-1322. |
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| 作者姓名： | 吕海洋 盛业华 李佳 段平 张思阳 |
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| 作者单位： | 1.南京师范大学虚拟地理环境教育部重点实验室, 江苏 南京, 210023 |
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| 基金项目： | 国家自然科学基金41271383国家自然科学基金41371374国家自然科学基金41471102 |
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| 摘 要： | 快速、准确地对地形进行重建以生成数字高程模型是地理信息表达的重要研究内容，径向基函数（radial basis function，RBF）作为一种插值性能较优的空间插值方法，特别适合于重建复杂的地形模型，但随着已知地形采样点数量的增加，RBF插值模型求解速度变慢，同时插值矩阵过于庞大而导致插值模型求解困难甚至求解失败。针对这个问题，本文基于区域分解和施瓦兹并行原理进行地形插值，以紧支撑径向基函数（compact support RBF，CSRBF）构建基于所有地形采样数据的全局插值矩阵，并自适应求解子区域CSRBF插值节点紧支撑半径，基于限制性加性施瓦兹方法（restricted additive Schwarz method，RASM）采用多核并行架构对各局部子区域的插值矩阵进行求解。以某地区数字高程模型（DEM）数据进行插值实验，结果表明，本文方法能够对大规模地形数据进行准确重建，并且具有较高的求解效率。
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| 关 键 词： | 地形重建 区域分解 并行 自适应 RASM 紧支撑径向基函数 |
| 收稿时间： | 2016-06-07 |
An Adaptive Parallel CSRBF Terrain Interpolation Method Based on RASM |
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| Institution: | 1.Key Laboratory of Virtual Geographic Environment, Ministry of Education, Nanjing Normal University, Nanjing 210023, China2.Jiangsu Center for Collaborative Innovation in Geographical Information Resource Development and Application, Nanjing Normal University, Nanjing 210023, China3.College of Tourism and Geographical Sciences, Yunnan Normal University, Kunming 650500, China |
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| Abstract: | Fast and accurate 3D terrain reconstruction to acquire a high resolution Digital Elevation Model (DEM) is one of the most important research areas in geographic information representation. As a kind of spatial interpolation method that is superior to other accurate interpolation methods, the Radial Basis Function (RBF) is particularly suitable for the reconstruction of complex 3D terrain models. However, the efficiency when calculating this interpolation model becomes lower and lower with an increasing number of sampling points, and the interpolation equation becomes too difficult or even fails as the interpolation matrix become bigger and bigger. To address this issue, a parallel interpolation method based on the principle of domain decomposition and restricted additive schwarz method (referred to as RASM) is proposed. A compact support RBF (CSRBF) based global interpolation matrix was built by taking all of the known sampling points, and the optimal local compact support radius is calculated for each of the local domains. The interpolation procedure operates in parallel through a message passing interface (MPI) based on the RASM. DEM data are used in an interpolation experiment. The results show that the method proposed in this paper could accurately reconstruct the terrain with massive terrain sampling data enabling a high efficiency solution. |
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