基于RASM的紧支撑径向基函数自适应并行地形插值方法

An Adaptive Parallel CSRBF Terrain Interpolation Method Based on RASM

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。

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 mod els. 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 interpola- tion 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 ma- trix was built by taking all of the known sampling points, and the optimal local compact support radi us 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 experi ment. The results show that the method proposed in this paper could accurately reconstruct the ter rain with massive terrain sampling data enabling a high efficiency solution.