顾及异向性的局部径向基函数三维空间插值

A 3D Local RBF Spatial Interpolation Considering Anisotropy

针对三维局部径向基函数(radial basis function,RBF)空间插值过程中合理设置待插值点的邻近搜索范围问题,提出了一种依据变异函数分析探索空间异向性的局部径向基函数插值方法。首先,构建采样点的协方差矩阵求解数据的三个轴向;然后,通过旋转变换将数据变换到新的坐标系下,根据地统计中的变异函数计算三个方向的变程,并将三个变程设置为局部搜索椭球体的三个轴;最后,对每个采样点构建节点RBF,通过对待插值点影响范围内的节点RBF进行线性加权组合,求出待插点的属性值。实验结果表明,该方法顾及了空间数据的异向性,计算精度高,插值结果可靠,是一种可行的顾及异向性的三维空间插值方法。

Aiming at the searching range of interpolation points in the process of three-dimensional （3D）, local radial basis function （RBF） interpolation based on exploring spatial anisotropy with vario- gram analysis was proposed. Firstly, three axes of the data was solved by constructing covariance ma- trix of the sampling point data and then the data was transformed into the new coordinate system by rotating transformation~ the range of each direction was calculated using geostatistical variograms; the three values of range was set as three axes of the ellipsoid; at last, node RBF at each sample point was built. The attribute values of interpolation were solved by linear combination of node RBF. Experi- mental results show that the proposed method is a feasible method for 3D spatial interpolation consid- ering anisotropy with high accuracy and reliable interpolation result.