Anisotropy Radial Basis Function Spatial Interpolation Model Research For 3D Spatial Field

Anisotropy is one of the features of 3D geographic spatial field.The appropriate reconstruction of anisotropy 3D geographic space field based on the observed data is the key issue of both 3D spatial analysis and 3D GIS.Radial Basis Function(RBF)as one kind of accurate interpolation method with the benefits of its simple form and its independence of dimension can be used in the reconstruction of 3D spatial field.However all kinds of RBFs are isotropy,which do not conform the real spatial field.Considering the anisotropy of real spatial field,the spatial structure analysis and RBF interpolation theory are combined together,so that the RBF reconstruction model of the geographical object with spatial distribution’s difference and anisotropy is proposed in this paper,and the calculation method correspondent to this model is explored.The target of this research is to provide a new valid and reliable spatial interpolation for spatial analysis of geographical objects.The main works of this research include:(1)The issue of shape parameter’s evaluation that has influence on precision of RBF interpolation is intensively studied.The RBF interpolation model is classified as positive definite and conditional definite.Under the positive definite,the deficiencies of shape parameters calculated by Leave Out One Cross Validation(LOOCV)and improved LOOCV(ILOOCV).Calculation of shape parameter based on Particle Swarm Optimization(PSO)and ILOOCV is proposed.Under the conditional definite,the solution expression of RBF’s most optimal shape parameter is deduced.Based on this it is verified that shape parameter’s calculation of PSO and ILOOCV is also suitable in the situation of conditional definite.It is experimentally showed that the shape parameter calculated by PSO and ILOOCV can minimize the precision of RBF interpolation model..(2)Aimed at the problem of 3D spatial field’s anisotropy orientation feature analysis,the average Principle Hessen Direction(PHD)anisotropy orientation analysis based on orthogonal transforms is proposed.In this method the spatial coordinates and attribute information of sampling points are used to build the average PHD matrix,orthogonalizing the non-orthogonal axis with the Orthogonal transforms,which can be used the anisotropy direction of spatial field.(3)On the basis of step 2,variogram is used to operate the 3D structure feature analysis.The angle computing method based on spherical coordinate is proposed.The expression of classification with angles is offered,which is condensing points pair to the spherical coordinate then classification with common expression.For the interpolate search space,the setting method based on integration area is proposed,in which the areas surrounded by fitted curves of experimental semivariation in three directions and the line y=sill value are calculated,then the ratio of the three areas can be used as the ellipsoid parameters of search space..(4)The 3D spatial field anisotropy node RBF interpolation model is proposed in this research.The anisotropy transformation matrix is consist of the rotation matrix which is built by the three axises calculated by anisotropy exploring method and scaling matrix which is built by the ratio of the three search spaces.Then the isotropy RBF can be transformed into the anisotropy interpolation model that conforms the geographic features.On the basis of this the RBF models on every nodes are linearly combined,meanwhile the shape parameters of node RBF models are optimized.With the experimental data of iron’s grade,the reliability of Multiquadic RBF,Inverse Multiquadic RBF,Gauss RBF and Multi-RBF are comparative analyzed,which turned out that Multiquadic RBF has the highest precision following by multi-RBF and Inverse Multiquadic RBF,and the Gauss RBF-has the lowest precision that must be used with caution in 3D spatial interpolation.At last,the 3D spatial field of iron’s grade is reconstructed.