Accumulated similarity surface for spatial interpolation

Spatial interpolation uses the geospatial features with known values and spatial relationships to predict unknown values. Spatial weights matrix is the most conventional way to represent spatial relationships when interpolating, where Euclidean distance is employed as the similarity measurement to tackle the spatial dependence problem. But spatial relationships of geospatial features should build on spatial nonstationarity besides spatial dependence. Therefore Euclidean distance is not suitable to represent spatial relationships over the whole geospatial space and local spatial analysis methods, which address the spatial nonstationarity should be employed to construct spatial weights matrix. This paper proposes accumulated similarity surface and brings in curve evolution and fast marching method to calculate the similarity of geographical features. Thus spatial weights matrix is constructed using accumulated similarity surfaces according to both spatial dependence and spatial nonstationarity. Experiments are conducted using ASTER DEM as experimental data. The interpolation results show that spatial weights matrix based on accumulated similarity surfaces performs better than Euclidean-distance-based spatial weights matrix.