Sibson (natural neighbour) and non-Sibsonian interpolation for digital elevation model (DEM)

A new interpolation scheme called as "non-Sibsonian interpolation" based on natural neighbours is proposed in [2]. The non-Sibsonian interpolation is reviewed in details and its performance in a Galerkin method for the solution of elliptic partial differential equations is studied in [17]. The purpose of this paper is to evaluate non-Sibsonian and Sibson interpolations for height interpolation in digital elevation model (DEM). Interpolations of non-Sibsonian, Sibson (natural neighbour), nearest neighbour, weighted average, polynomial, multiquadric, minimum curvature, and linear interpolation in triangles are tested on six theoretical test surfaces. For each test surface, 150 reference points in a scattered sampling pattern and 81 interpolation points in a regular sampling pattern are derived. True surface heights of the reference and interpolation points are calculated by the surface equations. For each test surface heights of the 81 interpolation points are interpolated based on the reference points by the use of eight different interpolation methods mentioned above. The accuracy measures (standard deviation, average of errors and maximum error) of the interpolation methods are derived by differences between true and interpolated surface values.