Modified Radial Basis Functions Approximation Respecting Data Local Features

This paper presents new approaches for Radial basis function (RBF) approximation of 2D height data. The proposed approaches respect local properties of the input data, i.e. stationary points, inflection points, the curvature and other important features of the data. Positions of radial basis functions for RBF approximation are selected according to these features, as the placement of radial basis functions has significant impacts on the final approximation error. The proposed approaches were tested on several data sets. The tests proved significantly better approximation results than the standard RBF approximation with the random distribution of placements of radial basis functions.