Abstract

Determination of the mathematical model of elevation computation is based on a discrete data set, which could be used for elevation modelling. Usually, interpolation or approximation techniques are used for function determination. We describe an aspect of radial basis function networks employment in a smooth surface representation using a sample of discrete 3D positional input-output data pairs. In this article we present a different solution using a neural network, which is trained upon given discrete input-output data pairs and uses radial basis functions for activation in hidden layer. Radial basis function network surface approximation is based on a single hidden-layer structure and uses pseudo-inversion as an alternative to
back-propagation learning algorithm to obtain optimal weights. Radial basis function network determines its own specific model for continuous function representation. In case study, we have shown that differences in quality surface modelling upon several activation functions exist. While using Gaussian activation function we have not reached desired results, the use of poly-harmonic lead to much more successful surface modelling results.

Key words: elevation model, interpolation, approximation, neural networks, radial basis activation functions, backpropagation, pseudo-inversion