Improvement of some interpolation methods for terrain reconstruction from scattered data

Abstract

Using GPS modules it is easy to obtain 3D data for areas that have not been digitized yet. Such terrain data are usually not arranged in a grid, and therefore we have to use scattered data interpolation methods. The aim of the paper is to create a digital terrain model from 3D data using modifications of known methods. Sibson interpolation method is often used when we need to interpolate large data sets. This method has low memory requirements, it is sufficiently fast, but creates undesired surface artefacts. Our aim is to have the resulting interpolation surface as similar as possible to the original surface. We have decided to replace the heights at specified points by local functions. We use biquadratic and bicubic polynomials, Hardy’s multiquadrics and thin plate spline as local functions. In the paper, we have evaluated the time requirements and the accuracy with which the interpolated area matches the actual 3D data on 2 terrain samples (the Little Carpathians and a small part of the Little Carpathians).