(Stellenbosch : Stellenbosch University, 2008-03) Du Toit, Wilna; Herbst, B. M.; Hunter, K. M.; Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. Applied Mathematics.
A popular method for interpolating multidimensional scattered data is using
radial basis functions. In this thesis we present the basic theory of radial basis
function interpolation and also regard the solvability and stability of the
method. Solving the interpolant directly has a high computational cost for
large datasets, hence using numerical methods to approximate the interpolant
is necessary. We consider some recent numerical algorithms. Software to implement
radial basis function interpolation and to display the 3D interpolants
obtained, is developed. We present results obtained from using our implementation
for radial basis functions on GIS and 3D face data as well as an image
warping application.