Analysing the Properties of Hierarchical RBFs for Interpolation

Interpolation methods using radial basis functions (RBF) are used for the creation and reconstruction of elevation and surface models, solving partial differential equations and reconstruction of noisy images. Hierarchical methods of RBF computation (HRBF) analysed in this article are based on the division of the domain of input points into subdomains, for which local interpolating radial functions are computed. These local functions are then combined into one global function interpolating the input points. The difference between HRBF methods lies in their approach to the division of the global domain and the subsequent joining of local functions. This article will focus on the analysis of advantages and disadvantages of HRBF methods, specifically methods using a balanced binary tree based on the kd-tree structure, or a grid to divide the global domain.