Abstract

In this paper, we consider two approaches of simplifying medium- and large-sized range datasets to a compact data point set, based on the Radial Basis Functions application. The first algorithm uses the Pseudo-Inverse Approach for the case of given basis functions, and the second one uses an SVD-Based Approach for the case of unknown basis functions. The novelty of this paper consists in a novel partition-based SVD algorithm for a symmetric square matrix, which can effectively reduce the dimension of a matrix in a given partition case. On the theoretical aspect, it is proven that the reduced matrix is an optimal approximation in least square sense. Furthermore, this partition-based SVD algorithm is combined with a standard clustering algorithm to form our SVD-Based Approach, which can then seek an appropriate partition automatically for dataset simplification. Experimental results indicate that the presented Pseudo-Inverse Approach requires a uniform sampled control point set, and can obtain an optimal least square solution in the given control point set case. While in the unknown control point case, the presented SVD-Based Approach can seek an appropriate control point set automatically, and the resulting surface preserves more of the essential structures and is prone to less distortions.