We review characterizations of (conditional) positive definiteness and show how they apply to the theory of radial basis functions. We then give complete proofs for the (conditional) positive definiteness of all practically relevant basis functions. Furthermore, we show how some of these characterizations may lead to construction tools for positive definite functions. Finally, we give new const...

We present techniques for modeling Variational Hermite Radial Basis Function (VHRBF) Implicits using a set of sketch-based interface and modeling (SBIM) operators. VHRBF Implicits is a simple and compact representation well suited for SBIM. It provides quality reconstructions, preserving the intended shape from a coarse and nonuniform number of point-normal samples extracted directly from the i...

Article history: Received 13 April 2012 Received in revised form 10 October 2012 Accepted 27 October 2012 Available online 8 December 2012

This paper compares radial basis function interpolants on diier-ent spaces. The spaces are generated by other radial basis functions, and comparison is done via an explicit representation of the norm of the error functional. The results pose some new questions for further research.

Monitoring nitrogen concentration of oilseed rape from hyperspectral data using radial basis function Fumin Wang, Jingfeng Huang, Yuan Wang, Zhuanyu Liu, Dailiang Peng & Feifeng Cao a Institute of Hydrology and Water Resources, Zhejiang University, Hangzhou, China b Institute of Agricultural Remote Sensing & Information Application, Zhejiang University, Hangzhou, China c Institute of Remote Sen...

A radial basis function (RBF) has the general form

Radial basis function networks (RBF) are efficient general function approximators. They show good generalization performance and they are easy to train. Due to theoretical considerations RBFs commonly use Gaussian activation functions. It has been shown that these tight restrictions on the choice of possible activation functions can be relaxed in practical applications. As an alternative differ...