In this paper, we identify univariate prewavelets on spaces spanned by translates of multiquadric functions and other radial basis functions with nonequally spaced centers (or "knots"). Although the multiquadric function and its relations are our prime examples, the theory is sufficiently broad to admit prewavelets from other radial basis function spaces as well.

The behavior of Radial Basis Function (RBF) Networks greatly depends on how the center points of the basis functions are selected. In this work we investigate the use of instance reduction techniques, originally developed to reduce the storage requirements of instance based learners, for this purpose. Five Instance-Based Reduction Techniques were used to determine the set of center points, and ...

Our goal is to create a natural Italian talking face with, in particular, lip-readable movements. Based on real data extracted from an Italian speaker with the ELITE system, we have approximated the data using radial basis functions. In this paper we present our 3D facial model based on MPEG-4 standard and our computational model of lip movements for Italian. Our experiment is based on some pho...

This paper presents a new approach for the Radial Basis Function (RBF) interpolation of a vector field. Standard approaches for interpolation randomly select points for interpolation. Our approach uses the knowledge of vector field topology and selects points for interpolation according to the critical points location. We presents the results of interpolation errors on a vector field generated ...

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Our goal is to create a natural talking face with, in particular, lip-readable movements. Based on real data extracted from an Italian speaker with the ELITE system, we have approximated the data using radial basis functions. In this paper we present our 3D facial model based on MPEG-4 standard and our computational model of lip movements for Italian. Our experiment is based on some phonetic-ph...

While it was noted by R. Hardy and proved in a famous paper by C. A. Micchelli that radial basis function interpolants s(x) = ∑ λjφ(‖x − xj‖) exist uniquely for the multiquadric radial function φ(r) = √ r2 + c2 as soon as the (at least two) centres are pairwise distinct, the error bounds for this interpolation problem always demanded an added constant to s. By using Pontryagin native spaces, we...

We propose an animation system for personalized human head. Landmarks compliant to MPEG-4 facial definition parameters (FDP) are initially labeled on both template model and any target human head model as priori knowledge. The deformation from the template model to the target head is through a multilevel training process. Both general radial basis function (RBF) and compactly supported radial b...

In this article we propose a general and robust technique for modeling surfaces through the analysis of multiple image acquisitions. Our method is based on the minimization of the multi-view texture mismatch and is inherently multi-resolution, as the surface is obtained through a progressive re0nement of hierarchical radial basis functions. ? 2002 Elsevier Science B.V. All rights reserved.