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 paper we investigate the approximation of a class of parabolic partial differential equations on the unit spheres S n ⊂ R n+1 using spherical basis functions. Error estimates in the Sobolev norm are derived.

To any graph G can be associated a toric ideal I G. In this talk some recent joint work with Enrique Reyes and Christos Tatakis will be presented on the toric ideal of a graph. A characterization in graph theoretical terms of the elements of the Graver basis and the universal Gröbner basis of the toric ideal of a graph will be given. The Graver basis is the union of the primitive binomials of t...

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.

H–bases are bases for polynomial ideals, characterized by the fact that their homogeneous leading terms are a basis for the associated homogeneous ideal. In the computation of H–bases without term orders, an important task is to determine the orthogonal projection of a homogeneous polynomial to certain subspaces of homogeneous polynomials with respect to a given inner product. One way of doing ...

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.

Numerical solutions of the Helmholtz equation suffer from numerical pollution especially for the case of high wavenumbers. The major component of the numerical pollution is, as has been reported in the literature, the dispersion error which is defined as the phase difference between the numerical and the exact wave. The dispersion error for the meshless methods can be a priori determined at an ...