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.

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.

As is now well known for some basic functions φ, hierarchical and fast multipole-like methods can greatly reduce the storage and operation counts for fitting and evaluating radial basis functions. In particular, for spline functions of the form

The Beppo-Levi native spaces which arise when using polyharmonic splines to interpolate in many space dimensions are embedded in Hölder-Zygmund spaces. Convergence rates for radial basis function interpolation are inferred in some special cases.

We introduce a class of matrix-valued radial basis functions (RBFs) of compact support that can be customized, e.g. chosen to be divergence-free. We then derive and discuss error estimates for interpolants and derivatives based on these matrixvalued RBFs.

Radial basis functions are well-known and successful tools for the interpolation of data in many dimensions. Several radial basis functions of compact support that give rise to nonsingular interpolation problems have been proposed, and in this paper we study a new, larger class of smooth radial functions of compact support which contains other compactly supported ones that were proposed earlier...

We describe a heuristic method for reconstructing a region in the plane from a noisy sample of points. The method uses radial basis functions with Gaussian kernels to compute a fuzzy membership function which provides an implicit approximation for the region.