In computer aided design (CAD), the availability of many types of surface editing which ease creating the geometric models is important. This paper describes a wavelets-based mulresolution representation for endpoint-interpolating cubic B-spline surface and algorithms to support the surface editing at different scales, allowing structural features (global shape) deformations as well as detail f...

In this article a new technique for the estimation of the distance of visibility in fog conditions is presented. It is based on a psychovisual model and on contrast estimation with wavelet transform. For this application, specific B–spline wavelets are introduced in order to have a good space and frequency localization and to enable a fast implementation. Using images stemming from situations o...

The problem of nonparametric function estimation has received a substantial amount of attention in the statistical literature over the last 15 years. To a very large extent, the literature has described kernel-based convolution smoothing solutions to the problems of probability density estimation and nonlinear regression. Among the subcultures within this literature has been a substantial effor...

This study focuses on identifying damage in reinforced concrete (RC) beams using time-domain modal testing and wavelet analysis. A numerical model of an RC beam was used to generate various scenarios with different severities locations. Acceleration time histories were recorded for both damaged undamaged structures. Two indices, DI_MW DI_SW, derived from the analysis, employed determine locatio...

Using results on syzygy modules over a multivariate polynomial ring, we are able to construct compactly supported wavelet bi-frames with few generators from almost any pair of compactly supported multivariate refinable functions. In our examples, we focus on wavelet bi-frames whose primal and dual wavelets are both derived from one box spline function. Our wavelet bi-frames have fewer generator...

We show how to construct a stable hierarchical basis for piecewise quadratic C continuous splines defined on Powell–Sabin triangulations. We prove that this hierarchical basis is well suited for compressing surfaces. Our compression method does not require the construction of wavelets which are usually expensive to compute, but instead we construct a stable quasi-interpolation scheme for our sp...

We prove that feedforward artificial neural networks with a single hidden layer and an ideal sigmoidal response function cannot provide localized approximation in a Euclidean space of dimension higher than one. We also show that networks with two hidden layers can be designed to provide localized approximation. Since wavelet bases are most effective for local approximation, we give a discussion...

We propose a new consistent, residual-based stabilization of the Stokes problem. The stabilizing term involves a pseudo-differential operator, defined via a wavelet expansion of the test pressures. This yields control on the full L2-norm of the resulting approximate pressure independently of any discretization parameter. The method is particularly well suited for being applied within an adaptiv...