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...

In this paper we use the lifting scheme to construct biorthogonal spline wavelet bases on regularly refined non-uniform grids. The wavelets have at least one vanishing moment and on each resolution level they form an L2 Riesz basis. Furthermore we are interested in determining the exact range of Sobolev exponents for which the complete multilevel system forms a Riesz basis. Hereto we need to ex...

We propose a generalization of the Cohen-Daubechies-Feauveau (CDF) and 9/7 biorthogonal wavelet families. This is done within the framework of non-stationary multiresolution analysis, which involves a sequence of embedded approximation spaces generated by scaling functions that are not necessarily dilates of one another. We consider a dual pair of such multiresolutions, where the scaling functi...

In this paper we consider polynomial splines with equidistant nodes which may grow as O|x|. We present an integral representation of such splines with a distribution kernel where exponential splines are used as basic functions. By this means we characterize splines possessing the property that translations of any such spline form a basis of corresponding spline space. It is shown that any such ...

The purpose of this presentation is to describe a recent family of basis functions—the fractional B-splines—which appear to be intimately connected to fractional calculus. Among other properties, we show that they are the convolution kernels that link the discrete (finite differences) and continuous (derivatives) fractional differentiation operators. We also provide simple closed forms for the ...

R. Mutihac Electricity and Biophysics, University of Bucharest, Bucharest, Romania Objective Analysis of an fMRI block-based visual stimulation paradigm was comparatively performed by wavelet analysis and statistical parametric mapping (SPM) [1] based on Gaussian Random Field Theory (RFT). The voxels were isotropic and the same general linear model (GLM) was employed in both SPM and the discret...

We present multiresolution B-spline surfaces of arbitrary order defined over triangular domains. Unlike existing methods, the basic idea of our approach is to construct the triangular basis functions from their tensor product relatives in the spirit of box splines by projecting them onto the barycentric plane. The scheme works for splines of any order where the fundamental building blocks of th...

A new method for manipulation of curves in several degrees is presented. When a point of curve is moved, it a ects a relative local segment, which size could depends of the propagation of the point through their lower resolution curves. So, for the same displacement of the point, could be generated relative local segments of di erent sizes, only varying a local parameter such sti ness constant....