Battle-Lemari e's wavelet has a nice generalization in the bivariate setting. This generalization is called bivariate box spline wavelets. The magnitude of the lters associated with the bivariate box spline wavelets is shown to converge to an ideal high-pass lter when the degree of the bivariate box spline functions increases to 1. The passing and stopping bands of the ideal lter are dependent ...

As a rule, an energy method is widely adopted for b-spline curve smoothing, but this method has the disadvantages such as massive calculation, computation complexity and low efficiency. Compared with the energy method, multi-resolution smoothing approaches nicely overcome these obstacles. Presently, some researches have been conducted on multi-resolution smoothing, but these efforts mainly aime...

The purpose of this note is to highlight some of the unique properties of spline wavelets. These wavelets can be classified in four categories: othogonal (Battle-Lemarié), semi-orthogonal (e.g., B-spline), shift-orthogonal, and biorthogonal (Cohen-DaubechiesFeauveau). Unlike most other wavelet bases, splines have explicit formulae in both the time and frequency domain, which greatly facilitates...

Battle-Lemarié’s wavelet has a nice generalization in a bivariate setting. This generalization is called bivariate box spline wavelets. The magnitude of the filters associated with the bivariate box spline wavelets is shown to converge to an ideal high-pass filter when the degree of the bivariate box spline functions increases to `. The passing and stopping bands of the ideal filter are depende...

In this paper we present a novel approach to construct B-spline wavelets under constraints, taking advantage of the lifting scheme. Constrained B-spline wavelets allow multiresolution analysis of B-splines which fixes positions, tangents and/or high order derivatives at some user specified parameter values, thus extend the ability of B-spline wavelets: smoothing a curve while preserving user sp...

This paper aims to obtain approximate solutions of the one-dimensional nonlinear Klein-Gordon equation by employing Cubic B-spline wavelets. Our scheme uses the Galerkin method and approximates the solution in the terms of cubic B-spline scaling and wavelet functions. These wavelets are applied as testing and weighting functions. Because of some properties of these wavelets such as having compa...

This paper presents an eecient algorithm to generate realistic images using spline wavelets. Our algorithm departs from the use of non-overlapping wavelets by providing a continuous solution at no extra cost. This in turn eliminates need for inaccurate Gouraud shading or expensive nal gather step. Advantage of spline wavelets come from the fact that scaling functions are n th order B-splines th...