We give a recipe for deriving local spline approximation methods which reproduce the whole spline space. The methods are obtained by solving a series of local approximation problems. Examples of speci c quadratic and cubic approximation methods are given. x

This paper generalizes the classical cubic spline with the construction of the cubic spline coalescence hidden variable fractal interpolation function (CHFIF) through its moments, i.e. its second derivative at the mesh points. The second derivative of a cubic spline CHFIF is a typical fractal function that is self-affine or non-self-affine depending on the parameters of the generalized iterated...

In this article, the cubic B-spline collocation method is implemented to find numerical solution of the problem arising from chemical reactor theory. The method is tested on some model problems from the literature, and the numerical results are compared with other methods.

We propose a new multiframe algorithm to enhance the spatial resolution of frames in video sequences. Our technique specifically accounts for the possibility that motion estimation will be inaccurate and compensates for these inaccuracies. Experiments comparing our results with other methods show that our multiframe enhancement algorithm yields perceptibly sharper enhanced images with significa...

This paper first describes an algorithm that finds the approximate finite impulse response (FIR) inverse of an FIR filter by minimizing the inversion (or reconstruction) error constrained to zero-bias. The generalization of the inverse filtering problem in the two channel case is the design of perfect reconstruction filter banks that use critical sampling. These considerations lead to the deriv...

Based on the cubic B-spline curve, new Chinese fonts are generated by wavelet transforms in this paper. The outlines of Chinese fonts are first transformed into B-spline curves. Then, using wavelet transforms, the control points of each curve are decomposed into hierarchies containing the detailed features of the Chinese fonts. Using the synthesis procedure of wavelet transforms, new fonts can ...

Uniform cubic B-spline functions have been used for mapping functions in various areas such as image warping and morphing, 3D deformation, and volume morphing. The injectivity (one-to-one property) of a mapping function is important to obtain good results in these areas. This paper considers the local injectivity conditions of 2D and 3D uniform cubic B-spline functions. We propose a geometric i...

Object-based video coding requires the transmission of the object shape. This shape is sent as a binary α-plane. In lossy packetbased networks, such as the Internet, this information has a nonnegligible probability of not arriving at the receiver, and hence its loss needs to be concealed. In this paper we propose a shape concealment technique utilizing Hermite splines. The algorithm has the fol...

A collocation method based on modified cubic B-spline functions has been developed for the valuation of European, American and barrier options of a single asset. The new approach contains discretization of temporal derivative using finite difference approximation of and approximating the option price with the modified B-spline functions. Stability of this method has been discussed and it is sho...