In this paper, we propose a new interpolation technique using exponential B-spline, which is super-set of the Bspline. An interpolation kernel of exponential B-spline was proposed using IIR based technique by Unser. As another approach, this paper presents an exponential B-spline interpolation kernel using simple mathematics based on Fourier approximation. A high signal to noise ratio can be ac...

Non-uniform B-spline dictionaries on a compact interval are discussed in the context of sparse signal representation. For each given partition, dictionaries of B-spline functions for the corresponding spline space are built up by dividing the partition into subpartitions and joining together the bases for the concomitant subspaces. The resulting slightly redundant dictionaries are composed of B...

We propose a learning approach to designing fuzzy controllers based on the B-spline model. Unlike other normalised parameterised set functions for deening fuzzy sets, B-spline basis functions do not necessarily span from membership values zero to one, but possess the property \partition of unity". B-spline basis functions can be automatically determined after each input is partitioned. Learning...

In this paper we propose a method to approximate a parametric 3 D-function by bicubic B-spline functions

The problems of determining the B–spline form of a C Pythagorean– hodograph (PH) quintic spline curve interpolating given points, and of using this form to make local modifications, are addressed. To achieve the correct order of continuity, a quintic B–spline basis constructed on a knot sequence in which each (interior) knot is of multiplicity 3 is required. C quintic bases on uniform triple kn...

By using straightforward frequency arguments we classify transformations of probabilities which can be generated by transition from one preparation procedure (context) to another. There are three classes of transformations corresponding to statistical deviations of different magnitudes: (a) trigonometric; (b) hyperbolic; (c) hypertrigonometric. Each class is characterized by a perturbation of t...

A collocation procedure is developed for the linear and nonlinear Fredholm and Volterraintegro-differential equations, using the globally defined B-spline and auxiliary basis functions.The solutionis collocated by cubic B-spline and the integrand is approximated by the Newton-Cotes formula.The error analysis of proposed numerical method is studied theoretically. Numerical results are given toil...

In this paper we prove that the degree elevation of B-spline curves can be interpreted as corner cutting process in theory. We also discover the geometric meaning of the auxiliary control points during the corner cutting. Our main idea is to gradually elevate the degree of B-spline curves one knot interval by one knot interval. To this end, a new class of basis functions, to be called bi-degree...