In this paper, we revisit wavelet theory starting from the representation of a scaling function as the convolution of a B-spline (the regular part of it) and a distribution (the irregular or residual part). This formulation leads to some new insights on wavelets and makes it possible to rederive the main results of the classical theory—including some new extensions for fractional orders—in a se...

In this paper, we revisit wavelet theory starting from the representation of a scaling function as the convolution of a B-spline (the regular part of it) and a distribution (the irregular or residual part). This formulation leads to some new insights on wavelets and makes it possible to rederive the main results of the classical theory—including some new extensions for fractional orders—in a se...

Nearest-neighbor, linear, and various cubic interpolation functions are frequently used in image resampling. Quadratic functions have been disregarded largely because they have been thought to introduce phase distortions. This is shown not to be the case, and a family of quadratic functions is derived. The interpolating member of this family has visual quality close to that of the Catmull-Rom c...

Spline curves are useful in a variety of geometric modeling and graphics applications and covering problems abound in practical settings. This work defines a class of covering decision problems for shapes bounded by spline curves. As a first step in addressing these problems, this paper treats translational spline covering for planar, uniform, cubic B-splines. Inner and outer polygonal approxim...

B-spline filter kernals have proved useful in many pixel sampling applications. A cubic B-spline filter kernal, having a width of four pixels, is particularly effective. In distribution ray tracing, pixel filters are evaluated implicitly by having the density of sampling proportional to the filter value. In this work we present a simple method to generate random samples having an underlying B-s...

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...