Adaptive osculatory rational interpolation for image processing

On the Osculatory Rational Interpolation Problem

The problem of the existence and construction of a table of osculating rational functins fj m for 1, m > 0 is considered. First, a survey is given of some results from the theory of osculatory rational interpolation of order s¡ — 1 at points x¡ for i > 0. Using these results, we prove the existence of continued fractions of the form c0 + c, -(x y0) + . . . + ck-(x y0) . . . (x yk_x) ck + l •<* ...

Bivariate Blending Thiele-Werner’s Osculatory Rational Interpolation

Adaptive Order Statistics Rational Hybrid Filters for Multichannel Image Processing

A new adaptive multichannel filtering approach is introduced and analyzed in this paper. The technique is simpler and more appropriate than traditional approaches that have been addressed by means of groupwise vector ordering information. These filters are a two-stage filters based on rational functions (RF) using fuzzy transformations of the Euclidean and angular distances among the different ...

Optimum-Point Formulas for Osculatory and Hyperosculatory Interpolation

Formulas are given for n-point osculatory and hyperosculatory (as well as ordinary) polynomial interpolation for f(x), over ( —1, 1), in terms of fixi), f'(xi) and f"(x/) at the irregularly-spaced Chebyshev points x¡ = —cos {(2i — l)ir/2n}, i = 1, • • ■ , n. The advantage over corresponding formulas for Xi equally spaced is in the squaring and cubing, in the respective osculatory and hyperoscul...

Cubic Convolution Interpolation for Digital Image Processing

Absfrucf-Cubic convolution interpolation is a new technique for resampling discrete data. It has a number of desirable features which make it useful for image processing. The technique can be performed efficiently on a digital computer. The cubic convolution interpolation function converges uniformly to the function being interpolated as the sampling increment approaches zero, With the appropri...