A new approach to image interpolation using the relationships between adjacent pixels in an image is introduced. In the first stage, the localized relationships are learned from the input image. In the second stage, the relationships and the concluded governing rules are used to build an interpolated image. Our method is compared with the main existing interpolation methods bilinear, bi-cubic a...

This paper is concerned with the spline interpolation of functions with a boundary layer component. It is shown that polynomial formulas of spline interpolation for such functions lead to significant errors. We proposed nonpolynomial spline interpolation formulas, fitted to a boundary layer component. Nonsmooth and smooth on whole interval interpolants are constructed. The accuracy of construct...

in this paper, a numerical method is developed for solving a linear sixth order boundaryvalue problem (6vbp ) by using the hyperbolic uniform spline of order 3 (lower order). thereis proved to be first-order convergent. numerical results confirm the order of convergencepredicted by the analysis.

A computationally inexpensive algorithm for signal interpolation using B-spline functions is presented in this work. Speciically, the convolution between the B-spline coeecients and the B-spline function itself, widely acknowledged as the most costly aspect of B-spline interpolation, is reformulated such that it is directly amenable to implementation at a much lower computational cost (16.25% o...

Image scaling is the process of resizing a digital image, wherein an image is converted from one resolution/dimension to another resolution/dimension without losing the visual content. It has many terminologies in literature such as Image Interpolation, image re-sampling, digital zooming, image magnification or enhancement, etc [1] [2]. Image interpolation algorithms can be grouped in two categ...

In this paper, an adaptive edge enhancement technique is proposed for two-dimensional (2-D) image scaling application. The anticipated image scaling algorithm consists of an edge detector, bilinear interpolation and sobel filter. The bilinear interpolation defines the intensity of the scaled pixel with the weighted average of the four nearest neighboring pixels, interpolated images become smoot...

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...

A personal account of the author's encounters with multivariate splines during their early history. 1 Tensor product spline interpolation My first contact with multivariate splines occurred in August 1960. In my first year at the Harvard Graduate School, working as an RA for Garrett Birkhoff, I had not done too well but, nevertheless, had gotten married and so needed a better income than the RA...