In this paper, a new method for gray-scale image and color zooming algorithm based on their local information is offered. In the proposed method, the unknown values of the new pixels on the image are computed by Moving Least Square (MLS) approximation based on both the quadratic spline and Gaussian-type weight functions. The numerical results showed that this method is more preferable to biline...

We propose a fast alternative to B-splines in image processing based on an approximate calculation using precomputed B-spline weights. During B-spline indirect transformation, these weights are efficiently retrieved in a nearest-neighbor fashion from a look-up table, greatly reducing overall computation time. Depending on the application, calculating a B-spline using a look-up table, called B-L...

This paper considers the problem of constructing a smooth surface to fit rows of data points. A special class of T-spline surfaces is examined, which is characterized to have a global knot vector in one parameter direction and individual knot vectors from row to row in the other parameter direction. These T-spline surfaces are suitable for lofted surface interpolation or approximation. A skinni...

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...

in this article, a numerical approximation to the solution of the newell-whitehead equation (nwe) and cauchy problem of ill-posed non-linear diffusion equation have been studied. the presented scheme is obtained by using the derivative of the cubic b-spline quasi-interpolation (bsqi) to approximate the spatial derivative of the dependent variable and first order forward difference to approximat...

The RKHS-based optimal image interpolation method, presented by Chen and de Figueiredo (1993), is applied to scattered potential field measurements. The RKHS which admits only interpolants consistent with Laplace's equation is defined and its kernel, derived. The algorithm is compared to bicubic spline interpolation, and is found to yield vastly superior results.

We derive knot insertion formulas for the B-spline basis for natural splines. We also show that this basis is totally positive and give necessary and su cient nesting conditions for uniqueness of interpolation. x

The problem of semi-cardinal spline interpolation was solved by Schoenberg exploiting the piecewise polynomial form of the splines. In the present paper, we propose a new construction for the Lagrange functions of semi-cardinal spline interpolation , based on a radial basis and Fourier transform approach. This approach suggests a way of extending semi-cardinal interpolation to polyharmonic spli...