Piecewise polynomial kernels for image interpolation: a generalization of cubic convolution

A well-known approach to image interpolation is cubic convolution, in which the ideal sine function is modelled by a finite extent kernel, which consists of piecewise third order polynomials. In this paper we show that the concept of cubic convolution can be generalized. We derive kernels of up to ninth order and compare them both mutually and to cardinal splines of corresponding orders. From spectral analyses we conclude that the improvements of the higher order schemes over cubic convolution are only marginal. We also conclude that in all cases, cardinal splines are superior