Cubic convolution interpolation for digital image processing

TLDR

Cubic convolution interpolation is a new, efficient resampling technique for discrete data that converges uniformly to the target function and offers accuracy between linear interpolation and cubic splines, making it useful for image processing. The paper derives a one‑dimensional interpolation function. The authors extend this function separably to two dimensions and apply it to image data.

Abstract

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 appropriate boundary conditions and constraints on the interpolation kernel, it can be shown that the order of accuracy of the cubic convolution method is between that of linear interpolation and that of cubic splines. A one-dimensional interpolation function is derived in this paper. A separable extension of this algorithm to two dimensions is applied to image data.