Cubic convolution interpolation for digital image processing

1981/12/01 by R. Keys, Robert G. Keys · 3,727 citations
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Algorithm #Artificial intelligence #Bicubic interpolation #Bilinear interpolation #Binary image #Computer science #Convolution (computer science) #Demosaicing #Digital Filter Design and Implementation #Discrete mathematics #Fourier analysis #Fourier transform #Image (mathematics) #Image and Signal Denoising Methods #Image processing #Image scaling #Interpolation (computer graphics) #Kernel (algebra) #Linear interpolation #Mathematical analysis #Mathematics #Monotone cubic interpolation #Nearest-neighbor interpolation #Overlap–add method #Spline interpolation #Stairstep interpolation #Statistics #Trilinear interpolation

paper · doi:10.1109/tassp.1981.1163711

published in IEEE Transactions on Acoustics Speech and Signal Processing 29(6), 1153-1160 (Institute of Electrical and Electronics Engineers)

openalex publication_date 1981/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

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