Quantitative comparison of sinc-approximating kernels for medical image interpolation

Abstract

Interpolation is required in many medical image processing operations. From sampling theory, it follows that the ideal interpolation kernel is the sinc function, which is of infinite extent. In the attempt to obtain practical and computationally efficient image processing algorithms, many sinc-approximating interpolation kernels have been devised. In this paper we present the results of a quantitative comparison of 84 different sinc-approximating kernels, with spatial extents ranging from 2 to 10 grid points in each dimension. The evaluation involves the application of geometrical transformations to medical images from different modalities (CT, MR, and PET), using the different kernels. The results show very clearly that, of all kernels with a spatial extent of 2 grid points, the linear interpolation kernel performs best. Of all kernels with an extent of 4 grid points, the cubic convolution kernel is the best (28% - 75% reduction of the errors as compared to linear interpolation). Even better results (44% - 95% reduction) are obtained with kernels of larger extent, notably the Welch, Cosine, Lanczos, and Kaiser windowed sinc kernels. In general, the truncated sinc kernel is one of the worst performing kernels.