Subunity coordinate translation with Fourier transform to achieve efficient and quality three-dimensional medical image interpolation

A new approach to the interpolation of three-dimensional (3D) medical image s is presented. Instead of going through the conventional interpolation sch eme where the continuous function is first reconstructed from the discrete data set and then resampled, the interpolation is achieved with a subunity coordinate translation technique. The original image is first transformed i nto the spatial-frequency domain. The phase of the transform is then modifi ed with n - 1 linear phase terms in the axial direction to achieve n - 1 su bunity coordinate translations with a distance 1/n, where n is an interpola tion ratio, following the phase shift theorem of Fourier transformation. Al l the translated images after inverse Fourier transformation are then inter spersed in turn into the original image. Since windowing plays an important role in the process, different window functions have been studied and a pr oper recommendation is provided. The interpolation quality produced with th e present method is as good as that with the sampling (sinc) function, whil e the efficiency, thanks to the fast Fourier transformation, is very much i mproved. The approach has been validated with both computed tomography (CT) and magnetic resonance (MR) images. The interpolations of 3D CT and MR ima ges are demonstrated. (C) 1999 American Association of Physicists in Medici ne. [S0094-2405(99)01209-2].