Methods for efficient, high quality volume resampling in the frequency domain

Resampling is a frequent task in visualization and medical imaging. It occurs whenever images or volumes are magnified, rotated, translated, or warped. Resampling is also an integral procedure in the registration of multimodal datasets, such as CT, PET, and MRI, in the correction of motion artifacts in MRI, and in the alignment of temporal volume sequences in fMRI. It is well known that the quality of the resampling result depends heavily on the quality of the interpolation filter used. However, high-quality filters are rarely employed in practice due to their large spatial extents. We explore a new resampling technique that operates in the frequency-domain where high-quality filtering is feasible. Further, unlike previous methods of this kind, our technique is not limited to integer-ratio scaling factors, but can resample image and volume datasets at any rate. This would usually require the application of slow discrete Fourier transforms (DFT) to return the data to the spatial domain. We studied two methods that successfully avoid these delays: the chirp-z transform and the FFTW package. We also outline techniques to avoid the ringing artifacts that may occur with frequency-domain filtering. Thus, our method can achieve high-quality interpolation at speeds that are usually associated with spatial filters of far lower quality.