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Imaging devices exploit the Nyquist-Shannon sampling theorem to avoid bothaliasing and redundant oversampling by design. Conversely, in medical imageresampling, images are considered as continuous functions, are warped by aspatial transformation, and are then sampled on a regular grid. In most cases,the spatial warping changes the frequency characteristics of the continuousfunction and no special care is taken to ensure that the resampling gridrespects the conditions of the sampling theorem. This paper shows that thisoversight introduces artefacts, including aliasing, that can lead to importantbias in clinical applications. One notable exception to this common practice iswhen multi-resolution pyramids are constructed, with low-pass "anti-aliasing"filters being applied prior to downsampling. In this work, we illustrate whysimilar caution is needed when resampling images under general spatialtransformations and propose a novel method that is more respectful of thesampling theorem, minimising aliasing and loss of information. We introduce thenotion of scale factor point spread function (sfPSF) and employ Gaussiankernels to achieve a computationally tractable resampling scheme that can copewith arbitrary non-linear spatial transformations and grid sizes. Experimentsdemonstrate significant (p<1e-4) technical and clinical implications of theproposed method.

Scale factor point spread function matching: Beyond aliasing in image resampling