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