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

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.