Oversampling Errors in Multimodal Medical Imaging Are Due to the Gibbs Effect

To analyze multimodal three-dimensional medical images, interpolation is required for resampling which—unavoidably—introduces an interpolation error. In this work we describe the interpolation method used for imaging and neuroimaging and we characterize the Gibbs effect occurring when using such methods. In the experimental section we consider three segmented three-dimensional images resampled with three different neuroimaging software tools for comparing undersampling and oversampling strategies and to identify where the oversampling error lies. The experimental results indicate that undersampling to the lowest image size is advantageous in terms of mean value per segment errors and that the oversampling error is larger where the gradient is steeper, showing a Gibbs effect.