Mutual information matching and interpolation artefacts

Registration algorithms often require the estimation of grey values at image locations that do not coincide with image grid points. Because of the intrinsic uncertainty, the estimation process will invariably be a source of error in the registration process. For measures based on entropy, such as mutual information, an interpolation method that changes the amount of dispersion in the probability distributions of the grey values of the images will influence the registration measure. With two images that have equal grid distances in one or more corresponding dimensions, a large number of grid points can be aligned for certain geometric transformations. As a result, the level of interpolation is dependent on the image transformation and hence, so is the interpolation-induced change in dispersion of the histograms. When an entropy based registration measure is plotted as a function of transformation, it will show sudden changes in value for the grid-aligning transformations. Such patterns of local extrema impede the optimization process. More importantly, they rule out subvoxel accuracy. Interpolation-induced artefacts are shown to occur in registration of clinical images, both for trilinear and partial volume interpolation. Furthermore, the results suggest that improved registration accuracy for scale-corrected MR images may be partly accounted for by the inequality of grid distances that is a result of scale correction