Image registration requires the transformation of one image to another so as to spatially align the two images. This involves interpolation to estimate gray values of one of the images at positions other than the grid points. When registering two images that have equal grid distances in one or more dimensions, the grid points can be aligned in those dimensions for certain geometric transformations. Consequently, the number of times interpolation is required to compute the registration measure of two images is dependent on the image transformation. When an entropy-based registration measure, such as mutual information, is plotted as a function of the transformation, it will show sudden changes in value for grid-aligning transformations. Such patterns of local extrema impede the registration optimization process. More importantly, they rule out subvoxel accuracy. In this paper, two frequently applied interpolation methods in mutual information-based image registration are analyzed, viz. linear interpolation and partial volume interpolation. It is shown how the registration function depends on the interpolation method and how a slight resampling of one of the images may drastically improve the smoothness of this function.