We provide conditions under which 2D digital images, considered in the two most common digital topology models (namely, dual adjacency and well-composedness), preserve their topological properties under rigid transformation. This study, that is developed in a discrete framework, leads to the proposal of efficient preprocessing strategies that ensure the topological invariance of images under further rigid transformation. These results and methods are proved to be valid for various kinds of images (binary, grey-level, label), thus providing a generic set of tools, that can be used in particular in the context of image registration and warping.