Image registration is an important procedure for medical diagnosis. Since the large inter-site retrospective validation study led by Fitzpatrick at Vanderbilt University, voxel-based methods and more specifically mutual information-based registration methods (see for instance [IEEE Trans. Med. Imag. 22 (8) (2003) 986] for a review on these methods) have been regarded as the method of choice for rigid-body intra-subject registration problems. In this study we propose a method that is based on the Iterative Closest Point algorithm and a pre-computed closest point map obtained with a slight modification of the fast marching method proposed by Sethian. Pre-computing the closest point map speeds up the process because at each iteration point correspondence can be established by table lookup. We also show that because the closest point map is defined on a regular grid it introduces a registration error and we propose an interpolation scheme that addresses this issue. The method has been tested both on synthetic and real images, and registration results have been assessed quantitatively using the data set provided by the Retrospective Registration Evaluation Project. For these volumes, MR and CT head surfaces were extracted automatically using a level-set technique. Results show that on these data sets this registration method leads to accuracy numbers that are comparable to those obtained with voxel-based methods.