We present in this paper a new registration and gain correction algorithm for 3D medical images. It is intensity based. The basic idea is to represent images by 4D points (xj,yj,zj,ij) and to define a global energy function based on this representation. For minimization, we propose a technique which does not require computing the derivatives of this criterion with respect to the parameters. It can be understood as an extension of the Iterative Closest Point algorithm or as an application of the formalism proposed by L. Cohen (Proceedings of the Fifth International Conference on Computer Vision (ICCV '95), Boston, June 1995). Two parameters enable us to develop a coarse-to-fine strategy both for resolution and for deformation. Our technique presents the advantage of minimizing a well-defined global criterion, to deal with various classes of transformations (for example, rigid, affine, volume spline, and radial basis functions), to be simple to implement, and to be efficient in practice. Results on real brain and heart 3D images are presented to demonstrate the validity of our approach. We also explain how one can compute basic statistics on the deformation parameters to constrain the set of possible deformations by learning and to discriminate between different groups.