The ability to register image data to a common coordinate system is a critical feature of virtually all imaging studies that require multiple subject analysis, combining single subject data from multiple modalities, or both. However, in spite of the abundance of literature on the subject and the existence of several variants of registration algorithms, their practical utility remains problematic, as commonly acknowledged even by developers of these methods because the complexity of the problem has resisted a general, flexible, and robust theoretical and computational framework. To address this issue, we present a new registration method that is similar in spirit to the current state-of-the-art technique of diffeomorphic mapping, but is more general and flexible. The method utilizes a Hamiltonian formalism and constructs registration as a sequence of symplectomorphic maps in conjunction with a novel phase space regularization based on the powerful entropy spectrum pathways (ESP) framework. The method is demonstrated on the three different magnetic resonance imaging (MRI) modalities routinely used for human neuroimaging applications by mapping between high resolution anatomical (HRA) volumes, medium resolution diffusion weighted MRI (DW-MRI) and HRA volumes, and low resolution functional MRI (fMRI) and HRA volumes. The typical processing time for high quality mapping ranges from less than a minute to several minutes on a modern multi core CPU for typical high resolution anatomical (~256x256x256 voxels) MRI volumes.