In this paper, a method for image deformation is presented. It is based upon decomposition of the deformation problem into basic physical laws. Unlike other methods that solve a differential or an energetic formulation of the physical laws involved, we encode the basic laws using computational algebraic topology. Conservative laws are translated into exact global values and constitutive laws are judiciously approximated. In order to illustrate the effectiveness of our model, we utilize the viscous fluid model to achieve neuroanatomy image registration