  We establish a new framework for image registration, which is based on linear
elasticity and optimal mass transportation theory. We combine these two
arguments in order to obtain a PDE constrained optimization problem that is
analytically investigated and further discretized with the finite difference
method and solved by an inexact SQP algorithm. This requires to solve in each
step a large sparse linear system, which has a saddle point form. Motivated by
stability arguments we use a fully staggered grid for the discretization of the
displacement vector field. Artificial and real world examples are presented to
underline the numerical robustness of the method.
