Numerical methods for volume preserving image registration

Image registration techniques are used routinely in a variety of today’s medical imaging diagnosis. Since the problem is ill-posed, one may like to add additional information about distortions. This applies, for example, to the registration of contrast enhanced images, where variations of substructures are not related to patient motion but to contrast uptake. Here, one may only be interested in registrations which do not alter the volume of any substructure. In this paper we discuss image registration techniques with a focus on volume preserving constraints. These constraints can reduce the non-uniqueness of the registration problem significantly. Our implementation is based on a constrained optimization formulation. Upon discretization, we obtain a large, discrete, highly nonlinear optimization problem and the necessary conditions for the solution form a discretize nonlinear partial differential equation. To solve the problem we use a variant of Sequential Quadratic Programming method. Moreover, we present results on synthetic as well as on real life data. 1