An Elasticity Penalty: Mixing FEM and Nonrigid Registration

Voxel-intensity based nonrigid image registration can be formulated as an optimization problem whose goal is to minimize a cost function consisting of two parts. One part characterizes the similarity between both images. The other part regularizes the transformation and/or penalizes improbable or impossible deformations. In this paper, we extend previous work on nonrigid registration by introducing a new penalty term expressing the elastic energy of the deformation, using the same expression as used in finite element modeling (FEM). We compare the new elasticity penalty, a volume penalty and a rigidity penalty with a biomechanical mass-tensor model (MTM), equivalent to FEM. Comparison is carried out on artificial images and volunteer breast MR images. We show that the results obtained using the elasticity penalty approximate the MTM registration up to less than 1 voxel for the artificial images and less than 3 voxels for the clinical images. The errors are mainly situated near the edges of the registered structures, and therefore can be attributed to differences in boundary conditions. We also show that the elasticity penalty, volume penalty and rigidity penalty give similar results.