Spline-based elastic image registration using solutions of the navier equation

We introduce a new hybrid approach for spline-based elastic image registration using both landmarks and intensity information. As underlying deformation model we use Gaussian elastic body splines (GEBS), which are solutions of the Navier equation of linear elasticity under Gaussian forces. We also incorporate landmark localization uncertainties, which are characterized by weight matrices representing anisotropic errors. To combine landmarks and intensity information, we formulate an energy-minimizing functional that simultaneously minimizes w.r.t. both the landmark and intensity information. The resulting functional can be efficiently minimized using the method of Levenberg/Marquardt. Since the approach is based on a physical deformation model, cross-effects in elastic deformations can be taken into account. We demonstrate the applicability of our scheme based on 3D synthetic images, 2D MR images of the brain, as well as 2D gel electrophoresis images. It turns out that the new scheme achieves more accurate results compared to a pure landmark-based approach.