Hybrid Spline-Based Elastic Image Registration Using Analytic Solutions of the Navier Equation

Abstract

We introduce a new hybrid approach for spline-based elastic image registration using both point 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 represented by weight matrices to cope with anisotropic errors. The hybrid registration approach is formulated as an energy-minimizing functional that incorporates landmark and intensity information as well as a regularization based on GEBS. 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 MR images of the brain. It turns out that the new scheme achieves more accurate results compared to a pure landmark-based as well as a pure intensity-based scheme.