Physics-based elastic registration using non-radial basis functions and including landmark localization uncertainties

We introduce a new approximation approach for landmark-based elastic image registration using Gaussian elastic body splines (GEBS). We formulate an extended energy functional related to the Navier equation under Gaussian forces which allows to individually weight the landmarks according to their localization uncertainties. These uncertainties are characterized either by scalar weights or by weight matrices representing isotropic or anisotropic errors. Since the approach is based on a physical deformation model, cross-effects in elastic deformations can be taken into account. Moreover, with Gaussian forces we have a free parameter to control the locality of the transformation for improved registration of local geometric image differences. We demonstrate the applicability of our scheme based on analytic experiments, 3D CT images from the Truth Cube experiment, as well as 2D MR images of the brain. From the experiments it turned out that the new approximating GEBS approach achieves more accurate registration results in comparison to previously proposed interpolating GEBS as well as interpolating and approximating TPS.