Analytic regularization for landmark-based image registration

Landmark-based registration using radial basis functions (RBF) is an efficient and mathematically transparent method for the registration of medical images. To ensure invertibility and diffeomorphism of the RBF-based vector field, various regularization schemes have been suggested. Here, we report a novel analytic method of RBF regularization and demonstrate its power for Gaussian RBF. Our analytic formula can be used to obtain a regularized vector field from the solution of a system of linear equations, exactly as in traditional RBF, and can be generalized to any RBF with infinite support. We statistically validate the method on global registration of synthetic and pulmonary images. Furthermore, we present several clinical examples of multistage intensity/landmark-based registrations, where regularized Gaussian RBF are successful in correcting locally misregistered areas resulting from automatic B-spline registration. The intended ultimate application of our method is rapid, interactive local correction of deformable registration with a small number of mouse clicks.