Non-rigid Registration Using Free-form Deformations

A deformable registration approach for medical images of same dimensionality is proposed. The popular free-form deformations (FFD) setting is utilized to characterize deformations based on a grid of control points. B-splines serve the purpose of interpolating the dense deformation field from a given control point configuration. The central idea is to combine the FFD method with well-understood techniques from the context of variational deformable registration problems. In particular, an energy functional is employed that consists of image dissimilarity and regularization terms which are both functions of the free-form deformation control points. An iterative optimization approach is chosen that is inspired by methods used to solve the partial differential equations that arise in the variational registration realm. In a sense, computations that take place on a per-pixel basis in the variational approach are transferred to the coarse grid of control points, leading to a potential efficiency gain. In order to best account for the complex deformations that body tissue is typically exposed to, a multi-resolution strategy is used that increasingly refines the control point grid. The algorithm is implemented in C++ and can be utilized for 2D-2D and 3D-3D registration. Several known techniques to increase computational efficiency are incorporated and either linear or cubic B-splines can be used. An evaluation is provided based on ground-truth experiments with synthetic 2D images and real patient CT scans, demonstrating the effectiveness of the proposed algorithm and its practical applicability to medical problems.