Non-rigid registration using free-form deformations

Free-form deformations are a powerful geometric modeling technique which can be used to represent complex 3D deformations. In recent years, freeform deformations have gained significant popularity in algorithms for the non-rigid registration of medical images. In this chapter we show how free-form deformations can be used in non-rigid registration to model complex local deformations of 3D organs. In particular, we discuss diffeomorphic and non-diffeomorphic representations of 3D deformation fields using free-form deformations as well as different penalty functions that can be used to constrain the deformation fields during the registration.We also show how free-form deformations can be used in combination with mutual information-based similarity metrics for the registration ofmono-modal and multi-modal medical images. Finally, we discuss applications of registration techniques based on free-form deformations for the analysis of images of the breast, heart and brain as well as for segmentation and shape modelling.