Image and surface registration

Image registration is one of the most useful and practical applications of image analysis. Among its many tasks are the tracking of changes between data from different time points or motion correction. Moreover, superimposing complementary information across image modalities is needed, as new imaging modalities emerge in the field. This chapter presents a review of the fundamental ideas and models in the field. The goal is to reflect the current state of the art of image registration (IR) to motivate the readers to refine these models, and to enable the tackling of new challenges as they arise. After discussing the background (Section 2), we review main components of a variational model: a distance measure or data fidelity term ( Section 3), regularization to ensure existence of solutions and constraints to further restrict the wanted transformation (Section 4). We also discuss diffeomorphic approaches which ensure local invertibility. We present the surface registration (SR) modelling in the same framework of variational models in Section 5 where the close relationship between IR and SR is also discussed, while we briefly discuss the numerical methods for IR and SR in Section 6. Finally in Section 7, we touch upon the main ideas in deep learningbased approaches for registration.