An extension of thin-plate splines for image registration with radial basis functions

Thin-plate splines are probably the most often used technique for landmark-based registration with radial basis functions. However, a disadvantage is that the locality of the transformation cannot be controlled. We introduce an extension of thin-plate splines which enables to control the spatial influence of acting forces and thus the locality of the transformation. Our approach is based on a new type of splines which we derived as closed-form solution of the biharmonic partial differential equation under certain forces. We have applied our approach to synthetic and real image data and have compared the results with standard thin-plate splines registration.