The paper presents a new parameter-free approach to non-rigid image registration, where displacements, obtained through a mapping of boundary structures in the source and target image, are incorporated as hard constraints for elastic image deformation. As a consequence, our approach does not contain any parameters of the deformation model (elastic constants). The approach guarantees the exact correspondence of boundary structures after elastic transformation provided that correct input data are available. We describe a linear and an incremental model, the latter model allows to cope also with large deformations. Experimental results for 2-D and 3-D synthetic as well as real medical images are presented.