Image registration seeks pointwise correspondences between the same or analogous objects in different images. Conventional registration methods generally impose continuity and smoothness throughout the image. However, there are cases in which the deformations may involve discontinuities. In general, the discontinuities can be of different types, depending on the physical properties of the tissue transitions involved and boundary conditions. For instance, in the respiratory motion the lungs slide along the thoracic cage following the tangential direction of their interface. In the normal direction, however, the lungs and the thoracic cage are constrained to be always in contact but they have different material properties producing different compression or expansion rates. In the literature, there is no generic method, which handles different types of discontinuities and considers their directional dependence.
The aim of this thesis is to develop a general registration framework that is able to correctly model different types of tissue transitions with a general formalism. This has led to the development of the eXtended Free Form Deformation (XFFD) registration method. XFFD borrows the concept of the interpolation method from the eXtended Finite Element method (XFEM) to incorporate discontinuities by enriching B-spline basis functions, coupled with extra degrees of freedom. XFFD can handle different types of discontinuities and encodes their directional-dependence without any additional constraints.
XFFD has been evaluated on digital phantoms, publicly available 3D liver and lung CT images. The experiments show that XFFD improves on previous methods and that it is important to employ the correct model that corresponds to the discontinuity type involved at the tissue transition. The effect of using incorrect models is more evident in the strain, which measures mechanical properties of the tissues
