Multiple material variational image registration

This thesis is concerned with non-parametric non-rigid image registration. Here, a vector field of displacements is searched such that each position in one image is mapped onto a corresponding position in the other image. Motivated by medical examples where after registration anatomical structures are deformed in a non-physical way, the overall aim lies in the incorporation of spatially varying material parameters to let each anatomical structure deform in a physically meaningful manner. In addition, it is observed that preservation of topology, as usually assumed in registration, may be an unsuitable property for certain applications like, e.g., brain shift. To this end, the notions of a ‘large gap change’ (that is, if two structures are separated by a large gap in one image but by a small gap in the other image) and a ‘topological change’ (here, the gap totally vanishes in one image) are introduced. The challenge is now to derive a regularisation of the resulting displacement field which is spatially varying and allows for settings including a large gap change or a topological change. Finally, locally a preservation of shape or volume may be reasonable, for instance in the treatment evaluation of tumors. Such a property, again, corresponds to a spatially adapted regularisation of the displacement field. The main contribution of this thesis is the development of a framework for multiple-material registration. By extending a state-of-the-art approach for non-parametric image registration, variable regularisers are derived allowing for prescribing individual material properties and, moreover, supporting large gap changes. By further extending the concept towards piecewise variable regularisers, even topological changes can be achieved.