Traditionally, different image processing tasks are mainly considered on their own. The main aim of this paper is a combination of registration, i.e., the spatial alignment of images and egmentation, i.e., the recognition of edges and object contours in images. A proper registration depends on a good initial segmentation and vice versa. In this paper, it is proposed to link these problems together by formulating a coupled variational problem. We will focus on an edge-based approach instead of considering image intensities and propose a variational formulation based on the MumfordShah free discontinuity problem. This paper is particularly devoted to a comparison of a sharp interface approach with the phase field analogue.