A Mumford-Shah Level-Set Approach for Geometric Image Registration

A new, fully automated method for non-rigid registration of multimodal images is presented. Due to the large interdependance of segmentation and registration, the approach is based on simultaneous segmentation and edge-alignment. The two processes are directly coupled and thus benefits from using complementary information of the entire underlying dataset. It is formulated as a variational joint free discontinuity problem in the MumfordShah framework, with respect to a geometric variable describing the contour set and a functional variable which represents the underlying deformation. The contour set is represented by a level set function. We derive a regularized gradient flow and describe an efficient numerical method using and Finite Element discretization and multigrid techniques. Finally, we illustrate the method in several applications, such as multi-modal intra-patient registration and reconstruction by registration to a reference object.