A Mumford–Shah Level‐Set Approach for Geometric Image Registration

Abstract

A new method for nonrigid registration of multimodal images is presented. Due to the large interdependence of segmentation and registration, the approach is based on simultaneous segmentation and edge alignment. The two processes are directly coupled and thus benefit from using complementary information of the entire underlying data set. The approach is formulated as a bivariate, variational, free discontinuity problem in the Mumford–Shah framework. A geometric variable describing the contour set and a functional variable which represents the underlying deformation are simultaneously identified. The contour set is represented by a level‐set function. We derive a regularized gradient flow and describe an efficient numerical implementation using finite element discretization and multigrid techniques. Finally, we illustrate the method in several applications, such as multimodal intrapatient registration and reconstruction by registration to a reference object.