Nonrigid Registration of Images with Different Topologies Using Embedded Maps

Changes in image topology occur in medical images due to normal variation in anatomy, image artifacts, and the presence of pathology. Non-rigid registration of images undergoing topological change for the purpose of atlas-based segmentation or deformation analysis is challenging since non-smooth geometric transformations must be introduced. As most registration methods impose a smoothness constraint on the allowable transformations they either do not model such changes or perform poorly in their presence. In this paper we describe an approach to non-rigid registration treating the images as embedded maps that deform in a Riemannian space. We show that smooth transformations representing topological changes in the original images can be obtained and describe the evolution in terms of a partial differential equation. Two-dimensional examples from brain morphometry are used to illustrate the method.