A curvature sensitive demons algorithm for surface registration

Registration, the problem of establishing correspondence between points of two objects, is one of the central problems in Computer Vision, Computer Graphics and Medical Imaging. In this paper we present a new appraoch for establishing point-to-point corre-spondence between two objects given as two-dimensional surfaces in three-dimensional space. In contrast to traditional approaches for surface registration, we do not register the surfaces directly. Rather, we represent the surfaces as the zero level-set of a signed distance function in three-dimensional space. Correspondence is then established for the distance function, and thus in particular for the zero-level set that represents the surface. Using this representation, the registration algorithm becomes independent of the surfaces topology and even topological changes can be dealt with. As the basis for our registration algorithm we use the well known Thirion's Demons algorithm. Our experiments showed that using this method, the surfaces are accurately matched. However, due to the lack of information on the surface, the correspondences do not always correspond to those a human expert would identify. Therefore we extend the algorithm, such that it consid-ers the curvature information on the surface. We show that the new term fits naturally into the original formulation of Thirion's Demons. Moreover, we provide an additional interpretation of our extension in the variational framework. We performed experiments on various synthetic and medical structures. Using the here presented representation, we were able to register extremely complex structures, such as the human skull, accurately. Our experiments show that for our data the extension yields considerably improvements compared to Thirion's original formulation.