3-D Diffeomorphic Shape Registration on Hippocampal Data Sets Hongyu Guo 1 , Anand Rangarajan 2 , and Sarang C. Joshi 3 1 Dept. of CAMS, Texas A&M University-Corpus Christi 2 Dept. of CISE, University of Florida 3 Dept. of Radiation Oncology, University of North Carolina at Chapel Hill Abstract. Matching 3D shapes is important in many medical imaging applications. We show that a joint clustering and diffeomorphism esti- mation strategy is capable of simultaneously estimating correspondences and a diffeomorphism between unlabeled 3D point-sets. Correspondence is established between the cluster centers and this is coupled with a si- multaneous estimation of a 3D diffeomorphism of space. The number of clusters can be estimated by minimizing the Jensen-Shannon divergence on the registered data. We apply our algorithm to both synthetically warped 3D hippocampal shapes as well as real 3D hippocampal shapes from different subjects. 1 Introduction Shape matching is ubiquitous in medical imaging and in particular, there is a real need for a turnkey non-rigid point feature-based shape matching algorithm [1,2]. This is a very difficult task due to the underlying difficulty of obtaining good feature correspondences when the shapes differ by an unknown deformation. In this paper, we attempt to formulate a precise mathematical model for point feature matching. Previous work on the landmark matching problem [3,4] ignored the unknown correspondence problem and assumed all the landmarks are labeled. And fur- thermore, there is a considerable amount of point feature data where the cardi- nalities in the two shapes are not equal and a point-wise correspondence cannot be assumed. On the other hand, previous work on the correspondence problem [5,6] did not solve the diffeomorphism problem. The deformation model used was splines, like thin-plate splines, Gaussian radial basis functions and B-splines. The principal drawback of using a spline for the spatial mapping or the deformation model is the inability of the spline to guarantee that there are no local folds or reflections in the mapping and that a valid inverse exists. Here, we are not interested in curve and surface matching because unlike a point-set representation of shapes, which is a universal representation, curve or surface representation of shapes usually require prior knowledge about the topology of the shapes. A point-set representation of shapes is especially useful when feature grouping (into curves and the like) cannot be assumed. J. Duncan and G. Gerig (Eds.): MICCAI 2005, LNCS 3750, pp. 984–991, 2005. c  Springer-Verlag Berlin Heidelberg 2005