CONSISTENT GROUPWISE NON-RIGID REGISTRATION FOR ATLAS CONSTRUCTION K.K. Bhatia , J.V. Hajnal , B.K. Puri , A.D. Edwards andD. Rueckert Visual Information Processing, Department of Computing, Imperial College London Robert Steiner Magnetic Resonance Unit, Imaging Sciences Department, Imperial College London Department of Paediatrics, Obstetrics and Gynaecology, Faculty of Medicine, Imperial College London ABSTRACT This paper describes a groupwise, non-rigid registration algorithm to simultaneously register all subjects in a population to a common reference (or natural) coordinate system, which is defined to be the average of the population. This natural coordinate system is calcu- lated implicitly by constraining the sum of all deformations from itself to each subject to be zero. To do this, the gradient projec- tion method for constrained optimization is applied to maximize the similarity between the images, subject to the constraint being satisfied. The algorithm has been tested on a group of 19 brain MR images acquired from a population of subjects with schizophrenia. 1. INTRODUCTION Image registration is an important tool in medical image analysis. The use of high-dimensional non-rigid registration algorithms en- ables computational morphometry for volumetric studies such as [1], or the creation of population-specific atlases. This requires spatial normalization of the population, where each image is trans- formed to the coordinate system of a chosen reference anatomy. Typically, a pairwise registration algorithm is used to find the map- ping from points in the reference space to points in the coordinate system of each image separately. This requires the a-priori se- lection of a reference subject from the population being studied. However, this reference may not be truly representative of the pop- ulation, particularly if there is wide variation within the groups, for example, in studies of neurodegenerative disorders or in neonatal brain development. Additionally, if the deformations required to transform one image into another are too large, the performance of the registration algorithm may be degraded. This can happen if the chosen reference subject represents one extremum of the popula- tion under investigation. Another problem associated with the use of pairwise image regis- tration is that the atlas created, and any resulting calculations (eg: volume measurements), are dependent on the choice of reference subject. For example, Figure 1 shows MR images of two subjects taken from a study of 19 schizophrenics. These were used as two separate references to register all images in the population to, and atlases produced by averaging over the group. This motivates the simultaneous registration of all subjects to a (yet unknown) reference that represents the average shape of the population. The distance between the images and the unknown reference is therefore minimized. Additionally, by registering all the images simultaneously, the resulting deformation fields will (a) (b) (c) (d) Fig. 1. Choice of reference image strongly affects atlas. (a) and (b): reference images; (c) and (d): atlases constructed from refer- ences (a) and (b) respectively. contain information about the variability across the group, and any inferences drawn will be with respect to the population as a whole. The aim of this work is to avoid altogether the need to choose a reference subject. Instead, all subjects are simultaneously reg- istered to an imaginary coordinate system that is at the average of the population being studied. This coordinate system is not defined explicitly, but is calculated implicitly by constraining the sum of all the deformations to be zero while maximizing the similarity of all images. In a previous work, Rueckert et al. [2] construct an atlas using pairwise registration from each subject in a group to a chosen ref- erence anatomy. The mean deformation of the group is then ap- plied to this atlas, to obtain a model in its natural coordinate sys- tem. If the registration were perfect, this would eliminate any bias