Groupwise registration of richly labelled images

We describe a method of registering 3D images in which regions have been segmented and labelled. Standard registration schemes cannot be naively applied to such images and several modifications to allow their registration have been proposed such as using vector valued images with one plane for each label [1] or a label consistency measure [2]. However, these either lead to impractically large images when a large number of labels are being considered, or cannot be applied to groupwise registration in a straightforward manner. The method we describe does not lead to impractically large images and can be applied to both groupwise and pairwise registration. It involves mapping each label value to a vector in a low dimensional space and applying a multi-plane registration algorithm to the resulting vector valued image. To obtain good results, the vectors representing each label should be well separated and chosen in such a way that there is minimal confusion between them. We demonstrate the method by using it to register a set of richly labelled images in a groupwise manner and use the resulting correspondences to construct a statistical shape model of a number of subcortical structures in the brain.