Constructing diffeomorphic representations of non-rigid registrations of medical images

The analysis of deformation fields, such as those generated by non-rigid registration algorithms, is central to the quantification of normal and abnormal variation of structures in the registered images. The correct choice of representation is an integral part of this analysis. This paper presents methods for constructing a general class of multi-dimensional diffeomorphic representations of deformations. We demonstrate that these representations are suitable for the description of deformations of medical images in 2 and 3 dimensions. Furthermore, we show that the non-Euclidean metric inherent in this representation is superior to the usual ad hoc Euclidean metrics in that it enables more accurate classification of legal and illegal variations.