A Non-Euclidean Metric for the Classification of Variations in 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 registered images. The correct choice of representation is an integral part of this analysis. This paper presents methods for constructing multi- dimensional diffeomorphic representations of deformations. We demonstrate that these representations are suitable for the description of medical image-based deformations in 2 and 3 dimensions. We show (using a set of 2D outlines of ventricles) 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.