A Point-Wise Quantification of Asymmetry Using Deformation Fields: Application to the Study of the Crouzon Mouse Model Hildur ´ Olafsd´ ottir 1,2 , Stephanie Lanche 1,2,3 , Tron A. Darvann 2 , Nuno V. Hermann 2,4 , Rasmus Larsen 1 , Bjarne K. Ersbøll 1 , Estanislao Oubel 5 , Alejandro F. Frangi 5 , Per Larsen 2 , Chad A. Perlyn 6 , Gillian M. Morriss-Kay 7 , and Sven Kreiborg 2,4,8 1 Informatics and Mathematical Modelling, Technical University of Denmark, Lyngby, Denmark 2 3D-Laboratory, School of Dentistry, University of Copenhagen; Copenhagen University Hospital; Informatics and Mathematical Modelling, Technical University of Denmark, Copenhagen, Denmark 3 Ecole Sup´ erieure de Chimie Physique Electronique de Lyon (ESCPE Lyon), France 4 Department of Pediatric Dentistry and Clinical Genetics, School of Dentistry, Faculty of Health Sciences, University of Copenhagen, Copenhagen, Denmark 5 Computational Imaging Lab, Department of Technology - D.326, Pompeu Fabra University, Barcelona, Spain 6 Division of Plastic Surgery, Washington University School of Medicine, St. Louis, MO, USA 7 Department of Physiology, Anatomy and Genetics, Oxford University, Oxford, UK 8 Department of Clinical Genetics, The Juliane Marie Centre, Copenhagen University Hospital, Copenhagen, Denmark Abstract. This paper introduces a novel approach to quantify asym- metry in each point of a surface. The measure is based on analysing displacement vectors resulting from nonrigid image registration. A sym- metric atlas, generated from control subjects is registered to a given subject image. A comparison of the resulting displacement vectors on the left and right side of the symmetry plane, gives a point-wise mea- sure of asymmetry. The asymmetry measure was applied to the study of Crouzon syndrome using Micro CT scans of genetically modified mice. Crouzon syndrome is characterised by the premature fusion of cranial sutures, which gives rise to a highly asymmetric growth. Quantification and localisation of this asymmetry is of high value with respect to surgery planning and treatment evaluation. Using the proposed method, asym- metry was calculated in each point of the surface of Crouzon mice and wild-type mice (controls). Asymmetry appeared in similar regions for the two groups but the Crouzon mice were found significantly more asym- metric. The localisation ability of the method was in good agreement with ratings from a clinical expert. Validating the quantification ability is a less trivial task due to the lack of a gold standard. Nevertheless, a comparison with a different, but less accurate measure of asymmetry revealed good correlation. N. Ayache, S. Ourselin, A. Maeder (Eds.): MICCAI 2007, Part II, LNCS 4792, pp. 452–459, 2007. c  Springer-Verlag Berlin Heidelberg 2007