Active Shape Analysis of Mandibular Growth Klaus B. Hilger 1 , Rasmus Larsen 1 , Sven Kreiborg 2 , Søren Krarup 2 , Tron A. Darvann 1,2 , and Jeffrey L. Marsh 3 1 Informatics and Mathematical Modelling, Technical University of Denmark, IMM, DTU, Richard Petersens Plads, Building 321, DK-2800 Kgs. Lyngby, Denmark 2 3D-Laboratory, Department of Pediatric Dentistry and Clinical Genetics, School of Dentistry, University of Copenhagen, DK-2200 Copenhagen N, Denmark 3 Department of Pediatric Plastic Surgery, St. Louis Children’s Hospital, Washington University School of Medicine, St. Louis, Missouri, USA kbh@imm.dtu.dk, http://www.imm.dtu.dk/∼kbh/ Abstract. This work contains a clinical validation using biological land- marks of a Geometry Constrained Diffusion registration of mandibular surfaces. Canonical Correlations Analysis is extended to analyse 3D land- marks and the correlations are used as similarity measures for landmark clustering. A novel Active Shape Model is proposed targeting growth modelling by applying Partial Least Squares regression in decomposing the Procrustes tangent space. Shape centroid size is applied as depen- dent variable but the method generalizes to handle other, both uni- and multivariate, effects probing for high covariation wrt. shape variation. 1 Introduction This work is primarily based on the theory of point distribution models, which are widely used in modelling biological shape variability over a set of anno- tated training data, [6,7], based on generalized Procrustes alignment, [10], and decomposition, [16], in shape tangent space. The data are mandibular surfaces acquired from computed tomography (CT) scans of subjects with Apert syn- drome. All scans are acquired for treatment and diagnostics purposes. In Apert syndrome, the mandible is not affected by the primary anomaly, [15]. In [1] the data are applied in a Geometry Constrained Diffusion (GCD) registration and a subsequent Principal Component (PCA) based growth analysis. A subset of the mandibles are annotated using 32 biological landmarks placed on distinct skeletal features in the CT volume. The landmarks are applied in this study to evaluate the dense correspondence obtained by GCD. Moreover, additional sub- jects with Apert syndrome are included into the data set, now representing 10 subjects, five males and five females, scanned at ages from 1 month to 14 years of age. Since the subjects are prepubescent and the sample size is small, the sexes are pooled in the subsequent analyses. The resulting data set consists of 36 CT scans. The remaining paper is organized in three sections. Section 2 contains an evaluation of the GCD based correspondence and an analysis of the underlying distribution of the biological landmarks. Section 3 presents derived Active Shape Models (ASM) of the biological landmarks that correlate to growth. In Section 4 we summarize and give some concluding remarks. R.E. Ellis and T.M. Peters (Eds.): MICCAI 2003, LNCS 2879, pp. 902–909, 2003. c  Springer-Verlag Berlin Heidelberg 2003