title: Growth modeling of human mandibles using non-Euclidean metrics.
abstract: From a set of 31 three-dimensional computed tomography (CT) scans we model the temporal shape and size of the human mandible for analysis, simulation, and prediction purposes. Each anatomical structure is represented using 14851 semi-landmarks, and mapped into Procrustes tangent space. Exploratory subspace analyses are performed leading to linear models of mandible shape evolution in Procrustes space. The traditional variance analysis results in a one-dimensional growth model. However, working in a non-Euclidean metric results in a multimodal model with uncorrelated modes of biological variation related to independent component analysis. The applied non-Euclidean metric is governed by the correlation structure of the estimated noise in the data. The generative models are compared, and evaluated on the basis of a cross validation study. The new non-Euclidean analysis is completely data driven. It not only gives comparable results w.r.t. previous studies of the mean modeling error, but seems to better correlate to growth, and in addition provides the data analyst with alternative hypothesis of plausible shape evolution; hence aiding in the understanding of cranio-facial growth.
authors.affiliation: Informatics and Mathematical Modeling, Technical University of Denmark, Richard Petersens Plads, Building 321, DK-2800 Kgs Lyngby, Denmark. kbh@imm.dtu.dk
authors.forename: Klaus Baggesen
authors.initials: KB
authors.lastname: Hilger
authors.forename: Rasmus
authors.initials: R
authors.lastname: Larsen
authors.forename: Mark C
authors.initials: MC
authors.lastname: Wrobel
mesh_terms: D002648:Child; D002675:Child, Preschool; D003627:Data Interpretation, Statistical; D005260:Female; D006801:Humans; D021621:Imaging, Three-Dimensional; D007223:Infant; D008297:Male; D008334:Mandible / Q000000981:diagnostic imaging / Q000254:growth & development*; D008953:Models, Anatomic; D014057:Tomography, X-Ray Computed