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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.