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Abstract:
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Manifold representations of three-dimensional shapes and other functional data can be used for nonlinear dimension reduction and to produce useful descriptions of shape variation. We use a manifold representation based on the medial axis to represent the shape of thoracic vertebrae in pediatric subjects, where the manifold coordinates describe geometrically meaningful properties such as widening, twisting and bending. Multiple vertebrae are observed within each subject. Our goal is to produce useful measures of shape variation within and between subjects, and assess changes across age, sex, and clinical status. Because the medial axis coordinates reside in a non-Euclidean space, standard regression and principal component techniques are not applicable. We propose a multilevel extension to recently proposed intrinsic regression models for Riemmanian manifolds. A two-stage Bayesian estimation procedure is proposed, as well as a test for shape differences across age and sex.
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