| Résumé | The spine is a complex assembly of rigid vertebrae surrounded by various soft tissues (ligaments, spinal cord, intervertebral discs, etc.). Its motion for a given individual and its shape variations across a population are greatly influenced by this fact. We show in this chapter how statistical shape models can be constructed, used, and analyzed while taking into account the articulated nature of the spine. We begin by defining what articulated models are and how they can be extracted from existing 3D reconstructions or segmented models. As an example, we use data from scoliotic patients that have been reconstructed in 3D using bi-planar radiographs. Articulated models naturally belong to a manifold where conventional statistical tools are not applicable. In this context, a few key concepts allowing the computation of statistical models on Riemannian manifolds are presented. When properly visualized, the resulting statistical models can be quite useful to analyze and compare the shape variations in different groups of patients. Two different approaches to visualization are demonstrated graphically. Finally, another important use of statistical models in medical imaging is to constrain the solution of inverse problems. Articulated models can readily be used in this context, we illustrate this in the context of 3D model reconstruction using partial data. More precisely, we will show the benefits of integrating a simple regularization term based on articulated statistical models to well known algorithms. |
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