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In-Depth Information
Articulated Statistical Shape Models
of the Spine
Jonathan Boisvert
Abstract 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 in
uenced
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 de
fl
ning 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 con-
ventional statistical tools are not applicable. In this context, a few key concepts
allowing the computation of statistical models on Riemannian manifolds are pre-
sented. 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 bene
ts of integrating a simple regularization term
based on articulated statistical models to well known algorithms.
1 Introduction
The human spine is naturally curved, and its exact shape varies from one individual to
another. These variations may be normal variations between healthy individuals, but
they may also be a sign of pathology. Unfortunately, healthy variations in shape are
large enough that they may be hard to distinguish from problematic deformations.
