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qualitative insight into the spinal anatomy, and have become indispensable inves-
tigative tools in related clinical decision making [ 44 ]. The CT imaging technique is
appropriate for observing bones and other dense structures of the spine, especially
relatively small and complex structures such as vertebral pedicles, facets and pro-
cesses. On the other hand, the MR imaging technique allows examination of soft
tissues, such as intervertebral discs, spinal cord and nerve roots. However, the
identi
cation, visualization and quantitative evaluation of many spinal disorders by
routine examinations is dif
cult because the spine is a complex and articulated
anatomical structure. The most common and straightforward visualization of 3D CT
and MR images of the spine and vertebrae is based on multi-planar cross-sections
that are de
ned in the coordinate system of the 3D image. However, such multi-
planar cross-sections may not provide suf
cient or qualitative enough diagnostic
information, because they cannot follow the curvature of the spine. As a result, not
all of the important details can be shown simultaneously in any cross-section. To
overcome this problem, cross-sections have to be generated in the coordinate
system of the spine, which can be achieved by curved-planar 3D image reformation.
The parameters for such cross-sectional image reformation are determined from the
spine-based coordinate system, which is de
ned by the curve representing the
vertebral column and by the rotation of vertebrae around the spine curve.
This chapter is focused on the techniques for automated determination of the
spine-based coordinate system for an efficient cross-sectional visualization of 3D
spine images. The geometrical representation of the spine in 3D images (Sect. 2 )is
used to de
ne the spine-based coordinate system, which provides means for
quantitative evaluation of the spine as the observed anatomical structure, and
represents the basis for cross-sectional reformation of 3D spine images (Sect. 3 ).
Cross-sectional image reformation reduces the structural complexity in favor of an
improved feature perception of the spinal anatomy, and results in valuable cross-
sections that enable not only easier navigation, manipulation and orientation in 3D
space, but can be also used for initializing spine image segmentation or other
automated image analysis techniques. Further development of spine visualization
and quantitative evaluation techniques may improve medical diagnosis and the
design of more effective strategies for the treatment of spinal disorders. The
fields of
visualization and quantitative evaluation of spine images are closely related, as
knowledge of spine parameters may provide a more effective spine visualization,
and, on the other hand, proper spine visualization may allow a more effective
measurement of spine parameters.
2 Geometrical Representation of the Spine in 3D Images
Geometrical representation of anatomical structures can be considered as a gener-
alization of the anatomical information, as the most relevant properties of the
observed anatomical structures are described by geometrical primitives such as
points, lines or line segments, curves or curve segments, etc. Geometrical primitives
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