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Fig. 2 Relative rigid
transformations are used to
represent a spine as an
articulated object. To obtain
absolute positions and
orientations with respect to a
global frame of reference, one
would need to compose a
series of inter-vertebral
transformations. For instance,
the position and orientation of
the third vertebra from the
bottom would be obtained by
applying the rigid
transformation T
0
T
5
◦ T
6
◦ ...
T
4
T
2
to
the global frame of reference
T
1
T
3
T
2
T
1
T
0
frame of reference, several transformations will need to be composed (see Fig.
2
,
for instance).
This representation of the spine is both intuitive and useful. The spine is a
complex anatomical structure, which supports a large portion of our body weight
and yet remains
flexible enough to allow for complex motions. It includes the
vertebrae as well as a variety of soft-tissues (inter-vertebral discs, ligaments, etc.).
Vertebrae do not deform signi
fl
cantly in typical circumstances, but because they sit
on top of one another; the orientation and position of one vertebra in
uence its
direct neighbors. These relative transformations between neighboring vertebrae
would not be captured correctly by a simple set of points and would result in an
overestimation of the variability of the spine
fl
s geometry.
'
2.1 Reconstructing Articulated Models from Existing
3D Data
Articulated representations can be obtained from several sources. Most medical
imaging modalities that are routinely applied to the spine can be used to produce
articulated spine models. The exact procedure used to extract
