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Fig. 22 A coronal orthogonal curved-planar cross-section CT
v¼v
c
of a 3D CT image of a scoliotic
spine, shown in a 3D view, b left sagittal view, c posterior coronal view and d superior axial view
of the image-based coordinate system (Note The image-based coordinate system and the spine
curve correspond to Figs.
1
and
7
)
C
v
¼
v
c
ð
x
;
c
z
ð
i
ÞÞ
¼ I
ð
R
z
ðuð
i
ÞÞ
½x
;
c
y
ð
i
Þþ
D
y
;
c
z
ð
i
ÞÞ;
ð
80
Þ
where matrix R
z
ðuð
i
ÞÞ
(Eq.
54
) represents the axial vertebral rotation for angle
uð
i
Þ
about axis z of the image-based coordinate system. In this case, the axial vertebral
rotation
uð
i
Þ
ned in transverse planes that are orthogonal to axis z of
the image-based coordinate system (i.e.
uð
has to be de
i
Þ
¼
u
z
ð
i
Þ
, Eq.
13
). As a result, the
resulting cross-sections are no longer de
ned on the basis of the spine-based
coordinate system, and therefore the spine curve is no longer represented by a
straight line.
