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Fig. 21 A sagittal orthogonal curved-planar cross-section CT
u¼u
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
)
rotation (Eq.
57
) for every point i on the spine curve cðiÞ.
. Exactly one sagittal
orthogonal curved-planar cross-section passes through the spine curve (i.e.
ð
i
Þ
0)
and therefore displays the spinal anatomy along its midline, which is represented by
a straight line (Fig.
21
).
However, in the resulting cross-sections, anatomical deformations are present that
result from the intersections of sagittal pro
x
¼
D
about
axis x of the image-based coordinate system. To avoid anatomical deformations, the
sagittal orthogonal curved-planar cross-section CT
u¼u
c
can be obtained as:
les due to the rotation for angle
að
i
Þ
C
u¼u
c
ð
y
;
c
z
ð
i
ÞÞ
¼
I
ð
R
z
ðuð
i
ÞÞ
½
c
x
ð
i
Þþ
D
x
;
y
;
c
z
ð
i
ÞÞ;
ð
77
Þ
