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3
S
Fig. 2 The spine-based coordinate system
of a 3D image of a scoliotic spine,
shown in a 3D view, b left sagittal view, c posterior coronal view and d superior axial view (Note
The spine corresponds to Fig. 1 )
u
;
v
;
w
Þ
R
C
:
c
ð
i
Þ ¼ ð
c x ð
i
Þ;
c y ð
i
Þ;
c z ð
i
ÞÞ;
i
2 ½
i sp ;
i ep ;
ð
1
Þ
where i
i ep represent the locations on the spine at its start and end
point of observation, respectively, and c x ð
¼
i sp and i
¼
represent the sagittal,
coronal and axial coordinate, respectively, of the same anatomical reference point at
any location i on the spine in the image-based coordinate system. Although arbi-
trary anatomical reference points can be chosen (e.g. the centers of the spinal canal),
the most established anatomical reference points are the centers of vertebral bodies.
For K observed consecutive vertebrae, let points
i
Þ
, c y ð
i
Þ
and c z ð
i
Þ
f
v
ð
k
Þ ¼ ð
v x ð
k
Þ;
v y ð
k
Þ;
v z ð
k
ÞÞ;
k
¼
1
;
2
; ...;
K
g
represent the corresponding centers of vertebral bodies. The spine
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