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(a)
(b)
Vertebral
body
Spinal
canal
Transverse
process
Spinal
process
(c)
(d)
Fig. 4 Spine segmentation. a Vertebra anatomical illustration; b vertebra template; c Initial
template superimposed on CT; and d segmentation results
X
n
w g *
2 f
E
¼
ð
u i ;
f
ð
u i ÞÞ
w 1 r
k
f
ð
u i Þ
k
w 2 r
ð
u i Þ
w p p
ð
u i ;
f
ð
u i ÞÞ
i¼1
*
ð 6 Þ
ð u i ; f ð u i ÞÞ is directional gradient
1
ð
u i ;
f
ð
u i ÞÞ
is occupied
p
ð
u i ;
f
ð
u i ÞÞ ¼
0
otherwise
Here (u i , f(ui)) i )) are the border atoms. The metric has four components, the direc-
tional gradient *
ð
u i ;
f
ð
u i ÞÞ
is to match the border atoms with the intensity edge of
r
ð
u i Þ
r
2 f
ð
u i Þ
the image,
are smoothness constraints on the border, and p(ui, i , f
(u i )) is a penalty function to prevent intersecting between model parts. Weights w g ,
w 1 , w 2 and w p are set empirically.
The extracted spinal canal de
f
and
nes the initial location and size of the vertebra
model. The model matching proceeds sequentially. First the vertebral body is
matched, followed by the spinous process, and at the end the transverse processes.
 
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