Information Technology Reference
In-Depth Information
the template with an intensity value I
ð
s
Þ
, the image appearance value of s is
computed as
e
ð
I
ðÞ
l
i
Þ
2
2
r
2
i
ps
ð
j
X
i
Þ¼
:
ð
3
Þ
e
x
I
c
I
, where c
I
We further de
ne p
I
I
ð
j
X
i
Þ¼
is the cross-correlation between the
image appearance values ps
and a binary template which sets value 1 to the
interior area of the template and 0 to the border region.
x
I
[
ð
j
X
i
Þ
0 is a weighting
factor. Intuitively this means that we assume that the interior region of the
template should obey the Gaussian distribution and the border area should have
a different intensity distribution. The Gaussian model
Nðli;
i
; r
i
Þ
can be learned
from the observed image(s) I once Xi
i
is given, i.e., to
fit a Gaussian distribution
with the intensity values of the interior region of the vertebral body determined
by X
i
.
Gradient observation model p
G
I
ð
j
X
i
Þ
: Similar to p
I
I
ð
j
X
i
Þ
, we can de
ne
e
x
G
c
i
G
, where c
i
G
is the cross-correlation between the gradient image
values of the observed image(s) in the template area and a binary gradient
template, which sets 0 in the interior area and 1 in the border region. This means
that the interior region of the vertebral body is homogeneous and high gradient
values should only happen on the border of the vertebral template.
p
G
I
ð
j
X
i
Þ¼
Local variance observation model p
V
I
ne the local variance image
I
V
of a pixel in the image(s) I as the intensity variance in a small window
centered at this pixel. We set p
V
I
ð
j
X
i
Þ
:Wede
e
x
V
c
i
V
, where c
i
V
is the cross-correlation
between the local variance values and a binary template identical to the gradient
template. Similar to the gradient observation model, this item is used to model
the observation that intensities of the interior area of a vertebral body should be
more homogeneous than those of the border region.
ð
j
X
i
Þ¼
We only consider the image observation model of the vertebral bodies but ignore
the observation model of the discs. This is due to the fact that for X-ray image(s)
with different view direction(s), the above mentioned observation model is more
reliable for the vertebral bodies than for the discs. A uni
ed observation model for
the discs is more dif
cult to be designed.
It can also be observed that the three components in the observation model do
not need to be trained with training data as done in [
1
,
2
,
5
]. Instead their parameters
can be directly learned from the target X-ray image(s) I.
2.3 Potentials Between Components
We de
ne inter-node potentials to apply geometric constraints between neighboring
nodes such that all the nodes will be assembled to a meaningful spinal structure.
More speci
cally, we have:
