Information Technology Reference
In-Depth Information
Algorithm III Optimization of the joint con
guration
1. For each component V
i
, run the step 1 and 2 of the inner iteration to
compute {X
i
;
k
¼
0
;
1
; ...;
K
1
g
with their correspondent beliefs
1}.
2. Run the outer iteration to compute the joint distribution p X
{
x
i
;
k
¼
0
;
1
; ...;
K
ðÞ
j
I
and update
fx
i
g:
3. For each component V
i
, run the step 3 of the inner iteration to update the
con
marginal distribution
guration of each component.
4. Repeat 1
-
3 until the procedure converges.
filter based inner iteration and the BP based outer iteration are
combined such that
The particle
The particle
filtering in the inner iteration is used to
find probable candidates for
each individual component.
The belief propagation (BP) in the outer iteration is used to set regularization on
multiple components so that only the candidates that can ful
ll the inter-com-
ponent constraint will be selected.
In our algorithm, the stop criteria is set to run Algorithm III for a
xed number
guration of Vi
i
is set as the sample X
i
with the
of iterations and the optimal con
highest probability
x
i
.
2.5 The Determination of the Number of Vertebrae
Vertebral number determination is a key factor for correct vertebral body detection.
In our approach we handle this problem by a semi-automatic method as described
below:
User clicks two landmarks on the X-ray image to indicate the centers of the
rst
and the last visible vertebral bodies.
From the locations of these two landmarks and the projection parameters of the
X-ray image(s), we can estimate a minimal number of vertebrae N
upper
,by
dividing the distance between the two landmarks by an empirical estimation of
the average vertebral height. Usually N
upper
is greater than the true number N of
the visible vertebrae in the image. We then construct a graph model with N
upper
nodes.
Carry out the inference procedure described in Algorithm III. Due to the dis-
tance potential between neighboring components as shown in Fig.
3
, neigh-
boring components will either be located side-by-side or overlap with each
