Information Technology Reference
In-Depth Information
the connection of two 8-adjacent image pixels. A local cost function is assigned to
the graph edges to weight their probability of being included in an optimal path. In
this work, we use two static feature components to form this cost function. The
rst
component f G is calculated from Canny edge detectors [ 27 ] at three different scales
(the standard deviations of the Gaussian smoothing operator in these three scales
are 1.0, 2.0, and 3.0, respectively) as follows.
Let
s denote the edges extracted by the Canny edge detector at three different
scales as E 1
'
, E 2
,andE 3
E i
ð
q
Þ
ð
q
Þ
ð
q
Þ
, respectively.
f
ð
q
Þ;
i
¼
1
;
2
;
3
g
are de
ned as
follows: if pixel q is a detected edge pixel at the ith scale, then E i
ð q Þ¼ 1; other-
wise, it equals to zero. Let
'
s further denote the gradient magnitudes at different
scales as G 1
, G 2
,andG 3
ð
q
Þ
ð
q
Þ
ð
q
Þ
, respectively. Then we have,
G 1
G 2
ð q Þ
ð q Þ
E 1
E 2
f G ð
q
Þ¼ð
1
:
0
ÞÞ
ð
q
ÞÞþð
1
:
0
ÞÞ
ð
q
ÞÞ þ ð
1
:
0
max
ð
G 1
ð
q
max
ð
G 2
ð
q
G 3
ð
q
Þ
E 3
ð q ÞÞ
ð
q
ÞÞ
ð
3
Þ
max
ð G 3
According to Eq. ( 3 ), if q is not a detected edge pixel at the ith scale, a constant
cost of 1.0 will be added to the cost function. Otherwise, the cost depends on the
gradient magnitude: the bigger the magnitude, the smaller the cost.
The second component, the gradient direction f D ð
;
Þ
, is calculated according to
the form proposed in the original paper [ 26 ], which is used to add a smoothness
term to the contour definition by assigning high costs to sharp changes.
Finally, these two static features are combined by weighted summation to form a
single statistic local cost function as follows
p
q
l
ð
p
;
q
Þ¼
0
:
6f G ð
q
Þþ
0
:
4f D ð
p
;
q
Þ
ð
4
Þ
where the weights for these two terms are empirically determined.
Based on the Livewire algorithm, the semi-automatic contour extraction starts
with a seed point, which is interactively placed by the user with a click of the left
mouse button. During the extraction, the user can add more seed points by clicking
the left mouse button. A click of the right mouse button will
nition of
one contour. After that, clicking the left mouse button again starts the extraction of
a new contour. Figure 2 shows an example of how the livewire segmentation
technique is used to extract contours from the input image.
finish the de
3.2 Landmark-Based Scaled Rigid Registration
for Initialization
Initialization here means to estimate the initial scale and the rigid transformation
between the mean model of the PDM and the input
fluoroscopic image. For this
purpose, we have adopted an iterative landmark-to-ray scaled rigid registration. The
fl
Search WWH ::




Custom Search