L. MA, T. Z. SU
Copyright © 2013 SciRes. ENG
2) Take the opening operation to remove some noises.
3) If there are several ROIs, then the ROI candidates
are marked and the one with the largest area is chosen to
be the final ROI.
3. Contour Evolution by GVF-Snake
Snakes [2], also active contours, firstly proposed by Kass
are deformable curves within an image domain that can
move under the influences of internal forces, coming
from and within the curve itself, and external forces
computed from the image data. The curve evolution un-
der both internal and external forces is mathematically
described as a process of energy minimization in Equa-
tion (4).
( )
( )
( )
( )
( )
1
int
0
int
snake ext
ext
EE vsEvsds
EE
= +
= +
∫
(4)
where
refers to a deformable curve energy,
represents internal forces and
corresponds to ex-
ternal forces.
3.1. Gradient Vector Flow Snake
In the traditional Snakes,
is computed by the nega-
tive gradient of the input image (
).
Although it is simple and easy to be implemented, there
are two key drawbacks both on setting an initial curve
close to the true boundary and hardly converging to
boundary concavity. In order to solve these difficulties,
GVF [8] method is proposed by Xu Chenyang and Prince
in 1997. In this model, a new version of external forces
called gradient vector flow (GVF) fields is presented.
These fields are dense vector fields derived from images
by solving a pair of decoupled linear partial differential
equations which diffuses the gradient vectors of a binary
edge map of the image to minimize an energy func tion.
1) GVF formation. For any gray-scale image
,
its GVF is defined as
( )( )( )
,,, ,V xyuxyvxy=
where
represen ts the coordinate. Then an energy func-
tion
is defined from the GVF field and the binary
edge map
of
:
( )
2
2
2222
xyxy
uuvvfVf dxdy
εµ
→
=++++ ∇−∇
∫∫
(5)
where
is a regularization parameter governing the
tradeoff between the first and the second term.
GVF field could be calculated by solving the Euler
equations of Equation (5) to minimize the energy func-
tion.
( )
( )
( )
( )
2 22
2 22
xx y
yx y
uuu ufff
vvv vfff
µ
µ
=+∇ −−+
=+∇ −−+
(6)
where
and
is the Laplacian Op-
erator,
should be set according to the amount of
noise present in the image (more noise, higher
).
2) GVF-snake. The active contour that us es the GVF
field as its external force is named as a GVF-Snake. It
effectively expands the scope and intensity of the exte r-
nal force. As for GVF -s nake considered, external force
term
in the energy functional
of Snake
[2] (Equation (7)) is replaced with
:
( )( )( )
'' ''''
,,,
t ext
E stx stxstE
αβ
= −−∇
(7)
where
is the ith pixel on the current contour.
The contour evolution is iteratively performed using Eq-
uation (8) by minimizing the Equation (7).
( )
( )
( )
( )
( )
( )
1
1 11
1
1 11
,
,
tt tt
tt tt
xAIxuxy
yAIyvxy
γγ
γγ
−
− −−
−
− −−
=+−
=+−
(8)
where, the matrix
is a pentadiagonal banded
matrix related to parameter
in Equation (7) . As
mentioned above, the curve profile could move into the
concave boundary regions because there are stronger ex-
ternal forces but still needs setting initial curves.
3.2. Contour Extraction of Skin Tumor s Based
on Visual Attention and GVF-Snake
As mentioned above, GVF-snake provides the solution
for one of major defects in conventional snake with re-
spect to contour concavity, but its initial contour is still
given by users. In this way the final curves may not be
guaranteed to reach the actual boundaries of objects es-
pecially when initial contours are located at the weaker
regions of GVF fields. However, visual attention based
ROI extraction would make contribution to initial con-
tour generation automatically and ensure the contour
derived from saliency map to locate at neighboring re-
gions of real object boundary. The proposed algorith m of
combination of visual attention and GVF-Snake for skin
contour extractions is described below:
Step 1. Visua l a ttention is used for the input image to
obtain the ROI of a skin tumor from a saliency map (see
the Section 2).
Step 2. The GVF field of input image is generated using
the Equation (6) where edge gradient
can be calculated from the gray scale image
.
Step 3. The initial contour
is ex-
tracted from the contour of ROI obtained in step1.
Step 4. The initial contour is iteratively evolved based
on Equation (8) whic h moves the deformable contour
towards the real contour of skin tumor in the image. Ite-
ration isn’t stopped until the most of points on the con-
tour are not change. Then the final result of contour ex-