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-