Journal of Software Engineering and Applications, 2013, 6, 554-558
http://dx.doi.org/10.4236/jsea.2013.610066 Published Online October 2013 (http://www.scirp.org/journal/jsea)
Color Cell Image Segmentation Based on Chan-Vese
Model for Vector-Valued Images
Jinping Fan, Shiguo Li, Chunxiao Zhang
Department of Electronic Communication Technology, Shenzhen Institute of Information Technology, Shenzhen, China.
Received September 9th, 2013; revised October 6th, 2013; accepted October 13th, 2013
Copyright © 2013 Jinping Fan et al. This is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
ABSTRACT
In this paper, we propose a color cell image segmentation method based on the modified Chan-Vese model for vector-
valued images. In this method, both the cell nuclei and cytoplasm can be served simultaneously from the color cervical
cell image. Color image could be regarded as vector-valued images because there are three channels, red, green and
blue in color image. In the proposed color cell image segmentation method, to segment the cell nuclei and cytoplasm
precisely in color cell image, we should use the coarse-fine segmentation which combined the auto dual-threshold
method to separate the single cell connection region from the original image, and the modified C-V model for vector-
valued images which use two independent level set functions to separate the cell nuclei and cytoplasm from the cell
body. From the result we can see that by using the proposed method we can get the nuclei and cytoplasm region more
accurately than traditional model.
Keywords: Cell Image; Color Image Segmentation; Level Set Method; Active Contour Model
1. Introduction
Worldwide, especially in middle and low income coun-
tries, cervical cancer is the second most common cancer
in women, and the third most frequent cause of cancer
death. But cervical cancer is more preventable than oth-
ers because it has a very long time precancerous stage
and can be easily detected by a routine screening test. So
it is necessary to develop the automated cervical smear
screening analysis system to assist the diagnosis of cer-
vical cancer. The quantitative analysis and automatic
recognition of cervical cell image contain the following
three steps: cell image segmentation, features extraction
and cell image recognition. Segmentation of cells in cy-
tological image is the fundamental and key point of
quantitative analysis and affects the classification result
directly.
The early cervical cell image segmentation method
was focused on the nuclear region segmentation [1-3].
After finding that the cytoplast region and the whole cell
body have played important role in cervical cell image
classification and diagnosis, some researchers employed
several methods to segment the cell nucleus and cell cy-
toplasm [4-6]. Because the cervical smear images are
frequently contaminated, the contrast between cell nu-
cleus and cytoplasm is lower, which makes the contours
of nuclei and cytoplasm very vague even for the abnor-
mal cells. In addition, the cells shape, size and topologi-
cal structure are strongly different from each other espe-
cially for the severe dysplastic cells. While the Chan-
Vese (C-V) active contour model without edges, pro-
posed in [7] has been used in gray cervical cell image
segmentation perfectly in [8]. The modified C-V model
can separate the cell nuclei and cytoplasm precisely. In
reality the collected and processed cell images are all
color images, so it’s necessary to research the method of
the color cell image segmentation. In this paper, we pro-
pose a color cell image segmentation method by using
vector-valued C-V model.
2. Cell Image Processing
The cells in the cervical smear image are poorly con-
trasted and more kinds of cells are found in high degree
of overlapping because of the diversity in the process of
collection, smear staining or the affection of bleeding and
inflammation. On the other hand, cells in different
growth stages or variant lesion degrees have diverse size,

Color Cell Image Segmentation Based on Chan-Vese Model for Vector-Valued Images 555
shape, morphology, color, texture and density. It’s hard
to use a global segmentation method to extract every
connected cell region from the cervical smear image pre-
cisely. These features brought us to use coarse-to-fine
segmentation strategy.
Before the cell coarse segmentation, we should do
some pre-processing steps to select regions of interest
(ROI) which contains the object cell. In each ROI, there
is only one object of interest in each field. So the next
fine segmentation can be implanted on the choosing ob-
ject. In this paper we use auto dual-threshold segmenta-
tion as the coarse segmentation method [8]. As there are
three components in cervical cell image: cell nucleus, cell
cytoplasm and background, we just need to segregate the
nucleus and cytoplasm from the background domain,
which means that two thresholds will be used in the al-
gorithm.
Combine cell nucleus region with cytoplasm region of
the result after auto-threshold segmentation and we can
get a binary image. Morphological opening operation,
which consists of an erosion operation followed by a
dilation operation, has been used to eliminate the small
isolated noise and void area. After the mathematical mor-
phology opening operation, isolated noise and hole smal-
ler than structure element will be eliminated. Scanning
the binary image after the processing mentioned above
again and labeling it by 8 neighborhoods searching algo-
rithm, we can segregate the minimum enclosing rectan-
gle of the connected region by its serial number. Expand
the rectangle to x pixels in up and down directions and y
pixels in left and right directions, the region after ex-
panding is deemed as the region of interest where the
fine segmentation will be operated on it.
3. Gray Cell Image Segmentation
Chan-Vese model (C-V model) proposed by T. F. Chan
and L. A. Vese is a classical level set based active con-
tour model [9-15]. The model is appropriate for seg-
menting the images containing the objects that have
fuzzy or discontinuous borders and complicated topolo-
gical structures. Here we use the modified C-V model to
segment the gray scale cervical cell image [8].
Let be the image domain, Ω1, Ω2 and Ω3
represent the cell nucleus, cell cytoplasm and back-
ground regions respectively. In general case, the intensity
of background is the highest among the three regions, the
cell cytoplasm is in the second place, and the cell nucleus
is the lowest. In addition the cell nucleus is always inside
the cell nucleus. The structure of the cervical cell image
shows in Figure 1.
d
R
In this section, we employ two independent level-set
functions 1

and 2

to segment the cervical cell image,
the contour curves C1 and C2 are represented by their
zero level set functions.
Ω
3
Ω
2
Ω
1
B
1
B
2
Figure 1. Structural representation of cervical cell image.
The level set functions and their regional classification
show in Figure 2. The definition of the level set function
is that if the point is inside the curve then 0

, if the
point is outside the curve the 0

 and if the point is
on the curve then 0


. The energy functional of this
model is defined as

 
1211 22112121 22
,,;, ,,,, ,Eccd dEccEd d


   (1)
where


1 121
,,Ecc

and

2122
,,Edd


are the energy
functional of level set functions 1

and 2

based on
Chan-Vese model; c1 and c2 denote the mean of the im-
age intensity inside and outside the contour curve C1; d1
and d2 denote the mean of the image intensity inside and
outside the contour curve C2.
Assuming c1, c2, d1 and d2 are constants and minimize-
ing energy functional


121 12 2
,,;, ,Eccd d

 with re-
spect to level set functions 1

and 2

yield the evolv-
ing equations of the two level set functions:
 

 
2
11
111 01
1
210 20
02 1211
11 12
div1 uc
t
cuc u
uccc AAAA


 








 




 



 
 




(2)
 

 
2
22
222 01
2
210 20
02 2212
21 22
div1 ud
t
dud u
uddd AAAA


 








 




 



 
 




(3)
where A is the area of the image, 11
A
 and 12
A

are the
area inside and outside the contour curve C1, 21
A

and
22
A

are the area inside and outside the contour curve C2,
λ1 and λ2 are adjustable weight values used in level set
evolving functions.


 
111 121
212 222
dd,1 dd
dd,1dd

A
HxyAH xy
A
HxyAH x


 
 
 




 
 y
11 122122
A
AA AA

 (4)
For cervical cell image, the intensity differences be-
tween cell nucleus or cell cytoplasm and the background

Color Cell Image Segmentation Based on Chan-Vese Model for Vector-Valued Images
556
0
1

1
Ω
1
C
32 ΩΩ 
0
1

3
Ω
0
2

21 ΩΩ 
0
2


2
C
(a) (b)
Figure 2. Level set functions and regional division: (a) Level
set function

1 and relevant regional classification, (b) Le-
vel set function

2 and relevant regional classification.
are much bigger than the intensity difference between
cell nucleus and cell cytoplasm. Let h1, h2 and h3 repre-
sent the mean of the image intensity within cell nucleus,
cell cytoplasm and background, then 321
. Asso-
ciating with the definition mentioned above we can ob-
tain the expression that 2322111
hhh
chddh ch

,
in addition we do fine segmentation in ROI, so the area
of background 22
A
 is small relatively. So the right side
of the Equation (3) is huge, considering the stabilization
of the algorithm, let 21
22
A
P
A
 and 22
21
A
P
A
, we can
rewrite the Equation (3) to the following equation.
 

 
22
22 2
2
22
01 02
22101 222 212
div 1
t
ud ud
ddu dPdP


 







 




  



  


 



(5)
Similarly for the fixed level set functions 1

and 2

minimizing the energy functional 121 1 2 2

,,,;,Ecc dd


with respect to c1, c2, d1 and d2, we can get the following
equations:




010 1
ΩΩ
12
1
ΩΩ
dd1 dd
,
dd1 dd
uHxyu Hxy
cc
1
H
xyH xy




 







(6)




020 2
ΩΩ
12
22
ΩΩ
dd1 dd
,
dd1 dd
uHxyu Hxy
dd
H
xyH xy




 






(7)
Generally the updating of the level set functions and
the computation of c1, c2, d1 and d2 are processing alter-
natively until the solution is stationary. When the evolv-
ing process has finished, the contour curves correspond-
ing to the zero level set functions of 1

and 2

are the
boundaries of the segmented domain. The contour curve
represented by zero-level set of 1

is entitled cell nu-
cleus contour curve, and the contour curve represented
by zero-level set of 2

is called cell body contour curve,
they are combined and defined as cell contour curve.
4. Color Cell Image Segmentation
Now we put the previous modified C-V model of the cell
image segmentation method to the vector case [12].
There are 3 channels in color cell image, red, green and
blue. Let 0,i u be the ith channel of an image on Ω,
while i=1,2,3 represent the red, green and blue channel
respectively. Let


13
cc c



 , ,

13
ccc
 



dd d
13



  and 13

dd

d


  be four un-
known constant vectors. The extension of the C-V model
to the color cell image segmentation model in vector case
is

 
112
,,; ,,,, ,EccddE ccEdd

212
,
 



(8)
According to the previous description of gray cell im-
age segmentation and Equations (2) and (5), assuming
c

, c

, d

and d

are constant vectors and mini-
mizing


1
,,, ,cd 2 ;dEc

 with respect to 1

and
2

, we can get the following equations:
 



3
11
11 1,
1
1
22
0, 0,
30,12 11
1, 1
111 12
1
di 1
3
1
3
i
i
ii ii
ii i
ii i
i
t
uc uc
ucPcP
PP


 

v
cc

















 









 





(9)


 
3
22
22 2,
1
2
22
0, 0,
3
2,0,2221 2
1
1
() div1
3
1
3
i
i
ii ii
ii iiii
i
t
ud ud
ddu dPdP


 







 












 









(10)
where 10

, 20

, 10

 and 20

 are the
fixed weight of the vector-valued C-V model, 1, 0
i


and 2, 0
i

 are the weight coefficients of each channel,
and


11 1
Ωdd
A
Hx 

 y

12 1
Ω1d, d
A
Hx 

 

 y


21 2
Ωdd
A
Hx 

 y

22 2
Ω1d, d
A
Hx 

 

 y
11
11
A
P
A
, 12
12
A
P
A
, 21
22
A
P
A
, 22
21
A
P
A

11 122122Ωdd
A
AA AAxy




Color Cell Image Segmentation Based on Chan-Vese Model for Vector-Valued Images
557
While minimizing the energy with respect to the con-
stants , , and d, we can obtain ccd spectively and we can see that the gray scale value are
great different from each other. The segmentation result
have been shown in Figures 3(e)-(h), where the red line
indicate the contour curve between the cell nuclei and
cytoplasm and the blue line the contour curve between
the cytoplasm and the background. Where the Figure 3(e)
is the result of using the method which is proposed in the
paper, Figures 3(f)-(h) are the result of gray scale cell
image segmentation using the modified C-V model.
 


 
0, 1
Ω
1
Ω
,,d
,dd
i
i
uxyH xyxy
cHxyxy






d
  
 
0, 1
Ω
1
Ω
,1,dd
1,dd
i
i
uxyHxyxy
cHxyxy












The conventional color cell image segmentation result
is applying gray cell image segmentation in each channel
and combined the result together to get the final segmen-
tation result. The cell body, cell nuclei and cytoplasm
being segmented by using the traditional method have
been shown in Figures 3(i)-(k) respectively. While the
cell body, cell nuclei and cytoplasm being segmented by
using the method proposed in this paper have been
shown in Figures 3(l)-(n). We can see that the edges of
the cell body and cell nuclei are accurate and smooth
than the traditional method, and approve the feasibility of
the proposed method.
 




0, 2
Ω
2
Ω
,,
,dd
i
i
uxyH xyxy
dHxyxy






dd
  
 
0, 2
Ω
2
Ω
,1, dd
1,dd
i
i
uxyHxyxy
dHxyxy












The segmentation result of single color cell image is
shown in Figure 3. Figure 3(a) is the color cell image of
being segmented, which is a high-grade squamous intra-
epithelial lesion (HSIL) cervical cell. Figures 3(b)-(d)
are the cell image of the red, green and blue channel re-
(a) (b) (c) (d) (e)
(f) (g) (h) (i) (j)
(k) (l) (m) (n)
Figure 3. Color cervical cell image segmentation results: (a) Original color cell image; (b)-(d) Red, green and blue channels
image of the cell; (e) The contour curve of the cell nuclei and the cell body of the color image using the method proposed;
(f)-(h): The contour curve of the nuclei and cell body of the red, green and blue channel; (i)-(k): The extracted cell body, nu-
clei and cytoplasm using traditional method; (l)-(n): The extracted cell body, cell nuclei and cytoplasm using the method pro-
osed in the paper. p

Color Cell Image Segmentation Based on Chan-Vese Model for Vector-Valued Images
558
5. Conclusion
This paper develops a color cervical cell image segmen-
tation method to segment the nucleus and cell cytoplasm
from a cervical smear image. In this paper, a coarse seg-
mentation method using auto-dual threshold segmenta-
tion method has been used firstly and region of interest
has been extracted. Then fine segmentation based on modi-
fied Chan-Vese model has been used in which two inde-
pendent level set functions have been used to approxi-
mate the boundary between nucleus and cytoplasm and
the boundary between cell body and background. On the
basis of gray scale cell segmentation method, we pro-
posed a color cell image segmentation method using
modified C-V model for vector-valued images. The nu-
merical simulation results are given to demonstrate the
validity and accuracy of the proposed method. It’s ob-
served that the proposed color cervical cell image seg-
mentation methods provide a good performance even the
original image has a vague boundary. Besides cervical
smear images, these proposed techniques can be employ-
ed to other color mages segmentation.
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