Color Cell Image Segmentation Based on Chan-Vese Model for Vector-Valued Images

doi:10.4236/jsea.2013.610066

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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.

Email: [email protected]

Received September 9th, 2013; revised October 6th, 2013; accepted October 13th, 2013

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.

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

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:

 



111 01

210 20

02 1211

11 12

div1 uc

cuc u

uccc AAAA





 

















 



















 













(2)

 



222 01

210 20

02 2212

21 22

div1 ud

dud u

uddd AAAA





 

















 



















 













(3)

where A is the area of the image, 11

 and 12



are the

area inside and outside the contour curve C1, 21



and



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



HxyAH xy

HxyAH x



 













 

 y

11 122122

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

1



Ω

32 ΩΩ 

1



Ω

2



21 ΩΩ 





(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

 is small relatively. So the right side

of the Equation (3) is huge, considering the stabilization

of the algorithm, let 21

 and 22

, we can

rewrite the Equation (3) to the following equation.

 



 

22 2

01 02

22101 222 212

div 1

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

dd1 dd

uHxyu Hxy

xyH xy























(6)



020 2

ΩΩ

dd1 dd

uHxyu Hxy

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





cc c







 , ,



ccc

 







dd d







  and 13









 be four un-

known constant vectors. The extension of the C-V model

to the color cell image segmentation model in vector case



 

112

,,; ,,,, ,EccddE ccEdd



212

 







(8)

According to the previous description of gray cell im-

age segmentation and Equations (2) and (5), assuming



, c



, d



and d



are constant vectors and mini-

mizing





,,, ,cd 2

;dEc



 with respect to 1



and



, we can get the following equations:







11 1,

0, 0,

30,12 11

1, 1

111 12

di 1

ii ii

ii i

uc uc

ucPcP





 





































 















 









(9)





 

22 2,

0, 0,

2,0,2221 2

() div1

ii ii

ii iiii

ud ud

ddu dPdP





 















 

























 



















(10)

where 10



, 20



, 10



 and 20



 are the

fixed weight of the vector-valued C-V model, 1, 0





and 2, 0



 are the weight coefficients of each channel,

and





11 1

Ωdd





 y



12 1

Ω1d, d











 y





21 2

Ωdd





 y



22 2

Ω1d, d











 y

, 12

, 21

, 22



11 122122Ωdd

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

,,d

,dd

uxyH xyxy

cHxyxy











 



0, 1

Ω

,1,dd

1,dd

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

,dd

uxyH xyxy

dHxyxy











 



0, 2

Ω

,1, dd

1,dd

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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