Liver Segmentation from CT Image Using Fuzzy Clustering and Level Set

doi:10.4236/jsip.2013.43B007

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Journal of Signal and Information Processing, 2013, 4, 36-42

doi:10.4236/jsip.2013.43B007 Published Online August 2013 (http://www.scirp.org/journal/jsip)

Liver Segmentation from CT Image Using Fuzzy

Clustering and Level Set

Xuechen Li1, Suhuai Luo1, Jiaming Li2

1The University of Newcastle, Australia; 2The CSIRO ICT Centre, Australia.

Email: [email protected]

Received April, 2013.

ABSTRACT

This paper presents a fully automatic segmentation method of liver CT scans using fuzzy c-mean clustering and level

set. First, the contrast of original image is enhanced to make boundaries clearer; second, a spatial fuzzy c-mean cluster-

ing combining with anatomical prior knowledge is employed to extract liver region automatically; thirdly, a distance

regularized level set is used for refinement; finally, morphological operations are used as post-processing. The experi-

ment result shows that the method can achieve high accuracy (0.9986) and specificity (0.9989). Comparing with stan-

dard level set method, our method is more effective in dealing with over-segmentation problem.

Keywords: Liver Segmentation; Fuzzy c-Mean Clustering; Level Set

1. Introduction

Liver segmentation from CT images is the key prepara-

tion work for the establishment of three dimension model

of liver, which has great significance on the diagnosis of

liver disease. A variety of liver CT image segmentation

methods have been proposed. These methods include

region growing [1-3], level set [4-6], clustering [7, 8],

statistic shape model [9], neural network [7] and support

vector machine (SVM) [10-12], etc. The following briefs

these progresses.

Ruskó et al. [1] presented an adaptive region growing

method. First, the seed region was determined based on

the intensity of gray level; second, the liver and heart

were separated based on the anatomical feature; thirdly,

an improved region growing was used to segment the

image; finally, a post-processing was employed to deal

with the under-segmentation. Their method can deal with

most cases well, but in some difficult cases (e.g. when

the gray level intensity of live is inhomogeneous), it will

cause under-segmentation. Li et al. [4] presented a dis-

tance regularized level set method. The main advantage

is that it allows the use of more general and efficient ini-

tialization of the level set function. Therefore, relatively

large time steps can be used in the finite difference

scheme to reduce the number of iterations. However, the

method needs user to select seed points, which makes it a

semi-automatic method. In [7] the initial image was seg-

mented by fuzzy c-means clustering (FCM) and smoothed

by morphological processing; then the candidate regions

were classified by neural network; finally, the regions

which belong to liver or node were extracted. However,

only gray level information was used in the original FCM

method, which may cause over-segment when other tis-

sues have similar gray level with liver. In [9], the author

presented an approach for automatic liver segmentation

which was based on statistic shape model (SSM) inte-

grated with an optimal-surface-detection strategy. First

the generalized Hough transform was used to build the

average shape model of liver; then the subspace of SSM

wasinitialize; finally, deform the shape model to adapt to

liver contour through an optimal-surface detection ap-

proach based on graph theory. The method achieves

higher accuracy compare with previous model based

methods. However, all model based methods suffer the

same problem. They need large number of training data

which must cover all shape cases. In [10, 11] wavelet

transform was used to achieve texture feature extraction;

then SVM was employed to make the classification; fi-

nally, region growing [10] ormorphological operations

[11] was utilized as the post-processing. However, region

growing may lead to over-segment when the gray level

intensity of liver and around tissues is similar; when us-

ing morphological operation as post-processing alone,

the parameters should be adjusted carefully, and the ro-

bustness may be a problem. Li et al. [5] presented a new

fuzzy level set algorithm. It begins with spatial fuzzy

clustering which presented by Chuang et al. [8] in 2006.

There salt was utilized to initialize level set segmentation

and estimated the parameters of level set evolution.

Liver Segmentation from CT Image Using Fuzzy Clustering and Level Set 37

Moreover, the fuzzy level set algorithm was enhanced

with locally regularize devolution which can facilitate

level set manipulation and lead tomorero bust segmenta-

tion. It is efficient when the background is simple and the

boundary between background and object is clear.

In this paper, we present a fully automatic segment-

tion method using fuzzy c-mean clustering combining

with level set. Sections 2 and 3 give introductions of

fuzzy c-mean clustering and level set method; Section 4

is the proposed segmentation method for liver CT scans;

Section 5 gives the result of segmentation and discussion;

Section 6 is conclusion and future work.

2. Fuzzy c-Mean Clustering

The FCM algorithm assigns pixels to each category by

using fuzzy memberships. Let (1,2,,

jn

denotes

an image with n pixels to be partitioned into c clusters,

where

represents features data. The algorithm isan

iterative optimization that minimizes the cost function

isdefined as:

ij ij



 (1)

iji j

dcx (2)

where presents the membership of

in the ith

cluster, .i is the ith cluster centre, and m is a

constant. The parameter m controls the fuzziness of the

resulting partition.

[0,1]

The cost function is minimized when pixels close to

the centroid of their clusters are assigned high member-

ship values, and low membership values are assigned to

pixels with data far from the centroid. The membership

function represents the probability that a pixel belongs to

a specific cluster. In the FCM algorithm, the probability

is dependent solely on the distance between the pixel and

each individual cluster centre in the feature domain. The

membership functions and cluster centres are updated by

the following:

2( 1)

ij m

cij

kkj













(3)

and

ij j

inm





 (4)

The standard FCM algorithm is optimized when the

feature data of pixels close to their cluster centre are as-

signed high membership values, while those that are far

away areas signed low values.

One of the disadvantages of standard FCM used in

image segmentation is that it only uses the gray level

intensity information for clustering rather than spatial

information of pixels. In fact, the probability that those

neighboring pixels share similar gray level intensity be-

long to the same cluster is great. Chuang et al. [8] pre-

sented a spatial FCM algorithm in which spatial informa-

tion can be incorporated into fuzzy membership func-

tions. The spatial function is defined as:

()

ij ik

kNBx

hu





(5)

where ()

NB x represents a square window centred on

pixel

in the spatial domain. Just like the membership

function, the spatial function ij represents the probabil-

ity that pixel

belongs to ith cluster. The spatial func-

tion of a pixel for a cluster is large if the majority of its

neighborhood belongs to the same clusters. The spatial

function is incorporated into membership function as

follows:

ij ij

ij c

kj kj

uuh



 (6)

where p and q are two parameters to control the rela-

tiveimportance of and .

uij

3. Level Set

Level set is a continuous deformable model method with

implicit representation. Its main idea is to embed the de-

formable model in a d+1 dimensional space, to segment

iteratively an object in a d dimensional space, using par-

tial differential equations. The main advantage of level

sets is that it allows changes of surface topology implic-

itly.

The standard level set function is defined as:



0, ,,















y

(7)

where





denotes the normal direction,0(, )



is the

initial contour and F represents the comprehensive-

forces. 0(, )



isusually defined as

 

,Cifxyisinside

xy Cotherwise













 (8)

here is a constant.

The original level set method needs reinitialization

because the level set function (LSF) typically develops

irregularities during its evolution which cause numerical

errors and eventually destroy the stability of the level set

evolution. Although reinitialization as a numerical rem-

edy is able to maintain the regularity of the LSF, it may

incorrectly move the zero level set away from the ex-

pected position Liver segmentation process. Moreover it

is time consuming for its large computation.

0C

Liver Segmentation from CT Image Using Fuzzy Clustering and Level Set

To deal with the problem, Li et al. [4] developed a

distance regularized level set evolution (DRLSE). Due to

the distance regularization term, the DRLSE can be im-

plemented with a simpler and more efficient numerical

scheme in both full domain and narrowband implementa-

tions than standard level set formulations. Moreover,

relatively large time steps can be used to significantly

reduce the number of iterations and computation time,

while ensuring sufficient accuracy.

Let :ΩR



 be a LSF defined on a domain Ω. The

energy function ()





is define as

 

()

pext







(9)

where ()



is the level set regularization term defined

as Equation (10), 0



 is a constant, ()

ext





is the

external energy.

()( )







dx

(10)

Here p is a potential function. The purpose of ()



to smooth the level set function and maintain the signed

distance property1





, at least at least in a vicinity of

the zero level set, in order to ensure accurate computa-

tion for curve evolution.

The gradient flow of the energy function is:



pext ext

Rdiv d









 

 





(11)

where



()

ds pss



.

The level set evolution an equation is discredited as

the following finite difference equations:



kk ext

tdivd )



 





 

 (12)

In our work, the potential function paned external en-

ergy





ext



are defined as:

  



11coscos2, 1

1(1) 1

if s













fs

(13)

and







()

ext g g





 (14)

where















dx

(15)



()

gH dx











(16)

1| (*)|

gGI



 (17)

here



and H are the Dirac delta function and the

Heaviside function respectively.

is edge indicator func-

tion and G



is a Gaussian kernel with a standard devia-

tion σ. In practice, we use





and



to approximate

δ and H in Equation (15) and (16) (their definition see

[4]). The final form of the energy function is:













()

dx gdx





 







 



dx







(18)

This energy function can be minimized by solving the

following gradient flow:



()

d g





div













 











(19)

Given an initial LSF





0( ),0



)



(

. The first term

on the right hand side is associated with the distance

regularization energyp



, while the second and third

terms are associated with the energy terms ()



and

()



, respectively.

4. Methodology

In developing an automatic segmentation of liver in CT

images, we have focused our attention mainly on three

aspects (see Figure 1): First, a contrast enhance cement

based on histogram operation is employed as preproc-

essing to make the boundary clearer; second, spatial

fuzzy clustering [8] combining with anatomical prior

knowledge are employed to extract liver region auto-

matically, and a distance regularized level set [4] is used

to refine the segmentation result; finally, morphological

filter is used as post-processing to fill holes and smooth

the final segmentation result.

Figure 1. The overview of the proposed liver segmentation.

4.1. Pre-Processing

The pre-processing contains three main steps: the range

of liver, contrast enhancement and median filtering

smoothing. First, the gray level range of live is deter-

mined by analyzing the histogram of CT slice. The prior

Liver Segmentation from CT Image Using Fuzzy Clustering and Level Set 39

knowledge shows that the gray level of live is between

130 and 150. Therefore, the peak of histogram in this

range is extracted and other parts will be set to 0. Second,

the liver peak is uniformed by contrast stretching. The

original and enhanced image and their histogram are

shown inFigure 2.After this step, most non liver tissues

are separate from liver and the boundary between liver

and the around tissues become clearer. It is benefit for

FCM and LSM. Thirdly, a median filter (10×10) is em-

ployed to reduce noise and smooth image.

050100 150 200 25030

2000

4000

6000

8000

10000

12000

14000

16000

(a) (b)

0.5

1.5

2.5

x 10

050100 150 200 250

Figure 2. The original and enhanced image and their histo-

gram (a is original image; b is histogram of a; c is contrast

enhanced image; d is histogram of c. Note: ∆ in b are the

thresholds of liver peak).

4.2. Fuzzy Clustering with Level Set

Segmentation

Our work is based on spatial fuzzy c-mean clustering [8]

and a distance regularized level set [4]. The problem of

both methods above is that they are semi-automatic

methods. The spatial fuzzy clustering needs user to

choose which class is the liver, so the level set refine-

ment can continue on that class. The distance regularized

level set needs user to select seed points. Moreover, the

number of cluster group is fixed. In some cases, liver

tissue may be clustered into different groups. For these

reasons, human participate is needed. To make the

method fully automatic and achieve better segment result,

we proposed the following improvements:

1. The image is cluster edict 4 groups based on Equa-

tion (1-6). One for liver, one for background, one for

other tissues brighter than liver (such as bones), and one

for tissues darker than liver (such as muscles). The

membership matrix u is initialized by random number;

repeat Equation (3-6) until J in Equation (1) less than

0.01. In our work,

represents the gray level of each

pixels, m = 2, p = 1, q = 1 and ()

NB x represents a (5 ×

5) window. The selection of liver group is done auto-

matically by using prior knowledge. Liver is the largest

organ located at upper left of CT slice. So we locate the

abdomen in the CT slice and divide it into 4 equal areas

(see Figure 3(a)). The group with most pixels locate at

the region 1(except background group) will most proba-

bly be the group contains liver. The background group

can be rejected by analysing the gray level intensity of

each group (it has the lowest average gray level inten-

sity).

2. In some cases, there are only a few other tissues in

the CT slice. The liver may be clustered into separate

groups. Therefore, merging similar groups is necessary.

Calculate average gray level intensity of each group on

original image instead of contrast enhanced image be-

cause the difference in enhanced image will always be

large even if the intensity is similar in original image. If

there is another group whose average intensity is similar

enough (difference less than 2.5) to liver group, add it to

the liver group.

3. Calculate the average intensity and standard devia-

tion of the liver group and reject tissues which are not

belong to liver based on statistic theory. Letk

x be the

gray level intensity of pixels of liver group,x be the

average intensity of liver group, and be the standard

deviation. The pixels which belong to liver are defined

as:

x(x3δ,x 3δ)



 (20)

4. The largest connected region of selected group

works as initialization of level set. In Li’s work [4], they

presented two kinds of application. One is the initial re-

gion contains all object and the other is the initial region

is all inside the object. In our work we use the first cases.

The reason is that there are less fake boundaries outside

liver. To make initial region contains all liver, we extend

the region out for 5 pixels. Then the level set is use on

the image after contrast enhancement which has clearer

boundary to avoid leakage. In our work, 0

C=2; ∆t=5 is

used in Equation (12); μ=0.04, λ=5, α=1.5 are used in

Equation (19) and the number of iterations is 40.

4.3. Post-Processing

There are three main problems in the output of level set.

One is that there may still be other tissues in the output

(such as heart tissues); another problem is that the con-

tour is not smooth where the boundary is not clear; the

final one is that there are holes in the liver area because

of contrast enhancement and statistic rejection. Therefore,

a post-processing based on morphology is needed.

There are two main morphological operations: dilate

and erode. By using them together, operations open and

Liver Segmentation from CT Image Using Fuzzy Clustering and Level Set

close are made. Open is separating whole object apart by

using erode first and then dilate; close is organising

smaller pieces together as one object by using dilate first

and then erode. To reject other tissues around liver, the

output of level set is processed by operation open (radius

is 2). After that, the liver should be separated from tis-

sues around. The liver can be extracted by selecting the

largest connected region. At the third step, a median filter

(3×3) is employed to smooth the boundary. The final step

is to fill holes inside liver. There are still some black

holes inside liver because some vessel or other tissues are

rejected in the processing fuzzy clustering and statistic

rejection. To refine the result, operation “hole-filling” is

employed. The final output is shown in Figure 3(f),

where the white curve is our segment result, black curve

is the manually segment result.

(a) (b)

(e) (f)

Figure 3. Liver segmentation processing(a is region defini-

tion for liver group selection; b is the selected liver group; c

is the initial region of level set; d is the output of level set; e

is the smoothed liver region before hole-filling; f is the final

segmentation. Note: white curve in f is result of our method,

black curve in f is ground truth).

5. Result and Discussion

We use three metrics to evaluate the segmentation result:

accuracy, sensitivity and specificity. The first one is used

to evaluate the general performance of our method; the

second one is used to evaluate the acceptance capability

of liver tissues and the last one focus on the rejection

capability of non-liver tissues.

Accuracy is a widely used metrics to evaluate per-

formance of segmentation methods. It is defined as:

TP TN

accuracy TP TNFPFN





where TP is the number of true positive cases; TN is true

negative cases; FP is false positive cases and FN is false

negative cases. The definition of TP, TN, FP and FN is

shown in Table 1.

Table 1. The definition of TP, TN, FP and FN.

Ground truth label

positive negative

positive TP FP

Test

outcome negative FN TN

Sensitivity is defined as:

sensitivity TP FN



It means how many liver tissues are accepted in the

outcome compare with ground truth.

Specificity is defined as:

specificity TN FP



It shows how many non-liver tissues are rejected in the

outcome.

We use two groups of data to test the performance of

our method. The data are from two different patients.

Each group has 64 slices and the size of each slice is

512×512 pixels. Table 2 shows the segmentation result.

The result shows that our method has high accuracy

and specificity. Compare with standard level set method,

our method shows more effectiveness on the unclear

boundary cases. Figure 4 is the comparison of standard

level set (left) and our method (right). It shows that when

the boundary between liver and around tissues is not

clear, standard level set will lead to over-segmentation

and our method will not. However, the sensitivity is

lower compare with other metrics. The under segmenta-

tion cases are shown in Figure 5. The main problem is

that the gray level intensity of vessels is much higher

than liver parenchyma. When vessels are completely

inside the liver, the under-segmentation can be corrected

Liver Segmentation from CT Image Using Fuzzy Clustering and Level Set 41

by hole-filling operation. However, when vessels and

other inhomogeneous tissues are at the edge of liver, the

under-segmentation would show as indentations instead

of holes. Our method shows less effectiveness to deal

with these cases.

Table 2. Performance metrics of the proposed liver seg-

mentation algorithm.

Data1 Data2

Average

(standard deviation)

0.9887

(0.0050)

0.9886

(0.0088)

Max 0.9977 0.9991

Accuracy

Min 0.9668 0.9195

Average

(standard deviation)

0.9330

(0.0258)

0.8703

(0.1024)

Max 0.9726 0.9766

Sensitivity

Min 0.8389 0.6397

Average

(standard deviation)

0.9987

(0.0006)

0.9991

(0.0022)

Max 0.9999 1

Specificity

Min 0.9959 0.9937

Figure 4. Comparison between standard level set and pro-

posed method.

Figure 5. Under-segmentation cases of proposed method.

6. Conclusions

In our work, a fully automatic fuzzy clustering segmen-

tation method combining with level set has been pre-

sented. It employed spatial fuzzy c-mean clustering and

anatomical prior knowledge to extract liver area from CT

scan automatically. The distance regularized level set

was used for refinement. The experiment result shows

high accuracy (average 0.9986) and specificity (average

0.9989) in all testing data. Compared with standard level

set method, our method is fully automatic and can

achieve better segmentation result even if the boundary is

not clear. The future work will focus on the under seg-

ment problem when there are vessels or other in homo-

geneous tissues on the edge of liver.

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