Proceedings of the 2012 International Conference on Machine Learning and Cybernetics, Xian, 15-17 July, 2012

DOUBLE WEIGHTED FCM ALGORITHM FOR COLOR IMAGE SEGMENTATION

DE-YU TANGl,2, JIN YANGl,2, YI-SHUAN HUANGl

1. Dept of Computer, College of Medical Information and Engineering, GuangDong Pharmaceutical

University, GuangZhou 510006 , China

2. Dept of Computer, College of Computer Science & Engineering,South China University of Technology, GuangZhou

510006 , China EMAIL: scutdy@126.com.goodskyfly@163.com.23220520@126.com

Abstract: In this paper, we propose a double weighted fuzzy

clustering method for color image segmentation. In order to improve the performance of image segmentation by FCM algorithm, we use the window-based point density weighted method to calculate the membership matrix, at the same time, the relietF algorithm is used to assign weights to the components of a true color image. Firstly, RGB color image is transformed into a HSI space. Then, by using the traditional FCM clustering algorithm, the initial membership values could be obtained, which are used to further conduct FCM in the next iteration. Finally, experiments show that by comparing with the standard FCM algorithm the proposed method can get good performances on image segmentation.

Keywords:

Window-based point density; FCM algorithm;

HSI ; ReliefF algorithm

1. Introduction

Image segmentation is an important image analysis technology. It aims at separating the image into different regions with different special significances, and these regions are mutually disjointed with each one meets some specific regional conditions. At present, image segmentation is widely used in industrial automation, security monitoring, biomedical image analysis, military engineering and many other fields [1] [9]. The traditional method of image segmentation is based on the brightness component with gray-scales. This method is simple and fast, but it ignores the color information which is a very important criterion. Currently, the segmentation of true color image is a hot research topic. A variety of color space models are proposed which make the image segmentation more comprehensive and accurate.

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HSI color space [2], which consists of Hue, Saturation and Intensity, comes from the human visual system. Usually, hue and saturation are known as chroma, which are used to represent the color category and the degree of depth. In human visual systems, HSI color space is often adopted, since human being's perception on brightness is far more sensitive than the color shade. Thus, when compared with RGB color space, HSI color space can better facilitate the color processing and recognition. Many algorithms are available in HSI color space for image processing, and they can greatly reduce the workload for color analysis.

Fuzzy C-Means (FCM) is the most famous clustering algorithm which has been widely used in the field of image segmentation. In this paper, we propose a new Fuzzy C-Means algorithm based on HSI color space [3] [10], which is further applied to color image segmentation. Since each pixel of the color image is multidimensional, we consider using the distance weighting method to improve the accuracy of the FCM algorithm. By combining with the color spatial information of the image, we could use a window-based point density weighted method to calculate the FCM membership degrees.

2. FCM algorithm

FCM clustering algorithm, as an iterative optimization method, was firstly proposed by Dune, and later promoted by Bezdek. The iteration process uses a so-called hill climbing technology to find the optimal solution. In image segmentation, the objective function is composed of the weighted measure between the image of each pixel and each cluster center.

FCM algorithm is presented as follows: Given a data set X={xl,x2, ... ,xn}, each data sample

xi contains d dimensions. Fuzzy clustering is to divide X

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Proceedings of the 2012 International Conference on Machine Learning and Cybernetics, Xian, 15-17 July, 2012

into c clusters where 2:::;c:::;n, and v={vl,v2, ... ,vc} are the c cluster centers. With fuzzy partition, a data sample is not strictly belonging to one class (cluster), but obtains some memberships indicating its belongingness to certain categories ( clusters).

FCM algorithm is realized by minimizing the following objective function:

n c

Jm = LLumij Ilxi-vj W,

i=1 j=1 2�m<oo

c

(1)

s.1.LUij = 1, Vi = 1,2, ... n (2)

j=1 where m is an arbitrary real number greater than or equal

to 2, xi is the ith data sample, uij is the membership

degree of xi belonging to the jth cluster, and

U=( uij li=1,2, ... ,n, j=1,2, ... ,m) is a class matrix.

In order to minimize the objective function, Lagrange multiplier method could be used. We can get the membership matrix and the cluster centers by the following formulas:

(3)

(4)

3. window-based point density

In general, given a data set, the characteristics of each sample are not clear. The density of a sample point should be larger if it is surrounded by lots of points lie together. This kind of samples influence the clustering very much [4][5]. The density of a sample is defined as:

n 1 J; = L --,dij =11 Xi -Xj II,dij � e,l � i,j � n

i=l,j=l dij + 1 (5)

where dij is the Euclidean distance between Xi and Xj,

e is the density range and mine dij) < e < max( dij) . When 1; is larger, Xi is surrounded by more data

samples. Otherwise, 1; is small, and Xi is surrounded

by fewer samples. By using the standardized treatment

for 1; , we obtain the weighted parameters as follows :

A.= f I n

L� j=l

(6) The point density function reflects the data intensity.

Larger Aj influences more on the clustering result of

sample Xi and cluster center Ci , while the e value

directly affects the point density weighted value. In order to select a reasonable e, we use a sliding window

method. When W = 1, the pixels of the sliding window could

be shown as in figure 1. The size of the window is 1, and all the directions are considered, which are used to

determine the pixel factor Ai' Then, the Euclidean

· th distances between the 1 pixel and its neighboring pixels in all the directions are calculated.

· th Figure 1 1 pixel window

However, if the size of the sliding window is too large, the computational cost will be increased in each iteration. Besides, the calculation must be dependent on

the size of the window W and the cluster center c, i.e.,

c(2w+1)2.

4. ReliefF algorithm

The Relief assessment was first proposed by Kira for classification problem. Later, Kononenko extended it to ReliefF which can solve both classification and regression problems [4-5]. The main idea of ReliefF algorithm is to evaluate the quality of the attribute

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Proceedings of the 2012 International Conference on Machine Learning and Cybernetics, Xian, 15-17 July, 2012

according to the ability of distinction between the attribute value and mutually adjacent sample. First, randomly select a training sample R, then find its k nearest neighbors in the same category from the training set, and these k examples are called Nhits (H); then find its k nearest neighbors in the other categories from the training set, these k examples are called Nmisses (M ). The weight W[ A] of each attribute A is updated based on R, NHits and Nmisses, where all NHits and NMisses have the same contribution for its updating. The formula is given as follows:

difJ(A I I) = I value(F,I)) -value(F,IJ I 1 , p 2 • max(F) -mm(F)

(7) k

W[A]= W[A]-Ldifj(A,R,H)I(mek)

+ L [ P(C) I.diff(A,R,M/C))] I (mek) C*class(R) 1-P(class(R)) j�1

(8)

5. Double weighted FCM algorithm

The objective function of double weighted FCM is given as follows:

n c

Jm = LLAi umij II Xi -Vj II�r),2 � m < 00

(9) where the constraints are same as formula (2). By using Lagrange method, we obtain the formula U ij with r

and Vj with Ai:

n

LAiUmij eXi V. = ....::.i=--"I ___ _

] n

Lumij

(10)

i=1 (11) The detailed processes of our method are described as

follows: 1) Give the initial membership of U and cluster number

cluster _ n, etc. 2) Implement the standard FCM algorithm. 3) According to the obtained cluster center and

membership degree, set the label for the clusters. If a data sample does not belong to any cluster, individually give it a label of isolated point, then implement the ReliefF algorithm and get the Euclidean distance weights r.

4) Fix the parameter C of the window-based density function and obtain all data sample point density A.

5) According to the point density A and membership U, implement formula (11) to get thye cluster center V .

6) According to the Euclidean distance weight r and cluster center v , implement formula (10).

7) According to formula (9), calculate the objective function value. If it satisfies the convergence condition, exit the loop, otherwise, go to 5).

6. The results of experiment and analysis

The data used in the experiment are 24-bit true color images as shown in Figures 1 and 2. The proposed method is compared with the traditional FCM algorithm. The platform is Microsoft Windows XP Professional (SP2) with a 2.09GHz CPC and a maximum 3GB memory. The parameter m is set to 2, the iteration number is 100, and the window-based point density parameter is 25. The ReliefF parameter cycle number M = 1000, k = 100. For Figure 2, the number of clusters is 2, and for Figure 3, the number of clusters is 3. We use two test index functions [8] for two different kinds of image segmentation methods. From tables 2 and 3, we can see that the value Vpc2 of our method is greater than the value Vpc1 of traditional FCM algorithm, and the value Vpe2 of our method is less than the value Vpel of traditional FCM algorithm, which shows the effectiveness of our approach.

1 n c

Vpc=-LL(Uij)2 n i=1 j=1 1 n c

Vpe =-LL(-Uij elogUij) n i=1 j=1

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Proceedings of the 2012 International Conference on Machine Learning and Cybernetics, Xian, 15-17 July, 2012

TABLE 1 HAND IMAGE VPC AND VPE

Clus 2 3 4 5 6 7 8 ter-n

Vpc 0.9 0.8 0.8 0.7 0.8 0.7 0.7 1 140 45 73 79 10 28 51

8 9 9 0 1 5

Vpe 0.1 0.3 0.2 0.4 0.4 0.5 0.5 1 521 00 65 24 16 49 49

8 6 7 4 3 3

Vpc 0.9 0.8 0.8 0.7 0.8 0.7 0.7 2 264 64 84 84 28 34 52

8 3 5 7 7 3

Vpe 0.1 0.2 0.2 0.4 0.3 0.5 0.5 2 23 41 38 04 61 11 39

5 4 9 6 0 9 5

TABLE 2 FRUITS IMAGE VPC AND VPE

Clus 2 3 4 5 6 7 8 ter-n Vpc 0.6 0.6 0.5 0.5 0.5 0.4 0.4 1 61 91 97 58 38 98 90

6 3 0 0 4 7 9

Vpe 0.5 0.5 0.7 0.8 0.9 1.1 1.1 1 13 63 68 96 69 01 40

1 8 2 1 8 4 7 Vpc 0.7 0.7 0.6 0.5 0.5 0.5 0.4 2 13 18 13 64 42 04 92

6 2 6 4 0 6 0 Vpe 0.4 0.5 0.7 0.8 0.9 1.0 1.1 2 47 15 30 76 44 83 37

2 6 8 3 9 2 8

Figure 2 hand image

Figure 3 fruits image

7. Conclusions

In image segmentation, FCM algorithm is widely used. But for color image, the data are multi-dimensiona1. Besides, the large amount of data also makes the processing difficult. By adopting the HSI color space and the spatial information, this paper proposes a double weighted FCM method for color image segmentation. Experimental results show that when comparing with the traditional FCM algorithm, our method can get good segmentation results.

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