SETIT 2009
5th International Conference: Sciences of Electronic, Technologies of Information and Telecommunications March 22-26, 2009 – TUNISIA
A Fuzzy Segmentation Approach for Images Application Lotfi TLIG*, Mounir SAYADI** and Farhat FNAIECH** * SICISI Unit, ESSTT, 5 Av. Taha Hussein, 1008, Tunis, TUNISIA
[email protected] **
Laboratory for Innovation Technologies (LTI-UPRES EA3899) University of Picardie Jules Verne, 7, rue du Moulin Neuf - 80000 Amiens - FRANCE
[email protected] [email protected] Abstract: Segmentation is a fundamental step in image description or classification. In recent years, several computational models have been used to implement segmentation methods but without establishing a single analytic solution. In this paper, the problem of textured images segmentation upon an unsupervised scheme is addressed. Until recently, there has been few interest in segmenting images involving possible complex random texture patterns. To overcome these adversities, we proposed a cascade clustering method combining a statistical features and fuzzy cmeans (FCM) clustering algorithm. For textured image segmentation, the performance of the proposed approach is compared to the standard FCM. Key words: Fuzzy clustering, Image segmentation, Statistical features, Textured images.
INTRODUCTION Textured image segmentation is one of the important tasks in computer vision systems, and many fields of application are concerned with it, including robotics, remote sensing medical imaging, etc. Techniques can be classified to be either supervised or unsupervised based on whether the number of textures is known in advance or not [CHU 97]. Segmentation consists to partition an input image into homogenous regions using clustering approach. The most widely used clustering method is probably the Fuzzy c-Means [RUS 69] [DUN 74] [BEZ 81] [MUK 96], called FCM algorithm, which is a “fuzzy relative” to the simple c-Means technique [HAR 73]. FCM is an unsupervised clustering technique which has been utilized in a wide variety of image processing applications such as medical imaging [HSI 99][BEZ 93] and remote sensing [RIG 92][CHU 00]. Its advantages include a straightforward implementation, fairly robust behavior, applicability to multichannel data, and the ability to model uncertainty within the data. A major disadvantage of its use in imaging applications, however, is that FCM does not incorporate information about spatial context, causing it to be sensitive to noise and other imaging artifacts. In this paper we propose a modified version of
standard FCM. The proposed approach is based on the following principle: the characterization is modified to include a statistical features vector to characterize every pixel, not only by their gray level values. For the time being we use the easiest way to include the statistical features vector: each pixel is represented by a set of the most commonly used features. Here a sliding window is used. For the application addressed, textured images, this proposed approach technique allows us to obtain a segmentation results, more performant than the standard use of fuzzy c-means. Mathematically, FCM is derived to minimize the (J ) with respect to the following objective function (µ ) (c ) membership functions i,k and the centroids k . This paper is organized as follows: next section discusses the FCM algorithm, section 2 presents a proposed method combining a statistic features and fuzzy c-means, called FCMF, and Section 3 shows the results of experiments with textured images, the performance of FCM using gray scale only is compared with performance of FCM using statistic features.
SETIT2009
1. Recall of FCM clustering algorithm
2. The proposed method
In the fuzzy clustering literature, the fuzzy cmeans, clustering algorithm, proposed by Dunn [DUN 74] and extended by Bezdek [BEZ 81] is the most popular, used and discussed technique [KUO 02] [GOU 02].Fuzzy c-means called FCM is an unsupervised clustering algorithm, has been applied successfully to a number of problems involving feature analysis, clustering and classifier design, in fields such as agricultural engineering, astronomy, chemistry, geology, image analysis, medical diagnosis, shape analysis, target recognition [BOU 93][MII 02]and image segmentation [BOU 97]. In this paper FCM algorithm is applied to clustering the set of vector of selected features.
In an image processing system an image or its derivatives can be represented in various feature spaces. Classification of objects can be achieved by grouping data points in the feature space with the same similarity into clusters. The dimension of the feature space depends on the representation of the image information. An image can be represented in terms of pixels, which are associated with a location and a gray level value. It can also be represented by its derivatives, e.g., regions with statistical features like Average grayscale value (Ag), Standard deviation (Sd), Variance(Va), Entropy(E), Skewness (Sk), Kurtosis(Ku) given in table 2 . Therefore, a proposed segmentation approach combining pixel characterization by a set of statistical features and fuzzy clustering approach, FCM, is discussed.
The fuzzy extension allows ui ( x ) to membership u function in fuzzy sets i on X assuming values in the c
∑ ui ( x) = 1 interval [0 1] such that
for all x in X in
i =1
{u ,..........., u }
c this case, 1 is called a fuzzy c-partition X of . The fuzzy c-means objective function J c
N
J = ∑∑ uim x j − ci
2
th c ; i is the center of i {u ,............, u c } is a fuzzy c-partition, cluster, Where 1 (m>1) is a degree of fuzziness and X = { x1 ,...........xN } i =1 j =1
becomes
represent the set of N data, in segmentation case X represent the pixels gray scales. Table 1: Standard FCM segmentation algorithm •
Step 1: Initialization: Fix the “fuzzifier” m f 1 and the number of clusters c with the constraint; 2 ≤ c ≤ N . Set l=1. Give any fixed thresholding parameter ε > 0 and an initial fuzzy
{
c-partition U 0 = u10 ,...............u c0 •
}
Step 2: Compute the vector of cluster centers c l with
U l −1 .
The proposed approach can be divided into two principal steps. The first consists to characterize each image pixel by a feature vector. Features can be (w × w) window. extracted from regions masked by Second step is a clustering procedure of the feature vector, initially extracted, using FCM clustering algorithm. By applying FCM, a partition of the feature vectors into new regions can be found. This section describes the proposed textured image segmentation called FCMF. As depicted in figure (1) the system scans the image using a sliding window and extracts a (w × w) block. The c-means feature vector for each algorithm is used to cluster the feature vectors into several classes with every class corresponding to one region in the segmented image [BEZ 81]. An alternative to the block-wise segmentation is a pixelwise segmentation by forming a window centered around every pixel. A feature vector for a pixel is then extracted from the windowed block. The spatial (N × M ) is performed, as scanning order of an image shown in Fig. 1, from left to right and top to bottom, pixel by pixel.
N
cil =
m ∑ (uik ) X k
k =1 N
∑ (uik )
m
k =1
•
Step 3: Update partition matrix U l with;
uikl =
1 d ∑ ik j =1 d jk c
Where
•
d ik
2
m −1
represent the Euclidean. d ik = xk − ci
Step4: Compare U l
to U l −1 : if U l − U l −1 ≤ ε ,
stop; otherwise l = l + 1 and go to Step 2
Figure 1. Pixel characterization by a feature vector.
SETIT2009 Table 2 : A set of statistical features M
∑∑
1 MN
Ag =
S=
N
g (i, j )
(1)
i =1 j =1
1
M N
Sd = ∑ ∑ ( g (i, j ) − Me) 2
(2)
Cp M ×N
× 100
(7)
With S , Cp and M × N are segmentation sensitivity (%), classified pixel and image size, respectively.
i =1 j =1
M N
1 MN
Va =
∑ ∑ ( g (i, j ) − Me) 2
(3)
i =1 j =1
M N
E = −∑ ∑ g (i, j ) log( g (i, j ))
(4)
I1
I2
I6
I7
i =1 j =1
I3
I4
I5
M N
Sk =
1 MN
Ku =
1 MN
∑ ∑ ( g (i, j ) − Me) 3
(5)
i =1 j =1 M N
∑ ∑ ( g (i, j ) − Me) 4
(6)
i =1 j =1
Note that g (i, j ) is the grey level of pixel (i, j ) .
As firstly mentioned each pixel becomes characterized by a set of statistical features given in table (2). Therefore, the standard FCM clustering algorithm will undergo the following modifications especially in two given steps (see table 3).
I8
I9
I10
Figure 2. Second group: Images with 2 similar textures
I1
I2
I3
I4
I5
Table 3 : Modification of two steps of the standard FCM
U l −1
Step 2: Compute cluster centers c l with
N
cil =
N
∑ (u
∑ (uik ) X k m
k =1 N
m ∑ (u ik )
ik
becomes Cil =
∑ (uik )
FCMF
th
pixel.
Step 3: Update partition matrix U with; = c
d ik d j =1 jk
∑
2
becomes m −1
=
95
1 c
Dik Djk j =1
∑
I10
FCM
m
l
l uik
I9
)m Fk
k =1
1
I8
100
With Fk the feature vector representing the K
l uik
I7
Figure 3. First group: Images with 2 non-similar textures
k =1 N
k =1
•
I6
.
Segmemntation Sensitivity (%)
•
90
85
80
75
70
2
m −1 65 I1
I2
I3 I4 I5 I6 I7 I8 Im ages w ithout visual sim ilarity (First im ages group)
I9
I10
100
With Dik = Fk − Ci .
FCM 95
FCMF
3. Experimental results 3.1. segmentation sensitivities In order to compare the performance of FCM and the proposed method FCMF, 20 bipartite images are used to test the segmentation sensitivity of each approach. As depicted in figures 2 and 3, textured images are divided into two groups; the first contains 10 images with similar textures while second group is formed by 10 textured images without visual similarity. Performance comparison of FCM and FCMF is based on their segmentation sensitivity ( S ) computed using equation (7).
Segmentaion Sensitivity (%)
90 85 80 75 70 65 60 55 50
I1
I2
I3 I4 I5 I6 I7 I8 Images w ith visual sim ilarity (Second im ages group)
I9
I10
Figure 4. Plot of segmentation sensitivity of two approaches, FCM and FCMF applied on bipartite textured images: (a) without visual similarity. (b) with visual Similarity Based on segmentation sensitivities obtained by FCM and FCMF applied to 20 test images, we can notice that the second method (FCMF) is more performant. The superiority of the proposed method is
SETIT2009 depicted in figure 4, here we can notice that the segmentation sensitivity using FCMF is superior compared to standard FCM, especially when textures are visually similar. Therefore, it’s clear that performance superiority resulted from the pixel characterization degree increased using a set of statistical features. (a)
3.2. segmentation results In this section, a set of textured images is used to test the validity of the proposed method FCMF compared with the standard clustering method FCM. Each method, FCM and FCMF, is applied on a set of textured images. The segmentation is done using; firstly, the fuzzy c-means clustering algorithm (FCM) based on pixel gray level only, secondly, the proposed method (FCMF) in which the pixel is presented by a feature vector.
(b)
(c)
(d)
(e)
Figure 6. Segmentation results of FCMF using a variety of sliding windows dimension (a)Original images (b) Corrupted images by Gaussian noise. Segmentation results with window dimension of; (c) (5× 5) . (d) (9 × 9) . (e) (15×15) . Based on experimental results illustrated by figure 5; it’s clearly shown that the efficiency and robustness of the proposed approach is proportional to sliding window’s size. When the window’s dimension increases, extracted features become more characteristic representative which effect directly on segmentation results.
4. Conclusion
(a)
(b)
(c)
Figure 5. (a) Original image. Segmentation results (b) using FCM based on pixel gray level only, (c) using FCMF based on feature vectors extracted with (9 × 9) sliding window. When working with this algorithm, one has to specify the number of clusters. This number was chosen according to the number of textures in the input image. The segmentation results obtained with the two methods are shown in figure 4. For segmented images, the pixels that correspond to the same cluster are assigned the same gray level. By visual inspection of the segmentation results given in figure (3), it’s found that in all images the proposed FCMF method make segmentation results more efficient than FCM. 3.3. windows size effect on segmentation results Refer to segmentation results depicted in figure 4, it’s clearly shown that the pixel representation by a set of statistical features makes the segmentation results more robust to grey level variation. Based on the performance superiority obtained by FCMF, our interest became oriented to the choice of window size, aiming to establish a comparative study between segmentation results. In this section three window’s sizes (5× 5) , (9 × 9) and (15×15) are used to test the window dimension effect on segmentation performance and robustness to an additive noise. Here, a set of corrupted images is used. For each image, a Gaussian noise is added.
Textured image segmentation is a difficult task in image processing. A unique segmentation approach will certainly never be established to be applied to all kinds of images. In this paper we have proposed an unsupervised fuzzy segmentation approach to be applied in textured image segmentation FCMF, aiming to increase the performance of the standard FCM segmentation technique. Starting from a well known algorithm, fuzzy c-means, we modified its standard use by including the pixel characterization using a set of statistical features containing the most commonly used. Experimental results on a set of various segmented images show better performance of the proposed method in terms of compactness of the segmented regions as compared to the standard fuzzy c-means. Based on experimental results, we have shown the superiority unsupervised fuzzy segmentation approach called FCMF. Furthermore, the search of other optimal features to characterize texture and the use of sliding window with a variable size are an important perspective of our present work.
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