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1、Medical Image Segmentation Based on Watershed Transformation and Rough Sets Ran Li Dept. of Electronic and Communication Engineering North China Electric Power University Baoding, China AbstractTraditional watershed algorithm often causes over-segmentation because of its high sensitivity to the wea
2、k edge and the noise. To overcome this drawback and in light of the characteristics of medical image, a new segmentation algorithm based on watershed transformation and rough set theory is proposed. The original image is partitioned into the edge-detail sub-image and smooth sub-image according to in
3、discernibility relation of rough set theory. Two enhancement methods are designed for the two sub-images, and watershed transformation is used for the further segmentation in the smooth sub-image. Finally, combine the two processed sub-images to obtain the segmentation result. The proposed algorithm
4、 has been executed on Magnetic Resonance Imaging (MRI) image, the analysis of compare between conventional watershed algorithm and the proposed algorithm is given. The experimental result shows that this method is efficient to restrain the over-segmentation, thus obtaining good segmentation results.
5、 Keywords-image segmentation; watershed segmentation; rough set; over-segmentation; MRI image I. INTRODUCTION Image segmentation is a process to partition an image into non-overlap regions, which is an important step in image processing area and is fundamental for analysis and identification in imag
6、e processing 1. Image segmentation is an important process for most of medical image analysis tasks, which is basic for higher-level image comprehension and analysis. A good segmentation will benefit clinicians and patients as it provides important information for surgical planning, early disease de
7、tection and 3-D visualization 23. Influenced by the complexity and variety of medical image, fuzzy edge of object, the asymmetry and squirming of human organ and noise caused by various medical image equipments(such as Computed Tomography (CT), Magnetic Resonance Imaging (MRI), Positron Emission Tom
8、ography (PET), etc.), medical image segmentation is a very difficult task. In order to solve the problems of medical image segmentation, many practical means have been advanced. These include watershed segmentation45, thresholding method6, region-growing method7, fuzzy cluster method8 and so on. The
9、 watershed algorithm is a classical and effective segmentation method by which one-pixel-wide continuous edge can be extracted. More importantly, it has the advantages of high segmentation precision and accurate positioning, and it is a fast, simple and intuitive method. Its drawbacks will include o
10、ver-segmentation and sensitivity to noise3. Several methods have been proposed to overcome these drawbacks. Watersnakes algorithm is a method of minimal energy, which improves the accuracy and continuity of edge location9. However, over-segmentation is not solved effectively. Method of combining pre
11、process and region merging in 5 can alleviate over-segmentation appropriately, meanwhile, it makes segmentation more complex. In this work, with a view to the preprocessing, we propose a watershed segmentation algorithm of introducing rough set. First, partition original image into edge-detail sub-i
12、mage and smooth sub-image using the rough set theory. Then, the two sub-images are enhanced via different enhancement methods. Moreover, further segmentation is practiced by watershed segmentation algorithm in the enhanced smooth sub-image. Finally, the two processed sub-images are fused into ultima
13、te image. The experiment result shows that the method is effective for inhibiting over-segmentation. The used elementary theories are in section 2 and the proposed methodology is described in section 3. Results and discussion are provided in section 4, with the paper concluded in section 5. II. SUB-
14、IMAGE DIVISION BASED ON ROUGH SET A. Rough Set Theory Knowledge system is an important concept in rough set theory, which has classification capability10. Generally speaking, information systems are used to represent knowledge. Rough set theory forms its information system by using undistinguished r
15、elationship to divide information1112, and the relationship between similar individuals is indiscernibility relation that is a kind of equivalent relation. When giving a finite and nonempty set U called the universe of discourse, and suppose R is an equivalence relation, the knowledge system ( , )KU
16、 R= is an approximate space. If x is an object of U, while X is a subset of U, then, ( )R x denotes a set composed of the 978-1-4244-4713-8/10/$25.00 2010 IEEEobjects which has the undistinguished relation from x. When X can be described by R accurately, Xis definable and is called accurate set of R
17、. When X can not be described by R accurately, X is called the rough set of R. The universe of discourse of the researched object is U. The subset XU denotes the concept in set U. The knowledge in set U is represented as the group-set of conception. The special sort is composed of the knowledge syst
18、em defined by the group in U. Normally the classification is replaced by the equivalence relation. If the equivalence relationship in U is denoted by R, objects of Ucan be represented as equivalent class-clusters based on R, marked as /UR. While PR and P , the intersection of all the equivalence rel
19、ationship in P(marked as P) is also a equivalence relation, which is called undistinguished relation of P, marked as ( )ind P: ()ind PRXX= PR (1) If the certain knowledge system ( , )KU R= is given, for subset XU and an equivalence relationship ()Rind K, the set X can be classified according to the
20、basic set of R. A category in Rcontaining an object xU is denoted by R(1,1)( ,1)(1,1)(1,1)( ,1)(1,1)Yf ijf i jf ijf ijf i jf ij=+ (10) Where i and j (1iM ,1jN) are coordinates of ( , )f i j. X denotes the sum of horizontal gradient, and Ydenotes the sum of vertical gradient. The pixel whose gradient
21、 is above threshold (W) belongs to edge-details region of the image, while the pixel whose gradient is below or equal to W belongs to smooth region of the image. Condition attribute is defined as 12,Cc c=. Where 1c stands for gradient attribute and 2c stands for noise attribute. 10,1c = is the gradi
22、ent attribute of pixel. Where 1 stands for the pixel with large gradient which satisfies the inequality ( , )I i jW, where 0 stands for the pixel with small gradient which satisfies the inequality ( , )I i jW. 20,1c = is the noise attribute of pixel. Where 0 denotes that the absolute values of avera
23、ge gray difference between block (s) of 3 3 and its adjacent blocks are all lower than some threshold (represented by Q), where 1 denotes that the absolute values are all higher than Q. The pixels of one image are categorized by attribute C. First, the image is divided into two sub-images based on 1
24、c, and the equivalent relation is defined as follows: 1( )( , )R xx I i jW= (11) Where 1( )R x stands for set of large gradient pixels, and 1( )R x stands for set of small gradient pixels. Then the image is divided into two sub-images based on 2c. Equivalent relation 2( )R s denotes set composed of
25、all noise pixels, and 2( )R s is defined as follows: 21,1( )()()ijijijijR ssm sm sQ= (12) Where 11,111()(,)9i jklm sf ik jl=+ (13) ,()i jm s denotes average gray value of 3 3 sub-block. Where 1,1ijs stands for adjacent block of , i js. Sub-block , i js and 1,1ijs constitute macro-block. Average gray
26、 value of the macro-block is as follows: 11,1119i ji k j lklMs+= (14) Combine the two kinds of sub-images obtained by different division manner. We obtain the de-noise set of large gradient pixels (represented by 1F) and the de-noise set of small gradient pixels (represented by 2F). 1F is correspond
27、ing to the edge of the image, and 2F is corresponding to the smooth region of the image. They are defined as follows: 112( )( )FR xR s= (15) 212( )( )FR xR s= (16) 1F and 2F are pixel sets that need to be further processed by enhancement and segmentation. III. ALGORITHM ILLUSTRATION The two sub-imag
28、es need to be processed in different way, the algorithm is performed based on the following procedure: 1) Obtain the gradients of all pixels in image F according to (8), (9) and (10), and ( , )I i j stands for the gradient image. 2) Generate two sub-images (1F and 2F) of F according to (15) and (16)
29、. Define the gray value of blank position of the two sub-images. To 1F, the gray values of low-gradient pixels are determined as half of the maximum gray-level, and the gray values of noise pixels are ijM obtained by (14). The complemented sub-image of 1F is denoted by 1F. Adopt the same method comp
30、lement 2F, and the complemented sub-image of 2F is denoted by 2F. 3) Enhance 1F and 2F by different means. Enhance 1F by exponential transform method whose transform equation is as follows: 1( )()g xF= (17) Where and are parameters. Enhance 2F by the method of histogram equalization. 4) Implement wa
31、tershed segmentation to enhanced 2F. Remove the pixels filled in procedure 2), and then obtain 1F and 2F. Combine 2F with 1F, and make sure the gray values of the pixels in combined image are all less than the gray-level of original image. So we obtain the segmentation result. Obviously, the above a
32、lgorithm is composed of three parts: classifying pixels of the image by property C, enhancement and segmentation. The original image is divided into edge-detail and smooth sub-images. The edge-detail sub-image is enhanced by exponential transform method, which can change the dynamic range of the ima
33、ge by gray stretch. The gray gradient of pixels nearby edge are even larger by choosing suitable parameters ( and ). While adopt the method of histogram equalization to smooth sub-image, which weaken the noise. This method is accord with the properties of human visual system (HVS). Watershed transfo
34、rm is only implemented in smooth part of the image, which can improve the over segmentation problem. IV. SIMULATION RESULTS AND DISCUSSIONS The proposed method is experimented on a MRI image to illustrate the effectiveness of our proposed method. The image we select is a human brain MRI image provid
35、ed by a hospital. Fig. 2(a) is original image. Fig. 2(b) is edge sub-image, and Fig. 2(c) is smooth sub-image. The segmentation result of smooth sub-image is show in Fig. 2(d). The ultimate segmentation result is shown in Fig. 2(e). Fig. 2(f) shows the comparison of segmentation result with the impl
36、ementation of the conventional watershed transformation on the original image. (a) (b) (c) (d) (e) (f) Figure 2. (a) Original MRI image, (b) Edge sub-image, (c) Smooth sub-image, (d)Smooth sub-image after watershed transform, (e) Segmentation result of our proposed method, (f) Segmentation result of
37、 conventional watershed segmentation From Fig. 2(f), we can see over-segmentation phenomenon. The image is segmented into a large number of small regions in Fig. 2(f), and the regions are scattered. Using the method proposed in our paper, the over-segmentation problem is evidently improved (shown in
38、 Fig. 2(e) ). In Fig. 2(e), the brain image is divided into white matter, grey matter, bone, other tissues and background. In the experiment, we set 0.395W =, 0.5Q =, 1.25= and 0.8=. V. CONCLUSIONS Excellent segmentation effect can not be obtained because of the drawbacks of conventional watershed a
39、lgorithm. Medical images contain much information of the research object, which has complex spatial correlation and uncertainty. Rough set theory is as a mathematical tool to describe problems with fuzzy and uncertainty knowledge. It can deal with uncertain information by special way and can deal wi
40、th the imprecision and incomplete information effectively. So if rough set theory is applied in image segmentation, the segmentation result will be good. In this paper, a new segmentation algorithm in which rough set theory and watershed transform are effectively combined is presented. The image is
41、divided into edge sub-image and smooth sub-image, and the two sub-images are implemented by different segmentation method. Watershed transform is only used on the smooth sub-image. The experimental results show our proposed method is effective in improving over segmentation problem and relieve the i
42、nfluence of noise in watershed segmentation process. But the edges of the result image obtained by the above-mentioned method are fuzzy in some degree. And this is our further work. REFERENCES 1 Dong Min, Li Xiangpeng, and Wang Li, “Image segmentation based on rough membership function, ” in Proc. I
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