Microsoft Word - 4-李国东.doc Advances in Systems Science and Applications (2010), Vol.10, No.1 19-24 ISSN 1078-6236 International Institute for General Systems Studies, Inc. Analysis B-scan Image by CNN and Polyfit* Guodong Li1,2 and Wenxia Xu3,4 1School of Mathematics and Physics, North China Electric Power University, Beijing 102206, China 2Industrial Systems Engineering, University of Regina, Wascana Parkway, Regina, Sask. S4S 0A2, Canada 3Dep of Electric Engineering, Chengdu University of Information Technology, Chengdu 610225, China 4Xinjiang Weather Modification Office, Urumqi 830002, China Email: lgdzhy@ncepu.edu.cn, xwxqiuye@live.cn Abstract In this paper, we have be processed ultrasound with Cell Neural Network(CNN). First we detected the edge from B-Scan images, and then we analysis the data that from the edge of image. Some interesting result has been finding. There are some regular between the number and the patient’s B-scan image. Keywords B-Scan image Edge detection Liver damages 10-degree polynomials fitting 1. Introduction In the last two decades, medical image processing technology has been developed rapidly. It can help doctor to diagnose patients' disease more accurately. Medical image processing with computer has attracted much attention recently [1]. A lot of methods for dealing with medical images have appeared [2],[3]. In Chua's articles (see [4] or [5]), many important and interesting CNNs are described. One of them is the edge detection CNN, which can detect the edge in gray-scale images. In a recent conference paper, a robustness theorem for designing edge detection CNNs is set up [6][7][8]. Detecting edges of gray-scale images may be required for a variety of purposes, such as machine vision, image analysis, and image pick-up and so on. Edge detection is one of the most important steps for image recognition since there is a direct relationship between edge and object recognition. A lot of scene information can be interpreted from the edges. In natural images, most edges are associated with abrupt changes in intensity distribution and can be approximately modelled as step edges. Pathological changes of chronic Hepatitis patient include liver fibrosis, heterotrichosis and liver cancer, etc; however, the three states of liver disease are difficult to distinguish from B-scan image by naked eyes. Digital analysis of the B-scan images will help doctors to diagnose the stage of the damages of patients' livers. 2. Edge Detection CNN In a Chua’s exposition [1], many important and interesting CNNs are described. One of them is Edgegray CNN, which can detect the edges in gray-scale images. The template of the standard Edge gray CNN has the form。 The standard M×N CNN architecture is composed of cells jic , . The dynamics of each cell is given via the following equation [1]: jiljki r rk r rk lkljki r rk r rk lkjiji zubyaxx ,,,,,,, +++−= ++−= −=++−= −= ∑ ∑∑ ∑ (1) * This work is supported by Meteorology Bureau of Xinjiang Uighur Autonomy, Science and Technical Item (Project no. 201012). Li: Analysis B-scan Image by CNN and Polyfit 20 ( )11 2 1 ,,, −−+= ++++++ ljkiljkiljki xxy NJMi NMljki ,2,1;,2,1 ],1[],1[),( == ×∈++ (2) Where jijijiji zuyx ,,,, ,,, represent state, output, input, and threshold respectively; lklk ba ., , are the elements of the A-template and the B-template respectively. Figure 1 The dynamic routes of the CNN The standard edge CNN's local rules and template are listed as follows: Local Ruler jiu , → )(, ∞jiy (1) white → white, independent of neighbours. (2) black → white, if all nearest neighbours are black. (3) black →black, if at least one nearest neighbours is white. (4) grey →black, if the Laplacian operator zU ji >∇ , 2 . (5) grey →white, if the Laplacian operator zU ji <∇ , 2 . (6) grey →0, if the Laplacian operator 0, 2 =∇ jiU . The standard CNN template has been generalized by the following theorem. Theorem 1[6]: Let the positions of CNN template parameters be described by (3).Then the CNN can perform the Local Ruler of the detection of edges in gray-scale images, if the following parameter inequalities hold: cbzzcz 6 .2 8 .1 −<<− 000 00 000 1,1 zz ccc cbc ccc BaA −= ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ −−− −− −−− = ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ = (3) Where a > 1, 1,1 >> cb ∑ ∑ ≠ −∈ ++−Δ∇ )0,0(),( }1,0,1{),( ,,, 2 lk lk ljkijiji ucbuU Where： Advances in Systems Science and Applications (2010), Vol.10, No.1 21 ⎪⎩ ⎪ ⎨ ⎧ − >Δ =Δ otherwise u if c ub ji jilk 1 g )( , ,, (4) 3. Segmentation of the B Scan Image Figures 3 show the ultrasound B-scan images (UBSIs) of six people's livers. Each original UBSI is an RGB image with 720×576 pixels. We chose the same eath part in the ultrasound B-scan images as that shown in Fig.2, which is on the left of the cholecyst and up of the portal vein. Expert doctors analyze this region when they diagnose sufferer according to B-scan image. So we cut this region and then processed it with edge gray detected CNN. Clinical diagnoses for the six UBSIs are listed as follows. Figure 3(1) is obtained from a healthy hepatitis B virus (HBV) carrier. Figure 3(2) is the UBSI of a normal liver without HBV infection. The UBSI of a young (under 20 years old) chronic hepatitis B patient without liver cirrhosis is shown in Figure 3 (3) and that of an old one (over 50 years old) is given in Figure 3 (4). Figure 3 (5) and Figure 3 (6) are the UBSIs of a patient with ascites and a patient with marked liver cirrhosis, respectively. 4. Application of the Edge Detection CNN In this section, we shall use edge detection CNN to process the part of B-scan image. The template parameters of the CNNs are given in Table 1. Table 1 Template parameters of the CD CNN a b c z g 4 16 2 0.4 0.4 The edge detection CNN can be used to process RGB images. An RGB image is usually represented by an M×N×3 (for the above UBSIs, M = 576, N = 720) data matrix P where M, N stand for the rows and the columns of the pixels in the image, and 3 represents 3 color planes ---red, green and blue, each color plane with 256 levels of intensity denoted as (R, G, B) = ( ) ( ) ( )( ),3:,:,~,2:,:,~,1:,:,~ PPP . Such an image is called an RGB 24-bit map. In order to use CNN to process RGB images, we use a transform *PP → (5) To change the 256 levels of intensity of each color plane into the levels of intensity in [-1, 1]. Consequently, the lighten pixels in the original RGB image P correspond to smaller values in the transformed image *P and vice versa. In the following discussions, we always assume that the levels of intensity of input RGB images 1P and 2P have been transformed via formula (5); the color planes of processed images have been changed into the RGB forms when the processed images are shown as color pictures. Firstly the edge detection CNN given in Table 1 is used to process the part of the UBSIs shown in Figure 3. The processing results are demonstrated in Figure 4. It is difficult to give a correct judgement for non medical researchers. However, we arrange the pixels of the three color planes P(:,:,1), P(:,:,2), P(:,:,3), of each processed image (the output ( )"" , ∞jiX , not the output ( )"" , ∞jiY ) in row-wise packing scheme [5]. Then wavelet transform is applied to process the images in Figure 4. Li: Analysis B-scan Image by CNN and Polyfit 22 Figure 2 The selected part of the B scan image The part in the white rectangle is chosen for EDGE CNN analysis. Patient liver NO1(a) Patient liver NO2(a) Patient liver NO3(a) Patient liver NO4(a) Patient liver NO5(a) Patient liver NO6(a) Figure 3 Segmentation of patient liver Patient liver NO1(b) Patient liver NO2(b) Patient liver NO3(b) Patient liver NO4(b) Patient liver NO5(b) Patient liver NO6(b) Figure 4 The result of the B scan image processed by edge detect CNN. 5. Introduction of Polynomial Fitting Given data ( )ii yx , (i=0,1,…，m)，we shall find a polynomial p(x) such that the error’s square sum is the least, i.e. ( )[ ] min 0 2 =−∑ = m i ii yxp Suppose that Φ is the set of polynomials of degree ( )mnn ≤ . Let ( ) ∑ = Φ∈= n k k kn xaxp 0 and Advances in Systems Science and Applications (2010), Vol.10, No.1 23 ( )[ ] min 0 2 00 2 =⎟ ⎠ ⎞ ⎜ ⎝ ⎛ −=−= ∑ ∑∑ = == m i n k i k ik m i ii yxayxpI (6) It is obvious that ∑ ∑ = = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ −= m i n k i k ik yxaI 0 2 0 is a function of ,,,, 10 naaa . So the problem is to find the extreme value of ( )naaaII ,,, 10= . By the necessary condition of extreme points, we have: 02 0 0 =⎟ ⎠ ⎞ ⎜ ⎝ ⎛ −= ∂ ∂ ∑ ∑ = = m i j i n k i k ik j xyxa a I nj ,1,0= (7) i.e. njyxax m i i j i n k k m i kj i ,1,0 00 0 ==⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ∑∑ ∑ == = + (8) In matrix form, (8) becomes ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ = ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ + ∑ ∑ ∑ ∑∑∑ ∑∑∑ ∑∑ = = = == + = = + == == m i i n i m i ii m i i nm i n i m i n i m i n i m i n i m i i m i i m i n i m i i yx yx y a a a xxx xxx xxm 0 0 0 1 0 0 2 0 1 0 0 1 0 2 0 00 1 (9) It is easy to show that the coefficient matrix of (9) is positive definite, therefore (9) has a unique solution. Solving (9), we obtain ka (k=0, 1,…，n)，and thus the polynomial ( ) ∑ = = n k k kn xaxp 0 　 (10) It is easy to show that (10) satisfies, i.e. (10) is the fitting polynomial. Figure 3 and Figure 4 are 6 livers’ original B-scan images and resulting images processed by CNN, respectively. Each original B-scan image is an RGB image with 720×576 pixels. In this paper we deal with these B-scan images by EDCNN. Then by polynomial fitting (10-degree), we find that the coefficients of the polynomials are related to the damage of the patients’ livers. 6. Concluding Remarks We have detected 6 B-scan images by CNN. Then using polynomial fitting, we obtain the following data as shown in Table 2. Data of normal liver is No. 1 in Table 2, From 2 to 5 are B-Hepatitis in Table 2. From the Tables 2, it is easy to see that the value of a1 is closely related to the condition of the liver. Most values of a1 are smaller than 7, and few are smaller than 12. Therefore, According statistic regular[9], we can conclude that if a1 is larger than 7, the liver is normal; and if a1 is smaller than 7, the liver is CHB. We can use this way to diagnose the CHB. Li: Analysis B-scan Image by CNN and Polyfit 24 Table 2 Data of edge B-scan analysis by CNN a10 e-47 a9 e-41 a8 e-35 a7 e-29 a6 e-24 a5 e-19 a4 e-13 a3 e-09 a2 e-04 a1 e-00 a0 e+5 1 -2.1535 4.9041 -4.7809 2.6041 -8.6754 18.181 -2.3715 18.313 -7.4913 12.252 1.8006 2 1.1509 -2.2140 1.7396 -0.7036 1.4633 -1.0387 -0.1564 3.6640 -2.5314 5.3752 2.0242 3 -0.3927 0.9139 -0.9437 0.5649 -2.1400 5.2406 -0.8123 7.4907 -3.6249 6.5730 1.9970 4 -0.8249 1.7516 -1.6135 0.8469 -2.7937 5.9910 -0.8262 6.8948 -3.0492 5.1082 2.0678 5 1.3496 -2.4470 1.7724 -0.6260 0.9187 0.6274 -0.4292 6.0397 -3.5273 6.9943 1.9646 6 0.5490 -0.8967 0.5185 -0.7841 -0.4708 2.6723 -0.5914 6.5870 -3.5138 6.6962 1.9830 References [1] B. Li. Evole and application of medicine image in technology of computer image processed. Journal of medicine engineer, 1993, 10(4): 360-363. [2] S. R. Xia. Medicine image searchers technology base on charpter fuse and feedback correlative. 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