Fuzzy Based Edge Guided Medical Image. Sharpening Technique Using Median Filtering. Method

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1 Contemporary Engineering Sciences, Vol. 10, 2017, no. 1, HIKARI Ltd, Fuzzy Based Edge Guided Medical Image Sharpening Technique Using Median Filtering Method L. Shyam Sundar Singh National Institute of Electronics and Information Technology Akampat, Post Box No. 104, Imphal, Manipur, India Anil K. Ahlawat Department of Computer Application Krishna Institute of Engineering and Technology Ghaziabad, UP Meerut Road, India Kh. Manglem Singh Department of Computer Science and Engineering NIT, ManipurImphal , Manipur, India T. Romen Singh Department of Computer Science Manipur University, India Copyright 2016 L. Shyam Sundar Singh et al. This article is distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract This paper presents a fuzzy edge guided image sharpening technique. Sharpened image is obtained by subtracting the smoothed image of an input image from itself. Image smoothening is carried out with median filtering technique. Median filtering technique is a process of replacing the concerned pixel by the median value of pixels within a block as the concerned pixel is at center. Smoothening is applied only at edge region within the image and hence edge detection

2 14 L. Shyam Sundar Singh et al. is important. It is carried out with the help of the fuzzy value of the second order derivatives along the horizontal, vertical, left and right diagonal directions. According to the degree of edge, image smoothening is applied only on the edge region of the input image. Keywords: Edge Detection, Fuzzy technique, Medical image, Edge sharpening Median filtering 1 Introduction Nowadays digital Image Processing takes a major role in the medical science to provide interior human anatomy visualization. It helps the medical practitioners in their diagnostic systems. Anatomy visualization assists to detect and locate the pathological deformations of human anatomy for analyzing the various internal structures of body of the patients. But images may suffer from noise and poor contrast due to the inadequate lighting while acquiring the image. So it is required to enhance the contrast of the image as well as remove the noise that decreases the image quality. Image segmentation, edge detection and enhancement are the significant steps in any digital image processing applications [9]. Its aim is to change the image representation by simplifying into something that is more meaningful so as to make easier to get the appropriate image information. Edges characterize boundaries of an object and hence edge detection is considered as one of the eminent and promising technique. Edges help to extract the suitable features of an object. The image enhancement technique s aim is to improve the quality and the visual appearance of the image to the human viewer by manipulating the existing image. The low contrast image is inconvenient for human visualization and hence image enhancement is one of the most challenging, interesting and important area of research in image processing. In medical imaging system, image enhancement is to improve the visual appearance to the human viewer. To human visual system, contrast is more sensitive than luminance/color. The contrast is the difference in luminance/color of the objects within the same field of view. Edge is the highly contrast region within the objects. Edge sharpening is a process of making more distinct the object by stretching the contrast within the region. Low contrast and noise presence in medical images due to device or environmental factors, the medical practitioners feel inconvenient in their diagnostic systems. So as to overcome this inconvenient, it is required to enhance the captured images.

3 Fuzzy based edge guided medical image sharpening technique 15 The traditional image enhancement algorithms [9] amplify the noise and it occurs inconvenience for clinical diagnosis and medical research. Hence efficient medical image enhancement techniques which are noise attenuation and enhancement of the texture details are necessary. This will provide great help to the medical practitioners for early diagnosis of some diseases. Not only the standard techniques, researcher apply many techniques on different domains like spatial [12, 14], transform domain [8, 13] and fuzzy domain [1, 2, 4, 5, 7, 8, 11] to enhance contrast and edge information of images. Fuzzy rule based techniques are also very powerful and nowadays it becomes a common technique for enhancement of images. In this proposed technique also, fuzzy membership function technique is applied to detect edges within the image and applied different enhancement functions on edge and non-edge area within the image itself. From the experimental result it is found that the proposed system outperforms. 2 Fuzzy Set Theory A fuzzy set is a mathematical tool for handling imprecision or vagueness [3, 6]. Let Z = {z} be a universal set of generic elements. A fuzzy set Y in Z is characterized by a membership function μ Y (z) that produces an association value of each element z in Z as positive real number in the range [0, 1]. Y can be expressed mathematically as follows Y = {z, μ Y (z) zεz} (1) The nature of participation of the element z in Y is given by the nature of membership function μ Y (z). According to desired application, we can define membership function or we can use the standard functions. 3 Proposed System This proposed system sharpens edge of medical images with fuzzy edge guided method. It involves edge region pixel detection and median value calculation within a w w block as prior process. Edge detection is based on the 2 nd ordered derivative around a concerned pixel at center with its two extreme boundary neighboring pixels within the block. Edge Detection. Let A [0, L 1] be an image with L-1 maximum intensity value. If the image is of one byte pixel value, L=256, i.e. A [0,255A can be expressed in normalized form as A [0,1].

4 16 L. Shyam Sundar Singh et al. Second order derivative around a pixel A ij with its two neighboring pixels A ij 1 and A ij+1 can be expressed as follows d v = A ij 1 + A ij+1 2A ij (2) The maximum possible value of d v is 2(L-1), i.e in the case of one byte pixel image and 2 in the normalized image pixel. If d v is greater than a certain threshold value t, A ij is said to be within edge region. In this system, second ordered derivative is calculated with the two extreme boundary neighboring pixels within a block of size w w (w is an odd) as the concerned pixel at center as shown in Figure 1. There will be four derivatives Dl, Dr, Dh and Dv along left, right diagonal, horizontal and vertical respectively as in Figure 2. They can be calculated as follows D l = A i d,j d + A i+d,j+d 2A i,j (3) D r = A i+d,j d + A i d,j+d 2A i,j (4) D h = A i,j d + A i,j+d 2A i,j (5) D v = A i d,j + A i+d,j 2A i,j (6) where d = w 1 2. Figure 1 shows a block of size w=3 and w=7 with d=1 and d=3 respectively. Different block size will give different width edge region area around the edge as in Figure 3. Based on these four derivatives, a certain value v is calculated so as to take decision whether the concerned pixel is within the edge region or not and calculated as v = D x D m p (7) where D x = max {D l, D r, D h, D v }, D m = min {D l, D r, D h, D v } and p is a constant value. But v is vague to decide for edge and hence fuzzy technique is applied to decide for edge. If the image is in normalized form then v [0,2].

5 Fuzzy based edge guided medical image sharpening technique 17 (i-3,j-3) (i-3, j) (i-3,j+3) (i-1,j-1) (i-1,j) (i-1,j+1) (i,j-1) (i,j) (i,j+1) (i,j-3) (i, j) (i,j+3) (i+1,j-1) (i+1,j) (i+1,j+1) (i+3,j-3) (i+3,j) (i+3,j+3) b. 3 3 a. 7 7 Figure 1. Pixel blocks as the concerned pixel at (i, j) as center. Dr Dh Dv Dl Figure 2. Different derivatives directions a. Input b. w=3 c. w=7 Figure 3.Width of edge at different block size w. Fuzzy edge domain plane. Since v is vague to decide for edge, a fuzzy membership function is designed with v as parameter to the function as follows μ(v) = { vg if v < p 1 otherwise It can be expressed in a single expression as (8) f v = μ(v) = [ p+v v p ] g (9) 2p where g is a positive constant which can give different shape of membership function and p is also a constant which can adjust the maxim participation level of

6 18 L. Shyam Sundar Singh et al. v as shown in Figure 4(a). Membership function shape at different values of p and g are shown in Figure 4. In this way, we can adjust the level of participation degree of a pixel within edge region by changing the parameter p and g keeping t at constant. Figure 4(b) shows the different degree of participation at different values of g with single value of p and t. Thus, we can detect edge region pixels within the image concerned. Figure 5 shows the corresponding fuzzy edge domain image plane of Figure 4 (b). p t a. Membership function at different p p g = 0.5 g = 1 g = 3 t v b. Membership function at different g Figure 4. Different shape of fuzzy membership function at different parameter values

7 Fuzzy based edge guided medical image sharpening technique 19 a. Original b. g =0.5 c. g =1 d. g =3 Figure 5. Fuzzy edge domain image plane of different function shapes at different values of g. Edge sharpening. In this proposed system, edge sharpening is carried out by subtracting blur/smooth image from its original image as in the following relation I = 2A B (10) where A is the input image while B is the blur/smooth image. Image blurring is carried out with the help of median filtering technique. But in this technique, blurring is applied only at the edge region pixels. Hence (10) can be expressed at pixel level as follows s = 2a b (11) where a and s are the input and output pixels while b is the median value of pixels within a block of size w w as a at center.

8 20 L. Shyam Sundar Singh et al. Original C= a. Brightness control at different values of C Original γ = b. Contrast control at different values of γ Figure 6. Brightness and contrast control at different parameter values. We can leave the non-edge pixels as it is, as follows s = a (12) Now, we can expressed in a single expression by combining (11) and (12) as 2a b s = { a if a is within edge region if a is not within edge region (13) Further it can be modified with edge and contrast controlling parameters as in the following relation I(i, j) = { Cx x (γ 1) C[A(i, j)] γ if f v > t otherwise (14) where x = A(i, j) + d(a(i, j) m x ), C, d and γare constants which can control brightness, edge sharpness level and global contrast respectively as in Figure 6. Here, d=2 is taken as most suitable value. fv and t are fuzzy edge participation degree obtained from (9) and fuzzy degree threshold value. t [0,1] can control level of belongingness of a pixel to edge region based on the shape of the membership function associated as in Figure7. mx is the an value of pixels

9 Fuzzy based edge guided medical image sharpening technique 21 within a block of size w w as A(i, j) at center. Its value depends on the size of w. The large value of w will give the more blurred image as in Figure 3 and Figure 8. Original g = a. Image result at different function shapes with different values of g keeping t =0.2 at constant. Original t= b. Image result at different threshold value of t keeping g=0.5 at constant. Figure 7. Result image at different threshold and different function shape. w=7 w=3 Figure 8. Different image blurring level and its visual effect to edge at different values of w.

10 22 L. Shyam Sundar Singh et al. System Algorithm: This proposed system can be summarized as the following algorithm - This paper will involve the following steps as Am n and Im n are the input and output images. 1. Determine the maximum and minimum double derivatives Dx and Dm of A(i,j) among the derivatives along four different directions as Dl, Dr, Dh and Dv for left & right diagonals, horizontal and vertical directions with the extreme boundary neighboring pixels of a block of size w w as A(i, j) at center. 2. Calculate v = D x D m p 3. Fuzzyfy v and assign its value at fv. 4. Calculate the median value mx of the pixels of the w w block. 5. Image transformation: x = A(i, j) + d[(a(i, j) m x ]) I(i, j) = { Cx x (γ 1) if f v > t C[A(i, j)] γ otherwise Repeat step 1 to 5 while I m- and j n- where = w Image Evaluation This proposed system provides the controls of brightness, contrast stretching, and edge sharpness/smoothness of an image. The enhancement measure by entropy (EME) [12, 14] is used to evaluate global contrast and Tenengrad [12, 14] is used to measure the edge sharpness/smoothness. Enhancement Measure by Entropy (EME). EME is based on entropy of contrast established on the foundation of the Michelson contrast measure [12, 14] and uses elements of human visual perception. It is expressed as EME = 1 p q l m (x,y) p q x=1 y=1 log (1 + l m(x,y) ) (15) l n (x,y) l n (x,y)+e where p q is the total number of non-overlapping blocks of size b b in the image I(m n) such that p = m b and q = n b. l m(x, y) and l n (x, y) are the maximum and minimum grey level values of pixels within the block (x, y), e is a very small constant added to the denominator to avoid division by zero. Higher value of EME denotes a higher contrast and information clarity in the image. Using a smaller block size b b produces a more accurate result, but increases processing time.

11 Fuzzy based edge guided medical image sharpening technique 23 Tenengrad Measure. TEN [12, 14] is used to measure edge information and based on gradient magnitude maximization. The gradient I(x, y) at each pixel location (x,y) of an image I is used to obtain Tenengrad value, where the partial derivatives are calculated by using a high pass filter like the Sobel operator, with the convolution kernels ix and iy. The gradient magnitude is given as S(x, y) = (i x I(x, y)) 2 + (i y I(x, y)) 2 (16) The Tenengrad criteria is then calculated as TEN = x y S(x, y) 2 for S(x,y) > T (17) where T is a threshold, for this application, it is 75% of the maximum magnitude Result Analysis. Table 1 and Figures 9-10 show the EME and TN comparison of results of PT with HE while Table 2 and Figures show the EME and TN values and output results of the proposed technique with their respective parameter values along the input image. The parameters C, γ, g and t are the respective controlling factors of brightness, global contrast, edge region and edge fuzzy threshold. But the values of p and d are kept constant as p=0.5 and d=2 for each experiment. We can adjust any level of output image by changing the respective parameter so as to get our desire result. Based on the visual results, EME and TN value as shown in the Tables and Figures, this system outperforms. For an algorithm, computational time complexity is a major factor. This system depends its computational time on local block size w. But this system is tested on different block size and found to be best at w=3. Hence, its computational time complexity is O (w 2 n) and it can be reduced to O(n), if w=3. From the above experimental results, it is observed that the proposed technique outperforms. Table 1. TN and EME comparison of Proposed Technique (PT) and Histogram Equalization (HE) of results shown in figure 10. Image No. HE Proposed Technique(PT) EME TN EME TN

12 24 L. Shyam Sundar Singh et al EME HE PT TN HE PT Figure 9. EME and TN Comparison chart of Table 1. a. Original b. HE c. PT Figure 10. Result Comparison of PT with HE

13 Fuzzy based edge guided medical image sharpening technique 25 Table 2. TN and EME of results shown in figures Figure No EME TN Figure 11. C=1.6, γ=1.05, g =0.9, t=0.2 Figure 12. C=1.6, γ=0.7, g =0.7, t=0.2

14 26 L. Shyam Sundar Singh et al. Figure 13. C=1.6, γ=1.2, g =0.9, t=0.2 Figure 14. C=1.5, γ=1.09, g =0.8, t=0.2 Figure 15. C=1.5, γ=1.09, g =0.8, t=0.2 5 Conclusion This proposed system is based on fuzzy based edge guided medical image contrast and edge enhancement technique. It can adjust contrast and local edge sharp-

15 Fuzzy based edge guided medical image sharpening technique 27 ness of an image with the respective parameters provided by the system. Fuzzy system is applied only on detection of edge region within the image. Sharpening technique is based on the subtraction of blurred image from the input image and blurring technique is carried out by the median filtering technique. References [1] J.J. Wang, Z-hong Jia, Xi-Zhong Qin, Jie Yang, Nikola Kasabov, Medical Image Enhancement Algorithm Based on NSCT and the Improved Fuzzy Contrast, International Journal of Imaging Systems and Technology, 25 (2015), [2] Khairunnisa Hasikin and NorAshidi Mat Isa, Enhancement of the low contrast image using fuzzy set theory, 14th International Conference on Modelling and Simulation, (2012), [3] L. A. Zadeh, Fuzzy sets, Inform. Contr., 8 (1965), [4] K. Venkateshwarlu, Image Enhancement Using Fuzzy Inference System, Master of Engineering Report, Thapar University, Patiala, , [5] Kh. Manglem Singh, Fuzzy Rule based Median Filter for Gray-scale Images, Journal of Information Hiding and Multimedia Signal Processing, 2 (2011), no. 2, [6] Klir. G. J and B. Yuan, Fuzzy Sets and Fuzzy Logic, Prentice - Hall, Upper Saddle River, NJ, [7] M.C. Hanumantharaju, S. Setty and N.K. Srinath, Development of multiscale Retinex algorithm for medical image enhancement based on multi-rate sampling, International Conference on Signal Processing Image Processing Pattern Recognition (ICSIPR), (2013), [8] R.A. King and S.K. Pal, Image enhancement using fuzzy sets, Electron. Letters, 16 (1980), [9] R.C. Gonzales, R. E. Woods, Digital Image Processing, 2 nd Edn., [10] S. Aghagolzadeh and O.K. Ersoy, Transform image enhancement, Opt. Eng., 31 (1992),

16 28 L. Shyam Sundar Singh et al. [11] S. KaurSohal, Er. S Singh, Performance Analysis of Fuzzy Based Image Enhancement Using Particle Swarm Optimization, International Journal of Engineering and Innovative Technology (IJEIT), 5 (2015), no. 1, [12] T. Romen Singh, O.I Singh, Kh. M Singh, T. Sinamand Th. R Singh, Image Enhancement by Adaptive Power-Law Transformations, Bahria University Journal of Information and Communication Technology, 3 (2010), no. 1. [13] T. Romen Singh, S. Roy, Kh. M. Singh, Global DCT Domain Power-Law Transformation in Image Enhancement Technique, International Symposium on Computational and Business Intelligence, (2013), [14] T. Romen Singh, Sudipta Roy, Kh. Manglem Singh, Histogram Domain Adaptive Power Law Applications in Image Enhancement Technique, International Journal of Computer Science and Information Technologies, 5 (2014), no. 3, Received: October 30, 2016; Published: December 23, 2016