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Procedia Engineering
Procedia Engineering 00 (2011) 000–000 Procedia Engineering 15 (2011) 1590 – 1594 www.elsevier.com/locate/procedia
Advanced in Control Engineering and Information Science
Adaptive Fuzzy Enhancement Algorithm of Surface Image based on Local Discrimination via Grey Entropy Gang Li a,* Yala Tonga,Xinping Xiaob a b
School of Science, Hubei University of Technology, Wuhan,430068 ，China School of Science, Wuhan University of Technology, Wuhan,430063 ，China
Abstract This paper used the value of grey entropy in the neighborhood window as parameters to measure the level of current pixel being edge point, which can be used to be the basis of image enhancement operation. Simulation results show that the algorithm can effectively improve the quality of surface image, and it supplied a good approach to surface image processing compared with other methods.
© 2011 Published by Elsevier Ltd. Open access under CC BY-NC-ND license. Selection and/or peer-review under responsibility of [CEIS 2011] Keywords:Fuzzy enhancement; grey entropy;image processing; local discrimination
1. Introduction In the process of acquisition of surface images, their visual quality will be inevitably reduced by all kinds of reasons. In order to facilitate the post-processing of the surface image, a lot of traditional methods have been put forward, one kind of which is the global histogram enhancement, the other is the * Corresponding author. Tel.: +86-27-88032284. E-mail address:
[email protected].
1877-7058 © 2011 Published by Elsevier Ltd. Open access under CC BY-NC-ND license. doi:10.1016/j.proeng.2011.08.296
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local contrast enhancement. With the development of time and science, a number of new disciplines and perspectives have been applied to image processing in the past, such as fuzzy mathematics[1], statistics in the new practical method, wavelet analysis[2], artificial neural networks[3], mathematical morphology[4], and so on, which greatly reduced the noise, increased the gray levels of pixels, and showed a more perfect effect after being dealt with them. Grey system theory is proposed by the professor Julong Deng[5], and it was applied to all kinds of areas in the past years. Grey entropy[6]is a very important part of grey system theory, and it is very popular in many areas. This paper applied the grey entropy to decide the level of edge of pixels, which will lay a good foundation for the following processing of automatic detection. 2. New Surface Image Enhancement Algorithm based on Grey Entropy 2.1. Idea of new algorithm proposed This Algorithm is divided into two stages: in the first stage, for each pixel in the 3 × 3 neighborhood window, calculate the grey entropy to measure the level of edge, and store the obtained grey entropy value in the corresponding sign matrix, and according to the order that from left to right and from top to bottom, figure out the grey entropy value of each point in turn, which shows that the smaller the gray entropy is, the more possible that this point's corresponding pixel can be an edge pixel; on the contrary, the larger the grey entropy is, the smoother the region is, indicating that maybe no edge point exists herein. The second stage, firstly, map the image to the fuzzy domain, calculate the fuzzy local contrast[7], set a threshold to judge whether the current local contrast of pixels in the neighborhood area should be enhanced or keep unchanged. By doing so, we can increase the local contrast of the corresponding edge area which is really needed to rich the gray levels of the image while maintaining the non-edge area still smooth. 2.2. Steps of new algorithm proposed Step1, suppose that the pixel of image with the size of M × N can be represented as I (i, j)(i = 1,L , M ; j = 1,L , N ) . L is the grey level of all the gray images, equal to 256.To avoid the case that the denominator or real number may be zeros in the calculation of grey entropy, we translate the grey value firstly ,then map it to fuzzy domain; f (i, j) =
I (i, j) + 1 (i = 1,L , M ; j = 1,L , N ) L
(1)
Step 2, calculate the corresponding grey entropy value of each pixel of the image; i +1
H (i, j) = − ∑
j +1
∑ g(k, l)ln(g(k, l)),
g(k, l) =
k =i −1 l = j −1
f (k , l) i +1
j +1
∑∑
f (k , l)
(k = i − 1, i, i + 1; l = j − 1, j, j + 1) (i = 2,L , M − 1; j = 2,L , N − 1)
(2)
k =i −1 l = j −1 j +1
H (1, j) = − ∑ g (1, l)ln( g (1, l)), l = j −1
i +1
H (i,1) = − ∑ g (k,1)ln( g (k ,1)), k =i −1
2
j +1
H (M , j) = − ∑ g (M , l)ln( g (M , l)) ( j = 2,L , N − 1) l = j −1
i +1
H (i, N ) = − ∑ g (k, N )ln( g (k, N )) (i = 2,L , M − 1)
2
k =i −1
2
H (1,1) = −∑∑ g (k , l)ln( g (k, l)); H (1, N ) = −∑ k =1 l =1
H (M ,1) = −
M
2
∑ ∑ g(k, l)ln(g(k, l));
k = M −1 l =1
N
∑ g(k, l)ln(g(k, l))
k =1 l = N −1
H (M , N ) = −
M +1
N +1
∑ ∑ g(k, l)ln(g(k, l))
k = M −1 l = N −1
This formula above make up a grey entropy table in which coordinates can match to the image.
(3) (4) (5) (6)
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Step 3,calculate the local contrast C(i, j) =
C (i, j) of
| f (i, j) − f3×3(i, j) | , f (i, j) + f3×3(i, j)
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the current central pixel in the neighborhood of image[7] ;
f 3×3(i, j) =
1 i +1 j +1 ∑ ∑ f (k, l) (i = 2,L, M − 1; j = 2,L, N − 1) 9 k =i−1 l = j −1
(7)
Step 4, enhance the local contrast like this:
⎧ C(i, j), H (i, j) > ξ Cˆ (i, j) = ⎨ α ⎩C (i, j) , H (k, l) ≤ ξ
(8)
The domain of α is between 0 and 1, and herein it can be set by 0.4, which can achieve a good effect. Step 5, from the (8), we can get the result; ⎪⎧((1 − Cˆ (i, j)) /(1 + Cˆ (i, j)))f3×3(i, j), fˆ (i, j) = ⎨ ⎪⎩((1 + Cˆ (i, j)) /(1 − Cˆ (i, j)))f3×3(i, j),
f (i, j) < f 3×3(i, j)
(9)
f (i, j) ≥ f 3×3(i, j)
Step 6, Inverse transform the enhanced image to the Spatial domain; Iˆ(i, j) = fˆ (i, j)L − 1;
(10)
The Structural framework and flow chart of the algorithm is: The overall translation and mapping the image to the fuzzy domain
Begin with the pixel ( 2 , 2 )
Move to the next
Normalize the pixels in the 3 × 3 neighborhood window Calculate the grey entropy value of each pixel in the image
No
Is it the pixel (M−1, N−1) ？ Yes Input results，end loop
Begin with the pixel ( 2 , 2 ) again Move to the next Yes
No
Is the grey entropy value of the central pixel in the neighborhood bigger than the threshold ξ ? D = C
D = Cα
Is it the pixel
(M−1, N −1) ?
Yes Reflect the image into spatial domain and anti-pan
Fig. 1. Structural framework and flow chart of the algorithm
No
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2.3. Results and their analysis of new algorithm proposed
(a.1)
(a.2)
(b.1)
(b.2)
(c.1)
(c.2)
(d.1)
(d.2)
Fig. 2. Experimental image enhancement and its corresponding edge detection results (a) original image; (b) traditional fuzzy enhancement; (c) new proposed method (ξ = 2.16, α = 0.4) ; (d) new proposed method (ξ = 2.18, α = 0.4) ;
(a.1)
(a.2)
(b.1)
(b.2)
(c.1)
(c.2)
(d.1)
(d.2)
Fig. 3. Surface image enhancement and its corresponding edge detection results (a) original image; (b) traditional fuzzy enhancement; (c) new proposed method (ξ = 2.18, α = 0.4) ; (d) new proposed method (ξ = 2.19, α = 0.4) ;
From the results of the experimental image, traditional fuzzy enhancement algorithm lead to the tendency that the gray values of image gather to low gray value, the whole image darkens, and gray levels
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of the image is lost; the new algorithm makes full use of grey entropy to describe the distribution of local area of the image, and the gray levels of the image in new algorithm are richer, and the vision of the whole image becomes better. Seen from the detection to crack of surface image, compared to the original image, the crack of image processed by the traditional method becomes clearer, but the texture of pavement also strengthens, and it also becomes clear; the part of crack darkens by new algorithm, but the area around the crack becomes smooth, which is the enhanced effect that we want. The edge detection corresponding to the enhancement algorithm also confirmed this from the other side. 3. Conclusion This paper described a fuzzy mapping based on translation transformation, which can increase the stability of the algorithm; making use the grey entropy of pixels in neighborhood to judge the level of edge for pixels, the dynamic adaptive selection of central point of neighborhood in fuzzy contrast enhancement was achieved, and can increase the local gray contrast of the image, rich the texture layer of the image ,improve the quality of the image , make it more adaptive for further treatment and analysis. However, the present improved effect was limited and not very satisfactory. How to overcome this disadvantage and restrain this situation through the implementation mechanism of the algorithm, will be a direction of further research. Acknowledgements We are very grateful to the anonymous referees for their insightful and constructive suggestions, which have led to an improved version of this paper. This work was supported by Hubei Provincial Department of Education Science and Technology Research Project (Grant No. Q20111408) and the Programs for Science and Technology Development of Wuhan (Grant No. 201010621218). References [1]Baoping Wang; Shenghu Liu; Jiulun Fan; Weixin Xie, An adaptive multi-level image fuzzy enhancement algorithm based on fuzzy entropy[J], Acta Electronica Sinica, 2005,33(4):730-734 [2]Peggy Subirats , Jean Dumoulin, Vincent Legeay and Dominique Barba，Automation of pavement surface crack detection using the continuous wavelet transform[A], //ICIP2006[C]:3037-3040 [3]Chou J, Cheng H D. Pavement distress classification using neural networks[C].//Proceedings,IEEE International Conference on Systems,Man and Cybernetics,1994:397-401. [4]Lei Zhang; Mei Xiao; Jian Ma; Hong-xun Song; Pavement crack detection based on visual model[J], Journal of Chang'an University(Natural Science Edition), 2009(5):21-24 [5]Julong Deng. The Basic of the Grey System [M]. Wuhan. Huazhong University of technology Press, 2002. [6]Qishan Zhang，Weiyou Han, Julong Deng，Information Entropy of Discrete Grey number[J], Journal of Grey Systems， 1994，6(4)：303-314 [7]A. Beghdadi and A. L. Negrate, Contrast enhancement technique based on local detection of edges,Comput.Vis. Graph. Imag. Proc., 1989,46: 162–174
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