An Image Edge Detection Algorithm using Wavelet Transform and Fuzzy Techniques

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1 An Image Edge Detection Algorithm uing Wavelet Tranform and Fuzzy Technique Bin Huang 1*, Jiaofeng Wang,Xiaomei Jin 3 1.College of Teacher Education, Quzhou Univerity, Zheiang Quzhou, china. Quzhou Vocational and Technical College Zheiang Quzhou, china 3. College of Teacher Education Quzhou Univerity, Zheiang Quzhou, china Abtract In thi paper we propoe an image edge detection algorithm baed on wavelet tranform and fuzzy technique. Sharpne of a reproduced image i one of the important criteria for quality of reproduction. Due to influence from ome external factor, image, which are tranferred between device and tranformed between colour pace, are not only changed in their colour and their gradation, but alo blurred in their detail. But the contour and edge information in image need uually to be extruded. Therefore, except for the colour correction and gradation adutment of image, the enhancement of image-harpne, which i the focu here, i very important in image proceing. The empirical tudy how that the image edge detection algorithm baed on wavelet tranform and fuzzy echnique can achieve better performance than the traditional algorithm in image edge detection. Keyword- Image edge detection; Wavelet tranform; Copula theory; Fuzzy algorithm I. INTRODUCTION In recent year, the tudy of wavelet tranform urged it uage in image coding. The multi-reolution analyi of wavelet tranform matche with the character of human viion. It can give ub-band for different level and different direction of an image. Studying the application of wavelet tranform in arbitrarily haped image coding, 3-D tranform coding of video, pot-proceing of decoded image, can promote the conummation of new image/video coding tandard, etc., MPEG-4, JPEG-000. The protection and enforcement of intellectual property right ha become an important iue in image/video coding ytem. Fuzzy method and MARCH model i the proce of encoding hidden copyright information in an image by making mall modification to it pixel. It can be ued for image authentication and forgery prevention. Studying watermark in wavelet domain of image/video, i helpful to include watermarking ytem into image/video coding tandard baed on wavelet tranform. In Zhang diertation, following the development of wavelet theory, epecially the econd generation wavelet tranform (the lifting algorithm), Zhang tudy the uage of wavelet tranform in arbitrarily haped image coding, 3-D tranform coding of video, pot-proceing of decoded image and watermarking in wavelet domain of image/video. The reearcher pointed out that coding of arbitrarily haped image wa one of core technology in MPEG-4 video compreion. They firt ue low-pa extrapolation to enhance the performance of Katata' approach uing claical wavelet tranform [1]. In order to make algorithm eaier, Zhang tudie the application of wavelet lifting cheme in tranform coding of arbitrarily haped image obect and preent three new approache baed on lifting algorithm. One need extrapolation of the image obect. The econd i a hapeadopted algorithm by modifying the compute of coefficient near the obect edge. The third i a hape-adopted algorithm baed on modifying boundary extenion method of the lifting cheme. The experiment reult how that the image compreion performance of approache uing lifting cheme, epecially the third one, are better than Katata' approach uing claical wavelet tranform and the approach uing SA-DCT. In Auin reearch, the motion etimation i combined with 3-D wavelet tranform for video coding []. In claical 3-D wavelet tranform of video, wavelet tranform of time domain i applied to pixel in the ame patial coordinate of each frame. But in hi paper, wavelet tranform i applied to pixel in one motion traectory which i contructed by motion vector in order to fully utilize the redundancy in the time domain. Becaue the length of motion traectory i arbitrarily, a new wavelet tranform method for arbitrary length ignal i needed. A length-adopted wavelet tranform algorithm baed on modifying boundary extenion method of the lifting cheme i preented in hi paper. The experiment reult how that for video equence with wide range of movement the compreion performance of thi approach i better than approach uing claical 3-D wavelet tranform. DOI /IJSSST.a ISSN: x online, print

2 In Zhou paper [3], the author ue de-noiing by integer wavelet threholding in pot-proceing of decompreed image. In Donoho' de-noiing algorithm, the high/high portion of wavelet coefficient can be ued to etimate noie level and threhold value. If the image ignal ha abundant high-frequency detail in high/high portion of wavelet domain, the etimation of threhold value will be interfered. So we ue adaptive tranform derived from lifting cheme to make ditribution of ignal energy more concentrative, o that the threhold value can be etimate more efficiently. We alo incorporate adaptively into redundant tranform to improve the de-noiing performance. From the experiment reult, we can ee that the PSNR value of recover image after DCT and wavelet tranform coding are increaed. Thi algorithm can efficiently remove blocking effect. The author preent a new trategy to embed watermark to image/video wavelet tranform domain. In many paper in literature, the coefficient in the cale ub-band (low-frequency coefficient) are explicitly excluded from watermark embedding in order to maintain tranparency. But the coefficient in cale ub-band are bigger than mot coefficient in other ub-band. Thi mean the coefficient in cale ub-band have higher perceptual capacity than coefficient in other ub-band. So in thi paper, watermark are embedded into the cale ub-band of image/video wavelet tranform domain. The experiment reult how that thi watermarking cheme i robut enough and maintain the character of tranparency. They alo ue adaptive wavelet tranform derived from lifting cheme to get bigger cale ub-band coefficient [4-5]. The reult how the image watermarking algorithm uing nonlinear wavelet tranform i more robut than algorithm uing uual wavelet tranform [6]. II. THEORY ABOUT WAVELWT TRANSFORM AND PREWITT OPERATOR The traditional edge detection method i rely on edge detection operator to detect, uch a Robert operator, Sobel operator, Prewitt operator, LOG operator, Canny operator, which ha the advantage of imple operation and trong real-time, but thee operator have diadvantage of peudo edge, while wavelet tranform [7] can well remove the noie and can effectively reflect the image grey level change. In order to effectively to image edge detection, operator of the improvement and a variety of detection algorithm fuion ha become a hot pot of image edge detection. Thi paper propoe a kind of edge image fuion detection Method baed on the improved Prewitt operator edge detection and wavelet tranform edge detection. The fuion algorithm combine the advantage of the two method, and achieved better fuion effect. The traditional Prewitt operator only ha two detection template of horizontal and vertical direction, edge detection accuracy i not high. In order to improve the edge detecting preciion and computing peed, the traditional Prewitt operator i improved in thi paper, the edge detecting operator i increaed from two to four. But Prewitt operator are enitive to noie, peudo edge prone to detection, and the detecting method baed on wavelet tranform edge not only ha good anti-noie, but alo can preerve the edge detail, thi paper put forward a kind of edge detecting algorithm baed on wavelet tranform and improved Prewitt operator edge image fuion: firt the ource image i proceed by uing median filter method, then the filtered image i enhanced by hitogram equalization method, the enhanced image i repectively detected by wavelet tranform edge detection method and improved Prewitt operator edge detection method, finally the two edge detecting image i done image fuion by uing wavelet image fuion algorithm baed on adaptive wavelet image fuion algorithm, Experiment how that the fued image combine the advantage of two kind of detection algorithm, the fuion detection method can uppre noie effectively, but alo can improve the accuracy of edge detection. It i an ideal method of image edge detection. Prewitt edge detection operator i an edge template operator, which ue grey level difference of upper and lower, left and right neighbouring point to detect edge. The principle of the traditional Prewitt edge detection i in the image pace uing the template in two direction and image neighbourhood convolution, the two direction template repectively detect horizontal edge and vertical edge. Thi operator i uually expreed by the following formula: Gx ( ) f( x1, y1) f( x1, y1) f( x1, y) f( x1, y) (1) f( x1, y1) f( x1, y1) G( y) f( x1, y1) f( x1, y1) f( x, y1) f( x, y1) f( x1, y1) f( x1, y1) P( xy, ) max[ Gx ( ), Gy ( )] or Pxy (, ) Gx ( ) Gy ( ) The Prewitt Operator template a follow: G x G y So, from the equation above, we can get: () (3) (4) (5) T X U V (6) ' T X 1U X (7) Evaluation index of dimenionle ue gravy ytem theory of effect meaure. For the indicator which became better and bigger: DOI /IJSSST.a ISSN: x online, print

3 ei (, ) mine(, i ) zi (, ) Smin ( Smax Smin )(8) max e( i, ) min e( i, ) For the indicator which became better and maller: ei (, ) mine(, i ) zi (, ) Smax ( Smax Smin )(9) max e( i, ) min e( i, ) For e-plu in ome appropriate value indicator: ei (, ) e zi (, ) S ( S S ) (10) 0 max max min ei (, ) e0 e0 In the evaluation of the ICP, it can be etimated the edge node for electing i that: w i ipc( k, ) ( cm( k, )) n n cm a c i1 w i (11) pc ( k, ) c ( ) ( ) i ak a ak a (1) Prewitt Operator think [8]: all that new pixel grey value greater than or equal to the threhold are edge point, becaue a lot of noie grey value i large, o the noie caued by miudgement for edge point, but alo for the maller amplitude of edge point, It edge have lot. The traditional Prewitt edge detection operator ha only horizontal and vertical direction of two template, Only the grey gradient change on the two horizontal and vertical enitivity, analyi of the two template, Gx template within the firt row i poitive, o the image can obtain better edge detection [9], Senitive image edge gradient i 1800 direction, Gy template within the third column i alway poitive, o the image on the right can get better edge detection, edge gradient i enitive to 90 direction and the other direction, uch a 0, 45, 135, 5, 70, 315 thee direction are not better edge detection. In order to increae the accuracy of operator in a pixel edge detection, template can be increaed from two to eight [10], Prewitt edge detection operator to increae from two to eight, the detection preciion i greatly increaed, the detection effect i increaed, but the peed of operation i greatly reduced, in order to imultaneouly determine the accuracy and peed, conidering only increaed two operator template. Analyi of the original two operator that Gx template: inide the firt row i poitive, o the image i get a good edge detection, template Gy within the third column i alway poitive, o the image on the right can get better edge detection, and image below and left i not outtanding, not good edge detection, and o conider the operator template increae the two direction, o that the image below and left can be better edge detection operator template, increaed operator template a follow: G xl (13) G yl (14) In order to effectively to image edge detection, operator of the improvement and a variety of detection algorithm fuion ha become a hot pot of image edge detection. Correlation ha been called a mine field for the unwary becaue it i a technique that i widely miued in finance and i applied to problem for which it i not uitable. A ditribution function i a function that aign probabilitie a a function of outcome that i for every outcome, the ditribution function give the probability. III. EDGE DETECTION ALGORITHM BASED ON VJAVELET TRANSFORMATION AND MARCH MODEL Suppoe (x, y) i a two-dimenional moothing function, and meet If we order: ( x, ydxdy ) 1 R (15) lim ( xy, ) 0 R x y 1 x y ( xy, ) (, ) (16) S Two dimenional ignal f(x,y) moothing i accomplihed at different cale of and (x, y) do convolution operation to achieve, the firt order derivative type along X and Y direction of two a the two baic wavelet i hown a follow: 1 ( xy, ) 1 1 x y ( xy, ) (, ) (17) x ( xy, ) 1 x y ( xy, ) (, ) (18) x Suppoe f(x, y) L (R ), Two dimenional wavelet tranform in the cale of include two part: 1 1 WT f ( x, y) f( x, y) ( x, y) (19) WT f ( x, y) f ( x, y) ( x, y) (0) Type a a vector in the form of 1 WT f ( x, y) WT f ( x, y) WT f ( x, y) (1) Be known a f (x, y) Binary wavelet, The WT f ( x, y), WT f ( x, y ), model of local maximum 1 point correponding to mooth image in the correponding DOI /IJSSST.a ISSN: x online, print

4 poition of the prominent point. It ize reflect the poition of the grey intenity, Therefore, the image edge point can be obtained a long a we detect wavelet tranform modulu local maxima along the gradient direction. The MARCH model can be formulated a follow: r ( ) () t t t 1/ t= H t( ) Zt (3) Z F ~ C( u, u,..., u ;,,..., ) t t 1 1t t nt 1 N (4) EZ ( t Ft 1) 0 (5) ' EZZ ( t t Ft 1 ) t( i, t), i, t 1 (6) D x, y, i given by,,,,,,, With the Gauian blur G x, y,, we have: Lxyk,, G xyk,, Ixy, D x y L x y k L x y (7) (8) The direction of the coefficient i calculated uing the following formula: T T D 1 T D DX D X X X X X Lx1, ylx1, y mx, y Lx, y1 Lx, y1 1 Lx, y1 Lx, y1 xy, tan L x1, ylx1, y The function, 1,,, 1 i1, i II 1 y0 x0 (9) (30) (31) f x y with of ize I1 and I can be hown a W i i I 1 I 1 1 f x y x y (3) I 1 I 1 k 1 W i i f x y x y 1 k,,,, (33) 1 i, 1, i II 1 y0 x0 where n n n n InJn A a1, a,..., a J n 1,,3 n repreent common factor. J1 J J3 1 3 Y g 1 a 3 a 1 a E (34) G A E Yˆ E that i: 1 D, ˆ F Y G A Y Y (35) IV. EDGE DETECTION METHODS BASED ON FUZZY ALGORITHM AND WAVELET TRANSFORM IMAGE FUSION Pre-proceing of image Edge detection include image filtering and image enhancement, edge detection algorithm i one order and two order derivative calculation baed on image intenity, but the calculation of derivative i very enitive to noie, eaily affected by noie, therefore, we mut ue the filter to reduce the noie, but in fact filter to reduce noie at the ame time alo led to the edge lo of trength. There are many method of image moothing filter, uch a the mean filter, median filtering and o on, the image can reduce the noie by uing the mean filter, but the filtered image edge become blurry and the median filter to filter the image can reduce the noie (epecially the alt and pepper noie), and can make the image edge i clear, epecially for the alt and pepper noie, filtering effect i good, o here the median filter to pre-proce the image edge detection. Image enhancement i to neighbourhood (or local) intenity value have highlighted ome ignificant change, Hitogram equalization through ome grey tranform of the original image, o that the tranformed image hitogram can be evenly ditributed, o a to be able to have imilar grey area grey and poeion of a large number of pixel in the original image to broadening, the tiny grey tranform a large area of the diplay, the image i more clear, in order to grey difference expand the target and background and enhance the intenity contrat between them, in order to more eaily detect the image edge detail, the image hitogram equalization enhancement method to pre-proce the image edge detection. In the proce of the image capture and image tranmiion, noie will be produced unavoidably. The exitence of image noie everely affect the effect of ubequent image proceing. To enhance the image quality, image de-noiing become a very important work of image pre-proceing. Now, a a new time-frequency analyi method, wavelet tranform (WT) ha important ignificance in the actual application. Combined with WT and fractional theory, fractional wavelet tranform (FWT) extend multireolution analyi to the time domain-general frequency domain. Image enhancement method can be divided into two roughly: The method of image enhancement in patial domain and the method of image enhancement in tranform domain. The firt method literally mean enhance the image in the patial domain, in other word, it mean proce each pixel in the image directly. In thi paper, we ue the fuzzy algorithm imilar to patial proceing method and ome improvement baed on the traditional fuzzy algorithm. The econd one mean tranform the original image to a pecific domain and enhance the image by modifying the correlation coefficient in tranform domain. There are ome method tranforming the Image from patial domain to tranform domain, uch a Fourier tranform, wavelet tranform, Contourlet tranform, NSCT tranform, Shearlet tranform and o on. In order to effectively to image edge detection, operator of the improvement and a variety of detection algorithm DOI /IJSSST.a ISSN: x online, print

5 fuion ha become a hot pot of image edge detection. Thi paper propoe a kind of edge image fuion detection Method baed on the improved Prewitt operator edge detection and wavelet tranform edge detection. If the image ignal ha abundant high-frequency detail in high/high portion of wavelet domain, the etimation of threhold value will be interfered. So we ue adaptive tranform derived from lifting cheme to make ditribution of ignal energy more concentrative, o that the threhold value can be etimate more efficiently. We alo incorporate adaptively into redundant tranform to improve the de-noiing performance. From the experiment reult, we can ee that the PSNR value of recover image after DCT and wavelet tranform coding are increaed. V. EXPERIMENT RESULTS Fig. 1 i the experiment of Lena image with Salt and pepper noie, Fig. 1(a) i the original Lena image, Fig. 1(b) i on the original image onto the alt and pepper noie, Fig. 1(c) i the Lena image after median filtering, filter will filter out alt and pepper noie in large, but alo retain many important detail of the image, the image i relatively clear, but in the de-noiing proce will inevitably loe ome detail edge. Fig. 1(d) i the image hitogram equalization after median filtering, the purpoe i to expand the grey difference of target and background and enhance the intenity contrat between them, In order to more eaily detect the image edge detail, After image hitogram equalization, image wa enhanced, and the detail of the image more clear. Fig. 1(e) i a fuzzy algorithm edge detection baed on image enhancement, from Fig. 1(e) can be een in Lena image edge detail, many are not detected, lot a lot of edge detection detail, the improved fuzzy algorithm edge detection reult i much better than Fig. 1(e), the edge i clearly, a hown in Fig. 1(f), but till lot ome grey value change lowly edge detail, Fig. 1(g) i the image by mean of image edge detection algorithm baed on wavelet tranformation, A can be een from the image, edge contain the image detail information richer and more continuou, but the edge i rough. image edge detect method Baed on improved Prewitt operator and wavelet tranform edge image fuion edge i combined with the advantage of the two algorithm, which preerve the edge detail, and remove the noie, no peudo edge appear, a hown in Fig. 1(h) how, it obtain the atifactory effect of edge detection. Table 1 how the comparion reult of GA algorithm and image edge detection algorithm baed on wavelet tranform and fuzzy algorithm a) origin image b) noie image c) filtered image d) Enhanced image e) Fuzzy detecting image f) Improved fuzzy edge detecting image g) Wavelet tranform edge detecting image (h) The edge detecting image of fuion algorithm DOI /IJSSST.a ISSN: x online, print

6 The number of experiment node TABLE I THE COMPARISON OF GA ALGORITHM AND IMAGE EDGE DETECTION ALGORITHM BASED ON WAVELET TRANSFORM AND FUZZY TECHNIQUES Probability of finding optimal Time for wavelet Average value for Probability of olution for wavelet Time tranform and wavelet tranform finding optimal tranform and fuzzy for GA fuzzy algorithm and fuzzy algorithm olution for GA algorithm Average value for GA 00 <1 5% % % % % % VI. CONCLUSIONS Thi paper preent a fuion method of edge detection of improved fuzzy algorithm and wavelet tranform image, by analyi of the experimental reult, the algorithm can uppre noie effectively, and can improve the accuracy of edge detection, detection effect i obviouly uperior to the ingle image edge detection. ACKNOWLEDGMENT Thi work i upported by Foundation of Zheiang Province Department of education reearch proect, China (No:Y ), Foundation of Quzhou city cience and technology proect, China(No:015018), Foundation of Quzhou Vocational and Technical College reearch proect, China(No:QZYZ1409). REFERENCES [1] Zhang YQ., Zafar S., Motion compenated wavelet tranform coding for cokor video comvreion, IEEE Tran. CSVT, vol., No.9, pp ,199. [] Auin, M. C. and Galeano, P., Bayeian etimation of the Gauian mixture GARCH model. Computational Statitic & Data analyi, Forth coming, vol.78, pp , 006. [3] G. Zhou, A. Cichocki, Q. Zhao et al., Nonnegative matrix and tenor factorization: an algorithmic perpective, IEEE Signal Proceing Magazine, vol. 31, No. 3, pp.54 65, 014. [4] Brave, Scott, and Clifford Na., Emotion in human computer interaction, Human-Computer Interaction vol.53, pp.35-41, 003. [5] Roell, Suan L., et al., Invetigating affective proody in pychoi: a tudy uing the comprehenive affective teting ytem, Pychiatry reearch, vol.10, No.3, pp , 003. [6] Roger, Yvonne, Helen Sharp, and Jenny Preece, Interaction deign: beyond human-computer interaction, John Wiley & Son, pp , 011. [7] Pan, Q.-K., Suganthan, P.N., Liang, J.J., Tagetiren, M.F. A Local- Bet Harmony Search Algorithm with Dynamic Subpopulation, Engineering Optimization, vol.4, pp , 010. [8] H. Ceylan, H. Ceylan, A hybrid harmony earch and TRANSYT hill climbing algorithm for ignalized tochatic equilibrium tranportation network, Tranp. Re. Part C Emerg. Technol, vol. 5, pp , 013. [9] R. Arul, G. Ravi, S. Veluami, Chaotic elf-adaptive differential harmony earch algorithm baed dynamic economic dipatch0, Int. J. Electr. Power Energy Syt.,vol.50, pp , 013. [10] Lee KS and Geem ZW, A new meta-heuritic algorithm for continuou engineering optimization: harmony earch theory and practice, Comput. MethodAppl. Mech. Engrg., vol. 194, pp , 013. DOI /IJSSST.a ISSN: x online, print