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- International Journal of Advanced Science and Technology Vol. 29, April, 2011 Novel Fuzzy logic Based Edge Detection Technique Aborisade, D.O Department of Electronics Engineering, Ladoke Akintola University of Tech., Ogbomoso. Oyo-state. doaborisade@yahoo.com Abstract This paper is based on the development of a fuzzy logic based edge detection technique indigital images. The proposed technique used three linear spatial filters to generate three edgestrength values at each pixel of a digital image through spatial convolution process. Theseedge strength values are utilized as fuzzy system inputs. Decision on whether pixels in focusbelong to an edge or non-edge is made in the proposed technique based on the Gaussianmembership functions and fuzzy rules. Mamdani defuzzifier method is employed to producethe final output pixel classification of a given image. Experimental results show the abilityand high performance of proposed algorithm compared with Sobel and Kirsch operators. Keywords: Fuzzy Logic, Fuzzy inference system, Edge strength, Edge detection.1. Introduction An Edge is defined as discontinuities in pixel intensity within an image. The edges of animage are always the important characteristics that offer an indication for higher frequency.Detection of edges in an image is used as a preprocessing step to extract some low-levelboundary features, which are then fed into further processing steps, such as object finding andrecognition. Many edge-detection methods have been suggested in the past years for the purpose ofimage analysis and had been attempted by many researchers to support different optimizationgoals. Traditional techniques, such as Sobel, Prewitt and Roberts provide false edge detectionand being very sensitive to noise. Canny [1] proposed a method to counter noise problems and minimize the probability offalse edges. In his work image is convolved with the first order derivatives of Gaussian filterfor smoothing in the local gradient direction followed by edge detection by thresholding [2].Canny edge detector has major drawbacks of being computational complexity and do not givea satisfactory results in varying contrast areas. However, improvement in the edge-detectionresearch area has now resulted in the use of some tools such as neural networks, ant colonyand, fuzzy logic by some presented algorithms [2]. In this paper, fuzzy logic based approach to edge detection in digital images is proposed.Firstly, for each pixel in the input image „edginess‟ measure is calculated using three 3 3linear filters after which three fuzzy sets characterized by three (3) Gaussian membershipfunctions associated to linguistic variable “Low”, “Medium” and “High” were created torepresent each of the edge strengths. The second phase involves application of fuzzyinference rule to the three fuzzy sets to modify the membership values in such a way that thefuzzy system output (“edge”) is high only for those pixels belonging to edges in the inputimage. Final pixel classification as edge or non-edge using Mamdani defuzzification methodis the last step. 75
- International Journal of Advanced Science and TechnologyVol. 29, April, 20112. Fuzzy Logic Based Application Fuzzy logic represents a powerful approach to decision making [3], [4], [5]. Since theconcept of fuzzy logic was formulated in 1965 by Zadeh, many researches have been carriedout on its application in the various areas of digital image processing such as image qualityassessment, edge detection, image segmentation, etc. Many techniques have been suggested by researchers in the past for fuzzy logic-basededge detection [6], [7], [8]. In [9], Zhao, et al. proposed an edge detection technique based onprobability partition of the image into 3-fuzzy partitions (regions) and the principle ofmaximum entropy for finding the parameters value that result in the best compact edgerepresentation of images. In their proposed technique the necessary condition for the entropyfunction to reach its maximum is derived. Based on this condition an effective algorithm forthree-level thresholding is obtained. Several approaches on fuzzy logic based edge detection have been reported based onfuzzy If-Then rules [10], [11]. In most of these methods, adjacent points of pixels areassumed in some classes and then fuzzy system inference are implemented using appropriatemembership function, defined for each class [12]. In Liang, et al. [13], adjacent points areassumed as 3 3 sets around the concerned point. By predefining membership function todetect edges. In these rules discontinuity in the color of different 3 3 sets, edges areextracted. It uses 5 fuzzy rules and predefined membership function to detect edges. In theserules discontinuity of adjacent point around the concerned point are investigated. If thisdifference is similar to one of predefined sets, the pixel is assumed as edge. A similar work is proposed by Mansoori, et al. [14], wherein adjacent points of each pixelare grouped in six different set. Then by using of appropriate bell shape membership function,the value from zero to one is determined for each group. Based on the membership values,and fuzzy rules, decision about existing/not existing and direction of edge pixels are obtained.3. Proposed Algorithm In this paper, at first an input image is pre-process to accentuate or remove a band ofspatial frequencies and to locate in an image where there is a sudden variation in the greylevel of pixels. For each pixel in the image edge strength value is calculated with three (3) 3 3 linear spatial filters i.e. low-pass, high-pass and edge enhancement filters (Sobel)through spatial convolution process. In carrying out a 3 3 kernel convolution, nineconvolution coefficients called the convolution mask are defined and labeled as seen below: a b c d e f g h i Every pixel in the input image is evaluated with its eight neighbors, using each of thethree masks shown in Figure 1 to produce edge strength value. The equation used for thecalculation of edginess values between the center pixel and the neighborhood pixels of thethree (3) masks using spatial convolution process is given by:76
- International Journal of Advanced Science and Technology Vol. 29, April, 2011 O( x, y) aI ( x 1, y 1) bI ( x 1, y) cI ( x 1, y 1) dI ( x, y 1) eI ( x, y) fI( x, y 1) (1) gI ( x 1, y 1) hI ( x 1, y) iI ( x 1, y 1)However, the result of convolution of the two Sobel kernels is combine thus, the approximateabsolute gradient magnitude (edge strength) at each point is computed as: Og Ox O y (2)The normalized edge strength is then defined as: NO( x, y) round (O( x, y) / max( O)) 100 (3)where x 0,1, . . . , M 1 and y 0,1, . . . , N 1 for an M-by-N image. 1 1 1 9 9 9 - 1 -1 -1 hHP - 1 - 1 1 1 1 hLP , 9 9 9 9 - 1 -1 -1 1 1 1 9 9 9 -1 0 1 1 2 1 hx - 2 0 2 , hy 0 0 0 -1 0 1 -1 -2 -1 Figure 1. 3 3 Kernels Used for Edge Detection The edge strength values derived from the three (3) masks served as the inputs used in theconstruction of the fuzzy inference system based on which decision on pixel as belonging toan edge or not are made. Membership functions are defined for fuzzy system inputs. Manymembership functions have been introduced in the literature. In the proposed edge detectionGaussian membership functions are used. To apply these functions, each of the edge strengthvalues of O g , O Hp , and O Lp are mapped into fuzzy domain between 0 and 1 , relative to thenormalized gray levels between 0 and 100, using Gaussian membership functions given as / 2 2 ] mn G( xmn ) e[( xmax xmn ) 2 (4)where G ( x mn ) is a Gaussian function, x m ax , x mn are the maximum and (m, n)th gray valuesrespectively and is the standard deviation associated with the input variable. Each of themapped values are partition into three fuzzy regions “Low”, “Medium”, and “High”. Thedefined regions and membership functions are shown in Fig. 2. 77
- International Journal of Advanced Science and TechnologyVol. 29, April, 2011 Po Figure 2. Gaussian Membership Functions Fuzzy inference rules are applied to assign the three fuzzy sets characterized bymembership functions Low , Medium , and High to the output set. The rules, tabulated inTable 1 are defined in such a way that in the fuzzy inference system, output setE L , E M , and E H correspond to pixels with low, medium and high probability valuerespectively. The output of the system PFinal representing the probability used for final pixelclassification as edge or non-edge was computed using a singleton fuzzifier, Mamdanidefuzzifier method given by; y ( ( )) M n 1 i 1 ki i p Final (5) ( ( )) M n 1 i 1 ki iwhere i are the fuzzy sets associated with the antecedent part of the fuzzy rule base, y isthe output class center and M is the number of fuzzy rules being considered.4. Experimental Results The proposed fuzzy edge detection method was simulated using MATLAB on differentimages, its performance are compared to that of the Sobel and Kirsch operators. Samples for aset of four test images are shown in Fig. 3(a). The edge detection based on Sobel and Kirschoperators using the image processing toolbox in MATLAB with threshold automaticallyestimated from image‟s binary value is illustrated in Fig. 3(b) and 3(c). The sample output ofthe proposed fuzzy technique is shown in Fig. 3(d). The resulting images generated by thefuzzy method seem to be much smoother with less noise and has an exhaustive set of fuzzyconditions which helps to provide an efficient edge representation for images with a very highefficiency than the conventional gradient-based methods (Sobel and Kirsch methods).5. Conclusion Effective fuzzy logic based edge detection has been presented in this paper. Thistechnique uses the edge strength information derived using three (3) masks to avoid detectionof spurious edges corresponding to noise, which is often the case with conventional gradient-78
- International Journal of Advanced Science and Technology Vol. 29, April, 2011based techniques. The three edge strength values used as fuzzy system inputs were fuzzifiedusing Gaussian membership functions. Fuzzy if-then rules are applied to modify themembership to one of low, medium, or high classes. Finally, Mamdani defuzzifier method isapplied to produce the final edge image. Through the simulation results, it is shown that the proposed technique is far lesscomputationally expensive; its application on digital image improves the quality of edges asmuch as possible compared to the Sobel and Kirsch methods. This algorithm is suitable for applications in various areas of digital image processingsuch as face recognition, fingerprint identification, remote sensing and medical imagingwhere boundaries of specific regions need to be determined for further image analysis.Acknowledgement The author is grateful to Engineer I. A Isaiah at Ladoke Akintola University ofTechnology, Ogbomoso, Nigeria for his helpful advice. Table 1. Fuzzy Inference Rules If edginess Lp is LO and edginessSo is LO and edginessHp is LO then p edge is E L If edginess Lp is LO and edginessSo is LO and edginessHp is MD then p edge is E L If edginess Lp is LO and edginessSo is LO and edginessHp is HI then p edge is E L If edginess Lp is LO and edginessSo is MD and edginessHp is LO then p edge is E L If edginess Lp is LO and edginessSo is MD and edginessHp is MD then p edge is E L If edginess Lp is LO and edginessSo is MD and edginessHp is HI then p edge is E M If edginess Lp is LO and edginessSo is HI and edginessHp is LO then p edge is E L If edginess Lp is LO and edginessSo is HI and edginessHp is MD then p edge is E H If edginess Lp is LO and edginessSo is HI and edginessHp is HI then p edge is E H If edginess Lp is MD and edginessSo is LO and edginessHp is LO then p edge is E L If edginess Lp is MD and edginessSo is MD and edginessHp is LO then p edge is E L . . . If edginess Lp is HI and edginessSo is LO and edginessHp is HI then p edge is E H If edginess Lp is HI and edginessSo is MD and edginessHp is HI then p edge is E H If edginess Lp is HI and edginessSo is HI and edginessHp is HI then p edge is E H 79
- International Journal of Advanced Science and TechnologyVol. 29, April, 2011 (a) (b) (c) (d) Figure 3. (a) Original Images, (b) Sobel Operator Results, (c) Kirsch Operator Results, (d) Proposed Fuzzy Edge Detection Algorithm Results80
- International Journal of Advanced Science and Technology Vol. 29, April, 2011References[1] Canny, J.F., “A computational approach to edge detection”, IEEE Trans. on Pattern Analysis and Machine Intelligence, 8(6), 1986, pp. 679-698.[2] Madasu H., John S., and Shantaram V., “Fuzzy Edge Detector Using Entropy Optimization” Proceedings of the International Conference on Information Technology: Coding and Computing, 2004.[3] L. A. Zadeh, “Fuzzy sets,” Information and Control, 8: 1965, pp. 338-353.[4] A. Kaufmann, “Introduction to the Theory of Fuzzy Subsets – Fundamentals Theoretical Elements, Vol. 1. Academic Press, New York, 1975.[5] L.C. Bezdek, “Pattern Recognition with fuzzy Objective Function Algorithm,” Plenum Press, New York, 1981.[6] K. Cheung and W. Chan, "Fuzzy One –Mean Algorithm for Edge Detection," IEEE Inter. Conf. On Fuzzy Systems, 1995, pp. 2039- 2044.[7] Y. Kuo, C. Lee, and C. Liu, "A New Fuzzy Edge Detection Method for image Enhancement," IEEE Inter. Conf. on Fuzzy Systems, 1997, pp. 1069-1074.[8] S. El-Khamy, N. El-Yamany, and M. Lotfy, "A Modified Fuzzy Sobel Edge Detector," Seventeenth National Radio Science Conference (NRSC2000), February 22-24, Minufia, Egypt, 2000.[9] M. Zhao, A. M. N. Fu, and H. Yan, “A Technique of Three-Level Thresholding Based on Probability Partition a Fuzzy 3-Partition”. IEEE Trans. on Fuzzy Systems, vol.9, no.3, June 2001, pp. 469- 479.[10] Tao, C. W. et al(1993), “A Fuzzy if-then approach to edge detection”, Proc. of 2nd IEEE intl.conf. on fuzzy systems, pp. 1356–1361.[11] Li, W. (1997), Recognizing white line markings for vision-guided vehicle navigation by fuzzy reasoning, Pattern Recognition Letters, 18: 771–780.[12] M. N. Mahani, M. K. Moqadam, H. N. pour, and A. Bahrololoom, “Dynamic Edge Detector Using Fuzzy Logic,” CSISS 2008, Sharif University of Technology, Kish, 2008, (In Persian).[13] L. Liang and C. Looney, “Competitive Fuzzy Edge Detection,” Applied Soft Computing, (3), 2003, pp. 123- 137.[14] G. Mansoori and H. Eghbali, “Heuristic edge detection using fuzzy rule-based classifier,” Journal of Intelligent and Fuzzy Systems, Volume 17, Number 5 / 2006, pp. 457- 469. Authors Aborisade, David O. received the B. Eng. degree in Electronic and Electrical Engineering Technology from Federal University of Technology, Owerri, in 1989. He received M.Eng. and Ph.D. degrees in Electrical Engineering from University of Ilorin, in 1995 and 2006, respectively. He is currently a Senior Lecturer with the Department Electronic and Electrical Engineering, Ladoke Akintola University of Technology, Ogbomoso. His research interests include computer vision, pattern recognition, image and signal processing, neural networks, and fuzzy logic. 81
- International Journal of Advanced Science and TechnologyVol. 29, April, 201182

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