Novel Fuzzy logic Based Edge Detection Technique

Transcription

1 Novel Fuzzy logc Based Edge Detecton Technque Aborsade, D.O Department of Electroncs Engneerng, adoke Akntola Unversty of Tech., Ogbomoso. Oyo-state. Abstract Ths paper s based on the development of a fuzzy logc based edge detecton technque n dgtal mages. The proposed technque used three lnear spatal flters to generate three edge strength values at each pxel of a dgtal mage through spatal convoluton process. These edge strength values are utlzed as fuzzy system nputs. Decson on whether pxels n focus belong to an edge or non-edge s made n the proposed technque based on the Gaussan membershp functons and fuzzy rules. Mamdan defuzzfer method s employed to produce the fnal output pxel classfcaton of a gven mage. Expermental results show the ablty and hgh performance of proposed algorthm compared wth Sobel and Krsch operators. Keywords: Fuzzy ogc, Fuzzy nference system, Edge strength, Edge detecton. 1. Introducton An Edge s defned as dscontnutes n pxel ntensty wthn an mage. The edges of an mage are always the mportant characterstcs that offer an ndcaton for hgher frequency. Detecton of edges n an mage s used as a preprocessng step to extract some low-level boundary features, whch are then fed nto further processng steps, such as object fndng and recognton. Many edge-detecton methods have been suggested n the past years for the purpose of mage analyss and had been attempted by many researchers to support dfferent optmzaton goals. Tradtonal technques, such as Sobel, Prewtt and Roberts provde false edge detecton and beng very senstve to nose. Canny [1] proposed a method to counter nose problems and mnmze the probablty of false edges. In hs work mage s convolved wth the frst order dervatves of Gaussan flter for smoothng n the local gradent drecton followed by edge detecton by thresholdng [2]. Canny edge detector has major drawbacks of beng computatonal complexty and do not gve a satsfactory results n varyng contrast areas. owever, mprovement n the edge-detecton research area has now resulted n the use of some tools such as neural networks, ant colony and, fuzzy logc by some presented algorthms [2]. In ths paper, fuzzy logc based approach to edge detecton n dgtal mages s proposed. Frstly, for each pxel n the nput mage edgness measure s calculated usng three 3 3 lnear flters after whch three fuzzy sets characterzed by three (3) Gaussan membershp functons assocated to lngustc varable ow, Medum and gh were created to represent each of the edge strengths. The second phase nvolves applcaton of fuzzy nference rule to the three fuzzy sets to modfy the membershp values n such a way that the fuzzy system output ( edge ) s hgh only for those pxels belongng to edges n the nput mage. Fnal pxel classfcaton as edge or non-edge usng Mamdan defuzzfcaton method s the last step. 75

2 2. Fuzzy ogc Based Applcaton Fuzzy logc represents a powerful approach to decson makng [3], [4], [5]. Snce the concept of fuzzy logc was formulated n 1965 by Zadeh, many researches have been carred out on ts applcaton n the varous areas of dgtal mage processng such as mage qualty assessment, edge detecton, mage segmentaton, etc. Many technques have been suggested by researchers n the past for fuzzy logc-based edge detecton [6], [7], [8]. In [9], Zhao, et al. proposed an edge detecton technque based on probablty partton of the mage nto 3-fuzzy parttons (regons) and the prncple of maxmum entropy for fndng the parameters value that result n the best compact edge representaton of mages. In ther proposed technque the necessary condton for the entropy functon to reach ts maxmum s derved. Based on ths condton an effectve algorthm for three-level thresholdng s obtaned. Several approaches on fuzzy logc based edge detecton have been reported based on fuzzy -Then rules [1], [11]. In most of these methods, adjacent ponts of pxels are assumed n some classes and then fuzzy system nference are mplemented usng approprate membershp functon, defned for each class [12]. In ang, et al. [13], adjacent ponts are assumed as 3 3 sets around the concerned pont. By predefnng membershp functon to detect edges. In these rules dscontnuty n the color of dfferent 3 3 sets, edges are extracted. It uses 5 fuzzy rules and predefned membershp functon to detect edges. In these rules dscontnuty of adjacent pont around the concerned pont are nvestgated. ths dfference s smlar to one of predefned sets, the pxel s assumed as edge. A smlar work s proposed by Mansoor, et al. [14], wheren adjacent ponts of each pxel are grouped n sx dfferent set. Then by usng of approprate bell shape membershp functon, the value from zero to one s determned for each group. Based on the membershp values, and fuzzy rules, decson about exstng/not exstng and drecton of edge pxels are obtaned. 3. Proposed Algorthm In ths paper, at frst an nput mage s pre-process to accentuate or remove a band of spatal frequences and to locate n an mage where there s a sudden varaton n the grey level of pxels. For each pxel n the mage edge strength value s calculated wth three (3) 3 3 lnear spatal flters.e. low-pass, hgh-pass and edge enhancement flters (Sobel) through spatal convoluton process. In carryng out a 3 3 kernel convoluton, nne convoluton coeffcents called the convoluton mask are defned and labeled as seen below: a b c d e f g h Every pxel n the nput mage s evaluated wth ts eght neghbors, usng each of the three masks shown n Fgure 1 to produce edge strength value. The equaton used for the calculaton of edgness values between the center pxel and the neghborhood pxels of the three (3) masks usng spatal convoluton process s gven by: 76

3 O( ai( x 1, y 1) bi( x 1, ci( x 1, y 1) di( y 1) ei( fi( y 1) gi( x 1, y 1) hi( x 1, I( x 1, y 1) (1) owever, the result of convoluton of the two Sobel kernels s combne thus, the approxmate absolute gradent magntude (edge strength) at each pont s computed as: O g O O (2) x y The normalzed edge strength s then defned as: NO ( round ( O( / max( O)) 1 (3) where x,1,..., M 1 and y,1,..., N 1 for an M-by-N mage h P, h P h , 1 x h y Fgure Kernels Used for Edge Detecton The edge strength values derved from the three (3) masks served as the nputs used n the constructon of the fuzzy nference system based on whch decson on pxel as belongng to an edge or not are made. Membershp functons are defned for fuzzy system nputs. Many membershp functons have been ntroduced n the lterature. In the proposed edge detecton Gaussan membershp functons are used. To apply these functons, each of the edge strength values of O, O, and O are mapped nto fuzzy doman between and1, relatve to the g p p normalzed gray levels between and 1, usng Gaussan membershp functons gven as 2 2 [ ( xmaxxmn ) / 2 ] mn G( xmn) e (4) where G( x mn ) s a Gaussan functon, x max, xmn are the maxmum and ( m, n) th gray values respectvely and s the standard devaton assocated wth the nput varable. Each of the mapped values are partton nto three fuzzy regons ow, Medum, and gh. The defned regons and membershp functons are shown n Fg

4 Fgure 2. Gaussan Membershp Functons Fuzzy nference rules are appled to assgn the three fuzzy sets characterzed by membershp functons,, and to the output set. The rules, tabulated n ow Medum gh Table 1 are defned n such a way that n the fuzzy nference system, output set E, E M, and E correspond to pxels wth low, medum and hgh probablty value respectvely. The output of the system P Fnal representng the probablty used for fnal pxel classfcaton as edge or non-edge was computed usng a sngleton fuzzfer, Mamdan defuzzfer method gven by; p M y n ( 1 Fnal M n ( ( )) k k ( )) where are the fuzzy sets assocated wth the antecedent part of the fuzzy rule base, the output class center and M s the number of fuzzy rules beng consdered. 4. Expermental Results (5) y s The proposed fuzzy edge detecton method was smulated usng MATAB on dfferent mages, ts performance are compared to that of the Sobel and Krsch operators. Samples for a set of four test mages are shown n Fg. 3(a). The edge detecton based on Sobel and Krsch operators usng the mage processng toolbox n MATAB wth threshold automatcally estmated from mage s bnary value s llustrated n Fg. 3(b) and 3(c). The sample output of the proposed fuzzy technque s shown n Fg. 3(d). The resultng mages generated by the fuzzy method seem to be much smoother wth less nose and has an exhaustve set of fuzzy condtons whch helps to provde an effcent edge representaton for mages wth a very hgh effcency than the conventonal gradent-based methods (Sobel and Krsch methods). 5. Concluson Effectve fuzzy logc based edge detecton has been presented n ths paper. Ths technque uses the edge strength nformaton derved usng three (3) masks to avod detecton of spurous edges correspondng to nose, whch s often the case wth conventonal gradent- P o 78

5 based technques. The three edge strength values used as fuzzy system nputs were fuzzfed usng Gaussan membershp functons. Fuzzy f-then rules are appled to modfy the membershp to one of low, medum, or hgh classes. Fnally, Mamdan defuzzfer method s appled to produce the fnal edge mage. Through the smulaton results, t s shown that the proposed technque s far less computatonally expensve; ts applcaton on dgtal mage mproves the qualty of edges as much as possble compared to the Sobel and Krsch methods. Ths algorthm s sutable for applcatons n varous areas of dgtal mage processng such as face recognton, fngerprnt dentfcaton, remote sensng and medcal magng where boundares of specfc regons need to be determned for further mage analyss. Acknowledgement The author s grateful to Engneer I. A Isaah at adoke Akntola Unversty of Technology, Ogbomoso, Ngera for hs helpful advce. Table 1. Fuzzy Inference Rules s O and edgnessps O then p edge s O and edgnessps MD then p edge s O and edgnessps I then p edge s MD and edgnessps O then pedge s MD and edgnessps MD then pedge s MD and edgnessps I then pedge M s I and edgnessps O then pedge s I and edgnessps MD then pedge s I and edgnessps I then pedge s MD and edgnessso s O and edgnessps O then pedge s MD and edgnessso s MD and edgnessps O then pedge... s I and edgnessso s O and edgnessps I then pedge s I and edgnessso s MD and edgnessps I then pedge s I and edgnessso s I and edgnessps I then pedge 79

6 (a) (b) (c) (d) Fgure 3. (a) Orgnal Images, (b) Sobel Operator Results, (c) Krsch Operator Results, (d) Proposed Fuzzy Edge Detecton Algorthm Results 8

7 References [1] Canny, J.F., A computatonal approach to edge detecton, IEEE Trans. on Pattern Analyss and Machne Intellgence, 8(6), 1986, pp [2] Madasu., John S., and Shantaram V., Fuzzy Edge Detector Usng Entropy Optmzaton Proceedngs of the Internatonal Conference on Informaton Technology: Codng and Computng, 24. [3]. A. Zadeh, Fuzzy sets, Informaton and Control, 8: 1965, pp [4] A. Kaufmann, Introducton to the Theory of Fuzzy Subsets Fundamentals Theoretcal Elements, Vol. 1. Academc Press, New York, [5].C. Bezdek, Pattern Recognton wth fuzzy Objectve Functon Algorthm, Plenum Press, New York, [6] K. Cheung and W. Chan, "Fuzzy One Mean Algorthm for Edge Detecton," IEEE Inter. Conf. On Fuzzy Systems, 1995, pp [7] Y. Kuo, C. ee, and C. u, "A New Fuzzy Edge Detecton Method for mage Enhancement," IEEE Inter. Conf. on Fuzzy Systems, 1997, pp [8] S. El-Khamy, N. El-Yamany, and M. otfy, "A Modfed Fuzzy Sobel Edge Detector," Seventeenth Natonal Rado Scence Conference (NRSC'2), February 22-24, Mnufa, Egypt, 2. [9] M. Zhao, A. M. N. Fu, and. Yan, A Technque of Three-evel Thresholdng Based on Probablty Partton a Fuzzy 3-Partton. IEEE Trans. on Fuzzy Systems, vol.9, no.3, June 21, pp [1] Tao, C. W. et al(1993), A Fuzzy f-then approach to edge detecton, Proc. of 2nd IEEE ntl.conf. on fuzzy systems, pp [11], W. (1997), Recognzng whte lne markngs for vson-guded vehcle navgaton by fuzzy reasonng, Pattern Recognton etters, 18: [12] M. N. Mahan, M. K. Moqadam,. N. pour, and A. Bahrololoom, Dynamc Edge Detector Usng Fuzzy ogc, CSISS' 28, Sharf Unversty of Technology, Ksh, 28, (In Persan). [13]. ang and C. ooney, Compettve Fuzzy Edge Detecton, Appled Soft Computng, (3), 23, pp [14] G. Mansoor and. Eghbal, eurstc edge detecton usng fuzzy rule-based classfer, Journal of Intellgent and Fuzzy Systems, Volume 17, Number 5 / 26, pp Authors Aborsade, Davd O. receved the B. Eng. degree n Electronc and Electrcal Engneerng Technology from Federal Unversty of Technology, Owerr, n e receved M.Eng. and Ph.D. degrees n Electrcal Engneerng from Unversty of Ilorn, n 1995 and 26, respectvely. e s currently a Senor ecturer wth the Department Electronc and Electrcal Engneerng, adoke Akntola Unversty of Technology, Ogbomoso. s research nterests nclude computer vson, pattern recognton, mage and sgnal processng, neural networks, and fuzzy logc. 81

8 82