A NEW FUSION METHODOLOGY FOR EDGE DETECTION IN A COLOUR IMAGE

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1 A NEW FUSION METHODOLOGY FOR EDGE DETECTION IN A COLOUR IMAGE M. Arf Laboratore d Informatque, Unversté Franços Rabelas 64, avenue Jean Portals, Tours, France Muhammad.arf@etu.unv-tours.fr T. Brouard Laboratore d Informatque Unversté Franços Rabelas 64, avenue Jean Portals Tours, France brouard@unv-tours.fr N. Vncent Laboratore CRIP 5 SIP Unversté René Descartes 45, rue des Sant Pères Pars Cedex 06 France ncole.vncent@math-nfo.unv-pars5.fr Abstract The most nterestng dea n ths paper s that we are not presentng a new edge detector but an evdental fuson methodology for edge detecton usng the results of some edge detectors. Our work concerns two man problems as hghlghted by others, (a) whch method to use for dfferent mages and (b) whch values to select for ts parameters. We are usng complementary nformaton provded by each ndvdual method to mprove the overall results. In our methodology, the edge structure of an mage s frst detected by ether some classcal methods lke Sobel, Canny, Roberts, LoG, Prewtt and Zerocrossng or by a same method wth dfferent values for ts parameters. Fnally, Dempster-Shafer evdence theory s appled to yeld the fnal output edge map whch s n fact a pxel to pxel fuson of the above mentoned methods. We propose to defne mass of belef to each proposton n an adapted way. To evaluate ts performance, experments are carred out on synthetc and real mages. The results show that the performance of the proposed evdental fuson of classcal edge detectors s more stable and relable than that of ndvdual classcal methods. Key words Edge detecton, classcal edge detectors, nformaton fuson, Dempster-Shafer evdence theory. 1. Introducton Edge detecton s a part of front-end processng step n most computer vson, mage processng, and pattern recognton systems. The accuracy and relablty of edge detecton s crtcal to the overall performance of these systems [1]. Edge features, whch are recognzed as an mportant aspect of human vsual percepton, are commonly used n shape analyss [2]. The edges n an mage are usually referred to as rapd changes n some physcal propertes, such as geometry, llumnaton, or ntensty values over number of scales. There are a lot of dfferent methods proposed to solve the problem of edge detecton [3]. Among classcal methods, dervatve edge detectors are straghtforward methods for edge detecton [4]. The frst-order dfferental operators such as Roberts, Sobel operators, are convolved wth mages to enhance spatal ntensty changes, then a threshold s appled to obtan edge ponts. Canny [5] formulated edge detecton as an optmzaton problem and defned an optmal flter. The second-order dfferental operator such as Laplacan operator, ndcates edge ponts by ts zero-crossng property [4]. Some common problems of these methods are senstvty to nose, ansotropy and thck lnes. Some more sophstcal methods have been developed. Some mathematcal PDE models proposed have been used n level sets [6]. In [7] some fuzzy approaches have been desgned. In recent years, hybrd methods have been ntroduced such as fuzzy neural networks [8]. As a matter of fact, the dversty of mages prevents a method from detectng all edges wth 100% confdence. All the technques developed so far faled to produce accurate results, although the locatons where each method fals are not necessarly dentcal. In partcular, f an mage s nosy or f ts attrbutes dffer by only a small amount between regons edge detecton may result n spurous and broken edges f the method reles entrely on local nformaton. Edge lnkng technques can be employed to brdge short gaps, although a very dffcult task. Approaches sometmes suffer from the use of lldefned hard thresholds [9], [10]. Complex archtectures have been elaborated n order to fnd the best edge detector to apply. Another way s to use the complementary nature of several methods to reduce the problems arsng n each ndvdual method. The trend towards ntegratng several technques seems to be the best way forward. Even though several approaches yeld

2 complementary nformaton, nevertheless, they nvolve conflctng and ncommensurate objectves. Thus, as prevously observed by [11], whle ntegraton has long been a desrable goal, achevng ths s not an easy task. Our contrbuton belongs to ths trend of trals [12], [13]. We are proposng an automatc methodology for ntegraton of several methods on the base of Dempster- Shafer evdence theory. In our strategy, the edge nformaton s extracted frst by each of the methods and a contour map s constructed usng ntensty to ndcate whether or nor a pxel belongs to contour. For each method, some pxels are selected as reference pxels belongng to boundary regon and non contour regon respectvely. For any pxel, we make the decson relyng on a dstance measured between the pxel and each of the reference pxels. So, for each of the mage pxels, a number of dstance values are obtaned on the base of one method whch can be consdered as a classfer. The results obtaned n ths way are then combned usng evdence theory. Our algorthm s explaned n secton 2. An ntroducton to some prncples of Dempster-Shafer theory s gven n secton 3. Secton 4 carres some applcaton results. Fnally, conclusons and perspectves of our work are descrbed n secton Our fuson algorthm The pxel by pxel decsonal fuson s realzed by the followng algorthm. 1. Load a colour (RGB) mage I. 2. Obtan a grey level mage I_GL (n our case, grey level ntensty = a.r + b.g + c.b, where a = 0.299, b = 0.587, c = 0.114) and/or extract 3 mages I_R, I_G, I_B.e ts 3 compostes from I. 3. Perform edge detecton wth several methods or same method wth dfferent threshold values. Name edge map as I_x_e_ where x ndcates GL, & R, G, B, and e denotes edge whle represents the method employed. 4. Select some small number of pxels u (u << Nt, where Nt s total number of pxels,.e. X 1, X 2,..., X u ) from I_x_e_ wth the largest ntensty values startng from the maxmum one. 5. Select another u number of pxels (X u+1, X u+2,..., X 2u ) from I_x_e_ wth the lowest ntensty values startng from the lowest one. 6. Use these 2u pxels selected as reference pxels. 7. Start fuson by takng one by one each pxel of I_x_e_. a. Calculate the dstances between current pxel and the reference pxels and compute evdence masses accordng to (5) and (6). b. Apply Dempster-Shafer theory to take the decson from nformaton ssued from dfferent methods as wrtten n (1) and (2). 8. Dsplay the fnal edge detected fuson mage I_e_f. 3. Dempster-Shafer evdence theory In order to combne nformaton comng from dfferent sources n a consstent manner, Shafer [14] has created the evdence theory on the bases formulated by Dempster. Ths theory has been used n many applcatons [15], [16], [17]. The most mportant factor s the modelng of belef functons. Once the belef functons are obtaned, fuson s carred out by Dempster orthogonal combnaton rule. In ths theory, let Ω = {H 1,., H M } be the set of all possble propostons, called the frame of dscernment. Let 2 Ω denotes the set of the 2 M propostons of Ω : 2 Ω = {H / H Ω} = {φ, {H 1 },, {H M }, {H 1 H 2 },., Ω}. Informaton brngng an opnon on the state of a system s characterzed by a degree of belef noted by m. Ths functon m s defned by : m : 2 Ω [0,1], and has the propertes that m( φ ) = 0 and = 1. The quantty m(h) s called basc probablty number of H. It measures the belef that s commtted exactly to H. The elements of 2 Ω whose mass s non null, are called focal elements. A stuaton of total gnorance s gven by m(ω) = 1 and of total certanty (on a sngleton assumpton) by m(h n ) = 1 where H n represents a sngleton proposton. The total belef commtted to a set H, the quanttes m(h ) must be added for all subsets H of H : Bel(φ) = 0, for H Ω, H φ, Bel(H) = H' H m(h ). There s one-to-one correspondence between the belef functon and the basc probablty assgnment. The man dffculty conssts n modelng knowledge to set the basc belef assgnment m(.), the belef functon. Most often, authors defne emprcally the m functon. H Ω m (H ) Now, wth several sources of nformaton S ( = 1,., J) provdng ther basc probablty assgnment functons m, a sngle belef functon can be obtaned by combnng them. Wth two sources S 1 and S 2 producng mass vectors m 1 and m 2, ther fuson mass vector m = m 1 m 2, accordng to Dempster s operator wll be: H Ω, H φ, m(h) = 1 K 1 A B= H m 1 (A).m 2 (B) (1) where K = A B= φ m 1 (A).m 2 (B) (2) The normalzaton coeffcent K represents the conflct between sources. It has value between 0 and 1. If K s equal to 0, the sources are n perfect agreement. But f K s equal to 1, they are n total conflct and fuson cannot be acheved by Dempster-Shafer theory. A conflct mass

3 K s generated when nformaton sources are nether ndependent nor perfectly relable and belef functons modelng s too vague. To solve ths problem, other combnaton operators have been proposed [18]. + ( NX( C)) 4. NX( C) 2 + 1/ VX( X) 4. 1/ VX( X) ] (4) Modelng of belef functons lacks of generalty. However, two types of approaches can be mentoned : () based on dstance calculaton, () based on smlarty measure. Accordng to the nature of our classfers we are more nterested n the frst approach but our work dffers from other propostons [16]. We now present our contrbuton to modelng of belef functons n an automatc way [19]. Indeed, we are dealng wth pattern recognton. An ncomng pattern X (pxel) has to be classfed n class C by combnng two or several dstance classfers. Dstance classfers gve the results by rank level outputs n form of the classes C ( = 1 to M) of prototypes X ( = 1 to N) accordng to ther dstance d(x, X ). We defne a proposton H n the frame of dscernment Ω as X C or smply C so: Ω = {C 1,..., C M } Now focal elements and ther belef functons are defned. Focal elements are the sets of n classes that are concerned by the nature of some nearest neghbors of X (n varyng from 1 to k). Before combnng results each classfer s consdered on ts own. For the purpose of modelng belef functon assocated wth each ncomng element, we are ntroducng a fuzzy membershp functon to X prototype classes. The prototypes are those n the neghborhood of ncomng X, we have noted our fuzzy membershp functon as F X (X). The functon has values between 0 and 1, and has to gve a maxmum value towards 1 when X belongs to the class. The man varables we have taken nto account for a gven classfer are (1) Choce of k nearest neghbors of ncomng pattern X and the dstances assocated wth. (2) Rank R X (X ) of the output classes of prototypes, ordered accordng to the dstance d(x, X ). (3) N X (C) whch s a class repetton number among the k nearest neghbors consdered. (4) V X (X), the rato between the dstances d(x, X ) and d(x, Rz()) where Rz() represents the precedng prototype n the rank level output of the classfer. Here s our prototype based formalsm : Each term has to be maxmum when X and k prototypes consdered belong to the same class. The weghts are chosen n order to balance the dfferent nfluences. Ths functon s then employed for modelng the belef functon. m ({A 1 }) = F Xσ(1) (X) (5)... m ({A 1, A 2,., A g }) = F Xσ(g) (X) (6) where X σ(j) (j = 1,.., g) represents the prototypes appeared n k nearest neghborng prototypes. m(ω) complements the evdence to 1. the results usng ths modelng approach and ts performance are shown n the followng secton. 4. Results In case of edge detecton, we have a two class problem.e. a pxel X belongs to ether contour (X C 1 ) or non contour regon (X C 2 ). In a smple way, we have Ω = {C 1, C 2 } and 2 Ω s {φ, C 1, C 2, C 1 C 2 }. Both classes have u = 10 pxels (prototypes) as reference pxels whch was found satsfactory from the results obtaned. We have carred out dfferent experments studyng sx classcal edge detectors ncludng the choce of ther parameter values. Due to space lmtaton, only some of the results obtaned are shown n the fgures 1, 2, 3. As s always the case, results are dffcult to evaluate. On the actual example, the use of standard thresholds gves dfferent results. The results are whte edges on black background, so we take the negatve to reduce the prntng nk consumpton. Dfferent experments carred out were : where f X ( X) F = X [ ( X ) = f X ( X ) f 1/ d( X, X) 4 1/ d( X, X) X ( X ) (3) 1/ RX ( X) + 4 1/ RX ( X) Category 1 : Intal colour mage was converted to a grey level mage and then dfferent edge maps were obtaned by applyng some well known edge detectors. Here frst part conssts of studyng the effect of ntensty threshold value for each edge detector. The threshold T can be nterpreted as the mnmum probablty for an edge to be an actual edge. Wth an only one method ntensty threshold varaton gves dfferent results as shown n the fgure 1 (c), (d), (e), (f) for Sobel operator wth four dfferent threshold values. Fnal edge structure was obtaned on employng our fuson methodology. We note from the results that the resultant fuson edge map s better than poor edge mages and comparable to other

4 ones (fgure 1). We can say that the method enables to select as edge pxels those for whch confdence evaluated by the mass of belef and the k-nn approach s large. Then false detecton s fewer than n poorest methods. The complementary peces of nformaton are taken nto account. The test operated wth an only method wth dfferent threshold values shows a threshold value selecton can be solved by a fuson methodology n an automatc way. (fgure 1b). Results obtaned employng other edge detectors wth dfferent ntensty threshold values had the same trends as shown n the fgure 1. In the second part of ths category of experments, dfferent methods were used wth same ntensty threshold value. Results obtaned for dfferent mages were stable nstead of varatons n the ratngs of each ndvdual method (fgure 2). (e) I_GL_e_Sobel (T = 0.025) (f) I_GL_e_Sobel (T = 0.075) Fgure 1: An ntal colour mage and ts edge detecton by Sobel wth four dfferent threshold values. Category 2. In the second category of experments, three components (Red, green & Blue) of a colour mage were extracted and studed along wth a grey level mage. A varaton n edge nformaton obtaned from these four mages on applyng an edge detector was observed dependng on the nature of ntal colour mage. Results obtaned n ths category of experments can be concluded n the same way as n the frst category,.e. for any method wth a fxed ntensty threshold value, the resultant fuson mage s very close to the optmum one whatever the ratngs of each ndvdual component s (as shown n the fgure 3). A comparson of our results wth those of others presented n ther bench works s under consderaton. (a) fnal fuson mage (I_e_f) (b) I_GL_e_Canny (c) I_GL_e_Sobel (a) Intal mage (b) Fnal mage by fuson (d) I_GL_e_Prewtt (e) I_GL_e_Roberts (c) I_GL_e_Sobel (T = 0.05) (d) I_GL_e_Sobel (T = 0.01) Fgure 2 : Fnal fuson mage and four edge detected mages by four common methods wth a same threshold value (T = 0.05).

5 (a) fnal fuson mage (I_e_f) (a) Intal mage (b) I_R_e_Sobel (c) I_G_e_Sobel (b) fnal fuson mage (I_e_f) (b) fnal fuson mage (I_e_f) (d) I_B_e_Sobel (e) I_GL_e_Sobel Fgure 3 : Comparson between a fnal fuson edge mage (I_e_f) and four Edge detected mages by Sobel (wth same threshold value, T = 0.05) when appled to three colour component mages (I_R, I_G, I_B) and grey level mage (I_GL). (c) I_G_e_Canny (c) I_GL_e_Canny The fuson of the colours n grey level mage seems here to gve a result comparable wth that obtaned by combnng the edge nformaton assocated wth each colour. Nevertheless, we have made use of only one method (Sobel operator) for detecton of contours n the 2nd part of category 1 experment. Some other results are shown n the fgure 4, where a comparson s made between the results obtaned wth the green colour component (the best colour component of a colour mage n general) and those of grey level mage (obtaned from the same colour mage) under the same parameters values for dfferent methods employed. (d) I_G_e_Sobel (d) I_GL_e_Sobel

6 (e) I_G_e_Prewtt (f) I_G_e_Roberts Category 3 (edge detecton based on green colour component) (e) I_GL_e_Prewtt (f) I_GL_e_Roberts Category 4 (edge detecton based on grey level mage) Fgure 4 : results of experment category 3 & Conclusons and perspectves Our purpose was not to elaborate a new edge detecton method but to take advantage of the numerous methods that already exst and fnd a way to combne them n an automatc way. We have shown that evdental fuson methodology can answer ths objectve. Of course our approach s lmted to methods that gve a quanttatve measurement of the belongng of a pxel to contour. Fnal results mprove average results of the nvolved methods. Besdes, the method s able, n an ntellgent way, to prevent the dffcult choce of a threshold on ndvdual methods. Indeed, the fuson process enables to combne dfferent values of the threshold and to decde n a better way than just a vote. We ntend to contnue mprove the results of the method by modfyng the defnton of the dstance used n the k-nn approach. Here we have only consdered the feature that s threshold, we are to nvolve other parameters that can characterze the pxels used as prototypes. A contextual learnng phase could then be ntroduced. [1] Zujun Hou and T. S. Koh. Robust edge detecton. Pattern Recognton 36(9), 2003, [2] D. Marr and E. Hldreth, Theory of edge detecton Proc. R. Soc. London B 207, 1980, [3] N. Pal, S. Pal, A revew on segmentaton technques. Pattern Recognton, 26(9), 1993, [4] R. Klette, P. Zamperon, Handbook of Image Processng Operators (Ed. Wley 1994). [5] J. Canny, A computatonal approach to edge detecton. IEEE Transactons. PAMI-8, 1986, [6] J. Sethan, Level set methods: evolvng nterfaces n geometry, flud mechancs, computer vson and materals (Cambrdge Unversty Press, 1999). [7] L. R. Lang and C. G. Looney, Compettve fuzzy edge detecton, App. Soft Comp., 3(2), 2003, [8] C.G. Looney, Radal bass functonal lnk nets &fuzzy reasonng, Neurocomputng, 48(1-4), 2002, pp [9] M. Salott and Garbay. A new paradgm for segmentaton. Internatonal Conference on Pattern Recognton, Vol. C, 1992, [10] X. Muñoz, J. Frexenet, X. Cufí and J. Martí. Strateges for mage segmentaton combnng regon and boundary nformaton. Pattern Recognton Lettres 24 (1-3), 2003, [11] T. Pavlds and Y. Low, Integratng regon growng and edge detecton. IEEE Trans. on Pattern Analyss and Machne Intellgence 12 (3), 1990, [12] L Xu, A Krzyżak, C. Y Suen. Methods of Combnng Multple Classfers and Ther Applcatons to Handwrtng Recognton. IEEE Transactons on Systems., Man and Cybernetcs, 22(3) 1992, [13] G.Ng & H. Sng, Democracy n pattern classfcaton: Combnatons of votes from varous pattern classfers. Artfcal Intellgence n Engneerng, 12, 1998, [14] G. Shafer. A mathematcal Theory of Evdence (Prnceton Unv Press., Prnceton New Jersey, 1976). [15] I Bloch. Some Aspects of Demspter-Shafer Evdence Theory for Classfcaton of Mult-Modalty Medcal Images Takng Partal Volume Effect nto Account, Pattern Recognton Letters 17, 1996, [16] T. Denoeux. A k-nearest Neghbor Classfcaton Rule Based on Dempster-Shafer Theory. IEEE Transactons on Systems, Man, and Cybernetcs, 25(5), 1995, [17] E. Mandler and J. Schurman. Combnng the classfcaton results of ndependent classfers based on Dempster-Shafer theory. Pattern Recognton and Artfcal. Intellgence, 1988, [18] R. R. Yager. On the Dempster-Shafer Framework and New Combnaton Rules. Informaton Scence, 41, 1987, [19] M. Arf, T. Brouard, N. Vncent. Non parametrc fuzzy modelng of belef functons n evdence theory. 15th IASTED Internatonal. Conf. on Modellng and Smulaton (MS 2004) March 1-3, 2004 Marna Del Rey, Calforna, USA, References