AN EFFICIENT METHOD BASED ON ABC FOR OPTIMAL MULTILEVEL THRESHOLDING *

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1 IJST, Transactons of Electrcal Engneerng, Vol. 6, No. E, pp 7-9 Prnted n The Islamc Republc of Iran, 0 Shraz Unversty AN EFFICIENT METHOD BASED ON ABC FOR OPTIMAL MULTILEVEL THRESHOLDING * S. A. MOHAMMADI, R. AKBARI ** AND S. H. MOHAMMADI Dept. of Electrcal and Computer Engneerng, Tabrz Unversty, Tabrz, I. R. of Iran Dept. of Computer Engneerng and Informaton Technology, Shraz Unversty of Technology, Shraz, I. R. of Iran Emal: akbar@sutech.ac.r Center for Spoken Language Understandng, Oregon Health & Scence Unversty, Portland, OR, USA Abstract Many effcent b-level thresholdng technques have been proposed n recent years. Usually, the objectve functons, whch are used by them, are not approprate for the multlevel thresholdng owng to exponental growth of computatonal complexty. Ths work presents a new multlevel thresholdng algorthm usng Artfcal Bee Colony algorthm (ABC) wth the Otsu s objectve functon. Also, a strategy s used to guess sutable thresholds for ntalzng the proposed. Ths ntalzng phase used the b-level Otsu to fnd the ntal thresholds. These guessed thresholds are used to create a food source around each of them for use n the ABC algorthm as ntal populaton. The presented thresholdng s tested on four popular mages. The results show that ths has compettve performance compared to other wellknown s such as Gaussan-smoothng, Symmetry-dualty, GA-based and PSO-based algorthms. Keywords Segmentaton, multlevel thresholdng, otsu, ABC algorthm. INTRODUCTION Image segmentaton s one of the most fundamental processes for mage analyss and explanaton. Ths process s used for dstnct objects n an mage from ts background or dstngushng an object from other objects wth dfferent gray-levels. One of the s used broadly n mage segmentaton s mage thresholdng. It can be categorzed nto two classes whch are called b-level thresholdng and multlevel thresholdng. B-level thresholdng parttons pxels nto two dstnct classes; one of the classes comprses those pxels havng gray level values above a predefned threshold and the other class ncludes the rest of the pxels. Multlevel thresholdng splts the pxels nto varous classes and the pxels wthn a class have a gray level nsde a partcular range. In ths, a sngle gray-level value s assgned to each class. One effectve and benefcal tool used for evoluton of mage segmentaton s mage gray level hstograms. Our purpose s to fnd thresholds, whch are gray level values, to classfy pxels. The smplest classfcaton s b-level thresholdng n whch one threshold should be found, but the problem becomes more complcated f more thresholds need to be found. Generally, t s not straghtforward to guess thresholds n the multmodal hstogram of an mage for mage segmentaton. Thus multlevel thresholdng s an nterestng and challengng area of research n the feld of mage processng. Many thresholdng technques have been proposed n the past years [-]. These technques can be classfed nto two dstnct groups: optmal thresholdng s [-8] and property-based thresholdng s [9-]. Optmal thresholdng s try to fnd an optmal threshold that segments classes to acheve approprated attrbutes. Conventonally, ths process s done wth optmzng an objectve functon. Property-based procedures evaluate some propertes of hstogram for detectng the thresholds. Receved by the edtors Aprl, 0; Accepted June 0, 0. Correspondng author

2 8 S. A. Mohammad et al. In recent years many algorthms have been proposed for optmal thresholdng, such as maxmzng a posteror entropy to measure the homogenety of the threshold classes [-7], an optmal thresholdng to maxmze the separateness measures of the classes based on dscrmnant analyss, whch was proposed by Otsu 8] or a mnmum error to mnmze the pxel classfcaton error rate proposed by Kttler and Illngworth [ ]. Because most of these algorthms were orgnally developed for b-level thresholdng, they encounter the computatonal complexty, whch s exponental when extended to multlevel thresholdng due to the exhaustve and comprehensve search. An teratve was proposed to overcome ths problem n [ ]. It assumed the multlevel thresholdng problem as successve b-level thresholdng problems. Then the threshold values were changed to optmze an objectve functon. Ths teratve scheme repeated none of the changed threshold values or the threshold could not move. Unfortunately, ths traps local optma wth three or more thresholds. There are also some proposed s for property-based thresholdng. For nstance, a whch frst smooths the gray-level hstogram by the Gaussan convoluton has been developed by Lm and Lee [ ]. Then the frst and second dervatves of the smoothed hstogram are used to detect thresholds. Another whch has been proposed by Tsa 0] works wth unmodal hstograms by ncludng a local maxmum curvature to recognze the thresholds. Property-based thresholdng s are rapd and approprate for the case of multlevel thresholdng, whle the number of thresholds s dffcult to determne and should be gven beforehand. Karaboga has represented artfcal Bee Colony (ABC) algorthm, whch s based on the foragng behavor of honeybees [ ]. ABC s one of the most recently ntroduced optmzaton algorthms. The prevous studes on ABC showed that ths algorthm s effcent and compettve performance may be obtaned by usng ths algorthm compared to the other algorthms n many engneerng felds. The performance of the ABC algorthm on multlevel thresholdng s compared wth the results of the Partcle Swarm Optmzaton (PSO) algorthm on the same benchmarks that are presented n [ ] and some other multlevel thresholdng algorthms. ABC and PSO algorthms are populaton-based optmzaton algorthms and they have been nspred by the socal behavor of anmals and swarm ntellgence, whch classfy them n the same class of swarm-based optmzaton algorthms. There are many other optmzaton algorthms proposed n lterature such as [ - 7] whch are used n other felds such as thermal unts 8], dscrete optmzaton [ 6] or contnuous optmzaton [ 7]. In ths work, a new algorthm based on ABC algorthm s proposed whch represents compettve results compared to the prevous algorthms. The proposed algorthm uses Otsu mult-level algorthm to ntalze thresholds snce t s very smple and the nearly optmal thresholds are selected based not only on local propertes such as valleys, but also based on the global propertes of the hstogram. However, t falls n the local mnma. Hence, for solvng ths problem, ABC s used as an algorthm to take t back from local mnma and perform a global search. The rest of the paper s organzed as follows: the Otsu s presented n secton. An teratve ntalzng s presented n secton. Proposed ABC multlevel thresholdng algorthm s ntroduced n secton. The expermental results are proposed n secton. Fnally secton 6 concludes ths work.. THE OTSU METHOD Otsu proposed a whch tres to maxmze the between class varance to dsjont the segmented classes as far as possble to detect the optmal threshold for segmentaton. Ths between class varance measure s used as the objectve functon n the ABC algorthm. It s formulated and defned as follows. Assume that an mage contans N pxels n whch the range of gray levels of a gven mage s located n the range of [0, L-] and h() ndcates the occurrence of gray level. We defne N as total number of pxels and P as the probablty of occurrences of gray level n the mage as follows: IJST, Transactons of Electrcal Engneerng, Volume 6, Number E June 0

3 An effcent based on ABC for 9 L N h( ),0 L () 0 h( ) P,0 L () N As a means to evaluate qualty of threshold (at level t) we shall brng between-class varance to the table. We should maxmze f(t) to fnd optmal threshold: where: f ( t) w w ( ) w w () t P () 0 N t P () P t (6) 0 w0 P N (7) t w Suppose we dvded the pxels nto two dstnct parts by a threshold t. The probabltes of each part occurrence are ndcated by w 0 and w and the mean of each part s denoted by μ 0 and μ. We could also wrte Eq. () n the other form as: where: f ( t) w w (8) 0 0 P (9) t 0 ( 0) 0 w0 P N ( ) (0) t w P N ( ) () 0 w N w P () 0 P N () 0 w The σ 0 and σ show varance of each class or part and σ denotes varance over all pxels. The w and the μ respectvely show the probabltes of all pxels occurrence and the mean level of all pxels. Thus, maxmzng Eq. 8 s dentcal to mnmzng: g( t) w w () 0 0 The g(t) functon s also known as wthn-class varance that should be maxmzed. Expandng ths logc to multlevel thresholdng s straghtforward as a result of dscrmnant crteron: f ( t) w w... w () 0 0 c c June 0 IJST, Transactons of Electrcal Engneerng, Volume 6, Number E

4 0 S. A. Mohammad et al. where c s the number of thresholds. Eq. () s used as an objectve functon for the ABC algorthm that should be mnmzed.. AN ITERATIVE INITIALIZING METHOD Otsu could fnd the optmal b-level threshold effectvely. Otsu also extends hs for the multlevel thresholdng but t suffers from computatonal complexty and tme, owng to the comprehensve search. Assume that we want to fnd c optmal thresholds. Due to an exhaustve search for fndng every possble set of thresholds, we obtan complexty of O(n c ) whch grows exponentally as the number of thresholds ncrease. Hence, these s are not approprate for use n practcal applcatons. An teratve s used for utlzng b-level Otsu to fnd several thresholds [ ]. If ths teratve scheme s used n the ntalzng phase of the proposed algorthm, notable computatonal tme n fndng multlevel thresholds s retaned due to lmtng the search space. Ths uses unformty measure as a crteron for evaluatng the qualty of the segmented mage whch s descrbed n secton.. At frst, the teratve procedure uses Otsu b-level thresholdng. Afterwards, to obtan hgher-level thresholds, Otsu b-level thresholdng s used n each sutable segmented class to maxmze the crteron functon (.e. unformty measure) as much as practcable. The pseudo-code of the teratve ntalzng algorthm s gven n Fg.. Apply b-level Otsu s to the whole hstogram. For n= to C Apply Otsu s n every segmented class separately. Compute the value of objectve functon n each case. Determne the class whch produced hghest value of the objectve functon. Store the new threshold value. End Fg.. The pseudocode of the teratve ntalzng ] The complexty of ths algorthm s the same as b-level thresholdng because all values n the range of [0, L-] are examned for every new threshold. It means that b-level thresholdng algorthms are used for c tmes, f we want to fnd c thresholds. Thus the tme complexty of the algorthm s O(c.n), whch s a lnear complexty. Table compares the algorthm runtme wth Gaussan-smoothng, Symmetrydualty, GA learnng-otsu and PSO based wth c = to for Lena and Pepper mages. As can be seen from Table, the CPU-tme results of teratve ntalzng are lnear and quck. Table. Tme complextes of the proposed teratve ntalzng, Gaussan-smoothng, Symmetry-dualty and GA-based Images Lena Peppers c Intal proposed thresholds 7 7,67 76,7,67 76,7,,67 76,7,,67,9 7 0,7 0,7,9,0,7,9,0,,7,9 Intal proposed Gaussan smoothng CPU-tme(s) Symmetry dualty GA-based IJST, Transactons of Electrcal Engneerng, Volume 6, Number E June 0

5 An effcent based on ABC for The unformty values are also computed n Table. The results ndcate that ths ntalzng s superor to other s. From these results one can see that mult-level thresholdng gves a better result n nearly no tme, so t can be consdered a good choce for ntalzng thresholds. Table. Unformty values of the proposed teratve ntalzng, Gaussan-smoothng, Symmetry-dualty and GA-based. Images Lena Peppers c Intal proposed thresholds 7 7,67 76,7,67 76,7,,67 76,7,,67,9 7 0,7 0,7,9,0,7,9,0,,7,9 Unformty values Intal Gaussan proposed smoothng Symmetry dualty GA-based PROPOSED ABC MULTILEVEL THRESHOLDING ALGORITHM Artfcal Bee Colony (ABC) algorthm was developed by Karaboga for numercal optmzaton [ ]. The nspraton behnd ths algorthm s the foragng behavor of honey bee swarms n fndng foods. Some popular and well-known evolutonary algorthms such as Partcle Swarm Optmzaton (PSO) and Genetc Algorthm (GA) have been compared wth the ABC algorthm on some unconstraned and constraned problems [-]. The ABC algorthm s also appled on the clusterng algorthms [ 6] and the tranng of neural networks [7, 8] wth the proposed objectve functon n 9]. The prevous studes showed that ABC outperforms other meta-heurstc algorthms on most of the engneerng problems. ABC algorthm dvdes artfcal bees nto three groups of bees: employed, onlooker and scout bees. Employed bees brng ther nformaton about food sources for onlooker bees. Ths nformaton s prepared for onlooker bees by dancng on dance area. From these dances, the onlookers could realze whch source s better. Another type of bee whch search the area stochastcally, s the scout bee. The artfcal bee colony s dvded nto equal parts. The frst part ncludes the employed bees and the other part conssts of the onlooker bees. If a food source s dscarded by other bees, the employed bee whch found that food source wll turn nto a scout bee. The pseudo-code of the ABC algorthm s presented n Fg.. Frst, P sze food sources or solutons are ntalzed around the results whch are found by the teratve n the preprocessng secton accordng to the followng constrant, that the numbers should be ascendng to not havng overlap between segmented classes. Then employed and onlooker bees are produced where the number of bees n each group s equal to the food sources. Each food source n ths algorthm ndcates a soluton for the optmzaton problem. The amount of nectar or the qualty measure known as ftness s computed as follows: ft (6) f where f s the Otsu s multlevel objectve functon whch s presented n Eq. (). June 0 IJST, Transactons of Electrcal Engneerng, Volume 6, Number E

6 S. A. Mohammad et al. Intalzaton: Generate a random populaton around the food sources suggested by teratve locaton. Z,=,,P sze //P sze denotes the sze of populaton Compute ftness of the populaton as defned by (6) Do For each employed bee Compute soluton v accordng to (7). Compute the value of f Update food source f the new food source s more relable. End Compute probablty of food selecton as specfed by (8). For every onlooker bee Select a soluton accordng to ts probablty. Compute soluton v accordng to (9). Compute the value of f Update food source f the new food source s more relable. End If there s an abandoned food source for the scout Replace soluton wth a new one as specfed by (0). Save the best soluton up to now. Untl termnaton condton s met. Fg.. The pseudocode of the proposed ABC algorthm for thresholdng The employed bees use ther prevous nformaton and ther current local nformaton around them to update ther locatons f the qualty of the found nectar s hgher than ther ex-locatons. Flyng Pattern of the employed bees s computed as follows from what s remembered before: v z ( z z ) (7) j j j j kj where j {,,...,D} and k {,,..., P sze } denote ndces whch are chosen arbtrarly. Coeffcent j s chosen randomly between [, ]. The ftness of v j s then compared wth the prevous food source ftness and f the recent one s better or equal to t, t s exchanged wth the old one. The employed bees return to ther hve to share ther nformaton wth the onlooker bees by some dancng styles, whch demonstrate the drecton and the amount of nectar n the food sources. The onlooker bees evaluate ths nformaton and choose to go to a food source accordng to some probablty functons defned as follows: p j Psze n ft ft n (8) where P sze s the number of food sources whch s equal to the number of both employed bees and onlooker bees, and ft s gven n Eq. (6). The onlooker bees also used ther memorzed best food poston and the newly chosen food source to update ther poston f the qualty of nectar s better than the prevous memorzed poston. The onlooker bees flyng trajectores are updated as follow: v z ( z z ) (9) j j j j wj where j {,,...,D} denote an ndex whch s chosen arbtrarly and w {,,...,P sze } denote an ndex whch s chosen wth probablty that s computed wth formula. Coeffcent j s chosen randomly IJST, Transactons of Electrcal Engneerng, Volume 6, Number E June 0

7 An effcent based on ABC for between [, ]. The ftness of v j s then compared wth the prevous food source ftness and f the new one s better or equal to t, t s replaced wth the old one. The scout bees change a deserted food source wth a haphazardly produced food source. If a food source poston does not change after a predefned number of teraton called lmt, t s assumed as deserted food source. If we presume that the deserted food source s z then the update rule s defned as follows: z z rand(0,)( z z ) (0) j j j j mn max mn where j {,,..., D}. In ABC algorthm, the exploraton s exerted by the employees and the onlooker n the search area and the scout bees n the search space do the explotaton.. EXPERIMENTAL RESULTS Ths secton presents the conducted experments to evaluate the performance of the proposed algorthm on the well-known benchmarks. a) Performance metrc The unformty measure was proposed by Levne and Nazf 9] for measurng mage segmentaton qualty. Next, Sahoo et al. [ ] recommended usng ths measure to test the performance of thresholdng algorthms. Ths qualty measure corresponds to Otsu crteron measure [ 0]. The unformty measure can be formulated as follows: j0 R j ( f ) U c N ( f f ) c where c denotes number of thresholds, R j ndcates the segmented regon j, f represents the gray level of pxel, μ j ponts to the mean of the gray levels of pxels n the segmented regon j, N ndcates the total number of pxels n the gven mage, f max represents the maxmum gray level of pxels n the gven mage, f mn demonstrates the mnmum gray level of pxels n the gven mage. The unformty value s between 0 and. The hgher values whch are closer to means that the qualty of thresholdng s better. b) Settngs of the algorthms The performance of the proposed algorthm n comparson wth the performances of Genetc Algorthm based multple thresholdng [ 0], Gaussan-smoothng [0, ] and Symmetry-dualty [9, ] are presented n ths secton. Four well-known mages (.e. Lena, Peppers, House, and Elane) are used here for comparson wth other s [ ]. The benchmark mages downloaded from ] and [ ] are of sze. c) Parameters tunng It seems that the proposed algorthm provdes effcency n multlevel thresholdng. However, ts performance may be affected by some parameters. The number of teratons and the sze of the colony are two man parameters whch nfluence the performance of the proposed algorthms. Two experments are conducted to observe the behavor of the proposed algorthm under dfferent confguratons. max j mn () June 0 IJST, Transactons of Electrcal Engneerng, Volume 6, Number E

8 S. A. Mohammad et al. In the frst experment, the effect of the colony sze s studed. The sze of colony vares between 0 and 0 n steps of 0. In ths experment, parameter c s set at and the number of teratons s fxed at 0. All the results are the average of 0 ndependent runs. Table shows the performance of the proposed algorthm wth a colony of dfferent szes. From Table, t can be seen that the sze of the colony affects the performance of the proposed algorthm. It seems that the unformty measures for a specfc colony sze of 0 could be the best choce wth dfferent number of teratons. Table. Unformty values for c = and dverse colony sze for four benchmark mages Iteraton 0 C Colony sze Lena Unformty values Peppers House Elane In the second experment, the effect of the teraton numbers s studed. The number of teratons vares between 0 and 0 n steps of 0. In ths experment, parameter c s set equal to and the sze of the colony s fxed at 0. All the results are the average of 0 ndependent runs. Table shows the performance of the proposed algorthm under dfferent number of teratons. From Table, t can be seen that the number of teratons affects the performance of the proposed algorthm. The best results are obtaned when the number of teratons s set at 0. Table. Unformty values for c = and dverse teratons for four benchmark mages Colony sze 0 C Iteratons Lena Unformty values Peppers House Elane These results show that ABC algorthm has better performance wth 0 teratons and a colony sze wth 0 bees. We choose these parameters not only because of slght changes n the results, but the less computaton tme that we gan. Ths could make our proposed algorthm faster than the PSO based snce 00 teratons were used to converge to the optmum soluton wth partcles. Coeffcents dd not affect the performance of the algorthm snce they were unformly generated n a fxed range. d) Comparatve study The performance of the proposed ABC multlevel thresholdng algorthm s compared wth the performance of PSO based, Gaussan-smoothng, GA-learnng-Otsu algorthm and Symmetry-dualty. The unformty values of the proposed algorthm n comparson wth other algorthms are shown n Table. The results show that the proposed s effcent and outperforms other s on most of the experments. The best result on Lena mage for c= s obtaned by the PSO based. Except for ths case, the best results on all other cases were obtaned by the proposed. IJST, Transactons of Electrcal Engneerng, Volume 6, Number E June 0

9 An effcent based on ABC for Table.Unformty values of the proposed ABC multlevel thresholdng, PSO based, Gaussan-smoothng, Symmetry-dualty and GA-based for Lena and Peppers mages Images Lena Peppers c Proposed thresholds 96,6 80,6,70 7,,7,79 7,06,6,9,9 0,9 68,,0 6,7,6,,0,,7,0 Proposed Unformty Values PSO based Gaussan Symmetry smoothng dualty GA-based The proposed s also compared wth basc PSO and adaptve PSO [] for Elane and House mages. Table 6 presents the unformty values of the proposed algorthm n comparson wth PSO and adaptve PSO. The results show that the proposed has compettve performance compared to the other s. The best results on the House mage for c= and c= are obtaned by Adaptve PSO. Except for these cases, the proposed performs better on other cases. As mentoned before, the proposed algorthm s appled for Lena, Peppers, House and Elane mages and dfferent thresholds are used to segment them. For other algorthms, the mentoned thresholds n ther papers are used to represent segmented mages. The results of hybrd GA, PSO and ABC, whch are derved thresholds on the hstogram of mages and ther correspondng mages wth thresholds are shown n Fgs. -6. In the prevous works lke Gaussan-smoothng and symmetry/dualty s, t can be seen that these s tend to put threshold at the valley of hstograms, whch s the best for mages wth dstnct foreground and background but populaton-based algorthms lke PSO or GA can work wth more complex hstograms whch may have unequal-sze peaks or flat valleys [ ]. These s care more about the characterstcs of mages based on dscrmnant analyss, whch can be seen n Fgs. -6. As t can be seen n Fg. b, Fg. b, Fg. b the qualty of mages wth thresholds s better than other mages, but the qualty of Fg. 6b and Fg. 6c are nearly the same as each other snce the founded thresholds are nearly smlar. Table 6.Unformty values of the proposed ABC multlevel thresholdng, Adaptve PSO and basc PSO for House and Elane mages Images House Elane c Proposed thresholds 97,6 7,9,7 70,7,,89 6,0,6,67,96 08,67 96,,86 8,,,96 8,,,7,0 Proposed Unformty values Adaptve PSO based Basc PSO June 0 IJST, Transactons of Electrcal Engneerng, Volume 6, Number E

10 6 S. A. Mohammad et al. (a) (b) (c) (d) Fg.. Gray scale mage and hstogram of a) Orgnal Lena b) Proposed Method c) Adaptve PSO d) GA for c= thresholds (a) (b) (c) (d) Fg.. Gray scale mage of and hstogram a) Orgnal Peppers b) Proposed c) Adaptve PSO d) GA for c= thresholds The hgher value of unformty measure means that the qualty of found thresholds by that algorthm s superor to others. In other words, t s a knd of class separablty crteron whch uses wthn-class and between-class varances for ts formulaton. If the wthn-class varance s mnmal and that of the between-class s maxmal then the class separaton s satsfactory. Therefore, the proposed algorthm represents a good separablty accordng to ts unformty values whch means that t s superor to other algorthms. IJST, Transactons of Electrcal Engneerng, Volume 6, Number E June 0

11 An effcent based on ABC for 7 (a) (b) (c) Fg.. Gray scale mage and hstogram of a) Orgnal House b) Proposed Method c) Adaptve PSO for c= thresholds 6. CONCLUSION In ths study, we proposed a new optmal multlevel thresholdng based on ABC algorthm and Otsu s. An teratve ntalzng was also used to make the algorthm converge faster. Ths dea makes the computaton complexty grow lnearly when hgher number of thresholds s selected. Owng to ths property, ths algorthm could be used n real stuatons. The results show that ths s superor to other well-known and popular s proposed prevously. (a) (b) (c) Fg. 6. Gray scale mage and hstogram of a) Orgnal Elane b) Proposed Method c) Adaptve PSO for c= thresholds June 0 IJST, Transactons of Electrcal Engneerng, Volume 6, Number E

12 8 S. A. Mohammad et al. REFERENCES. Sezgn, M. & Sankur, B. (00), Survey over mage thresholdng technques and quanttatve performance evaluaton. Journal of Electronc Imagng, Vol., pp Sahoo, P. K., Soltan, S., Wong, A. K. C. & Chen, Y. C. (988). A survey of thresholdng technques, Computer Vson Graphcs Image Process, Vol., pp Lee, S. U., Chung, S. Y. & Park, R. H. (990). A comparatve performance study of several global thresholdng technques for segmentaton, Computer Vson Graphcs Image Process, Vol., pp Kapur, J. N., Sahoo, P. K. & Wong, A. K. C. (98). A new for gray-level pcture thresholdng usng the entropy of the hstogram. Computer Vson Graphcs Image Processng, Vol., pp Kttler, J. & Illngworth, J. (986). Mnmum error thresholdng. Pattern Recognton, Vol. 9, pp Pun, T. (98). Entropy thresholdng: A new approach. Computer Vson Graphcs Image Processng, Vol. 6, pp Pun, T. (980). A new for grey-level pcture thresholdng usng the entropy of the hstogram. Sgnal Processng, Vol., pp Otsu, N. (979). A threshold selecton from gray-level hstograms. IEEE Transactons on Systems, Man, Cybernet, SMC-9, Yn, P. Y. & Chen, L. H. (99). New for multlevel thresholdng usng the symmetry and dualty of the hstogram. Journal of Electroncs and Imagng, Vol., pp Tsa, D. M. (99). A fast thresholdng selecton procedure for multmodal and unmodal hstograms. Pattern Recognton Letters, Vol. 6, pp Lm, Y. K. & Lee, S. U. (990). On the color mage segmentaton algorthm based on the thresholdng and the fuzzy c-means technques. Pattern Recognton, Vol., pp Yn, P. Y. & Chen, L. H. (997). A fast teratve scheme for mult-level thresholdng s. Sgnal Processng 60, pp Karaboga, D. (00). An dea based on honey bee swarm for numercal optmzaton. Techncal Report-TR06, Ercyes Unversty, Engneerng Faculty, Computer Engneerng Department.. Chander, A., Chatterjee, A. & Sarry, P. (0). A new socal and momentum component adaptve PSO algorthm for mage segmentaton. Expert Systems wth Applcatons, Vol. 8, Issue, pp Akbar, R., Mohammad, A. & Zarat, K. (00). A novel bee swarm optmzaton algorthm for numercal functon optmzaton. Communcatons n Nonlnear Scence and Numercal Smulaton, Vol., pp.. 6. Hatam, M. & Masnad-Sraz, M. A. (008). Analytcal dscrete optmzaton. Iranan Journal of Scence & Technology, Transacton B, Engneerng, Vol., No. B, pp Akbar, R. & Zarat, K. (0). A Cooperatve approach to bee swarm optmzaton algorthm. Journal of Informaton Scence and Engneerng, Vol. 7, No., pp Nknam, T. & Golestaneh, F. (0). Enhanced bee swarm optmzaton algorthm for dynamc economc dspatch. IEEE Systems Journal, DOI: 0.09/JSYST.0.98, Issue Levne, M. D. & Nazf, A. M. (98). Dynamc measurement of computer generated mage segmentatons. IEEE Trans. Pattern Analyss and Machne Intellgence, Vol. 7, pp Ng, W. S. & Lee, C. K. (996). Comment on usng the unformty measure for performance measure n mage segmentaton. IEEE Transactons on Pattern Analyss And Machne Intellgence, Vol. 8, No. 9.. Karaboga, D. (00). An dea based on honey bee swarm for numercal optmzaton. Techncal Report-TR06, Ercyes Unversty, Engneerng Faculty, Computer Engneerng Department.. Basturk, B. & Karaboga, D. (006). An artfcal bee colony (ABC) algorthm for numerc functon optmzaton. IEEE Swarm Intellgence Symposum, Indana, USA.. Zarat, K., Akbar, R. & Zegham, V. (0). On the performance of bee algorthms for resource constraned project schedulng problem. Journal of Appled Soft Computng, Vol., No., pp IJST, Transactons of Electrcal Engneerng, Volume 6, Number E June 0

13 An effcent based on ABC for 9. Karaboga, D. & Basturk, B. (007). A powerful and effcent algorthm for numercal functon optmzaton: Artfcal Bee Colony (ABC) algorthm. J. Global Optm. Vol. 9, Issue, pp Akbar, R., Zegham, V. & Zarat, K. (0). Artfcal bee colony for resource constraned project schedulng problem. Internatonal Journal of Industral Engneerng Computatons, Vol., No., pp Karaboga, D. & Ozturk, C. (0). A novel clusterng approach: Artfcal Bee Colony (ABC) algorthm. Appled Soft Computng, Vol., pp Karaboga, D., Basturk, B. & Ozturk, C. (007). Artfcal Bee Colony (ABC) optmzaton algorthm for tranng feedforward neural networks, LNCS: Modelng Decsons for Artfcal Intellgence, MDAI. Vol. 67, Sprnger Verlag, pp Karaboga, D. & Ozturk, C. (009). Neural networks tranng by Artfcal Bee Colony Algorthm on pattern classfcaton. Neural Network World, Vol. 9, Issue, pp De Falco, I., Della Coppa, A. & Tarantno, E. (007). Facng classfcaton problems wth partcle swarm optmzaton. Journal of Appled Soft Computng, Vol. 7, Issue, pp Yn, P. Y. (999). A fast scheme for optmal thresholdng usng genetc algorthms. Sgnal Processng, Vol. 7, pp Yn, P. Y. & Chen, L. H. (99). New for multlevel thresholdng usng the symmetry and dualty of the hstogram. Journal of Electroncs and Imagng, Vol., pp ftp://sp.usc.edu/pub/database/msc.zp June 0 IJST, Transactons of Electrcal Engneerng, Volume 6, Number E