Development of a New Optimal Multilevel Thresholding Using Improved Particle Swarm Optimization Algorithm for Image Segmentation

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1 Inernaonal Journal of Elerons Engneerng, (1), 010, pp Developmen of a New Opmal Mullevel Thresholdng Usng Improved Parle Swarm Opmzaon Algorhm for Image Segmenaon P.D. Sahya 1 & R. Kayalvzh 1 Deparmen of Eleral Engneerng, Annamala Unversy, Chdambaram, INDIA Deparmen of Insrumenaon Engneerng, Annamala Unversy, Chdambaram, INDIA Absra: Image hresholdng s a very ommon mage proessng operaon, sne all mage proessng shemes need some sor of operaon of he pxels no dfferen lasses. In order o deermne hresholds, mos mehods analyze he hsogram of he mage. The opmal hresholds are ofen found by eher mnmzng or maxmzng an objeve funon wh respe o he values of he hresholds. In hs paper, mproved parle swarm opmzaon (IPSO) based mullevel hresholdng has been proposed for he mnmzaon of objeve funon. The hao sequenes are nluded n he nera wegh faor of he lassal PSO o mprove he searhng apably of he algorhm. The expermenal resuls show ha he proposed mehod an mae opmal hresholdng applable n ase of mullevel hresholdng and he performanes are beer han hose of some propery based mullevel hresholdng mehods. Keywords: Image Thresholdng, Image Segmenaon, Parle Swarm Opmzaon, Improved Parle Swarm Opmzaon. 1. INTRODUCTION Thresholdng s an mporan ehnque for mage segmenaon. Beause he segmened mage obaned from hresholdng has he advanage of smaller sorage spae, fas proessng speed and ease of manpulaon, ompared wh a gray level mage onanng 56 levels, hresholdng ehnques has drawn a lo of aenon durng he las few years. Thresholdng s used n many mage proessng applaons suh as opmal haraer reognon where he goal s o exra he haraer n a doumen mage and hen reognze [1], auoma vsual nspeon of defes where s adoped o dee defes of eleron omponens for ndusral applaons [], deeon of vdeo hange where ulzes an adapve hreshold o dee he hanges beween a urren mage and a pre-esablshed baground [3], movng obje segmenaon where an mage s segmened no objes wh homogeneous haraerss o aheve effen ompresson by odng he onour and exure separaely for real-me onen-based applaons [4] and medal mage applaons where s used o exra he bran regon from a magne resonane mages (MRI) for deeng ssue deformes suh as aners and njures [5]. The am of an effeve segmenaon s o separae objes from he baground and o dfferenae pxels havng nearby values for mprovng he onras. Thresholdng ehnques an be dvded no b-level and mullevel aegory, dependng on number of mage segmens. In b-level hresholdng, mage s segmened no *Correspondng Auhor: pd.sahya@yahoo.n, mhuvg.nr@gmal.om wo dfferen regons. The pxels wh gray values greaer han a eran value T are lassfed as obje pxels, and ohers wh gray values lesser han T are lassfed as baground pxels. Mullevel hresholdng s a proess ha segmens a gray level mage no several dsn regons. Ths ehnque deermnes more han one hreshold for he gven mage and segmens he mage no eran brghness regons, whh orrespond o one baground and several objes. The mehod wors very well for objes wh olored or omplex a baground on whh b-level hresholdng fals o produe sasfaory resuls. Over he years, many researhers have proposed several algorhms for b-level and mullevel hresholdng of mage hsograms [7-1]. The man objeve of many suh shemes s o aheve opmal hresholdng, suh ha he hresholded lasses aheve some desred haraers. Many of hese mehods aemp o aheve opmzaon of an objeve funon by maxmzng poseror enropy ha ndaes homogeney of segmened lasses [7], maxmzng some measure of separably [8], employng ndex of fuzzness and fuzzy smlary measure [10], mnmzng Bayesan error [1] e. Several suh mehods have been orgnally developed for b-level hresholdng and laer exended o mullevel hresholdng [7-8]. However nsead of employng opmzaon of a fness funon, hey have mplemened hsogram hresholdng based on a smlary measure beween gray levels. The presen paper proposes he developmen of a new opmal mullevel hresholdng algorhm, espeally suable

2 64 Inernaonal Journal of Elerons Engneerng for mul-model mage hsograms employng Improved Parle Swarm Opmzaon algorhm. In he reen years parle swarm opmzaon (PSO) has ganed muh populary n dfferen nd of applaons beause of s smply, easy mplemenaon and relable onvergene [13-15]. I has been found o be robus n solvng onnuous non-lnear opmzaon problems. However he radonal PSO hghly depends on s parameer and ofen suffers he problem of beng rapped n loal opma [16-17]. To overome hese drawbas, he mproved parle swarm opmzaon (IPSO) algorhm has been nrodued.. PROBLEM FORMULATION OF ENTROPY BASED MULTILEVEL THRESHOLDING The popularly employed enropy reron for sasfaory deermnaon of opmal hresholds of mage hsograms as ulzed n segmenaon problems was proposed by apur (1985). The orgnal algorhm was developed for b-level hresholdng and was laer exended for mulple levels. The b-level algorhm an be desrbed as follows: Le here be L gray levels n a gven mage and hese gray levels are n a gven mage and hese gray levels are n he range {0, 1, (L 1)}. Then one an defne h()/n, (0 (L 1)) where h() denoes number of pxels wh gray-level L and N denoes oal number of pxels n he mage where L 0 h() Then he objeve s o maxmze he fness funon H 0 H 1 f() H 0 + H 1. (1) In, 0 0 0, and 0 0 L L In, P. The opmum hreshold s whh maxmzes f(). The opmal mullevel hresholdng problem an be onfgured as a P-dmensonal opmzaon problem, for deermnaon of P opmal hresholds for a gven mage [ 1 p] where he am s o maxmze he objeve funon: f([[ 1, p ]) H 0 + H 1 + H +.+ H () Where H 0 H 1 H 1 1 In, P In, In,, H L L In, P. Ths enropy reron based measure res o aheve more and more enralzed dsrbuon for eah hsogram based segmenaon regon n he mage. In hs proposed IPSO algorhm, opmum -dmensonal veor [ 1, 3. ] s obaned, whh an maxmze he objeve funon as gven n equaon (). As PSO algorhms are usually desgned o solve mnmzaon problems, we solve hs maxmzaon problem, gven n (), by onsrung he fness funon as he reproal of f ([ 1, 3. ]). 3. GENERAL PSO METHOD Parle swarm opmzaon (PSO) frs nrodued by Kennedy and Eberhar s one of he heurs opmzaon algorhms. A smple PSO manans a swarm of parles ha represen he poenal soluons o he problem on hand. The smple PSO onsss of a swarm of parles movng n he D-dmensonal spae of possble problem soluons. Eah parle embeds he relevan nformaon regardng he D deson varables and s assoaed wh a fness ha provdes an ndaon of s performane n he objeve spae. Eah parle has a poson X [X, 1, X,.X, D ] and a flgh veloy V [V, 1, V, V, D ]. Moreover a swarm onans eah parle own bes poson pbes (pbes, 1, pbes,,., pbes, D ) found so far and a global bes parle poson gbes (gbes, gbes,., gbes D ) found among all he parles n he swarm so far. In essene, he rajeory of eah parle s updaed aordng o s own flyng experene as well as o ha of he bes parle n he swarm. The sandard PSO algorhm an be desrbed as V, d + 1 W V,d + C 1 rand 1 (pbes,d X, d ) + C rand (gbes d X, d ) (3) X,d + 1 X, d + V,d + 1 (4) 1,, n; d 1,., D Where W s a weghng faor; C 1 s a ognon aeleraon faor; C s a soal aeleraon faor; rand 1 and rand are wo random numbers unformly dsrbued beween 0 and 1; V, d s he veloy of parle a eraon ; X, d s he dh dmenson poson of parle a eraon ; pbes, d s he dh dmenson of he own bes poson of parle unl eraon ; gbes d s he dh dmenson of he bes parle n he swarm a eraon. The me varyng weghng funon W usng [13] s gven by W W max (W max W mn ) Ier / Ier max (5) Where W max and W mn are nal and fnal wegh respevely, Ier s urren eraon number and Ier max s maxmum eraon number. The model usng (5) s alled

3 Developmen of a New Opmal Mullevel Thresholdng Usng Improved Parle Swarm Opmzaon Algorhm nera weghs approah (IWA). The nera wegh s employed o onrol he mpa of he prevous hsory of veloes on he urren veloy. Thus he parameer W regulaes he rade-off beween he global and he loal exploraon ables of he swarm. A large nera wegh falaes exploraon whle a small one ends o falae exploaon. 4. PROPOSED IPSO METHOD One of he smples dynam sysems evdenng hao behavor s he eraor alled he logs map, whose equaon s desrbed as follows: f µ.f -1.(1 f 1 ) (6) where µ s a onrol parameer and has he real value beween [0,4]. Despe he apparen smply of he equaon, he soluon exhbs a rh varey of behavors. The behavor of he sysem represened by equaon (6) s grealy hanged wh he varaon of µ. The value of µ deermnes wheher f sablzes a a onsan sze, osllaes beween a lmed sequene of szes, or behaves haoally n an unpredable paern. And also he behavor of he sysem s sensve o nal value of f [15]. Equaon (6) s deermns, dsplayng hao dynams when µ 4.0 and f 0 {0, 0.5, 0.5 0, 0.75,1.0}. In hs paper, he new wegh s equal o he mulplaon of equaon (5) by equaon (6) n order o mprove he global searhng apably as follows: Wnew W f (7) Whereas he onvenonal wegh dereases monoonously from W max o W mn, he proposed new wegh dereases and osllaes smulaneously for oal eraon as shown n Fg. 1. Sep 1: Ge he hreshold value as npu. Sep : Inalze parameers W max, W mn, C 1, C and Ier max. Sep 3: Generae nal populaon of N parles wh random posons and veloes. Sep 4: Calulae Fness: Evaluae he fness value of urren parle usng objeve funon (1) or (). Sep 5: Updae Personal Bes: Compare he fness value of eah parle wh s pbess. If he urren value s beer han pbes, hen se pbes value o he urren value. Sep 6: Updae Global Bes: Compare he fness value of eah parle wh gbes. If he urren value s beer han gbes, se gbes o he urren parle s value. Sep 7: Updae Chao Wegh: Calulae wegh Wnew +1 usng equaon (7). Sep 8: Updae Veloes: Calulae veloes V + 1 usng equaon (3). Sep 9: Updae Posons: Calulae posons X + 1 usng equaon (4). Sep 10: Reurn o sep (4) unl he urren eraon reahes he maxmum eraon number. Sep 11: Oupu he opmal soluon n he las eraon. 5. PERFORMANCE EVALUATION The performane of he proposed mehod s evaluaed by omparng s resuls wh he onvenonal PSO and GA mehods. Fgure 1: Comparson of Weghs 4.1. IPSO Algorhm The proposed IPSO algorhm no only mproves he sandard PSO algorhm bu also adds new sraegy n order o fnd he global soluon beer han PSO algorhm by applyng he hao sequenes for wegh parameer. The proposed algorhm an be summarzed as follows: Fgure : Lenna Image (51 51)

4 66 Inernaonal Journal of Elerons Engneerng Fgure 3: Pepper Image (51 51) Two well-nown mages (namely Lenna and pepper mages eah of sze 51 51) are aen as es mages. I s shown n he Fgs. and 3 respevely. Table 1 show he opmal hresholds obaned wh, 3, 4 and 5 respevely and orrespondng objeve funon values aaned usng IPSO, onvenonal PSO and GA mehods. I s observed ha he IPSO ouperforms well as ompared wh PSO and GA mehods. For a vsual nerpreaon of he segmenaon resuls, he segmened Lenna and pepper mages wh 3 and 5 are presened n Fg. 4 and 5 respevely. I an be easly seen ha he qualy of segmenaon s beer, n eah ase, when 5 s hosen. To quanavely judge he qualy of several hresholdng based segmenaon algorhms, he unformy measure s ulzed whh has also been exensvely ulzed n several leraures. Ths unformy measure s gven as Where, j R j Σ 0Σ () f µ j u 1 * * N *() f f R j f max number of hresholds jh segmened regon mn gray level of he pxel µ j mean gray level of pxels n jh regon N f max f mn oal number of hresholds n he gven mage maxmum gray level of pxels n he gven mage and mnmum gray level of pxels n he gven mage. The value of hs unformy measure, u, should be a posve fraon.e. should le beween 0 and 1. A hgher value of u ndaes ha here s beer unformy n he hresholded mage, depng beer qualy of hresholdng and ve versa. I an be also seen ha he proposed IPSO ould aheve sgnfanly beer segmenaon resuls as demonsraed by que hgher values of u n eah ase, ompared o oher mehods. Fgure 4: The Thresholded Images of Lenna (a) 3-levelhresholds, (b) 5-level hresholds. Fgure 5: The Thresholded Images of Pepper (a) 3- level Thresholds, (b) 5-level Thresholds.

5 Developmen of a New Opmal Mullevel Thresholdng Usng Improved Parle Swarm Opmzaon Algorhm Table1 Comparave Sudy of IPSO, PSO and GA mehods Images Opmal hresholds Objeve values Unformy measure IPSO PSO GA IPSO PSO GA IPSO PSO GA Lenna 98, , , ,13,179 79,15,176 90,131, ,110,153,186 74,114,149,186 75,105,143, ,10,136,170,198 69,104,137,169,197 74,103,133,166, Pepper 73,14 75,145 84, ,110,161 6,113,166 7,119, ,78,15,171 46,80,16,17 57,90,13, ,71,111,15,190 43,78,118,154,193 56,88,11,157, CONCLUSION In hs paper an opmal mullevel hresholdng usng mproved parle swarm opmzaon (IPSO) algorhm has been desrbed. The IPSO uses hao sequenes for wegh parameer o mprove he global searhng ably and esape from loal mnma. The performane of he proposed algorhm has been ompared wh onvenonal PSO and GA mehods. The expermenal resuls show ha he proposed sheme an aelerae he opmal hresholdng mehods n he mullevel hresholdng ase and he qualy of he hresholded mages s beer ha hose of properybased mullevel hresholdng mehods. REFERENCES [1] A. T. Aba, U. Bars and B. Sanur, The Performane Evaluaon of Thresholdng Algorhms for Opmal Charaer Reognon, IEEE Pro. Inerna. Conf. Doumen Analyss and Reognon, Ulm, Germany, pp , Augus [] D. Aleanu, D. Rs and A. Graser, Conen based Threshold Adapaon for Image Proessng n Indusral Applaon, Inerna. Conf. Conrol and Auomaon, Budapes, Hungary, pp , June 005. [3] C. Su, A. Amer, A Real-me Adapve Thresholdng for Vdeo Change Deeon, IEEE Inerna. Conf. Image Proessng, Alana, Georga, USA, pp , Oober 006. [4] S. Y. Chen, Y. W. Huang, B. Y. Hseh, S. Y. Ma, and L. G. Chen, Fas Vdeo Segmenaon Algorhm wh Shadow Canellaon, Global Moon Compensaon and Adapve Threshold Tehnques, IEEE Trans. Mulmeda, 6(5), pp , 004. [5] M. S. Ans, B. T. Maewh, Fully Auoma Segmenaon of he Bran n MRI, IEEE Trans. Med. Imagng, 17(1), pp , [6] N. R. Pal. S. K. Pal, A Revew on Image Segmenaon Tehnques, Paern Reognon, 6, Year 1993, pp [7] J. N. Kapur, P. K. Sahoo, A. K. C. Wong, A New Mehod for Gray-level ure Thresholdng usng he Enropy of he Hsogram, CompuerVson Graphs and Image Proessng, 9, Year 1985, pp [8] N. Osu, A Threshold Seleon Mehod from Gray-level Hsograms, IEEE Transaons on Sysems, Man, Cybernes SMC-9, Year 1979, pp [9] P-Y. Yn, A Fas Sheme for Opmal Thresholdng usng Gene Algorhms, Sgnal Proessng, 7, Year 1999, pp [10] L.K. Huang, M. J. Wang, Image Thresholdng by Mnmzng he Measure of Fuzzness, Paern Reognon, 8, Year 1995, pp [11] H. D. Cheng, J. L, Threshold Seleon based on Fuzzy -paron Enropy Approah, Paern Reognon, 31, Year1998, pp [1] J. Kler, J. Illngworh, Mnmum Error Thresholdng, Paern Reognon, 19, Year 1986, pp [13] R.C. Eberhar and J. Kennedy, Parle Swarm Opmzaon, IEEE In. Con. Neural Newors, 4, pp , Year [14] Y. Sh and R.C. Eberhar, A Modfed Parle Swarm Opmzer, IEEE In. Con. Evoluonary Compuaons, pp , Year [15] Y.Sh and R.C. Eberhar, Empral Sudy of Parle Swarm Opmzaon, IEEE In. Pro. Evoluonary Compuaons, 3, pp , Year [16] Lu Bo, Wang Lng, Jng T-Hu, Tang Fung, and Huang De-Xan, Improved Parle Swarm Opmzaon Combned wh Chaos Soluons, Chaos Soluons and Fraals, pp , Year 005. [17] Lu Bo, Wang Lng, Jng T-Hu, Tang Fung, and Huang De-Xan, Improved Parleswarm Opmzaon Combned wh Chaos Soluons, Chaos Soluons and Fraals, pp , Year 005.