A Novel Hybrid Bat Algorithm for the Multilevel Thresholding Medical Image Segmentation

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1 RESEARCH ARTICLE Copyrght 2015 Amercan Scentfc Publshers All rghts reserved Prnted n the Unted States of Amerca Journal of Medcal Imagng and Health Informatcs Vol. 5, 1 5, 2015 A Novel Hybrd Bat Algorthm for the Multlevel Thresholdng Medcal Image Segmentaton Yongquan Zhou 1 2, Langlang L 1, and Mngzh Ma 1 1 College of Informaton Scence and Engneerng, Guangx Unversty for Natonaltes, Nannng , Chna 2 Guangx Hgh School Key Laboratory of Complex System and Computatonal Intellgence, Nannng , Chna In ths paper, a novel hybrd bat algorthm usng Otsu s method for multlevel thresholdng medcal mage segmentaton optmzaton s proposed. We use the modfed random localzaton strategy to mprove the bats exploratory abltes and ncrease search effcency and convergence speed. The proposed algorthm s used to fnd the optmal thresholds by maxmzng Otsu s objectve functon, and ts performance was tested two medcal mages. The expermental results show that the proposed algorthm provdes better solutons and hgher computaton accuracy. Keywords: Bat Algorthm, Otsu s Method, Hybrd Bat Algorthm, Multlevel Thresholdng, Medcal Image Segmentaton. 1. INTRODUCTION Generally speakng, mage segmentaton dvdes the mage nto related sectons consstng of mage pxels wth related data feature values. The problem of multlevel thresholdng s regarded as an mportant area of research. Thresholdng technques can be classfed nto two categores: b-level and mult-level. B-level thresholdng means that the mage s segmented nto two classes: the object of the nterest and the background. Mult-level thresholdng means that there are multple threshold values that are selected to slt the mage. In ths paper, mult-level thresholdng s consdered. Among the global thresholdng technques, Otsu s method 1 s one of the best selecton methods to maxmze the between class varances of the hstogram. It s smple and effectve for b-level thresholdng problems. However, when Otsu s method s extended to multlevel thresholdng problems, ts effcency becomes very low; computatonal complexty ncreases exponentally due to ts exhaustve search to optmze the objectve functon. To mprove mage segmentaton accuracy, many methods have been proposed to optmze multlevel thresholdng problems, ncludng conventonal methods and ntellgent methods. In partcular, swarm ntellgent algorthms such as dfferental evoluton (DE), 2 partcle swarm optmzaton (PSO), 3 ant colony optmzaton (ACO), 4 bacteral foragng (BF), 5 artfcal bee colones (ABC), 6 Cuckoo Search (CS), Frefly Algorthm, 7 and artfcal mmune system optmzaton 8 have been used n multlevel thresholdng. Frst presented by Yang n 2010, 9 the bat algorthm (BA) s a metaheurstc search algorthm that was nspred Author to whom correspondence should be addressed. by the echolocaton behavor of the bats wth varyng pulse rates of emsson and loudness. The BA s easy to mplement, so t has devleoped much n recent years. Many hybrd approaches have been proposed TheBAsalsousedtosolvemanyreal-world optmzaton problems In ths paper, a novel hybrd bat algorthm usng Otsu s method for multlevel thresholdng medcal mage segmentaton optmzaton s proposed. We use the modfed random localzaton (MRL) 19 strategy, whch allows bats to cover the whole search space, mprovng the exploratory ablty of the bats and ncreasng search effcency and convergence speed. The proposed algorthm s used to fnd the optmal thresholds by maxmzng Otsu s objectve functon, and ts performance has been tested by medcal mage segmentaton. The expermental results show that the proposed algorthm provdes better solutons and hgher computaton accuracy. 2. OTSU s METHOD Otsu s a basc mage segmentaton method that s wdely popular wth researchers. Assumng that the gven mage s presented n L gray levels 0 1 L 1, the number of pxels at level s denoted by n, and the total number of pxels s denoted by N = n 1 + n 2 + +n L. The probablty of gray level s denoted by: p = n N p 0 L 1 p = 1 (1) In the b-level thresholdng method, the pxels of the mage are dvded nto two classes: C 1 wth gray levels 0 1 t and C 2 =0 J. Med. Imagng Health Inf. Vol. 5, No. 8, /2015/5/001/005 do: /jmh

2 RESEARCH ARTICLE J. Med. Imagng Health Inf. 5, 1 5, 2015 wth gray levels t + 1 L 1 by the threshold t. The gray level probablty dstrbutons for the two classes are gven as: w 1 = t p and w 2 = =0 The means of C 1 and C 2 are: u 1 = t =0 p w 1 u 1 = L 1 =t+1 The total mean of gray levels s denoted by u T : The class varances are: 2 1 = t =0 u 1 2 p w = The wthn-class varance s: The between-class varance s: p (2) L 1 =t+1 p w 2 (3) u T = w 1 u 1 + w 2 u 2 (4) L 1 =t+1 u 2 2 p w 2 (5) N 2 w = w k 2 k (6) k=1 2 B = w 1 u 1 u T 2 + w 2 u 2 u T 2 (7) The total varance for grey levels s: 2 T = 2 w + 2 B (8) Otsu s method chooses the optmal threshold t by maxmzng the between-class varance, whch s equvalent to mnmzng the wthn-class varance, snce the total varance (the sum of the wthn-class varance and the between-class varance) s constant for dfferent parttons. The objectve functon obtaned by Otsu s method s: t = arg max 1 t L 2 B t = arg mn 1 t L 2 B t (9) 3. BASIC BAT ALGORITHM 3.1. The Velocty and Poston Updatng of the Bat Assume that the bat populaton s random, and the dmenson of search space s set at n, the poston of the bat at tme t s x t, and the velocty s v t. Therefore, the poston xt+1 and velocty at tme t + 1 are updated by the followng formula: f t = f mn + f max f mn (10) = v t + xt best f t (11) x t+1 = x t + vt+1 (12) where f represents the pulse frequency emtted by bat at the current moment. f max and f mn represent the maxmum and mnmum values of pulse frequency, respectvely. s a random number n 0 1, andbest represents the current global optmal values. We select a bat from the bat populaton randomly and update the correspondng poston of the bat accordng to formula (13). Ths random walk can be understood as a process of local search strategy, whch produces a new soluton by the chosen soluton. x new = x old + A t (13) where, x old represents a random soluton selected from the current optmal soluton, A t s the loudness, s a random vector, and ts arrays are random values n Loudness and Pulse Emsson Usually, at the begnnng of the search, loudness s strong and pulse emsson s small. When a bat has found ts prey, loudness decreases whle pulse emsson gradually ncreases. Loudness A and pulse emsson r are updated accordng to formulas (14) and (15): r t+1 = r 0 1 exp t (14) A t+1 = A t (15) where both 0 < <1and >0 are constants. A = 0 means that the bat has just found ts prey and temporarly stops emttng any sound. It s not hard to fnd optmzaton values that when t, we can get A t 0andr t = r Basc Bat Algorthm The steps of the basc bat algorthm as follow: 9 Step 1: Intalze the basc parameters: the attenuaton coeffcent of loudness, the ncreasng coeffcent of pulse emsson, the maxmum loudness A 0 and mnmum pulse emsson r 0,andthe maxmum number of teratons Maxgen; Step 2: Defne pulse frequency f f mn f max ; Step 3: Intalze the bat populaton x and v; Step 4: Enter the man loop. If rand <r, update the velocty and current poston of the bat accordng to formulas (14) and (15). Otherwse, make a random dsturbance for the poston of the bat,andgotostep5; Step 5: If rand <A and F x <F x, accept the new solutons, and fly to the new poston; Step 6: If F x <F mn, replace the best bat, and adjust the loudness and pulse emsson accordng to formulas (10) and (11); Step 7: Evaluate the bat populaton, and fnd out the best bat and ts poston; Step 8: If the termnaton condton s met (.e., reached the maxmum number of teratons or satsfed the search accuracy), Table I. Objectve functon values and optmal threshold values obtaned by Otsu method. PSO + Otsu BA + Otsu HMRLBA + Otsu Images Methods Mean Std Mean Std Mean Std Lung 1-level e e e e e e 12 2-level e e e e e e 12 3-level e e e e e e 01 Plls 1-level e e e e e e 13 2-level e e e e e e 12 3-level e e e e e e

3 J. Med. Imagng Health Inf. 5, 1 5, 2015 RESEARCH ARTICLE Table II. The objectve values obtaned by dfferent methods. 1t 2t 3t Images Threshold Value Threshold Value Threshold Value Lung e+03 47, e+03 39, e+03 Plls e , e , e+06 go to step 9; otherwse, go to step 4, and execute the next search. Step 9: Output the best ftness values and global optmal soluton. Where rand s a unform dstrbuton n MODIFIED RANDOM LOCALIZATION BAT ALGORITHM (MRLBA) In ths secton, a modfed verson of the BA based on the Modfed Random Localzaton (MRL) strategy 19 s proposed to mprove the performance of the BA Modfed Random Localzaton (MRL) Strategy Frstly, accordng to the ftness value, the ntal populatons are sorted, and dvded t nto three regons: R-I, R-II, and R-III. Where, R-I represents the regon havng the elte ndvduals, R-II represents the set of medan ndvduals, and R-III represents the remanng ndvduals. Select from three ndvduals R-I, R-II, and R-III, respectvely. The MRL strategy can be cover the maxmum of the search space and the exploratory ablty s mproved. The sze of parameters are taken as popsze %, popsze %, popsze %, respectvely Hybrd Bat Algorthm wth Modfed Random Localzaton and Otsu s Method (HMRLBA) The HMRLBA algorthm generates a randomly dstrbuted ntal populaton of popsze solutons (bats) n the range 0 L 1. The ftness values of all solutons are evaluated by Otsu s method, where the new solutons are generated by adjustng the vector of frequences. = v t + xt xt r1 f t + x t r2 xt r3 (16) x t+1 = x t + vt+1 (17) = Gmax gen Gmax 2 (18) Pseudo code of HMRLBA 1: BEGIN 2: Input the mage 3: Intalze the bat populaton 4: Evaluate ftness usng Otsu s method 5: Sort f X 6: Get the best soluton 7: gen 1 8: Whle gen <= G max 9: For = 1topopsze 10: /*Modfed Random Localzaton (MRL) strategy*/ 11: Dvde the search space nto three regons, R-I, R-II, and R-III, respectvely 12: Select r 1, r 2,andr 3 13: r 1 = nt rand 14: r 2 = nt + rand 15: r 3 = nt + rand 16: Update veloctes and locatons/solutons [formulas (16) to (17)] 17: If rand >r, then 18: Generate a local soluton around the best soluton 19: End If 20: Generate a new soluton randomly 21: If rand <p m, then 22: Modfy the real and magnary part by DE/best/2/bn 23: End f 24: Calculate ftness f X 25: Evaluate the ftness usng Otsu s method 26: If rand <A and f X <f X, then 27: Accept the new solutons 28: Reduce A and ncrease r 29: End f 30: Get the best soluton 31: gen gen : End Whle 33: Memorze the best soluton acheved 34: END Table III. Computaton tme obtaned by Otsu and Otsu embedded wth PSO, BA, and HMRLBA for three thresholds. Three thresholds Images Methods Mn Max Mean Std Lung Otsu Otsu + PSO Otsu + BA Otsu + HMRLBA Plls Otsu Otsu + PSO Otsu + BA Otsu + HMRLBA

4 RESEARCH ARTICLE J. Med. Imagng Health Inf. 5, 1 5, 2015 (a) (b) Fg. 1. Images thresholded obtaned by the Otsu-HMRLBA method: Represents 3-level thresholdng. 5. SIMULATION RESULTS In ths paper, all the algorthms were mplemented n Matlab R2012 (a). The test envronment was set up on a computer wth AMD Athlon (tm) II X4 640 Processor, 3.00 GHz, 3GB RAM, runnng on Wndows Parameter Settng The parameter settng for each algorthm n the comparson s descrbed as follows: the pulse frequency range s f 1 1,the maxmum loudness s A 0 = 0 9, the mnmum pulse emsson s r 0 = 0 1, the attenuaton coeffcent of loudness s = 0 95, and the ncreasng coeffcent of pulse emsson s = 0 9. In PSO, we use the lnear decreasng nerta weght max = 0 9and mn = 0 4, and the learnng factor s c 1 = c 2 = 2 0. In HMRLBA, the value of,, and are fxed at 20, 40, and 40, respectvely. The populaton sze of all algorthms s popsze = Expermental Results In ths secton, two well-known test medcal mages, namely Lung ( and Plls ( wth 256 grey levels, are taken as test nstances (Table I). The results are compared wth two other hybrd algorthms: Otsu s method, PSO + Otsu; and the BA + Otsu method. To test results are correctly and vablty of the proposed algorthm, the aforementoned technque for multlevel mage thresholdng n medcal mage segmentaton has been tested. Fg. 3. ANOVA tests of the computaton tme for Plls Soluton Qualty In ths secton, we set the G max = 100. The proposed algorthm s compared wth the PSO and BA algorthms. Table II shows the correspondng objectve functon values obtaned out of 100 trals by Otsu and Otsu embedded wth the PSO, BA, and HMRLBA methods. As seen n Table II, the proposed HMRLBA algorthm always provdes better results than the PSO and BA algorthms. For the four test medcal mages, as seen n Table III, the results obtaned by HMRLBA for the eghth mage s somewhat poor, but t s stll better than the results obtaned by Otsu method s and the PSO and BA algorthms Computaton Effcency In order to compare the computaton effcency of the PSO, BA, and HMRLBA algorthms for multlevel thresholdng, the value of the best ftness F T correspondng to the best threshold soluton T s used as the comparatve crteron. The run of each algorthm wthn dfferent threads was stopped when: F T F opt = 10 9,whereF opt s the optmal value of the objectve functon, and s a threshold value that fxes the accuracy of the measurement. In ths secton, the computed tme taken by each algorthm to acheve the desred accuracy. In ths way, the stoppng condton for all algorthms s based on the ftness functon value and s not on the number of teratons. The results of the segmented medcal mages are shown n Fgure 1. The expermental results shown n Fgures 2 and 3 are the ANOVA tests of the computaton tme for the two medcal mages. These tests show that the proposed HMRLBA algorthm s also the most robust method, and ts superorty s even more obvous. Therefore, HMRLBA s an effectve and feasble method for multlevel thresholdng medcal mages segmentaton. Fg ANOVA tests of the computaton tme for lung. 6. CONCLUSIONS Ths paper, a novel HMRLBA algorthm s proposed for multlevel thresholdng medcal mage segmentaton problems. The modfed random localzaton strategy enables the bats to cover the maxmum of the search space, mprovng the bats exploratory abltes. To verfy the effcency and effectveness of

5 J. Med. Imagng Health Inf. 5, 1 5, 2015 RESEARCH ARTICLE the proposed HMRLBA algorthm, the proposed algorthm was tested usng medcal mages. The results obtaned by ths method are compared wth those obtaned by the Otsu, PSO, and BA methods, and the HMRLBA algorthm delvered better solutons and hgher computaton accuracy. Acknowledgments: Ths work s supported by Natonal Scence Foundaton of Chna under Grant Nos and References and Notes 1. N. Otsu, A threshold selecton method from graylevel hstograms. IEEE Trans. Systems, Man and Cybernetcs 9, 62 (1979). 2. E. Cuevas, D. Zaldívar, and M. Pérez-Csneros, A novel mult-threshold segmentaton approach based on dfferental evoluton optmzaton. Expert Systems wth Applcatons 37, 5265 (2010). 3. V. Osuna-Encso, E. Cuevas, and H. Sossa, A comparson of nature nspred algorthms for mult-threshold mage segmentaton. Expert Systems wth Applcatons 40, 1213 (2013). 4. Y. Zhwe, Z. Zhaobao, Y. Xn, and N. Xaogang, Automatc threshold selecton based on ant colony optmzaton algorthm, Proceedngs of the Internatonal Conference on Neural Networks and Bran (2006), pp P. D. Sathya and R. Kayalvzh, Optmal multlevel thresholdng usng bacteral foragng algorthm. Expert Systems wth Applcatons 38, (2011). 6. E. Cuevas, F. Sencón, D. Zaldvar, et al., A mult-threshold segmentaton approach based on artfcal bee colony optmzaton. Appl. Intell. 37, 321 (2012). 7. I. Brajevc and M. Tuba, Cuckoo search and frefly algorthm appled to multlevel mage thresholdng. Studes n Computatonal Intellgence 115, 516 (2014). 8. E. Cuevas, V. Osuna-Encso, D. Zaldívar, et al., A novel multthreshold segmentaton approach based on artfcal mmune system optmzaton. Advances n Computatonal Intellgence 116, 309 (2009). 9. X. S. Yang, A new metaheurstc bat-nspred algorthm, Nature Inspred Cooperatve Strateges for Optmzaton (NICSO 2010) (2010), pp X. S. Yang, Bat algorthm for mult-objectve optmzaton. Int. J. Bo-Inspred Comput. 3, 267 (2011). 11. X. He, W. Dng, and X.-S. Yang, Bat algorthm based on smulated annealng and gaussan perturbatons. Neural Comput. Appl. (publshed onlne) (2013). 12. J. Xe, Y. Zhou, and H. Chen, A novel bat algorthm based on dfferental operator and Lévy flghts trajectory. Computatonal Intellgence and Neuroscence 2013, (2013). 13. G. G. Wang and L. H Guo, A novel hybrd bat algorthm wth harmony search for global numercal optmzaton. Journal of Appled Mathematcs 2013, (2013). 14. G. G. Wang, L. H. Guo, H. Duan, L. Lu, and H. Q. Wang, A bat algorthm wth mutaton for UCAV path plannng. The Scentfc World Journal 2012, (2012). 15. O. Hasançeb, T. Teke, and O. Pekcan, A bat-nspred algorthm for structural optmzaton. Computers and Structures 128, 77 (2013). 16. O. Hasançeb and S. Carbas, Bat nspred algorthm for dscrete sze optmzaton of steel frames. Advances n Engneerng Software 67, 173 (2014). 17. J. Xe, Y. Zhou, and H. Zheng, A hybrd metaheurstc for multple runways arcraft landng problem based on bat algorthm. Journal of Appled Mathematcs 2013, (2013). 18. Y. Zhou, J. Xe, and H. Zheng, A hybrd bat algorthm wth path relnkng for capactated vehcle routng problem. Mathematcal Problems n Engneerng 2013, (2013). 19. Sushl Kumar, Pravesh Kumar, and Tarun Kumar Sharma, B-level thresholdng usng PSO, artfcal bee colonyand MRLDE embedded wth Otsu s method. Memetc Comp. 5, 323 (2013). Receved: 7 March Revsed/Accepted: 3 June