Image Segmentation of Thermal Waving Inspection based on Particle Swarm Optimization Fuzzy Clustering Algorithm

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1 0.478/v Image Segmentaton of Thermal Wavng Inspecton based on Partcle Swarm Optmzaton Fuzzy Clusterng Algorthm Jn Guofeng, Zhang We, Yang Zhengwe, Huang Zhyong, Song Yuanja, Wang Dongdong, Tan Gan. 60 offce, X an Research Insttute of Hgh Technology, Hongqng Town, X an 7005, Chna, douhao66@6.com. Chna Aerodynamcs Research and Development Center, Manyang 6000, Chna The Fuzzy C-Mean clusterng (FCM) algorthm s an effectve mage segmentaton algorthm whch combnes the clusterng of non-supervsed and the dea of the blurry aggregate, t s wdely appled to mage segmentaton, but t has many problems, such as great amount of calculaton, beng senstve to ntal data values and nose n mages, and beng vulnerable to fall nto the shortcomng of local optmzaton. To conquer the problems of FCM, the algorthm of fuzzy clusterng based on Partcle Swarm Optmzaton (PSO) was proposed, ths artcle frst uses the PSO algorthm of a powerful global search capablty to optmze FCM centers, and then uses ths center to partton the mages, the speed of the mage segmentaton was boosted and the segmentaton accuracy was mproved. The results of the experments show that the PSO-FCM algorthm can effectvely avod the dsadvantage of FCM, boost the speed and get a better mage segmentaton result. Keywords: Image segmentaton, thermal wave nspecton, partcle swarm optmzaton, fuzzy C-Mean clusterng algorthm I. INTRODUCTION NFRARED THERMAL WAVE testng method s a nondestructve testng method that has developed rapdly n recent years. The nteracton of the varous heated exctatons and the materals are used for the nfrared thermal wave technque method to detect the unevenness or anomaly nsde the materals []. Compared to X-ray testng, ultrasonc testng and other tradtonal non-destructve testng methods, the nfrared thermal wave testng method has the followng advantages: hgh-speed, non-contact, safe, sngle-sde test, quanttatve detecton, and others. It has ganed great acceptance n wde applcaton areas, e.g., avaton, navgaton, power, automotve, constructon and other areas []-[0]. The mage sequences captured by thermal camera contan abundant defect nformaton, whch s used for recognzng the defects. However, the testng process s mpacted by a varety of factors of mages, ther narrow dynamc range, low-resoluton and hgh nose. So, the nfrared mage sequences have to be analyzed quanttatvely and qualtatvely to calculate defect szes and depths accurately. Image segmentaton s the basc problem of mage processng whch ams to partton mages nto meanngful regons and extract the target out of the complex background for the subsequent quanttatve dentfcaton []. Infrared thermal mage segmentaton s the process that separates regons of devant temperature from the mage. Ths segmentaton can be seen as a clusterng process for pxels that have dfferent characterstcs, as pxel gradent and ther pxel neghborhood characterstcs. Clusterng s an unsupervsed classfcaton method. The overall dstrbuton pattern of data and the nterrelatonshps among data can be found by ths approach, so t s a powerful ntellgent mage segmentaton method. FCM s a clusterng algorthm that s wdely used because of better results and hgher effcency. The dsadvantages of FCM are: t can easly be trapped to local mnma and t s senstve to ntal values and noses. If the ntal values are not selected sutably, the data may be msclassfed. To overcome shortages of the FCM, a fuzzy C-mean clusterng algorthm based on the partcle swarm optmzaton (PSO) s proposed n ths paper.. THEORY OF ALGORITHMS.. Partcle Swarm Optmzaton Algorthm Partcle swarm optmzaton (PSO) algorthm proposed by Kennedy and Eberhart n 995, s a technque of evoluton computaton. Ths swarm ntellgence s motvated by the search strategy of defense and huntng behavor of brds, fshes and other bologcal communtes. It has been wdely used n the functon optmzaton, neural network tranng, pattern recognton, mage processng and other engneerng felds. In D-dmensonal space, the evoluton equaton of the standard PSO algorthm s expressed as: ν = + + () + ( ) ωv d cr ( pd xd ) c d r( pgd xd ) x = x + v () + ( ) d d d Here, =,,,n; d=,,,d. ω s the nerta weght that usually decreases lnearly from 0.9 to 0.. The learnng factors c and c are non-negatve constants whch represent the weght of the partcle preferences, c represents the preference of ther own experence, c represents the preference of the group experence. Accordng to the experence, c and c are set to.05 n practce []. The random numbers r and r get the values between (0, ). The velocty vector v d [-v max, v max ], v max s a constant, set accordng to dfferent problems, a smaller value of v max wll slow down the convergence rate and effcency. Accordng to specfc ssues, the teraton termnaton condton s 96

2 generally chosen as the maxmum number of teratons, or t can be set as the partcle swarm best poston satsfyng the mnmum threshold scheduled... Fuzzy C-Mean Clusterng Algorthm Clusterng s an unsupervsed method of machne learnng whch does not have any pror understandng about the dstrbuton of the data. It s a process that assorts the objects nto groups (called clusters), so that the objects n the same clusters are more smlar (n some sense or another) to each other than to those n other clusters. FCM was advanced on the hard C-means (HCM) algorthm. Based on the least square prncple, the clusters of data feld were obtaned by applyng the teratve method to optmze the objectve functon. Basc prncple of the FCM that parttons the target data set X (wth n samples) nto classes c (where c n) s to fnd the membershp functon (u j ) c n and the center B=(v, v,, v c ) of all c classes to search for a mnmum of the gven objectve functon that s expressed n the form: = j= ( j ) (, j ) c n m J = u d x x (3) Here, m [, ) s the weght ndex, a constant that controls the degree of fuzzy clusterng results. d(x, x j ) s the Eucldean dstance of the j-th sample to the -th class. When c uj = = accordng to the Lagrange multpler method, the necessary condtons of the objectve functon takng the mnmum are expressed as: u = j c dj k = d kj m n m = n ( ) m k k ( ) k = uj j= v u x If the data set X, the number of clusterng categores c and the weght ndex m are known, the best classfcaton matrx and the cluster centers are expressed by the above two equatons. The effcency ndcator PBMF s chosen to evaluate the effect of the clusterng results, whch s the maxmum ndex of the optmal number of the clusters; the greater ts value, the better the clusterng results. It s defned as [3]: ( ) PBMF c E max v v = j, j c n c m uj xj x = j= (4) (5) (6) where E s a constant assocated wth the data sets; m s the ambguty; x j, v, u j represent a sngle sample, the center vector of a cluster and an element of the plottng matrx, respectvely..3. Prncple of the FCM based on PSO When FCM s appled to mage segmentaton, the gray hstogram of the mage s used to substtute the sample data to reduce computaton and to ncrease the speed level [4]- [5]. The objectve functon of the fast FCM based on the gray hstogram s defned as: L C m m j j j= 0= (, ) ( ) ( ) ( ) W U V = u d h j (7) where h(j) s the gray level hstogram of the obtaned mage, j denotes a level of the gray scale, j=0~l, L s the maxmum level. u j s the membershp of the j-th gray level n the -th class, d j s the dstance of the j-th gray level to the -th class, whch s defned by ( dj ) = j z, z s the gray value of the -th cluster center. When the FCM-PSO s appled to mage segmentaton, each pxel n the mage s evaluated by ftness functon, defned as: f ( x ) λ = (8) W m ( U, V) Here, λ s a constant, W m (U,V) s the sum of the total between-class dsperson number. The smaller the W m (U,V), the better effect of the cluster, the hgher ndvdual ftness. The mplemented steps of the algorthm are: Step : Intalze the partcle swarm parameters. Gven the fuzzy ndex m, the populaton sze n, the learnng factors c and c, the nerta weght ω max and ω mn, the maxmum number of teratons I max, the number of the classfcaton categores c. Then, select the ntal cluster center of the c sample ponts randomly, calculate the membershp matrx composed of a partcle from the cluster center, and ntalze the partcle velocty. Fnally, n partcles were produced after n tmes computaton. Step : Intalze the cluster parameters. Set the number of fuzzy ndex m, the ntal number of clusters c, the maxmum number of clusters c max, and the threshold e. Step 3: Calculate the degree of membershp and membershp matrx. Accordng to the basc steps of the clusterng algorthm, calculate the new cluster center and the correspondng membershp matrx by (4) and (5). The calculated results form a partcle. Step 4: Accordng to (8) evaluate the suffcency of the partcles, then track and record the extreme value of each ndvdual partcle and the global extreme of the partcle swarm. Update the poston and the velocty of the partcle usng () and (). Step 5: Recalculate the degree of membershp and membershp matrx. For the new partcle obtaned from the partcle swarm, calculate the membershp matrx of ts correspondng cluster center. 97

3 Step 6: Determne whether the teraton termnaton condtons meet the requrements. If the terated result s satsfed, calculate the valdty of the ndcators PBMF(c) by (6), then fnsh the algorthm, otherwse return to step 4. Step 7: If c<c max, then c=c+, go to step 3. Otherwse contnue. Step 8: Identfy the maxmum value of PBMF(c), correspondng to whch c s the optmal number of clusters, and the correspondng U and V are the optmal clusterng results. 3. EXPERIMENTS AND IMAGE CAPTURING The experments were performed on the pulsed heatng nfrared thermal wave non-destructve test system, produced by the Thermal Wave Imagng (TWI), Inc., USA. The testng system s shown n Fg.. Two lnear xenon flash lamps were assembled as the pulsed thermal exctaton devce, wth the maxmum power output of each flash beng 4.8 KJ. The type of the nfrared camera s Thermal CAM TM SC3000, whch s produced by the FLIR Company n Sweden, and the workng wave band of the thermal camera s 8~9 μm, the temperature senstvty at room temperature s 0.0 K, the magng camera for the 40 wde-angle lens, the testng area at a fxed dstance of 4 cm s 4 cm 3 cm. The specmens used n the experment are shown n Fg.. (a) s a steel shell specmen map contanng fve dfferent dameter flat-bottomed holes to smulate the debondng defect. (b) s a composte specmen, whch s made of two layers of composte materals suppressed, t contans three artfcal crcular defects of dfferent dameters. The surfaces of the expermental specmens are panted wth black lacquer because t can mprove the emssvty and absorptvty of the specmens [6]-[7]. When testng, the frequency of IR camera was set to 60 Hz, the capturng tme was set to 30 s. The orgnal thermal mage sequences of test surfaces of the two specmens ganed n the experments are shown n Fg.3 and Fg.4, respectvely, whch were captured by the camera and recorded by computer. Abundant defect nformaton s contaned n thermal mages. The areas of the surface temperature anomaly (hot spots) correspond to the defects n the specmen. From Fg.3, t s clearly seen that the defects appear frstly at tme 0.43s, the bgger the defect, the bgger the hot spot. Along wth the tme, the contrast of defects and other area s growng, reachng the maxmum at 4.7s. Then the contrast s droppng wth the hot spots becomng fant because of the lateral thermal dffuson. At last, the surface temperature dstrbuton becomes balanced and no defect nformaton can be seen n the mage. The smallest defect, however, s not vsble at all. Compared wth the testng for steel shell, we can see from Fg.4 that the frst tme the defect s observed s 9.s, and the tme for the maxmum temperature contrast s.4s. Ths shows that the testng for composte by the thermal wave testng method s better than for metal, because the heat conducton coeffcent of composte s smaller than metal, whch makes the nfrared camera capture more defect nformaton. Fg.. The pulsed heatng nfrared thermal wave non-destructve test system (a) The steel shell specmen (b) The composte specmen Fg.. Specmens of the experment 0.s 0.43s.5s 3.93s 4.7s 5.53s 6.58s Fg.3. Thermal mage sequences of steel shell 7.67s Fg.4. Thermal mage sequences of the composte materal 98

4 4. IMAGE PROCESSING The orgnal mages are nosy, dstorted and ther contrast s low. In order to avod the nfluence of the nose, the homomorphc flterng technque s used. The enhanced results are shown n Fg.5 and Fg.6. In order to evaluate the performance of the three algorthms, the correct segmentaton rate was ntroduced, whch s defned as [8]: correct pxels accuracy = 00% (9) all pxels The accuracy and the segmentaton tme of the three segmentaton algorthms are shown n Table. (a) Orgnal mage (b) Enhanced mage Fg.5. The enhancement mage of the steel shell (a) Orgnal mage (b) Enhanced mage Fg.6. The enhancement mage of the composte materal The threshold-based segmentaton method, FCM clusterng algorthm and the proposed segmentaton algorthm are appled to the enhanced thermal mages of the steel shell ( pxels) and the composte ( pxels). In the threshold segmentaton, the gray levels the threshold selected were 0 and 80. The parameters of the clusterng algorthm based on the PSO were set as: c=3, the populaton sze n= 40, c =c =, ω max =0.9, ω mn =0.4, m=, the maxmum number of teratons 500. The algorthm was mplemented n MATLAB7.0. The values of cluster centers were calculated accordng to the obtaned partcle swarm algorthm for mage segmentaton. The results are shown n Fg.7 and Fg QUANTITATIVE IDENTIFICATION OF THE DEFECTS Thermal mages obtaned n the detecton process provded abundant nformaton for analyss of the defects. Every mage reflected the temperature feld dstrbuton of nternal defects. The dentfcaton of the defects manly ncludes evaluaton of ther type, depth, sze and shape. After the process of enhancement and segmentaton, the external nose and nterference of the thermal wave mages were elmnated. For quanttatve evaluaton of mage segmentaton, the quanttatve dentfcaton of the defects was explored usng regonal processng. The obtaned results are shown n Fg.9. Table. Results of the three algorthms Algorthm the segmented mages accuracy tme/s threshold the steel shell 77.58% the composte 87.0% FCM the steel shell 87.95% 7.53 the composte 93.75% PSO & FCM the steel shell 95.53%.8406 the composte 97.86% (a) The mage of the steel shell (a) threshold (b) FCM (c) PSO & FCM Fg7. Segmentaton mages of the steel shell (b) The mage of the composte Fg.9. The area dsposal results of the segmented mages (a) threshold (b) FCM (c) PSO & FCM Fg.8. Segmentaton mages of the composte materal After the mage processng, the defects nformaton can be descrbed as follows:. The mvew functon of MATLAB has been used to determne locatons of the defects. For the mage of steel shell, centers of the defects are (38, 04) (0, 05), (63, 99) and (7, 98). For the composte materals, they are (47, 66), (0, ) and (64, 36). 99

5 . The defects were extracted separately by the functon bwselect of MATLAB, and then the areas of the defect (.e., pxel sze, n pxels) have been calculated by the functon bwarea. For the mage of steel shell, the pxel areas are 4.49, 86.43, and The pxel areas of the composte materals are , and The calculated area of the defects has been obtaned by the proportonal relatonshp (n mm ) expressed as: S S totle S = P totle S S ε = 00% S (0) () where S s the pxel area, S totle s the total area of the specmen, P totle s the total pxel number, S s the theoretcal area, ε s the absolute error. For the steel shell, the thermal mage s 490 lnes, the column s 85, so the total pxel number P totle = = 39650, and S totle = = mm. For composte mages, the mage s 490 lnes, the number of column s 460, so the total pxels P totle = = 5400, and S totle = = 6500 mm. All the dentfcaton results are lsted n Table and 3. From Table and 3, t can be seen that the detecton effect for the composte materals s much better than for the steel shell, and the greater the defect, the better the dentfed result. Table. Postons and superfcal characters of the steel shell Name Defect Defect Defect 3 Defect 4 Center poston (39.60, ) (0.69, ) (63.40, ) (4.940, ) S S ' S ε Table 3. Postons and superfcal characters of the composte materal specmen Name Defect Defect Defect 3) Center poston (47.377, ) (08.09, ) (64.975, 36 S S ' S ε CONCLUSIONS In order to quanttatvely recognze the defects of thermal wave non-destructve detecton, the fuzzy C-mean clusterng algorthm based on the partcle swarm optmzaton was appled to the thermal mage segmentaton. The threshold segmentaton method and the tradtonal Fuzzy C-Mean algorthm for mage segmentaton were appled to contrast wth the algorthm proposed n ths paper, usng the segmentaton accuracy rate. Results show that the speed of the proposed method s fve tmes greater than n the case of the tradtonal fuzzy C-means algorthm, and the algorthm proposed has the best correct segmentaton rate wthn the three compared methods. The algorthm proposed n ths paper s not senstve to nose or local mnmum. It yelds accurate mage segmentaton, and acceptable dentfcaton errors. The Fuzzy C-Mean clusterng algorthm based on the partcle swarm optmzaton can boost the speed and t can be effectvely appled to the thermal wave non-destructve detecton for mage segmentaton. ACKNOWLEDGMENTS We gratefully acknowledge the Natonal Natural Scence Foundaton of Chna (No , No ) and Natural Scence Basc Research Plan n Shanx Provnce of Chna (No.0JQ808) for support for ths project. REFERENCES [] Lu, B., Zhang, C.L., Feng, L.C. et al. (007). Edge detecton method on thermal wave mages for skncore dsbonds n carbon fber renforced honeycomb materal. Infrared and Laser Engneerng, 36 (), -3, 73. [] Maldague, X.P.V. (00). Introducton to NDT by actve nfrared thermography. Materals Evaluaton, 6, [3] Yang, X.L., Jang, T., Feng, L.C. (009). Thermographc testng for mpact damage of arplane composte. Nondestructve Testng, 3 (), 0-, 43. [4] Steven, M.S., Tasdq, A., Yu, L.H. (003). Thermographc nspecton of composte structures. SAMPE Journal, 39 (5), [5] Takahde, S., Shro, K. (00). Applcatons of pulse heatng thermography and lock-n thermography to quanttatve nondestructve evaluatons. Infrared Physcs & Technology, 43, -8. [6] Wang, X., Jn, W.P., Zhang, C.L. (004). Infrared thermography NDT methods and development. Nondestructve Testng, 6 (0), [7] Barrera, E., de Fretas, V.P. (007). Evaluaton of buldng materals usng nfrared thermography. Constructon and Buldng Materals,, 8-4. [8] Marnett, S., Vavlov, V. (00). IR thermographc detecton and characterzaton of hdden corroson n metals. Corroson Scence, 5, [9] Přbl, J., Zaťko, B., Frollo, I. et al. (009). Quantum magng X-ray CT systems based on GaAs radaton detectors usng perspectve magng reconstructon technques. Measurement Scence Revew, 9 (), 7-3. [0] Mkulka, J., Geschedtova, E., Bartusek, K. (0). Soft-tssues mage processng: Comparson of tradtonal segmentaton methods wth D actve contour methods. Measurement Scence Revew, (4),

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