2009-2010 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe

Cheung, CF

Hu, K

Jiang, XQ

Kong, LB

PolyU Institutional Repository

????:1001-2265(2009)09-0007-04????:2009-04-16　＊????:????????????????????(MEMS)???????????(50535030);???????????(G-YE95)????:??(1981—),? ,????? ,?????????????????? ,?????????????? ,???? ,????? ,(E-mail)hukai hust@163.com。微镜阵列的缺陷提取与识别＊胡凯 1, 2 ,张志辉 2 ,蒋向前 1, 3 ,孔令豹 2(1.华中科技大学 机械学院仪器系 ,武汉　430074;2.香港理工大学 工业工程系先进光学制造中心 ,香港;3.哈德斯菲尔德大学 ,英国哈德斯菲尔德　HD1 3DH)??:微镜阵列作为现在广泛应用的一种微米量级的微小型光学元件 ,缺陷识别是其加工制造的一个重要问题 。文章着重于微镜特征提取和微镜阵列的评定。使用 Gabor滤波和灰度共生矩阵提取缺陷特征 ,提出了基于支持向量机的多类分类缺陷识别方法.根据统计学原理 ,使用核函数将样本映射到高维空间进行训练.综合各种核函数的测试准确率 ,得到解决该问题的最佳核函数.通过比较不同的多类分类算法 ,提出了基于 DAGSVM的诊断模型。并通过不同的特征向量与和不同的分类器的比较 ,实验结果表明该方法识别率高 ,识别速度快 ,容错性好 ,而且能够正确识别有缺陷的微镜图像。???:微镜阵列;Gabor;滤波;支持向量机?????:TG156　　　?????:ADefectsRecognitionofMicrolensArrayUsingGaborFiltersandSupportedVectorMachineHUKai1, 2 , ZHANGZhi-hui2 , JIANGXiang-qian1, 3 , KONGLing-bao2(1.DepartmentofInstrumentation, SchoolofMechanicalScienceandEngineering, HuazhongUniversityofSci-enceandTechnology, Wuhan430074, China;2.AdvancedOpticsManufacturingCentre, DepartmentofIn-dustrialandSystemsEngineering, TheHongKongPolytechnicUniversity, HungHom, Kowloon, HongKong)Abstract:DefectsrecognitionisanimportantproblemwithapplicationtofabricationofMLA(MicrolensAr-ray).ThefocusofthispaperisontheproblemoffeatureextractionandclassificationfordefectsrecognitionofMLA.Specificaly, weproposeusingGaborfiltersforMLAfeatureextractionandSVM(SupportVectorMa-chine)fordefectsdetection.amulti-clasificationmethodbasedonsupportvectormachine(SVM)ispro-posed.Accordingtostatisticlearningtheory, weusekernelfunctionstomapthetrainingsamplesintoahighdimensionalspacefortraining.Combiningthetestingaccuracyofdiferentkernelfunctions, anoptimalkernelfunctionisobtainedtosolvethisproblem.Bycomparingdiferentmulti-calssificationstrategies, adiagnosismodelbasedonDAGSVM(directedacyclicgraphSVM)isconstructed.Extensiveexperimentationandcom-parisonsusingrealdata, diferentfeaturesanddiferentclasifiers(e.g., NeuralNetworksandSupportVectorMachine)demonstratethesuperiorityoftheproposedapproachwhichhasachievedanaverageaccuracy.Keywords:MLA;Gaborfilters;SVM0　???????????????????????? ,????????????????????????????????? 。?????????? ,??????? 、????? ,??????? 、???????? ,????????????????? ,????????? ,?????????????? ,????????????? ,??????·7·2009?? 9? ·????? ·??????????? ,?????????????????????? [ 1] 。????????????????????????????? ,??????????? ,??????????????????? 。???????????????? ,????????????????????????。????????????????? ,???????????????。???????????? , ?????????????????????????? ,???????????? , ?????????。????????????? 、?????? 、?????? 、????? Laws?????[ 2] 。???? , ??????? Gabor?????????????????????????? , ??????? 2??????????????。?????????????????????? ,?????????? ,????? 、??????????????????????? ,????????????????? 。BP???????????????? sigmoid????? ,???????????????????? 。?? ,???????????????????? ,??????????????????。?????? , ????????????? 、??????????。?? ,???????????????? ,??????????????????? ,????????????????? 、????? 、????? 、?????????? ,????????????????? 。??????????? (supportvectorma-chine, SVM)????????????????。SVM???????????????????? ,??????????????????? ,??????????????? ,????????? ,????????????????????。1　??????????????? WYKONT8000?????????? 24???? 512 ×512? 256??? 。????????? ,?????????? ,???????????????? 、????????????? ,????????。???????????????? 。1.1　????????????(graylevelco-occurrencematrix)???????????? , ?????????????????? ,??????????????????????????? ,??????? 、?? 、????????????? , ???????????????????[ 3] 。????????????????????????????????? ,?????:?? i? j??????????? θ??? ,??? d??? ,?? P(i, j, d, θ), ?? , θ?????:0°、45°、90°、135°,??? I(k, l)=i? I(m, n)=j?????????????:P(i, j, d, θ)=λ{[ (k, l), (m.n)] /k-m =d, l-n=d,I(k, l)=i, I(m, n)=j} (1)P(i, j, d, π/4)=λ{[ (k, l), (m.n)] /k-m=d, l-n=d,I(k, l)=i, I(m, n)=j} (2)P(i, j, d, π/2)=λ{[ (k, l), (m.n)] /k-m=d, l-n=d,I(k, l)=i, I(m, n)=j} (3)P(i, j, d, 3π/4)=λ{[ (k, l), (m.n)] /k-m=-d, l-n=-d, I(k, l)=i, I(m, n)=j} (4)?? , λ????????????? 。?? ,?????????? ,?P(i, j, d, θ)=P(j, i, d, θ) (5)???????????????? Haralick?????????????? 14??? , ??????????? 、??? 、?? 、??? 4???[ 2-4] 。? 1　Haralick? 4??????? 12 ∑ii.P s(i)?? ∑i(j2.P d(j))?? 12 ∑i(i-2μ)2.P s(i)-∑ij2.P d(j)??? ∑i∑j 11+i2P d(j)1.2　Gabor??????????????????????????????? “? ”,???????????????????? 。???????????????????????。???????????????? ,??????????? ,?????????????。?? ,?????? Gabor???????????·8··????? · ??????????????? [ 5] 。Gabor?????????????????? ,???????????????????? ,???????????????? 。???Gabor?? g(x, y)?????:g(x, y)= 12πσxσy＊exp-12 x2σ2x+ y2σ2y exp[ 2πjW x] (6)Gabor????:gm, n =a-mg( x,  y)a≥ 1 m, n∈ z (7) x=a-m(xcosθ+ysinθ) y=a-m(-xsinθ+ycosθ) (8)k???? , a-m?????。??????? Gabor????:Im, n(x, y)= i(x, y)＊gm, n(x, y) (9)?? i(x, y)?????? , Im, n(x, y)???????? , ＊???? ,  ＊ ???????。?? 6?? 4?? Θ ={0, π/4, π/2, 3π/4}, 2????? Ψ={0.5, 0.4}??????????? 。?? ,??? 48?(4?? ＊2???? ＊6??)Gabor???????? , ?? 48? Gabor?? ,?? 4? Haralick???? , ?? 52??? 。??? ,????? 2???????????? ,???????????????????。????????? 54??? 。2　??????????????? ,??????????。????????? ,? 2????????????? ,????????? 。???? , 2????????????????????。?? ,???????????? 2??????????? 。? 1　????2.1　BP?????????????????????? , ??????????????????????? , ???? ?? ?? (? ? )? ?? ?? ? BP(Back-Propagation)?? , ????????? BP??。BP??????????????????????? “?? ”, ???????????????????????? “?? ”????? , ??????????????????????? 。??? BP?????????? , ????? 2?? 。??????? , ??????? , ??????? 。??????????????? , ?????????????? , ???????????????? 。????:???????????????????? , ???????????????????????????? , ????????????????????????[ 6] 。2.2　???????????????????????? ,???????? 。??????? 1992 ～ 1995????? ,??????????? 。SVM???????????????????? ,???????? 2??????? 。? 2　???????????? ,??????????? 2??? , H???? , H1? H2?????????????????????????? , ?????????????(margin)。?????????????????? 2????? ,?????????。????? ,????? (x1 , y1), … , (xn, yn)∈Rdx{1, -1},???????????? ω·x+b=0??????? ,???????? 。??????? 2/‖ω‖ 2 , ?????????? ‖ω‖ 2??。Vapnik?? , ‖ ω‖ 2??????? VC????? ,???????????:R(ω, ξ)= 12ω· ω+c∑ni=1ξi (11)?????:y1[ ω· x+b] ≥ 1 -ξi, ξi≥ 0, i=1, 2, … , n?? , ξi???? ,?????????? ,??????? 。???????????? VC? ,????·9·2009?? 9? ·????? ·????? ,?????????? 。????????? ,????? 0 , VC??????。?????????? ,?????????? VC????? 。?? SVM??????????????? , ???????????????????????????? ,????? SVM???? ANN??? 。??????????????:???????????:??????????????? ,?????????????????? ,???????????? ?? , one-against-almethod, one-against-onemethod? DAGSVM?????。?? C.W.HsuandC.J.Lin[ 7-11]????????????? ,???????????????????????????? ,?????????;?????????? ,one-against-onemethod? DAGSVM?? ?? ?(trainingphase)????????? ,????? 2??????? 。one-against-one?? , ??????? K???? ,???????????? ,?????????? k?????????? , ?????? k(k-1)/2??????。???? ,????????????????? 。?????????????? ,???????????????。DAG???????????????? ,? k(k-1)/2??? SVM??? ,????????????????? , ??k(k-1)/2??? ,??????? ,????????????????????? ,????? k,???????????? SVM??? ,?????????? ,??????????????? ,??????????????????。? 3　????3　??????????? 54????????????????? 3?? 。???????? 30%, 60%,90%????? ,??????????。???????????????????????? ,?????????? “???”?? , “???”??? “???? ” ??????????????。SVM?DAGSVM?????? ANN??。? 2　??????????????????????? (%) ANN SVM(1vs1) DAGSVM30 75.0 81.3 91.760 81.3 81.3 91.790 75.0 100 100　　???????????? DAGSVM????????? ,????????????? , ??????????? (50%???????? ,?????? 3)。????? ,???? ,????????????? ,???????????????。? 3　??????????????? ANN SVM(1vs1) DAGSVM?? 100 100 100?? 83.3 91.7 100?? 83.3 91.7 91.74　????????????? ,???? Gabor????????????????????????????????????? ,???????? ,????????????????????????? ,???????????????? , ???????????? 。?? BP????? SVM????? ,????????????????????。????? SVM????????????? BP?????? , ???????????。????????? , ??????????????? , ?SVM?????????????。?? 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Defects recognition of microlens array using gabor filters and supported vector machine

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