翻譯以.原文和在同一文件中前

針對有光澤表面三維微觀測量的基于條紋邊界的高精度高穩(wěn)定性結(jié)構(gòu)光方法ZhanSong,RonaldChung,SeniorMember,IEEE,andXiao-Ting：關(guān)鍵字：邊緣檢測，有光澤表面，結(jié)構(gòu)光系統(tǒng)，三維重建緒(CMMs)，timeofflightsystems[3]，stereovision[4]，shapefromshading[5]，laserscanning6]structuredlightsystemsSLSs)等幾種方法。每種方法都有各CMMs相比，基于光學(xué)的方法具有非接觸、快速（3-5微米，并且表面分布不均勻）將會對最終測量結(jié)果帶來明顯的物理特性，操作速度是受限的。測量精度也會受到激光散斑的影響[14]。SLSs包含KonicaMinoltaVIVID9iFAROLaserScanArm。另外也有專門針對微米級精30mm300Hz的頻率下測量到被激光束照亮的目標(biāo)點(diǎn)0.01mm。在文獻(xiàn)[16]中，研究了9%的誤差百分率。除了激光線，用投影設(shè)備照射出光條紋也可以用在[12],[18]。在空間編碼方案中，一個圖案元素的代號是用元素附近圖案的值SLSs可以得到更大的數(shù)據(jù)密度張二進(jìn)制條紋的序列來編碼這個場景。這樣，域中的場景會被分割成2n個子區(qū)域，像素的中心或者碼圖案的邊緣[24]通常會被編碼。為了實(shí)現(xiàn)更高的測量精度，圖1中的一些方法比如相位移動[9]-[11],[25],[26]，和算法被提出[28][29]。在實(shí)際應(yīng)用中，為了提高展開過程的穩(wěn)定性，通常會使用一系列的碼。通過結(jié)合局部相位值和全局碼值，每個圖像點(diǎn)可以獲得一個150mm的球體的實(shí)驗(yàn)中，統(tǒng)計了0.05mm的平均誤差[25]。在文獻(xiàn)[26]中，提出用正弦位移的方法來對倒裝焊接凸起進(jìn)行三維測量。在對一個標(biāo)準(zhǔn)的1mm塊規(guī)的測量中，得到了2微米的平均精度。不過，受位移方法中[27]，正弦周期圖案被并行線圖案所代替，如圖1（b）所示。通過把直線圖案分別在x和y方向平移6次，可以獲得x方向的6和y方向的6張圖。由于直線圖案也是周期性的，它有其固有的歧義，但是碼會被引入來減少歧義性。在一個測量平面度的實(shí)驗(yàn)中，報告記錄了測量200x200mm的平面區(qū)域時具有0.028mm的標(biāo)準(zhǔn)偏差。在文獻(xiàn)[30]中，一個和主動視覺系統(tǒng)被影結(jié)構(gòu)光的主動視覺用來三維重建。在一次使用11.65x7.35cm矩形板誤差均在1mm以內(nèi)。然是一個。由于反射，圖像數(shù)據(jù)中被投影圖案[9]-[11],[25],[26]的正弦結(jié)構(gòu)了消除帶狀圖案的周期性誤差，傳統(tǒng)碼圖案被引入。為了更加確切的檢測帶基于條紋邊界的編碼策略P=G+{G∈{0,1,2,…,(2???S∈{0,1,2,…,(m?

其中，S是條紋邊界產(chǎn)生的局部編碼，G是全局碼編碼，P是最終具有唯圖2.碼結(jié)合條紋圖案平移的編碼策略。上：一系列碼圖案（其中n=9）用來構(gòu)造亞像素精度條紋邊界檢測受到光學(xué)限制（調(diào)制傳遞參數(shù)，景深，等等，投影出的條紋邊界在獲3（a反射而增加。這使得fpfn的交叉線無法辨別。這樣直接使用零叉邊界????=????? fd+和fd-的零叉位置分別用 精度條紋邊界位置可以用如下公式獲得：xedge=(x{?2fD+=0}+x{?2fD?=0}) 系統(tǒng)標(biāo)定和三位深度計算圖4.相機(jī)、投影儀和世界坐標(biāo)系之間的幾何關(guān)系。幾何關(guān)系標(biāo)定之后，表面任意點(diǎn)P的深度值都可以通過三角算法從相機(jī)和投影儀中的兩個對應(yīng)點(diǎn)和計算出來。CP表示這是相機(jī)或者投影儀的測量參數(shù)，mM表示這是特定 集體表示成3x3的矩陣Ac或Ap，其 表示傳感器陣列中u軸和v軸方向的比例因子 表傳感器軸的傾斜度，u0v0表示傳感器平面的原點(diǎn)[32]其中R和T分別表示相機(jī)和投影儀坐標(biāo)系之間的旋轉(zhuǎn)和平移矩陣相機(jī)和投影儀分別有6個外參數(shù)（ 集體表示成4x4的矩陣在標(biāo)定過程中，如圖5（a）所示的標(biāo)定板被用來標(biāo)定相機(jī)。打印出的圖案128255，并且該圖案構(gòu)成了標(biāo)定板在標(biāo)定過程中代替對象表面。 夠被標(biāo)定出來。關(guān)于標(biāo)定的細(xì)節(jié)可以在文獻(xiàn)[33]中找到。255標(biāo)定過程可以計算出相對于同一世界坐標(biāo)系的內(nèi)參數(shù)Ac和Ap，相機(jī)和投影儀的畸變參數(shù)，以及他們的外參數(shù)Rc，Tc，Rp，Tp。得到Rc，Tc，Rp，Tp之后，相機(jī)和投影儀之間的變換矩陣E可以通過公式（6）得到。假設(shè)相機(jī)圖像平面上提取出的條紋邊界點(diǎn)（這里 示m的投影和投影儀圖案平面上提取出的的條紋邊界點(diǎn)，與同一個場景點(diǎn)相關(guān)聯(lián)。假設(shè)二維位置通過x維度編碼。我們可以通過匹配編碼聯(lián)的場景點(diǎn)的深度zc就能通過傳統(tǒng)的三角測量算法[8]得到，如下所示：圖實(shí)驗(yàn)系統(tǒng)配置了一個現(xiàn)成的微型投影儀（3M硅液晶顯示，分辨率30ft/s-30°的夾角。雖然大的夾角可以提高測量精度，但是也會帶來的閉塞和散序用來進(jìn)行三維計算。在標(biāo)準(zhǔn)PC平臺（Core2Duo3.3GHz，4G內(nèi)存）上它測量精度評估如圖7（a）所示，在迎面方向?qū)?zhǔn)投影儀。該平面向著投影儀平移15次，每次0.1mm。每次移動之后，用該系統(tǒng)重建這個平面?？偣灿?6個平面被重建。面相對于投影儀坐標(biāo)系的方向是[0.027,0.055,0.998]（單位法向量，也就是幾乎7（b）中。圖有光澤硬幣的三維重建9（a（b）..對比與結(jié)論（x,y強(qiáng)度值：I1，I2，I3，I4。相位值可以按照如下方式求解：。投影線的峰值中心由以為信號的卷積圖像發(fā)生變化的位置進(jìn)行線性插值得到[27]。采用相同的碼策略來消除正弦圖案和直線圖案中的周期性歧義。用第三部分C中介紹的相同過程。圖14展示了一個球形網(wǎng)格陣列樣品的實(shí)驗(yàn)。BGA上的凸起被相移法、直線平移法和本文方法三維重建。重建結(jié)果分別在圖14（b）-（d。12.傳統(tǒng)的相和（f）是由形態(tài)、有光澤表面的視覺測量仍然遺留著一個有性的問題。有光澤表面的測量精度微小厚度和不均勻。為了定量地評估這個參考結(jié)果和原本有光澤表面（圖11所示）Geomagic如圖14所示，一個凸起高度0.4mm的標(biāo)準(zhǔn)BGA樣品被重建。BGA上0.1mm14（d）所示的用本文所提方見，得到了所有凸起的平均高度為0.396mm，標(biāo)準(zhǔn)偏差只有0.012mm。結(jié)論及將來的工作澤的硬幣、金屬工件和BGA凸起，證明了該系統(tǒng)強(qiáng)大的穩(wěn)定性和高測量精度。域由于遮擋問題不能被和重建。一個額外的相機(jī)安裝在投影儀的另一端可以當(dāng)前系統(tǒng)需要3秒來完成一次完整掃描。將來，一種具有更快響應(yīng)時間的微型投 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m n xPPPX;xCPm n xPmxCnmn個相機(jī)中的像。PPm

n n

PI0mI P m 式中，αm（αm≥0）是相應(yīng)模式的反射率相機(jī)觀測約束的可能情況當(dāng)只考慮相機(jī)觀測約束時，三維重建問題是一個非常典型的多視點(diǎn)MVS的最大問題之一，特征稀少表面。另一方面，當(dāng)深度相機(jī)的數(shù)量很小的時候（例如23個深度相機(jī)）MVS可能仍然會由于自我和相互遮擋導(dǎo)致信在我們的實(shí)現(xiàn)中，我們計算了相關(guān)區(qū)塊之間的均值移除交叉關(guān)聯(lián)（MRCCX，我們用公式（1）取，并表示為ICn。MRCC是通過如下公式計算得出： ICICiICjICj ,

Cj

ICi

CC Iij其中，ICIC分別為相機(jī)Ci和Cj相應(yīng)區(qū)塊的亮度平均值。我們?nèi)〔煌鄼C(jī)對之間MRCC的最大值作為整個系統(tǒng)的相機(jī)觀測約束可能情況：CC IijLmaxMRCCIC,IC i j MRCCI0，用來計算投影儀-

1 2 1

Cj

投影儀-相機(jī)約束的可能2投影儀-相機(jī)約束需要地復(fù)雜性探索，因?yàn)楣剑?）中的線性權(quán)重αm是未知的。實(shí)際上，αm的取值至少跟表面點(diǎn)到每個投影儀之間的距離，表面取2m?margminmmIPmIm

投影儀-I0MRCC ,

L1LL 具體實(shí)現(xiàn)是一個非常具有性的問題。另一方面，雖然多個深度相機(jī)會由于隨1（c4桌子或者桶，用流行的射線追蹤軟件POV-Ray2[11]渲染。每一個場景中，兩個深圖（a（顯示了每個相機(jī)獨(dú)立地通過基于互相關(guān)的方法進(jìn)行深MCC.（MCC（dMS，在平面掃描期間為每條光線將公式（）最大化，來重建中心視點(diǎn)的深度圖。在5（e）顯示了該方法（（PSNR出的方法執(zhí)行效果遠(yuǎn)好于直接深度合并或者M(jìn)VS。56Batlle,J.,Mouaddib,E.andSalvi,J.,“Recentprogressincodedstructuredlightasatechniquetosolvethecorrespondenceproblem:asurvey,”PatternRecognition,Vol.31,No.7,pp.963—982,1998.Cai,Q.,Gallup,D.,Zhang,C.,andZhang,Z.,“3ddeformablefacetrackingwithacommoditydepthcamera,”inECCV,2010.Crabb,R.,Tracey,C.,Puranik,A.,andDavis,J.,“Real-timefore-groundsegmentationviarangeandcolorimaging,”inCVPRWorkshoponToF-CamerabasedComputerVision,2008.Cui,Y.,Schuon,S.,Chan,D.,Thrun,S.,andTheobalt,C.,“3Dshapescanningwithatime-of-flightcamera,”inCVPR,2010.Faugeras,O.et.al,“Real-timecorrelation-basedstereo:algorithm,implementationsandapplications,”INRIAtechnicalreport#2013,1993.Kang,Y.-S.andHo,Y.-S.,“High-qualitymulti-viewdepthgenerationusingmultiplecoloranddepthcameras,”ICME2010.Kolmogorov,V.andZabih,R.,“Multi-cameraSceneReconstructionviaGraphCuts,ECCVKutulakos,K.andSeitz,S.,“Atheoryofshapebyspacecarving,”IJCV,Vol.38,No.3,pp.199—218,2000., Ray,J.Zhu,L.Wang,R.Yang,andJ.Davis,“Fusionoftime-offlightdepthandstereoforhighaccuracydepthmaps,”CVPR,2008.QingxiongYang,Kar-HanTan,Culbertson,B.,andApostolopoulos,J.,"Fusionofactiveandpassivesensorsforfast3Dcapture,"MultimediaSignalProcessing(MMSP),2010.Sun,J.,Zheng,N.-N.andShum,H.-Y.,“StereoMatchingUsingBeliefPropagation,”IEEETrans.OnPAMI,Vol.25,No.7,pp.787-800,2003.IEEETRANSACTIONSONINDUSTRIALELECTRONICS,VOL.60,NO.3,MARCH AnAccurateandRobustStrip-Edge-BasedStructuredLightMeansforShinySurfaceMicromeasurementin3-DatDigitalObjectIdentifier—Three-dimensionalmeasurementofshinyorreflec-tivesurfaceisachallengingissueforoptical-basedinstru-mentations.Inthispaper,wepresentanovelstructuredlightapproachfordirectmeasurementofshinytargetsoastoskipthecoatingpreprocedure.Incomparisonwithtraditionalimage-intensity-basedstructuredlightcodingstrategieslikesinusoidalintheilluminatedpatterns.Withstripedgesgenerallybetterpthanindividualimageintensityintheimagedatainthepresenceofsurfacereflections,suchacodingstrategyismorerobust.Toremovetheperiodicambiguitywithinstrippatterns,traditionalGraycodepatternsareadopted.Tolocalizethestripedgesmoreprecisely,bothpositiveandnegativestrippatternsareaccuracyisproposedforstrip-edgelocalization.Theexperimentalsetupisconfiguredwithmerelyanoff-the-shelfpico-projectorandacamera.Extensiveexperimentsincludingaccuracyevaluation,comparisonwithpreviousstructuredlightalgorithms,andthere-constructionofsomerealshinyobjectsareshowntodemonstratethesystem’saccuracyandenduranceagainstreflectivenatureofIndexTerms—Edgedetection,shinysurface,structuredlightsystem(SLS),3-Dreconstruction.WWITHTHEdevelopmentofmicrofabricationandelec-tronicpackagingtechnology,thereisinindustryanincreasingneedofdemandingthree-dimensional(3-D)infor-mationinmicrometer-levelprecisionforsurfaceinspectionandqualitycontrolpurposes[1],[2].Eveninmundanetaskslikecoinanticounterfeitingandsignaturerecognition,ithasbeenrecognizedthat3-DmeasurementsthatarenecessarilyatmicrometerlevelconstituteanotherlevelofManuscriptreceivedMay21,2011;revisedAugust12,2011,November2011,December12,2011,andJanuary11,2012;acceptedFebruary13,2012.DateofpublicationFebruary24,2012;dateofcurrentversionOctober16,2012.ThisworkwassupportedinpartbytheNationalNaturalScienceFoun-dationofChina(NSFC)underGrant61002040,inpartbyNSFC-GuangDongunderGrant10171782619-2000007,andinpartbytheIntroducedInnovativeR&DTeamofGuangdongProvince-RobotandInligentInformationTech-nologyTeam.Z.SongandX.T.ZhangarewiththeShenzhenInstitutesofAdvancedTechnology,ChineseAcademyofSciences,Shenzhen518055,China(: ;xt R.ChungiswiththeDepartmentofMechanicalandAutomationEngi-neering,TheChineseUniversityof,Shatin,(:Colorversionsofoneormoreofthefiguresinthispaperareavailabletotheexisting2-Dmethods.However,instrumentsandmeansformicrometer-level3-Dmeasurementinadequateaccuracyandeconomyarestilllacking.Thefactthatmanyofthetargetobjectsareshinyorreflectiveposesadditionalchallengetothemeasurementprocess.Bytheworkingprinciples,3-Dmeasuringsystemscanbeclassifiedintocoordinatemeasuringmachines(CMMs),timeofflightsystems[3],stereovision[4],shapefromshading[5],laserscanning[6],andstructuredlightsystems(SLSs).Eachapproachcomeswithitsownlimitations,advantages,andcost.ComparedwithCMMs,optical-basedmethodshavethead-vantagesofbeingnoncontactandfastandhavebeenwidelyadoptedinthecommercialsector[7].Inthesemethods,laserbeamsorstructuredlightpatternsareprojectedontotheobjectsurface,andthereflectionsarecapturedbyimagingdevices.Depthinformationattheseilluminatedareascanthenbecalcu-latedviatriangulationHowever,existingopticalmethodsgenerallyencounterdiffi-cultieswithshinyorspecularobjects.Surfacesthatareshinygenerallyhavemostofthe inglightbeamsreflectedoffthesurfacestovariousdirections

thanthatoftheimagingdevice,andthatgreatlycompromisesthequalityofthecapturedimages.Subjecttothelowimagequality,exist-ingstructuredlightmeanswhichareusuallyintensitybased[9]–[11]aredifficulttooperate.Theoften-usedpracticeistocoattheshinysurfaceswithathinlayerofwhitepowdertosurfaceswithathinopaquelacquerjustformeasuringpurposeisacommonpractice.However,forapplicationswherehighac-thicknessof3–5μm,whichcouldbeunevenlydistributedoverthesurface)willinducedistincteffecttothefinalmeasurementaccuracy.Moreimportantly,suchatreatmentcomplicatesthewholescanningprocedureandcouldcausecorrosionstothetargetsurface.Allthesemakeexistingstructuredlightscanningtechniquesimpracticalinmanyapplications[12].Inthispaper,anovelstrip-edgebasedstructuredlightcodingstrategyispresented.Informationencodedinthepatternisnotindividualimageintensitybutstrip-edgeposition.Comparedwithrawimageintensities,stripedgeshavepreciselocationsintheimagedatathataremoredistinguishabledespitethepresenceofinfluencefromthespecularnatureoftheimagedscenetotheoverallimage-intensitydistribution.Thatmakesitscodinginformationmorerobust.Toremovetheperiodicambiguitywithstrippatterns,thetraditionalGraycodepatterns0278-0046/$31.00?2012 IEEETRANSACTIONSONINDUSTRIALELECTRONICS,VOL.60,NO.3,MARCHareadopted.Bytheuseofbothpositiveandnegativestrippatternsandazero-crossing-basedfeaturedetectorthatwedeveloped,stripedgescanbeextractedaccuray.Weshowexperimentalresultsfromasystemsetupthatisconfiguredwithmerelyanoff-the-shelfpico-projectorandanindustrialcamera.Bothdevicesareconsumergradetomakethesystemeconomicalandapplicableforwideindustrialapplications.Thispaperisorganizedasfollows.SectionIIgivesabriefreviewofthepreviousworkonoptical3-Dmeasuringtech-nologies.Theproposedstructuredlightcodingstrategy,strip-edgedetector,systemcalibration,and3-DreconstructionaredescribedinSectionIII.Experimentsonaccuracyevaluation,micrometer-levelmeasurementofsomerealshinyobjects,andcomparisonswithsometraditionalmethodsarepresentedinSectionIV.AconclusionandpossiblefutureworkareofferedinSectionV.PreviousThisworkfocusesonhowhigh-accuracy3-Dmeasurementcanbeconductedovershinymicro-objects.Traditionalme-chanicalprobingmeansadoptedinCMMscanachievehighprecision,butattheexpenseofmeasuringspeed[13].Non-contacttechniques,includinglaserscanningandSLS,havebeenadvancingquicklyinthelastdecade.Suchtechniquesaretriangulation-basedopticalmeasuringtechnologies.Laserscannerisoperableonalmostallsurfaces,butbecauseofitsphysicalscanning-basednature,theoperationspeedislimited.Themeasuringaccuracyisalsoaffectedbylaserspeckleeffect[14].SLSsconsistofaprojectiondeviceandcameras.Byprojectingsomespeciallydesignedlightpatternsontothetargetsurfaceandimagingtheilluminatedscene,imagepointsundertheilluminationscaneachbelabeledwithauniquecodeword.Suchcodewordsarep intheimagedata.Sincecode-wordsontheprojectionsideareknownapriori,point-to-pointcorrespondencesbetweentheimageplaneandtheprojectionplanecanbeestablishedreadily.Three-dimensionalinforma-tionatsuchpositionscanthenbedeterminedviatriangulation[8].SLSshavethebenefitsofdemandingonlyasimplesetup,lowcost,andfastoperationspeed,althoughitsperformancehascertaindependenceuponthesurfaceconditionoftheinspectedobjectandupontheworkingenvironment.Inthelaserscanningapproach,abeamoflaserlightpassedovertheobjectwhileacameramountedasideistorecordthepositionoftheprojectedlaserprofiles.Thereareanincreasingnumberofoff-the-shelf3-Dlaserscannersavailableinthemarket.Differencesofthevarioussystemsliemainlyonthelaserstrength,wavelength,workingdistance,andscanningspeed.RepresentativesystemsinthemarketincludeKonicaMinoltaVIVID9iandFAROLaserScanArm.Therearealsosystemsspecificallyformeasuringinmicrometer-levelof0.1×0.5×0.05mminameasuringfieldof150×25mm.wrinklesonlaminatedplasticsheets.Thesensoruses

spotlaserilluminationandperformspositiondetectionthroughsubpixelpeakdetection.ThelaserdisplacementequipmentisslightlytiltedtominimizetheeffectofspecularreflectionfromFig.1.(a)Sinusoidalpatternisshiftedfourtimestoletthephasevalueateachimagepointbedetermined[25].(b)Linepatternisshiftedsixtimestoencodeeachimagepointontheline[27].plasticsurfaces.Thesensorissetataheightof30mmabovetheplaneofthemechanicalstageandmeasuresthedistancetothetargetspotilluminatedbythelaserbeamatarateof300Hz.Intheexperiment,adepthresolutionof0.01mmwasreported.In[16],alaserlinescanningsystemisstudied.Intheimplementation,thecameraandthelaserarefirstcalibrated.Havingfoundthetopandbottomboundariesofthelaserlineintheimage,thecenterofthelaserlinebetweenthetopandbottomboundariesisfoundalongitslength.Thesecenterpointsareusedforraytracinganddepthcalculation.Whenmeasuringaweldpoolofdepthabout0.38mm,apercentageerrorofabout9%wasreportedintheexperiment.Insteadoflaserline,alightstripilluminatedbyaprojectiondevicecanalsobeusedwiththesamescanningstrategy[17].Intheuseofstructuredlightpattern,thecodingstrategiescanbecategorizedtospatialcodingandtemporalcodingschemes[12],[18].Inthespatialcodingscheme,codewordatapatternelementisdefinedbythepatternvaluesintheneighborhood,whichcanbeaboutvariousgraylevels[19],colors[20],orsomegeometricalprimitives[21]inthepattern.De-Bruijnsequences[22]andM-array[23]arethemaincodingschemesoftenemployed.Sinceuniquelabelatanypatternpositioncomeswithonlyacertain“spread”ofpatternvaluesinthevicinityoftheposition,thepatternpositionsthatcanbeuniquelycoded,andinturntheirdepthvaluessubsequentlyrecovered,cannotbetoodense.Inthetemporalcodingscheme,codingisachievednotinthespatial butinthetime.Aseriesofpatternsisprojectedatdifferentinstantsontothetargetsurface.Thecodewordforanygivenpixelonthecamera’simageplaneisdecidedbytheilluminationsatthatpixelovertime.SLSsusingthisencodingschemecanresultinstrongerdatadensityandhigheraccuracyinthemeasurement.Inparticular,Graycodeisawidelyusedcodingschemebecauseofitssimplicityandrobustness.IfabinaryGraycodepatternofcodewordlengthnistobeused,animagesequenceconsistingofn+1binarystrippatternsneedbeprojectedsequentiallytoencodethescene.Withthat,thesceneintheimage canbeseparatedinto2nsubregions,andthepixelcenterortheGraycodepattern’sedges[24]areusuallyencoded.

shifting[9]–[11],[25],[26]andlineshifting[27]areusuallyusedasshowninFig.1.Tosolvetheperiodicambiguitybetweensinusoidalandlinepatterns,variousphaseunwrapalgorithmshavebeenproposed[28],[29].Inrealapplications,SONGetal.:STRIP-EDGE-BASEDSTRUCTUREDLIGHTMEANSFORSHINYSURFACEMICROMEASUREMENTIN3- Theilluminatedobjectsurfaceisthenimaged,andthestripedgesintheimagedataarepreciselylocated.toimprovetherobustnessoftheunwrapprocedures,aseriesofGraycodepatternsareusuallyused.BycombiningthelocalphasevalueandtheglobalGraycodevalue,auniquecodewordforeachimagepointcanbeobtained.Inexperiment-ingwithasphereof150-mmdiameter,aagedeviationof0.05mmwasreported[25].In[26],asinusoidalshiftingSLSisproposedforthe3-Dmeasurementofflipchipsolderbumps.Inthemeasurementofastandard1-mmgaugeblock,aageaccuracyof2μmwasobtained.However,subjecttostrongreflectionsofbumpsurfaces,thereconstructed3-Dmodelsofthebumpshaveobviousdiscrepancywiththeactualones.Intheline-shiftingmethod[27],thesinusoidalperiodicprofileissubstitutedbyaparallellinepatternasshownin1(b).Byconsecutivelyshiftingthelinepatternsixtimesinthex-andy-directions,respectively,siximagesforthex-coordinateandsiximagesforthey-coordinatecanbeob-tained.Sincethelinepatternisalsoperiodic,ithasinherentambiguity,buttheGraycodepatternscanbebroughtintoastandarddeviationof0.028mmisreportedinmeasuringaplanarregionof200×200mm.In[30],apassiveandactivestereovisionsystemwasusedforreconstructingthesurfacethedeformedplate.Inthesystem,passivestereovisionisusedtodetectthesurfaceboundary,whileactivestereovisionwithaprojectionofstructuredlightisusedfor3-Dreconstruction.Inanexperimentwitharectangularplateofsize11.65×7.35cm,ataworkingdistanceofabout40cm,themeasuringerrorindepthwaswithin2mm,andtheerrorinthex-andy-directionswaswithin1mm.Shinysurfacewithstrongreflectivenatureisstillachallengetooptical-basedinstrumentationsincludingstructuredlightmeans.Sinusoidalstructureintheprojectedpattern[9]–[11],[25],[26]isdestroyedintheimagedataowingtothestrongreflections,andtheprojectedlinesarealsousuallyfloodedandundistinguishableinthecapturedimage[27].Toimprovethestructuredlightpattern’santireflectioncapability,astrip-edge-basedcodingstrategyisproposedinthispaper.Comparedwiththeimage-intensity-basedsinusoidalpatternandthethin-line-basedline-shiftingpattern,thestripscanbebetterpintheimagedatainthepresenceofsurfacereflections,andthatmakesthecodingproceduremorerobust.Toremovetheperiodicambiguitywithinstrippatterns,traditionalGraycodepatternsarebroughtin.Todeterminethestripedgesmoreprecisely,boththepositiveandnegativepatternsareused.Inparticular,animprovedzero-crossingedgedetectorisproposedforstrip-edgelocalizationinsubpixelaccuracy.Strip-Edge-BasedStructuredLightPatternDesignandStrip-EdgeDetectionThemajorprocessesinvolvedinthedevisedsystemarethusthefollowing.Inthestructuredlightpattern,auniquecodewordisassignedtoeachstrip-edgepoint,whichisacombinationofalocalstrip-edgecodevalueandaglobalGraycode

betweentheilluminatedpatternandtheimageplanecancolumnoftheFig.2.CodingstrategyofGraycodecombinedwithstripshiftingpat-tern.Top:SeriesofGraycodepatterns(withn=9)isusedtoconstruct256subregionseachwithauniquecodeword.Bottom:Strippatternofwidth4pixelsisshiftedthreetimestoencodepositionswithineachsubregion.Stripedgesoftheshiftingpatternwillbedetectedandencodedinfineraccuracy.established,andspatialdepthatthestrip-edgepointscanbeComparedwiththerawimageintensitiesandthinimagelinesthatarevulnerabletothereflectivenatureofshinysurfaces,edgesofbinarystripsintheilluminatedpatternaremorelocalizableandbetterp intheimagedatadespitethespecularnatureoftheobjectsurfaces.HigherlocalizabilityoftheedgescomeswithmoreaccuratereconstructionandhigherrobustnessofthemeasurementIntheimplementation,aseriesof(n+1)Graycodepatternsisfirstprojectedinordertodividethetargetsurfaceinto2nsubregions(itisnot2n+1regionsbecausetheall-zerocodewordisnotdistinguishableintheimagedataandgenerallynotused),eachwithauniquen-b-longGraycodeword.Supposethateachofsuchsubregionsismpixelwideontheprojector’spatterngenerationplane.Then,astrippatterninhalfofthefineststripwidthoftheGraycodesequenceisshiftedm?1times,instepsSuchaperiodicpattern,byitself,hasaperiodicambiguityofmpixels(i.e.,thewidthofthestrippatternontheprojector’spatterngenerationplane)indistinguishingdifferentpointsofthetargetsurface.However,bycombiningthetwocodewordstogether,onefromtheGraycodeandtheotherfromthestrippattern,themsubdivisionscanbeintroducedtoeachofthe2nsubregionstoachievefiner3-Dreconstruction.TheprocedurecanbeexpressedasP=G+G∈{0,1,2,...,(2n?S∈{0,1,2,...,(m? whereSisthelocalcodewordgeneratedbythestrippat-tern,GistheglobalGraycodewordusedtoremoveperiodicambiguityamongstrippatterns,andPisthefinaluniquecodeword.Forapatterngenerationplaneof1024-pixelwidthintheprojector,Graycodeof9-blength(i.e.,n=9)canseparateitinto256subregions.Then,astrippatternofwidth4pixelsisshiftedthreetimesinsteplengthof1pixelasillustratedbyFig.2.Upontheshifting, IEEETRANSACTIONSONINDUSTRIALELECTRONICS,VOL.60,NO.3,MARCHFig.3.(a)Zero-crossingedgedetector.(b)Withoutsurfacereflect