翻译以原文和在同一文件中前

基于自动地交通场景监视中视点独立的物体分作者：ZhaoxiangZhang,MinLi,KaiqiHuangandTieniu 介中自动物体分类是计算机视觉和视觉中的重要内容，在实际应用中具有巨大潜力。知道物体类型信息，更具体和准确的方法能够用于运动物体的高级别动作。尤其是对交通场景而言，移动物体分类成预先定义好的类别能够允许操作者编程实现系统，这是通过将不同的物体区分为我们感的部分，像是当一个行人将进入时予以警告或者像是当机动车逆行时予以警告等等。这在智能视觉中是很普遍的。等人在[14]中应用Boosting进行自动特征选择与物体分类，这给我们提供了一工校准总是需要对场景进行大量[12]并且限制了分类算法在不同情形 辨率中也是个事实上，有一个普遍的约束：交通场景中大多数我们感的物体是在地平面上或者地平面上运动的。我们可以利用基于地平面和图像平面间的单应关系处理畸变。Stauffer等人在[13]中实现了数据在确 决相机中的畸变问题。这种方法已经在[16]中详细阐述过了。首先，路的方法在[16]中被提出。这种方法拓展到费直线道。然后在第四地平面x,与真实世界平面上的点x相对应的，对应关系为xHx。正如[12]中描述H （2-纯投影部分主要是由地平面上 线

l,l,l

112 0 P 0 3 A，其形式为 0 A 0 1

（2-变换中保持不变，但是度量坐标却通过仿射矩阵从(1,i,0)T变成仿射坐标(i,1,0)T地平面的仿射矫正需要识别地平面上的线l，线可以由两个地面上的点求得。这个部分我们提出基于交通场景中的移动车辆找到两个地平面上的点的方法。源于单位时间内位置的改变。第二个方向是主轴方向，它能通过轮廓矩分析arctan

02pq是数对p,q的中心矩。事实证明移动车辆的这个主轴方向角的变化很小，然而行人和自行车的主轴方向角变化急剧，这在图2-1中阐明。代K-Mean聚类算法，我们采用一个更可靠地策略：只有那些主轴角度偏差小于T5的目标才被标注为车辆，其他的全部舍弃。之后的点估计受益于图们不在平行，而是相交于图像平面中一个叫做地平面点的位置。垂直方向上也是同样的情况。我们使用投票策略来估计这两个地平面上的点。每一个从车辆中提取出的直线l,其上的每一个点sx,y都能产生一个 在投票空间中以x,y为中心。随着时间的积聚，一个投票表产生了，并且全局值的位置对应交叉点。图2-3展示了一个投票空间域道路方向相对应的例图2-3估计点的示意图（引自这些情况下，之前讨论的方法不能用于估计出地平面的两个点。幸运的平面点估计问题，以下进行详细讨论。线段。图2-4（a）展示了一种拐点的情况，这是能把整个道路分成两个直线个直线段用于估计地平面上的点。2-4平面点。（a括：直行，左转，右转和转圈。一个可靠地策略类似于直线段情况。如2-段，我们能够用传统方式估计出多组两个正交的地平面点。显然，段1与断估计出的点对应该和段3、段4估计出的接近。事实上，我们仍可以用传统方式估计十字路口情形下的点。这种情况下，估计正交点对的投票空间将会有两个显著地峰顶。一个对应段1与段234的。交通流量在十字路口总是调度经常避免可以求出两组地平面点。现在我们讨论2-5（b）中描述的弯道情况。他是最复杂的情况。因为哦我们从这种道无法检测到任何一条直线段。相反，我们能够应用车辆运动信息监测道路区域，然后把整个道路分成随机的小部分，正如2-6（a）中所向上移动。因此，对于每个部分我们能够估计一对两水平正交点，运用基如此多的小部分，有车辆驶过的部分将会提供大量点。因为假设车辆在同一方向上移动是确的，我们应该选择这个大的集合中最准确的部分。我们知道，所有的点应该在一条线上。每个部分估计出的点，Hough变换能用于估计线，这在图2-6（b）中展示。那些与线距离和最近的点对被选作正交点。 计出正交点。其他情况的道路布局可以看做是以上三种基本布局的组合，我们能够估计出若干点对，并选择其中最准确的部分。两个点就能确定一条线，进而实现地平面的仿射变换。度量如[4]中描述的，真实世界平面上的每个已知角度在图像平面直线la与直线lb间，给出了一种约束,，它是在以c,c为圆心，r为半径的圆上c,cab,abcot,ra 这里ala2blb2

一个关于,的圆。因为从中有充足的被检测的车辆，我们能从一大堆圆中找到交叉点，如图3-1（a）所示。由于对称性质，我们只关心轴上面的交叉点。每两个圆就能确定交叉说 投票策略。估计了,，我们能 仿射矩阵A，因此实现度物体密度：等于面积/周长2这些特征中的大部分在近景中能有效进行分类，但是由于畸变而无法在远景中应用。幸运的是，地平面矫正使得这些特征归一化为独立于视角，表示为sizeRvelocityR,compactnessR,sizeR,angleR。K-Mean分类的自动目标类为了利用监督学习方法将移动目标自动分类，我们采用K-Mean聚类算法和决策级融合来实现自动标注。我们使用三个特征compactnessR,sizeR,angleR3个聚类。每一个对应各自的 compactnessR车辆和行人、自行车的优势；size‘R有区别车辆和自行车的优势；

Pivv,i,i,i1, 使用规则，我们获得如下的推导结果Pcategoryi|vPivpi,i1, 的前验概率要进行初始化，利用每个聚类中经过自动标注后的总数。每个聚类中的分布通过以下方式估计：

1Nr

vi,r,

r

j pk,new1pk,oldMk,t,k1,

1 vˆ ˆ i, i, x,yBtx,yBt1x,y （4-时，我们能够轻松检测场景改变。T是一个阈值，BtBt1分别是恢复实验结果与我们之前，目标形态由于相机投影产生显著的变形。地平面矫正再5-1中说明。我们可以发现，经矫正后，目标轮廓再远景场景中几乎保持图（a）-前后的表现，如图5-2所示。可以看出，矫正的特征要比原始特征更易于分五部分假设。图该方法的平均分类准确度如表5-1表表5-2聚类距离的分类矩此外，我们同样对比了[15]中提到的方法，分类准确度如表3所示。显在我们的方法中，初始与优化分类是进行的。随着场景变化检测的模块化，我们的方法能够自动场景改变并适应新的场景。传统的目标能够处理每秒15帧速度额，这基本实现了实时性。我们方法的简化情形是自上而下的视角。然后畸变在这种视角下不是很显然。因为，地平面矫正用于处理畸变，自上而下的视角在我们的方法中不会成为一个大问题。此外，交通场景更倾向于倾斜安装头结这篇中，我们提出了基于地平面矫正视角独立的目标分类方法。基于新能够实现化并独立于人工标注。算法是有效的，并对条件改变具有鲁棒参考文B.BoseandE.Grimson.Groundnerectificationbytrackingmovingobjects.InProceedingsoftheJointInternationalWorkshopsonVS-PETS,2003.L.M.Brown.Viewindependentvehicle/classification.InProc.oftheACM2ndinternationalworkshoponSurveillanceandSensorNetworks,2004.J.Deutscher,M.Isard,andJ.MacCormick.Automaticcameracalibrationfromasinglemanhttanimage.InProceedingsofECCV,2002.D.LiebowitzandA.Zizzerman.Metricrectificationforimagesofnes.InProceedingsofIEEEConferenceonCVPR,1998.E.Rivlin,M.Rudzsky,R.Goldenberg,U.Bogomolov,andS.Lepchev.Areal-timesystemforclassficationofmovingobjects.InProceedingsofthe16thInternationalConferenceonPatternRecognition,2002.M.Everingham,A.Zisserman,C.K.I.Williams,and...The2005pascalvisualobjectclasseschallenge.LectureNotesinComputerScience,3944:117–176,Jan.W.Grimson,L.Lee,R.Romano,andC.Stauffer.Usingadaptivetrackingtoclassifyandmonitoractivitiesinasite.IninIEEEConferenceonComputerVisionandPatternRecognition,1998.F.Han,Y.Shan,R.Cekander,H.S.Sawhney,andR.Kumar.Atwo-stageapproachtopeopleandvehicledetectionwithhog-basedsvm.InPerformanceMetricsforInligentSystems2006Workshop,2006.D.Liebowitz,A.Criminisi,andA.Zisserman.Creatingarchitecturalmodelsfromimages.InProceedingsofEuro-Graphics,1999.[10]Z.Liu,K.Huang,andT.Tan.Castshadowremovalwithgmmforsurfacereflectancecomponent.InProceedingsofICPR,2006.[11]F.Lv,T.Zhao,andR.Nevatia.Usingvanishingpointsforcameracalibration.[12]R.I.HartleyandZizzerman.Multipleviewgeometryincomputervision.CambridgeUniversityPress.,2000.[13]C.Stauffer,K.Tieu,andL.Lee.Robustautomatednarnormalizationoftrackingdata.InProceedingsofVS-PETS2003,2003.[14]P.A.Viola,M.J.Jones,andD.Snow.Detectingpedestriansusingpatternsofmotionandappearance.InProceedingsof9thIEEEInternationalConferenceofComputerVision,2003.[15]Z.Zhang,Y.Cai,K.Huang,andT.Tan.Real-timemovingobjectclassificationwithautomaticscenedivision.InIEEEConferenceofImageProcessing2007,[16]Z.Zhang,M.Li,K.Huang,andT.Tan.Robustautomatedgroundnerectificationbasedonmovingvehiclesfortrafficscenevisualsurveillance.InProceedingsofIEEEConferenceonImageProcessing,2008.[17]Q.ZhouandJ.K.Aggarwal.Trackingandclassifyingmovingobjectsfrom.InProc.of2ndIEEEInternationalWorkshoponPETS,2001.inria-Authormanuscript,publishedin"TheEighthInternationalWorkshoponVisualSurveillance-VS2008,Marseille:FranceViewIndependentObjectClassificationBasedonAutomatedGround RectificationforTrafficSceneSurveillanceNationalLaboratoryofPatternRecognition,InstituteofAutomation,Academyof{zxzhang,mli, ,,version1-29SepWeaddresstheproblemofviewindependentobjectclas-sification.Ouraimistoclassifymovingobjectsoftraf-ficscenesurveillancesintopedestrians,bicyclesandvehicles.However,thisproblemisverychallengingduetolargeobjectappearancevariance,lowresolutionsandlimitedobjectsize.Especially,distortionofsurveillancecamerasmakesmost2Dobjectfeatureslikesizeandspeedrelatedtoviewanglesandnotsuitableforobjectclassification.Inthispaper,weadoptthecommonconstraintthatmostobjectsofinterestintrafficscenesaremovingonthegroundne.Firstly,werealizethegroundnerectificationbasedonappearanceandmotioninfor-mationofmovingobjects,whichcanbeappliedfornormal-izationof2Dobjectfeatures.Anonlinelearningframeworkisthendescribedtoachieveautomaticobjectclassificationbasedonrectified2Dobjectfeatures.Experimentalresultsdemonstratetheeffectiveness,efficiencyandrobustnessoftheproposedmethod.Automaticobjectclassificationin sisanimportantissueincomputervisionandvisualsurveillancewithgreatpotentialforrealapplications.Withobjectstypeinforma-tionknown,morespecificandaccuratemethodscanbede-velopedtomonitorhighlevelactionsofmovingobjects.Especiallyfortrafficscenesurveillance,classificationofmovingobjectsintopredefinedcategoriesallowstheopera-tortoprogramthemonitoringsystembyspecifyingeventsofinterestfordifferentobjectstypeslike’alarmingwhenapedestrianiscomingintoaforbiddenarea’or’alarmingwhenavehicleisrunninginareversedirection’,whichisverycommonininligentvisualsurveillance.Duetoitsimportance,muchworkhasbeendoneonau-tomaticobjectclassification.In[2,5,7,17],shapefeatures

likearea,compactness,boundingboxaspectratioandmo-tionfeatureslikespeedandmotiondirectionsareextractedmotionfeaturesarebasedonimagenesothattheycan-notavoiddistortion,whichismuchmoresig-nificantinfar-fieldtrafficscenesurveillance s.Forexample,nearbyobjectsinimagesappeartobelargerandthese2Dobjectfeaturesforclassificationisnotsuitableandlimitstheaccuracyofobjectclassification.In[15],scenesaredividedintosubregionstobetreatedrespectivelytodecreasetheeffectofdistortion.In[6],aseriesofalgorithmsaredescribedtodemonstratetheeffec-tion.However,mostofthealgorithmsaretime-consumingandnotapplicabletolowresolution s.In[8],SVMisappliedwithHistogramofOrientatedGradientfeaturesforclassification.Violaetal[14]giveusagoodframeworkforautomaticfeatureselectionandobjectclassificationbyBoosting.However,thisframeworkneedstocollectlargesamplesoftrainingdatainallkindsofconditionsandlabelallofthemmanually.fromdistortion,whichmakeoriginal2Dfea-turenotapplicabletoobjectclassification.Howtocon-quertheeffectofdistortionisthekeytouse2Dfeaturesforefficientobjectclassification.Thecommonsolutiontodistortionistouseapre-calibratedcamera.However,manualcalibrationalwaysneedawidecalityofclassificationalgorithmstodifferentscenes.Vari-ousapproaches[3,9,11]areproposedforauto-calibrationfrominherentscenestructuresoraccuratepedestriandetec-lancescenesandprecisepedestriandetectionisverychal-lenginginlowresolutionsurveillance interestintrafficscenesurveillance saremovingonornearthegroundne.Wecandealwithdistor-tionofcamerasbasedonhomographybetweenthegroundneandimagene.Staufferetal[13]achievednormal-

Extendingaffinerectificationtometricrectificationin-izationoftrackingdataonaninaccuratelinear

⎛ Boseetal[1]achievedmetricrectificationofthe — nebyextractingaseriesofmovingobjectsalonglinearpathwithconstantspeed.However,theconditionsare

A=⎝ 0

tobeInthispaper,wesolvedistortionofsurveil-lancecamerasbasedonarobustautomatedgroundnerectificationwhichhasalreadybeenproposedindetailin[16].Firstly,bothaffinerectificationandmetricrectifica-tionareachievedbasedonappearanceandmotioninforma-tionofmovingobjects.Theserectificationscanbeeffec-tivelyusedfornormalizationof2Dobjectfeatures.Anovelonlinelearningframeworkisthenappliedtomakeuseofrectified2Dobjectfeaturesforclassification.Experimentalresultsdemonstratetheeffectiveness,efficiencyandrobust-nessofourapproach.Theremainderofthepaperisorganizedasfollows.InSection2,webrieflyintroducetheprincipleofthegroundnerectification.InSection3,weintroducethemethodofaffinerectification.Detailsofthismethodinthecaseofthemethodtothecasesofnon-straightroadways.ThentheprincipleofmetricrectificationisintroducedinSection4.InSection5,weproposeouronlinelearningframeworkforclassification.Experimentalresultsandysisarepre-sentedinSection6.Finally,wedrawourconclusionsinSection7. ne projection,thegroundneismappedtoimage ne,x,arerelatedtopointsontheworldne,x,asx=Hx.Ashasbeendescribedin[12],thehomogra-phymatrixHcanbe poseduniquelyintothreema-trices,S,A,P,representingthesimilarity,affineandpure-

Thismatrixhastwodegreesofdomrepresentedbyαandβ,whichspecifytheimageofthecircularpoints[12].Thecircularpointsareinvariantundersimilarityformations,butaretransformedfrommetric(1,±i,0)Ttoaffinecoordinate(α±iβ,1,0)TbythetransformationTheabovepartinthissectionisreferencedto[16]andspectivelyfrommovingobjectsintrafficscenesurveillancesaredescribedasfollows.AffineAffinerectificationofthegroundnerequiresidentifi-cationofthevanishinglinel∞ofthegroundne,whichcanbedeterminedbytwohorizonalvanishingpoints.Inthissection,weproposeourapproachtorecovertwovan-ishingpointsofthegroundnebasedonmovingvehiclesintrafficscenesurveillance CoarseMovingVehicleMovingobjectsintrafficscenescanbedetectedaccu- ywithshadowsremovedbyimprovedGMM[10],butmore.Thedifferenceofthefollowingtwodirectionsaretakenasadistinctivefeatureforcoarsevehicledetection.Thefirstdirectionisthevelocitydirectionofobjectsins,whichcanbecalculatedduetopositionchangeofunittime.Thesecondoneisthemainaxisdirectionθ,whichcanbeestimatedfrommomentysisofsilhouette:μprojectivecomponentsofhomography θ=μ

−

H= ThesimilaritycomponentSisasimilaritytransforma-tionwhichhasnorelationtotheaffineandmetricrectifica-Thepure-projectivecomponentischaracterizedbyavanishinglinel∞=(l1,l2,l3)Tofthegroundne,which

Here,μpqisthecentralmomentoforder(p,q).Itisevidentthattheangledifferenceisverysmallformovingvehicleswhileitissignificantforpedestriansandbicyclesasillus-tratedinFigure1.InsteadofK-Meanclustering,weadoptamorereliablestrategythatonlythoseobjectswithangledifferencelessthanθT=5◦arelabeledasvehicleswithalloftherestdiscarded.Thelatterestimationofvanishinghasthe

⎛ 0P=⎝ 0

pointsbenefitsfromthisstrictdetectionLinearEquation,version1-29SepRecoveryof,version1-29Sep

Inmostviewanglesofsurveillancescenes,vehiclesinsarerichinlinesegmentsalongtwoorientationscor-,,version1-29SepIllustrationof (b)Illustrationof(c)IllustrationofFigure1.Directiondifference(Redarrowheadstandsforvelocitydirection;bluearrowheadstandsformainaxisdirection)respondingtothesymmetricalaxisdirectionanditsper-pendiculardirection.Wemakeuseofimagegradienttoextractthesetwoaccuratelineequationsforeveryvehicledetectedfrom s.AsshowninFigure2,thesetwoori-entationsareextractedbytwostagesofHistogramofOri-entationGradient(HOG)andtherespectivelineequationsaredeterminedbycorrelationtoimagedata.Motiondi-rectioncanhelpustodistinguishthesetwolines.Theonewithorientationclosetomotiondirectioncorrespondstothesymmetricalaxisdirectionwhiletheotheronecorrespondstoitsperpendiculardirection.Figure2.Estimationoflineequationsfromvehicles(citedfrom[16])IntersectionItiscommonthatmostvehiclesintrafficscenesaremov-ingalongroadwayswhicharemostlystraightorcontainaseriesofapproximaystraightlinesegmentsintheviewfield.Here,weassumethatthereisonlyonestraightroad-wayintheviewfield.So,symmetricalaxisofmostvehi-

clesshouldbeparalleltoeachotherin3Dworld.Duetoimageprojection,theyarenolongerparallelbutintersecttothesamepointcalledhorizonalvanishingpointonimagene.Theperpendiculardirectionisofthesamecase.Wevanishingpoints.Foreverylinelextractedfromvehicles,eachpoints(x,y)lyingonlgeneratesaGaussianimpulseinvotingspacewith(x,y)asitscenter.Withtimeaccu-mulated,avotingsurfaceisgeneratedandthepositionofitsglobalextremecorrespondstotheestimatedintersectionpoint.OneexampleofvotingspacecorrespondingtotheroadwaydirectionisshowninFig.6.Traffic Figure3.Illustrationofestimatingvanishingpoints(citedfrom[16])SpecialCasesofRoadwayever,thesolutionshaveonlydiscussedtotheassumptionofonlyonestraightroadwayinviewfield.However,thisas-sumptionisnotalwaystrueinreality.Theremaybemorethanoneroadwayintheviewfiled,likeacrossroad.Theroadwaymaybenotstraightatall,likeabend.Inthesecases,themethoddescribedabovecannotappliedtoesti-matethetwohorizonalvanishingpoints.Fortunay,thevarianceofroadwaylayoutsinrealitycanbeseenascom-binationsofseveralprimitivelayoutswhichcanbesolvedforhorizonalvanishingpointsestimationandarediscussedrespectivelyasfollows.StraightInreality,itisverycommonthatthewholeroadwayisnotstraight,butiscontainsseriesofstraightsegments.Fig.4(a)showsthecaseofoneinflexionwhichdividesthewholeroadwayintotwostraightsegments.Fig.4(b)showsaroad-waywhichisconsistastraightsegmentandabend.Theroadwayinthesecasescontainsatleastonestraightseg-ment,whichcanbeappliedforhorizonalvanishingpointsThedetectionofstraightsegmentscanbesimplyreal-izedbymotioninformation.Withobjectsextractedbymo-cidents.Asaresult,thetwopeaksshouldbeofdifferentheightsothattheycanbedistinguishedfromeachother.Thisstrategycanalsorecovertwogroupsoforthogonalhorizonalvanishingpoints.Case

Case

3.4.3NowwediscussthecaseofabendasshowninFig.5(b).ItisthemostcomplicatedcasebecausewecannotdetectFigure4.Straightsegmenttiondetectionandclassifiedasvehicles,conventionaltrack-ingcanhelpustomonitorthechangetrendofvelocitydi-rections.Asweknow,thevelocitydirectionofavehiclechangeslittleinastraightsegmentbutboundattheinflex-ionorbendpart.Inthisway,wecandetectallstraightseg-mentsfromscenesandeachstraightsegmentcanestimatetwoorthogonalhorizonalvanishingpoints.

onestraightsegmentfromthisroadway.Instead,wecandetecttheroadwayregionbyvehiclemotioninformationanddividethewholeroadwayrandomlyintomanysmallpiecesasshowninFig.6(a).Ifthevehiclewithitscen-troidwithinthepiece,weconfirmthatthevehicleispass-ingbythepiece.Weassumethatmostvehiclespassingsult,wecanestimateacoupleoftwohorizonalorthogonalvanishingpointsforeverypiecebythestrategyofthecon-ventionalcasebasedonmotionandappearanceinformationofvehiclespassingbytheverypiece.Sincewedividethewholeroadwayintosomanysmallpieces,thosepieceswithenoughvehiclespassingbycansupplyusalargenumberofcouplesofhorizonalvanishingpoints.Sincetheassumptionofvehiclesmovinginthesamedirectioninonepieceisnotveryaccurate,weshouldselectthemostaccuratecouplesfromthelargeset.3124(a)Thecaseof (b)Thecaseof3124Figure5.CrossroadandThecaseofcrossroadismorecomplicatedasillustratedinFig.5(a).Theactivitiesofvehiclesinthecrossroadcon-tains:runningahead,turningleft,turningrightandturning

Divisionof

Estimationofhorizonalvanish-ingline,version1-29Separound.Atrustystrategyissimilartothestraightsegmentcase.ForthecrossroadshowninFig.5(a),wecandetectfourstraightsegmentsbymotiondirectioninformation.Foreverystraightsegment,wecanestimateacoupleoftwoor-thogonalhorizonalvanishingpointswiththestrategyoftheconventionalcase.Evidently,thecouplesestimatedfromSegment1andSegment2shouldbeapproximatetoeachotherwhilethoseofSegment3,version1-29SepInfact,wecanstillusethestrategyofconventionalcaseforvanishingpointsestimationforcrossroad.Inthiscase,therewillbetwoevidentpeaksinthevotingspacesforhori-zonalvanishingpointsestimation.OnepeakcorrespondstothedirectionofSegment1and2whiletheotherpeakcor-respondstothedirectionofSegment3and4.Trafficflowincrossroadarealwaysattemperedregularlytoavoidac-

Figure6.IllustrationofroadwaydivisionandestimationofvanishinglineAsweknow,allhorizonalvanishingpointsshouldlieonthehorizonalvanishingline.Forallthehorizonalvanish-ingpointsestimatedfromeverypieces,HoughTransformcanbeappliedtoestimatethisvanishingline,whichisil-lustratedinFig.6(b).Thosecoupleswiththesmallestsumofdistancestotheestimatedvanishinglinearetakenasef-fectivehorizonalorthogonalvanishingpoints.Foronestraightroadway,wecanestimateexclusivecou-pleoforthogonalhorizonalvanishingpointsfromappear-anceandmotioninformationofmovingobjectsin Sinceothercasesofroadwaylayoutscanbeseenascombi-nationsoftheabovethreeprimitivelayouts,wecanestimateachievestheaffinerectificationofthegroundne.MetricAsdescribedin[4],eachknownangleθontheworldnebetweenlinelaandlinelbonimagenegivesaconstraintof(α,β)tolieonacirclewithcenter(cα,andradius(c (a+b),(a− r=|(a−b)|

αβ)= Outputwherea=−la2/la1andb=−lb2/lb1arethelinedirec-pendiculardirectionsontheworldnetodetermineacir-cleabout(α,β).Sincethereareredundantdetectedvehi-clesfrom s,wecandetermine(α,β)astheintersec-tionofalargesetofestimatedcirclesasshowninFig.7(a).oo(a)Illustrationof Figure7.Illustrationofestimatingintersec-tionsofcircles(citedfrom[16])Duetosymmetricproperty,weonlyfocusontheinter-sectionabovetheαaxis.Everytwocirclescandeterminetheintersectionconvenientlybydifferentialofthesetwocir-cleequations.ForNcircles,wecanobtainN(N−candidatepointsand(α,β)isdeterminedsimplybasedGaussianvotingstrategydescribedaboveasshownin7(b).With(α,β)estimated,wecancalculatetheaffinema-trixAsothatthemetricrectificationisrealized.Theabovepartinthissectionisreferencedto[16].ObjectInthissection,wedescribeourapproachforviewinde-pendentobjectclassification.TheflowchartofthemethodisshowninFigure8.Inourframework,wemainlyusethefollowing

Figure8.Classificationsize:sizeofobjectsinvelocity:timederivativeofcentroidofthetperiaersize:timederivativeofangle:anglebetweenmotiondirectionanddirectionofmajoraxisofthesilhouetteMostofthesefeaturesareefficientforclassificationinnearfield s,butnotavailableinfarfield sduetosignificantdistortion.Fortunay,thegroundnerectificationenablesnormalizationofthesefeaturestobeindependentofviewangles,whicharedenotedas(sizeR,velocityR,compactnessR,sizR,angleR).Theonlineclassificationframeworkiscomposedofthreeperiods.Thefirstperiodachievesthegroundnerectifi-cationbasedonmotionandshapeinformationofcoarselyobjecttypelabelingbasedonunsupervisedK-Meanclus-tering.Thethirdperiodachievesonlineobjectclassificationandrefinementofclassifiers.AutomaticInordertoclassifymovingobjectsautomaticallywith-outsupervisedlearning,weadoptK-Meanclusteringanddecisionlevelfusionforautomaticlabeling.Weusethethreefeatures(compactnessR,sizeR,angle)forK-Meanclusteringandautomaticlabeling.After sprocessedframebyframeforaperiodoftime,K-Meanclusteringisadoptedtoestablish3clusters.Eachclustercorrespondstoeachcategory,respectively.Thedecisionlevelfusionbasedonthefollowingthreeintuitiverulesisadoptedtoestablishthecorrespondences:(1)compactnessRhastheadvantagesofdistinguishingvehiclesfrompedestriansand,version1-29Sepshapeandmotion bicycles.(2)areaR,version1-29Seppedestriansfromvehiclesandbicycles.(3)anglehastheadvantagesofclassifyingpedestriansandvehicles.Usingvotingstrategy,wecanconvenientlyachieveautomaticla-Bayesianviewanglechanges.Herewemakeanassumptionthatv=(areaR,speedR,compactnessR)ofeverycategorysatisfiesamultivariateGaussiandistribution.TheassumptionwillbetestedinSection6andthedistributionsaredenotedas:Pi(v)=η(v,μi,Σi)i=1,2,3 P(category=v)∝Pi(v)· i=1,2, whereP(category=v)andpiareposteriorandpriorprobabilityofeachcategory,respectively.Thepriorprob-dividualsbelongingtoeachclusterafterautomaticlabelingperiodandtheGaussiandistributionisestimatedfromeachclusterinthefollowingway:N

whereTisathresholdandBtandBt−1arerecoveredback-groundofthecurrentandpreviousframes,respectively.Asweusereflectancecomponentforbackgroundmodeling,thedetectionisrobusttofastilluminationchanges.WhenneandinitializetheFurthermore,theclassificationresultscanfeedbacktothegroundnerectification.Theobjectswhichareclas-sifiedasvehiclescansubstitutecoarsevehicledetectionandcontributethetheaffineandmetricrectificationofthegroundne.ExperimentalResultsandNumerousexperimentsareconductedandexperimentalresultsarepresentedinthissectiontodemonstratetheper-formanceoftheproposedapproach.AllexperimentsareconductedonacomputerofP43.0CPUand512MDDR.IllustrationofAppearanceRectifica-Aswehavedescribedbefore,objectappearancehassig-nificantdistortionduetocameraprojection.Thegroundnerectificationenablesnormalizationofappearance.μˆi= i=1,2, Here,wetakeobjectsilhouetteasanexampleto

N

−μˆ)i,j=1,2,

theperformanceofappearancerectification.Experimentsareconductedtoavehiclemovingacrossafar-fieldscene.TheoriginalprojectedsilhouettesandrectifiedsilhouettesareshowninFigure9.AswecanThecategoryisdeterminedbytheposteriorprobabilityandtheclassifierisrefinedatthesametimetoberobusttoconditionchanges:pk,new=(1−β)pk,old+ k=1,2, ˆneγ)ˆold

variantinfar-fieldscenes,whichillustratestheeffectivenessofappearancerectification.Thispartisreferencedto[16].ˆ2

,version1-29Sepi,j,new=(1−γ)ˆi,j,old+γ(vi,t−ˆt)(vj,t−ˆt)(12)whereβandγaretherefinementrate.M(k,t,version1-29Sepisclassifiedasthecategorykand0otherwise.Thepriorisposteriorprobabilityoutputforeverymovingobjects.Wecandeterminethecategoryusingthesumofposteriorprob-abilityoftrackedframestoimproverobustnessofclassifi- Mostscenechangesin surveillanceareabrupttran-sitionscausedbyzoomingormovingofcamerasratherthangradualtransitions.Wecansimplydetectscenechangesyt,y)−Bt−1(x,y)>T

Figure9.Rectificationofsilhouetteforamov-ingvehicle((a)-(f)areoriginalsilhouettes;(g)-(l)arerectifiedsilhouette)IllustrationofFeatureThegroundnerectificationenablesnormalization

testtheperformanceoftheproposedobjectclassificationposedmethodisshowninTable1.

Sizebefore

0.098.2

Sizeafter

Table1.Classificationconfusionmatrixus-ingrectifiedfeatures

Speedbefore

Speedafter

originalfeatureswithoutrectification,theclassification,version1-29SepCompactnessbefore,version1-29SepFigure10.Effectoffeatureabundantmovingobjectsextractedbymotiondetectionandlabeledmanually,weyzetheclass-conditionaldensi-tiesofthethreeobjectfeaturesbeforeandafternormaliza-tionasshowninFigure10.Aswecansee,therectifiedfeaturesaremucheasiertobeclassifiedthanoriginalfea-tures.Furthermore,theclass-conditionaldensitiesofthesethreefeaturesapproximaysatisfyGaussiandistributions,whichconfirmstheGaussianassumptiondescribedinSec-tion5toacertainextent.Classification(a)Scene (b)Scene(c)Scene (d)SceneFigure11.IllustrationoftrafficWetesttheperformanceofourapproachinfourscenesofdifferentviewanglesasshowninFigure11

formanceisshowninTable2.Aswecansee,featureTable2.Classificationconfusionmatrixus-ingdistancefromclusterficationcangreatlyboosttheperformanceofobjectFurthermore,wealsocomparetheperformanceofthemethoddescribedin[15],withclassificationaccuracyshowninTable3.Evidently,theperformanceofourmethodTable3.Classificationconfusionmatrixus-ingGaussianAssumption0.097.3groundnerectificationcandealwithdistor-tionmuchbetterthansimplescenedivision.Inourapproach,initializationandrefinementofclassi-fiersarecarriedoutonline.Withthescenechangedetectionmodular,ourapproachcandetectscenechangesandadapttonewscenesautomatically.Conventionalobjecttracking,,version1-29Sepcanimprovetheperformanceofobjectclassificationwithtemporalinformationbasedondecisionlevelfusion.Inourimplementation,ouralgorithmcandealwith swithreal-timeperformance.Therearestillmanyotherapplicationsofthegroundnerectificationlikecameracalibration.Insteadofatiringwidesitesurvey,completecalibrationcannowbeachievedonlybymeasuringfewmetricslikeahorizonallinelengthandthecameraheight,whichgreatlythedifficultyforcameratop-downcameraview.However,distortionisnotevidentintop-downviews.Sincethegroundnerec-tificationistakentodealwithdistortion,top-downviewisnotabigproblemofourapproach.Furthermore,trafficscenesurveillance