翻译以.原文和在同一文件中前

一种灰度直的阈值选择方本文提出了一种关于图像分割的无参数、非监督的自适应阈值。通过一个1 概将直限制在导数（或梯度值）绝对值大的像素点上。还有差值直法，息来修改直使其更便于找到阈值。另一类方法通过参数技术直接处理灰度直。例如，直的分布的总和接近于最小二乘法意义下的值，这里用到了统计决策过2 并且像素的总数量为N=𝑛1+𝑛2+⋯+𝑛𝐿。为了简化讨论，灰度直被标准化并且𝑝𝑖=𝑁，𝑝𝑖≥0，∑𝑝𝑖=

分类的阈值为灰度k；𝐶0表示的像素的灰度级是[1,…,k],𝐶1表示的像素的灰度级是𝜔0=Pr(𝐶0)=∑𝑝𝑖= 𝜔1=Pr(𝐶1)=∑𝑝𝑖=1− 𝜇=∑𝑖Pr(𝑖|𝐶)(=

=

0

𝜇=∑𝑖𝑃𝑟(𝑖|𝐶)=∑𝑖𝑝

=𝜇𝑇−

1

1−ω(k)=∑μ(k)=∑

𝜇𝑇=𝜇(𝐿)=∑

𝜔0𝜇0+𝜔1𝜇1=𝜇𝑇，𝜔0+𝜔1=

∑𝑘(𝑖−𝜇)2𝜎2=∑(𝑖−𝜇)2Pr(𝑖|𝐶)

(𝑖−𝜇1)2𝜎2=∑(𝑖−𝜇)2Pr(𝑖|𝐶)

者叫做类分离方法

λ 𝐵 𝜅 𝑇 𝜂=

𝜎2=𝜔0𝜎2+ 𝜎2=𝜔0(𝜇0−𝜇𝑇)2+𝜔1(𝜇1−𝜇𝑇)2=𝜔0𝜔1(𝜇1− (由(9)可得)并𝜎2=∑(𝑖− 问题，即找到一个阈值k使得（12）中的一个目标函数（标准方法）最大。ηλ/(λ1),𝜎2+𝜎2= 这意味着𝜎2、𝜎2k的函数，但是𝜎2k的值有关。同时说明𝜎2 阶统计量（类方差）的，而𝜎2是基于一阶统计量（类均值）的。由此可见，η是最简单k的度量值。所以，我们采用ηk的“完美程度”（或者称为分离的。搜索可以基于简单的累加（6）和（7），或者显式地使用（2）-（5η(k)=𝐵

𝜎2(𝑘)

[𝜇𝑇𝜔(𝑘)−

𝜔(𝑘)[1−𝜎2(𝑘∗)=max 1≤𝑘<𝐿从这个问题看出，k𝑆∗={𝑘;𝜔0𝜔1=𝜔(𝑘)[1−𝜔(𝑘)]> 𝑜𝑟0<𝜔(𝑘)<我们称之为灰度直的有效范围。从公式（14）的定义，标准量度𝜎2(或者η)取最小0当k∈S−𝑆∗={𝑘;𝜔(𝑘)=0𝑜𝑟1}(也就是让所有的像素值不是在𝐶0中就在𝐶1中)并且取得一个正的边界值，k∈𝑆∗,显而易见，最大值是一直存在的。3 对于选定的阈值𝑘∗,类概率（2）和（3）分别表示阈值化程度很高的类所占据的区域上的仿射变换的不变性（即:对于任意的变换和扩张，𝑔𝑎𝑔𝑖+𝑖𝑏。它被唯一确0≤𝜂∗≤三部分的情况下，我们假设两个阈值：1≤𝑘1≤𝑘2≤𝐿,将类划分成为三部分，𝐶0[1𝑘1],𝐶1是[𝑘1+1𝑘2],𝐶2是[𝑘2+1L]。于是，标准尺度𝜎2(也就是η)就成了𝑘1和𝑘2两个变量的函数。同时，最佳的一组阈值𝑘∗和𝑘∗的选择原则就是将𝜎2的值最 𝜎2(𝑘∗,𝑘∗) 𝜎2(𝑘1, 1≤𝑘1≤𝑘2≤𝐿况，所以，基本不需要再去寻找一种简化阈值选取流程的方法。应该，本方法中，M分割所需要的参数是M-1个本身的离散阈值，而那些参数化方法，比如用分布的和来近的灰度直，需要3M-1个连续参数量。始的灰度级图像；（b）(也可以是（f）)是阈值分割之后的结果；（c）(也可以是（g）)是一组灰度直（标注出了阈值）和相对应的标准度量η(k);（d）(也可以是(h))是通过分析得到的结果。所有的原始灰度尺寸都是64*64,并且在Fig.1中的的灰度级是16级灰度值上的有相等的输出结果，所以可能在灰度级上会稍微损失精度。1（a，另外一个的老式的（e在i.2，示纹理果其中灰直代性显（）（g这个方也成功用到了胞中，结果示在Fi.3中。其中𝐶代表，𝐶1代表细胞质目标函数𝜎2(𝑘),或者说标准度量η(k)Fig1-2中的实4 总本文从判别分析的角度提出了一种通过灰度直自适应选择出阈值的方法。这个谷，而是基于直的整体综合（全局量。这个方法的应用范围不仅仅局限在以上所灰度级的阈值选取，它还涵盖件亲切和有益的建议。 分类 用于车辆检测的增强分类院（系）称专业称学生指导称师20146近年来，ViolaJones已经提出了一种用检测器[1]AdaBoost来从一个很大的RealAdaBoost算法，拟合参数函1 概3.1章节中会有展示。因此，我们决定将脸部检测的方2 AdaBoost/ViolaJones脸部检45000个在[1]140000个特征被检测过。但是这Viola等人的最大贡献就是将检测器的效率提高到实时的地步。这之所以成为可能，是因为一些聪明的观察：仅仅估算AdaBoost选择的必要的特征值，使用级联结构迅速筛为了减少评估一张所花费的时间，减少花费在分出错误样本的时间十分重要。假设10倍，而检测的精度仅仅下降一点点。级联的一个不为人知的好（尤其是存在的错误样本的时候。级联的每个阶段都仅仅训练那些已经通过了之在Viola-Jones基础上的扩例如Lennart等人做了特征集合方面的扩展[4],Wu等人做了弱分类器和提升方面的工作[2],Huang等人提出了关于多个人脸检测的树结构级联的理论[5]等等。在这篇文章中，我们也对Viola等人的工作做了验证和扩充。3 数据车尾部的是从驾驶员的驾驶座位上拍摄的，拍摄地点是在匹兹堡。1（a）展示了我们到的一些车尾部的，1（b）是裁剪以后车尾部的部分。1其次是左侧和右侧的轮胎特征。这个检测器的质量通过了329张的测试以及评估。在这些640*480的上，一个扫描窗口的大小是50*50，用每次3像素的移动幅度进比较ROC曲线来评估其效率。RealAdaboost算给出示例(𝑥1,𝑦1),…,(𝑥𝑛,𝑦𝑛),其中𝑦𝑖=-1,1分别代表错误样本和正确样本初始化权重𝑤=

,

分别对应𝑦=−1,1.ml对于ℎ𝑗=1log(𝑃𝑡,𝑗 其中𝑃𝑡,𝑗、𝑛𝑡,𝑗j的特征值权重大于0，就是正样本，当它小于0就是负样本。𝜔𝑖←

𝜔𝑖 ∑∑

h(𝑥)=∑法。这些结果在4中被描绘出来。最开始的两个方法用的二元分类器，用的是离散拟合参Simoncelli[6]已经通过经验发现了我们数据集中的特征直遵循着下面的公式h(x)∝不应该符合，因为它们具有差异性。我们可以在估算𝑛𝑡,𝑗的时候去完善上面的公式，但是我们就无法再使用𝑤𝑖来表示直的权重，因为直不能遵循上面的公式。我们首先对非的直𝑝𝑡,𝑗和𝑛,𝑡,𝑗做了实验，然后尝试拟合非的负样本直。二者都产生了比直略差的性能。提可以大幅提高速度。7显示了最后的强分类器和弱分类器数目关系的曲线图。随着数量从500降到7，一张640*480的的计算时间降到100ms，同时对精度无任何损图像配3.1节中已经简短的提到过，我们已经知道最为显著的检测车辆的特称就是阴影方式，一个是对准两个车胎的位置，另外一个是对准车顶部的两个角。8比较了程序选择的前面的10个特征，结果是如果选择顶部对齐，那么上部区域会有的特征4 总我们认真的学习研究了Viola等人人脸识别的方法，并且将其运用于车辆识别。用探索出来的最好的组合方式得到的最终的结果显示在10中。在预留的用于最终检测的80张中，一共有149辆车，检测到了143辆。漏检率仅为4%,并且有BoostedClassifierforCarDavidC.ECEDepartmentCarnegieMellonUniversityRecently,ViolaandJones[1]haveproposedadetectorusingAdaboosttoselectandcombineweakclassifiersfromaverylargepoolofweakclassifiers,andithasbeenproventobeverysuccessfulfordetectingfaces.Wehavefollowedtheirapproachandappliedittodetectrearviewsofcars.Thedetectorwascarefullyexaminedandwasexpandedinanumberofways,suchasvaryingthetypeandcomplexityofweaklearners,usingRealAdaboost,fittingparametricfunctionstotheprobabilitydistributions,aligningtrainingimagesatdifferentpositions,andexploitingatendencyintheclassifiertospeeduptherunningWeadoptedthemethodsfromfacedetectionandapplieditforcarrear-viewdetection.Webelievethatfacedetectionandcardetectionaresimilarinnatureandapplyingfacedetectionmethodsforcardetectionisanaturalchoice.Thesuccessoffacedetectionmayhavebeenduetothefactthatfaceimageshaverichinternalfeatures.Someimagecategories,suchaspe-destrian,canonlybecharacterizedbythecontouroftheobjectsincethereisnotacharacteristicpatternthatstandsoutinsidetheregionoftheobject.Ontheotherhand,faceshaveverydis-tinctivepattern,causedbyeyes,nose,mouth,etc,thatcanbewellcapturedbysimplefiltersencodingtheintensitydifferenceasinViolaandJones[1].Similarly,rearviewsofcarsalsohavedistinctivepatterns,suchasthedarkshadowregionrightbelowthecar,anddarktireregion,asshowninsection3.1.Therefore,wedecidedtoapplythemethodsdevelopedforfacedetectiontocardetection.PreviousAdaboost/ViolaJonesfaceAdaboost[3]isametaalgorithmthatisdesignedtoboosttheperformanceofanyexistingclassifier.Apopularchoiceofweaklearnerisdecisiontreeofdepth1,whichissimplyaclas-sifierthatdependsonlyonasinglefeature.Whenthenumberoffeaturesisverylarge,asinthecaseofrectangularfeaturesin[1],Adaboostcanbeviewedasafeatureselectionprocedure.Morethan45,000featuresweretestedin[1]andmorethan140,000featuresweretestedinourwork,butthediscriminativefeaturesareonlyaverysmallfractionofit.Findingandcompu-tingonlythediscriminativeonesisfarmoreefficientthanat-temptingtoevaluatethemall.ThebiggestcontributionofViolaetal.[1]wasinimprovingthespeedofthedetectortorealtime.Thiswaspossibleduetosomecleverobservations:evaluatingonlythenecessaryfeatureschosenbyAdaboost,usingcascadingstructuretoquicklyrejectnegativesamples,andusingverysimplefeaturesthatarefasttoevaluateusingintegralimage.

Reducingthetimespentonclassifyingnegativesamplesistheveryimportantinreducingthetimetoevaluateanimage,sinceatypicalimagehasaround1~10carsand130,000sub-windowsofnon-car.Violaetal.haveusedacascadestylede-tectorthatcouldquicklyrejectnegativesamplesbyevaluatingonlyafewfeatures.Itismentionedintheirpaperthatcascadingimprovestherunningtimeby10timeswhileslightlydecreasingtheaccuracy.Alessknownbenefitofcascadingisthatiteffec-tivelyusesmoretrainingdata(morenegativesamplesinpartic-ular)thanonewouldnormallybelimitedbythetimeandcom-putationalresourceneededfortraining.Eachstageofcascadeonlytrainsonthesamplesthatpassedthepreviousstages,andsinceonlyaverysmallfractionofthenegativesamplespassthroughthepreviousstages,eachstagecantrainonasmallsamplewhilehavingtheeffectoftrainingonamuchlargerset.Figure1(a)ImagescollectedwhiledrivingaroundPittsburgh(b)croppedregionsofcars(c)croppedregionsofnon-carsAfterthesuccessofViolaetal.[1],therehasbeenalotofextensionstotheirmethod,suchasextensionofthefeaturesetbyLienhartetal.[4],extensionsontheweakclassifierandboostingmethodbyWuetal.[2],atreestructuredcascadeformultiviewfacedetectionbyHuangetal.[5],andsoon.Inthispaper,wehavealsoexaminedandexpandedtheoriginalworkofViolaetal.[1]OwnTheimagesofcarswerecollectedinsideacarfromthepas-sengerseatwhiledrivingaroundthePittsburgharea.Figure1(a)showssomeoftheimagesthatwerecollected,figure1(b)showscroppedregionofcars,andfigure1(c)showscroppedregionsusedfornegativetrainingimages.Atotalof621imagesofcarswerecollectedand80imagesweresetasideforthefinaltesting.Oftheremaining561images,629croppedregionsofcarswereextractedandtheywererandomlydividedinto300fortrainingand329fortestingforuseincomparingdifferentmethodsandplottingtheReceiverOperatingCharacteristic(ROC)curve.Figure2showsthefirst3filterschosenbytheboostingprocess.Theshadowbelowthecaristhemostdiscriminativefeature,andtheleftandrighttireregionarethesecondandthirdmostdiscriminativefeature.Thequalityofthedetectorwasmeasuredonthe329imagesfortesting.Onthe640x480images,ascanningwin-dowofsize50x50wasevaluatedwithslidingstrideof3pixelsandrepeatingtheprocessbyresizingtheimagewithscale0.9,leadingto128918subwindows.PerformancewasmeasuredbycomparingtheROCcurve. Figure2Firstthreefiltersselectedbyyi1,1fornegativeandpositiveexamplesrespective-Initializeweightswi2m1,foryitively,wheremandlarethenumberofnegativeandpositivesrespectivelyfortForeachfeaturearealvaluedweaklearnerisdefinedh 1j pt,2 whereand ist,t,t,jweightedhistogramoffeaturejforpositivenegativerespectivelyweightedwith

ChooseChoosetheclassifierhtwiththelowesterrortwhereerroriscomputedbythresholdingthereal-valuedconfi-denceatzeroandclassifyingaspositivewhengreaterthanzeroandclassifyingasnegativewhenlessthanze-Updateandnormalizethewiwiexpyihtxiw i nwThefinalstrongclassifierh(x)htTtFigure3RealAdaboostViolaetal.[1]haveuseddiscreteAdaboostanddecisionstump(singleleveldecisiontree)astheweakclassifier.WehavecomparedtwoversionsofdiscreteAdaboostandalsocomparedRealadaboost.Thethreesettingswere(1)adecisionstump,(2)aslightlymorecomplexbinaryclassifier,and(3)RealAdaboostandtheyaredepictedinFigure4.ThefirsttwomethodswithbinaryclassifieraretrainedwithdiscreteAda-boostandthethirdmethodwastrainedwithrealAdaboost.Thealgorithmformethod(3)isgiveninFigure3.Experimentsshow(Figure5)thatmethod(3)givesthebestperformanceandmethod(2)and(1)givesslightlylowerperformance.Eveninthesecondandthirdcase,nocompromiseinspeedneedstobemadeiftheweakclassifierisstoredasalookuptable[2].Wehavealsoexperimentedwithweakclassifierusing2fea-turestocreatea2dimensionalhistogram.Thisyieldedinbetterperformanceintrainingsetbutgaveslightlyworseperformanceintestingset,whichsuggeststheclassifierhaveoverfittedthetrainingsetgiventhepowerofamorecomplexclassifier.FittingSimoncelli[6]havenoticedempiricallythathistogramsofthefeaturesusedinoursettingfollowtheform:ph(x)ex/Weobserved(Figure6)thatthehistogramsoffeaturesfornegativesamplesfollowtheaboveform,butthehistogramsofpositivesdonot(andshouldnot,forthemtobediscriminative!).Wecantrytofittheabovefunctionwhenestimatingnt,jbutthenwecannolongerweightthehistogramswithwisinceweightedhistogramwouldnolongerfollowtheaboveform.Wehavefirstexperimentedwherethehistogramspt,jandnt,wereunweighted,andthentriedfittingtheunweightednegativehistogram.Bothyieldedaslightlyworseperformancethanusingweightedhistograms.Figure4Firstrow:histogramofpostiveandnegativesamples,second,third,fourthrow:weakclassifierformethod(1),(2),Figure5Performancecomparisonoftwodifferentweak

Figure6FittedhistogramwithequationgivenSimoncelliSpeedAlthoughwedidnotusethecascadingstructureforquickre-jectionofnegativesamples,wedidobserveatendencyintheclassifierthatcouldincreasethespeeddrastically.Figure7showsthescoreofthefinalstrongclassifierplottedagainstthenumberofweaklearners.Asthenumberofweaklearnerin-creases,thescoreforbothpositiveandnegativesamplesin-creaseordecreasealmostlinearly.Samplesthatgetlowscoreearlyonintheevaluationcouldberejectedtosavetime.Byadjustingthethresholdforrejection,wecouldreducetheaver-agenumberofevaluatedfeaturesfrom500to7featuresachiev-ingarunningtimeofabout100msfora640x480image,with-outcompromisingtheaccuracy.Figure7TendencyinthescoreofthefinalImageAsbrieflymentionedinsection3.1,wehavenoticedthatthemostdiscriminativefeaturefordetectingcarsistheshadowregion.Theremaybetworeasonsforthis;theregionmayac-tuallybethemostcharacteristicpartindetectingcars,oritmighthavebeencausedbythefactthatthetrainingimagesofcarswerealignedatthetipsofthetwotires,thusmakingthebottomregionmoreconsistentacrosscarimages.Thisbringsustothequestionofhowweshouldalignthecarimages.Sowehavecomparedtwodifferentalignments,onealignedwiththetwotipsofthetiresandtheotheralignedthetoptwocornersofthecar.Figure8comparesthefirst10fea-tureschosenbytheprocess,anditshowsthatmorefeaturesFigure10Thefirstrowandtheleftmostimageofsecondrowshowsresultswithnoerrors.Thethreerightmostimagesonthesecondrowshowexampleswherethereareeitherfalsedetectionsormisseddetection.WehavecarefullystudiedandobservedthefacedetectionmethoddevelopedbyViolaetal.[1]andappliedittocardetec-tion.Thefinalresultswiththebestcom