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4Tw o-dimensionalFaceRecognition4.1FeatureLocalizationBeforediscussingthemethodsofcomparingtwofacialimageswenowtakeabrieflookatsomeatthepreliminaryprocessesoffacialfeaturealignment?Thisprocesstypicallyconsistsoftwostages:facedetectionandlocalization.Dependingontheapplication,ifthepositionofthefacewithinaaforexample)thenthefacedetectionstagecanoftenbeskipped,astheregionofisweabriefdiscussionoffacedetectionintheliteraturereview?Theeyelocalizationmethodisusedtoalignthe2Dfaceimagesofthevarioustestsetsusedthroughoutthissection.However,toensurethatallresultspresentedarerepresentativeofthefacerecognitionaccuracyandnotaproductoftheperformanceoftheeyelocalizationroutine,allimagealignmentsaremanuallycheckedandanyerrorscorrected,priortotestingandevaluation.Wedetectthepositionoftheeyeswithinanimageusingasimpletemplatebased?Asetofofisandimagecroppedtoanareaaroundbotheyes?Theaverageimageiscalculatedandusedasatemplate?Figure41Theaverageeyes?Usedasatemplateforeyedetection.Botheyesareincludedinasingletemplate,ratherthanindividuallysearchingforeacheyeinturn,asthecharacteristicsymmetryoftheeithersideofthenose,provideausefulfeaturethathelpsdistinguishbetbeupin?Althoughthismethodishighlysusceptibletoscalei?e.subjectdistancefromthecamera)andalsointroducestheassumptionthateyesintheimageappearnearhorizonta1.SomepreliminaryexperimentationalsorevealsthatitisadvantageousPAGEPAGE9 /12toincludetheareaofskinjustbeneaththeeyes?Thereasonbeingthatinsomecasestheeyebrowscancloselymatchthetemplate,particularlyifthereareshadowsintheeye-sockets,buttheareaofskinbelowtheeyeshelpstodistinguishtheeyesfromeyebrows(theareajustbelowtheeyebrowscontaineyes,whereastheareabelowtheeyescontainsonlyplainskin)?Awindowispassedoverthetestimagesandtheabsolutedifferencetakentothatoftheaverageeyeimageshownabove?Theareaoftheimagewiththelowestdifferenceistakenastheregionofinterestcontainingtheeyes?Applyingthesameprocedureusingasmallertemplateoftheindividualleftrighteyesthenrefineseacheyeposition.Thisbasictemplate-basedmethodofeyelocalization,althoughprovidingfairlyofteneyes.weareabletoimproveperformancebyincludingaweightingscheme?Eyelocalizationisperformedonthesetoftrainingimages,whichistheninwhicheyedetectionfailed?Takingthesetofsuccessfullocalizationswecomputetheaveragedistancefromtheeyetemplate(Figure4-2top)?Notethattheimageisquitedark,indicatingthatthedetectedeyescorrelatecloselytotheeyetemplate,aswewouldexpect?However,brightpointsdooccurnearthewhitesofthesuggestingthatthisareaisofteninconsistent,varyinggreatlyfromtheaverageeyetemplate?Figure4-2-Distancetotheeyetemplateforsuccessfuldetections(top)indicatingvarianceduetonoiseandfaileddetections(bottom)showingcrediblevarianceduetomiss-detectedfeatures?Inthelowerimage(Figure4-2bottom),wehavetakenthesetoffailedlocalizations(imagesoftheforehead,nose,cheeks,backgroundetc.falselydetectedbythelocalizationroutine)andonceagaincomputedthedistancefromtheeyetemplate?Thebrightpupilssurroundedbydarkerareasindicatethatafailedmatchisoftenduetothehighcorrelationofthenoseandcheekboneregionsoverwhelmingthepoorlycorrelatedpupils?Wantingtoemphasizethedifferenceofthepupilregionsforthesefailedmatchesminimizethevarianceofthewhitesoftheeyesforsuccessfulmatches,wedividethelowerimagevaluesbytheupperimagetoproduceaweightsvectorasshowninFigure4-3?Whenappliedtothedifferenceimagebeforesummingatotalerror,thisweightingschemeprovidesamuchimproveddetectionrate.Figure43-Eyetemplateweightsusedtogivehigherprioritytothosepixelsthatbestrepresenttheeyes?4.2TheDirectCorrelationApproachWebeginourinvestigationintofacerecognitionwithperhapsthesimplestapproach,knownasthedirectcorrelationmethod(alsoreferredtoastemplatematchingbyBrunelliandPoggio)involvingthedirectcomparisonofpixelysnml?eeemtftoencompassalltechniquesinwhichfaceimagesarecompareddirectlywithoutanyformofimagespaceanalysis,weightingschemesorfeatureextraction,sfeec?,eotrt?scorrelationisappliedasthesimilarityfunction(althoughsuchanapproachwouldobviouslycomeunderourdefinitionofdirectcorrelation)?WetypicallyusetheEuclideandistanceasourmetricintheseinvestigations(inverselydon?sndnedsaedsensitiveformofimagecorrelation),asthispersistswiththecontrastmadebetweenimagespaceandsubspaceapproachesinlatersections?Firstly,allfacialimagesmustbealignedsuchthattheeyecentersarelocatedattwospecifiedpixelcoordinatesandtheimagecroppedtoremoveanybackgroundinformation.Theseimagesarestoredasgrayscalebitmapsof65by82pixelsandpriortorecognitionconvertedintoavectorof5330elements(eachelementcontainingthecorrespondingpixelintensityvalue)?Eachcorrespondingvectorcanbethoughtofasdescribingapointwithina5330dimensionalimagespace?Thissimpleprinciplecaneasilybeextendedtomuchlargerimages:a256by256pixelimageoccupiesasinglepointin65,536-dimensionalimagespaceandagain,similarimagesoccupyclosepoints?space,whiledissimilarfacesarespacedfarapart?CalculatingtheEuclideandistancedbetweentwofacialimagevectors(oftenreferredtoastheqyandgalleryimageg),wegetanindicationofsimilarity?Athresholdisthenappliedtomakethefinalverificationdecision.4.2? 1VerificationTestsTheprimaryconcerninanyfacerecognitionsystemisitsabilityyyadyrean5styasetofpotentialmatchesinadatabase?Inordertoassessagivensystem'sabilitytoperformthesetasks,avarietyofevaluationmethodologiesa(i?securesiteaccessorsurveillance),whileothersprovideamoremathematicaldescriptionofdatadistributioninsomeclassificationspace?addition,theresultsgeneratedfromeachanalysismethodmaybepresentedina?usetheverificationtestasourmethodofanalysisandcomparison,althoughwealsouseFishersLinearDiscriminatetoanalyzeindividualsubspacecomponentsinsection7andtheidentificationtestforthefinalevaluationsdescribedinsection?Theverificationtestmeasuresasystem'stocorrectlyathisreducestotwoimagesbeingpresentedforcomparison,forwhichthemustreturneitheranacceptance(thetwoimagesareoftherejection(thetwoimagesareofdifferentpeople)?Thetestisdesignedto?aaaproximitychiporPINnumber?Thisnumberisthenusedtoretrieveastoredimagefromadatabaseofknownsubjects(oftenreferredtoastheorgalleryimage)andcomparedwithaliveimagecapturedatthepointofentry?isondecision.Theresultsofthetestarecalculatedaccordingtohowmanytimesaccept/rejectdecisionismadecorrectly.Inordertoexecutethistestwemustfirstdefineourtestsetoffaceimages?Althoughthenumberofimagesinthetestsetdoesnotaffecttheresultsproduced(astheerrorratesarespecifiedaspercentagesofimagecomparisons),itisimportanttoensurethatthetestsetissufficientlylargesuchthatstatisticalanomaliesbecomeinsignificant(forexample,acoupleofbadlyalignedimagesmatchingAlso,thetypeofimages(highvariationinlighting,partialocclusionsetc?)?multiplefacerecognitionsystems,theymustbeappliedtothesametestset?ofsystemperformanceinarealworldsituation,thenthetestdatashouldbeapplicationenvironment?Ontheotherhand,ifthepurposeoftheexperimentationistoevaluateandimproveamethodoffacerecognition,whichmaybeappliedtoarangeapplicationenvironments,thenthetestdatashouldpresenttherangeofdifficultiesthataretobeovercome?Thismaymeanincludingagreaterperceconditionsandhencehighererror:ratesintheresuItsproduced?Belowalgorithmforexecutingtheverificationtest?Thealgorithmisappliedtoasingletestsetoffaceimages,usingasinglefunctioncalltothefacerecognitionalgorithm：CompareFaces(FaceA,FaceB)?Thiscallisusedtocomparetwofacialimages,:returningadistancescoreindicatinghowdissimilarthetwofaceimagesare:thelowerthescorethemoresimilarthetwofaceimages?Ideally,imagesofthesamefaceshouldproducelowscores,whileimagesofdifferentfacesshouldproducehighscores?Everyimageiscomparedwitheveryotherimage,noimageiscomparedwithitselfandnopairiscomparedmorethanonce(weassumethattherelationshipissymmetrical)? Oncetwoimageshavebeencompared,producingasimilarityscore,theground-truthisusedtodetermineiftheimagesareofthesamepersonordifferentpeople? Inpracticalteststhisinformationisoftenencapsulatedaspartoftheimage(bymeansofauniquepersonidentifier)?Scoresarethenstoredinoneoftwolists:alistcontainingscoresproducedbycomparingimagesofdifferentpeopleandalistcontainingscoresproducedbycomparingimagesofthesameperson.Thefinalacceptance/rejectiondecisionismadebyapplicationofathreshold? Anyincorrectdecisionisrecordedaseitherafalseacceptanceorfalserejection.Thefalserejectionrate(FRR)iscalculatedasthepercentageofscoresfromthesamepeoplethatwereclassifiedasrejections? Thefalseacceptancerate(FAR)iscalculatedasthepercentageofscoresfromdifferentpeoplethatwereclassifiedasacceptances?twotheoftheataspecificthresholdvalue? Ideally,boththesefiguresshouldbezero,butinrealityreducingeithertheFARorFRR(byalteringthethresholdvalue)in?thefulloperatingrangeofaparticularsystem,wevarythethresholdvaluethroughtheentirerangeofscoresproduced?TheapplicationofeachthresholdvalueproducesanadditionalFAR,FRRpair,whichwhenplottedonagraphproducestheerrorratecurveshownbelow?Figure45-ExampleErrorRateCurveproducedbytheverificationtest?Theequalerrorrate(EER)canbeseenasthepointatwhichFARisequal?arecognitionperformanceofabiometriesystemandallowsforeasycomparisonofmultiplemethods?However,itisimportanttonotethattheEERdoesnotindicatetheleveloferrorthatwouldbeexpectedinarealapplication.Itisunlikelythatanyrealsystemwoulduseathresholdvaluesuchthatthepercentageoffalseacceptanceswasequaltothepercentageoffalserejections?Securesiteaccesssystemswouldtypicallysetthethresholdsuchthatfalseacceptancesweresignificantlylowerthanfalserejections:unwillingtotolerateintrudersatthecostofinconvenientaccessdenials?Surveillancesystemsontheotherhandwouldrequirelowfalserejectionratestosuccessfullyidentifypeopleinalesscontrolledenvironment?ThereforeweshouldbearinmindthatawithalowerEERmightnecessarilybethebetterperformertowardstheextremesofitsoperatingcapability?Thereisastrongconnectionbetweentheabovegraphandthereceiveroperatingcharacteristic(ROC)curves,alsousedinsuchexperiments?BothusestheTrueAcceptanceRate(TAR),whereTAR二1.0-FRRinplaceoftheFRR,effectivelyflippingthegraphvertically.AnothervisualizationofverificationtestresultsistodisplayboththeFRRandFARasfunctionsof?atothethresholdvaluenecessarytoachieveaspecificFRRandFAR?TheEERcanbeseenasthepointwherethetwocurvesintersect?Figure46ExampleerrorratecurveasafunctionofthescorethresholdThefluctuationoftheseerrorcurvesduetonoiseandothererrorsisontheoftotheAsmalldatasetthatonlyallowsforasmallnumberofcomparisonswillresultsinaintoofaimageonahighproportionofthecomparisonsmade?Atypicaldatasetof720(asin4.2?2)840aof1%anthequalityofasingleimagecouldcausetheEERtofluetuatebyupto44.1。這通常有由檢測(cè)和眼睛如果是事門禁系統(tǒng)主題那么檢測(cè)階段通常是可以跳。因此眼睛中有個(gè)檢測(cè)文獻(xiàn)短討適用于對(duì)齊各種測(cè)試為了確保所有結(jié)果都代外表準(zhǔn)確率所有結(jié)果發(fā)現(xiàn)個(gè)使用眼睛個(gè)基于模板置方法。個(gè)區(qū)域中對(duì)手動(dòng)對(duì)齊進(jìn)行采取和裁剪以平均計(jì)算作為模板。4-1平均眼睛用作模板眼睛檢測(cè)兩個(gè)眼睛都包括在一個(gè)模板，而不是單獨(dú)為單個(gè)搜索，因?yàn)檠劬υ诒亲觾?邊對(duì) 稱特點(diǎn)，這樣就提供了一個(gè)可用方法，可以幫助區(qū)分眼睛和其他可能誤報(bào) 背景。雖然 這種方法介紹了假設(shè)眼睛水平形象出現(xiàn)后很容易受到小距離影響 〔即主體和相機(jī)距 離〕，但初步試驗(yàn)顯示，還是利于包括眼睛下方皮膚區(qū)域得 到校準(zhǔn)去結(jié)果。因?yàn)樵谀?些情況下，眉毛可以密切配合模板，特別是如果在眼 睛區(qū)域陰影周圍。此外眼睛以下 皮膚面積有助于區(qū)分眉毛〔眉毛下方面積眼中 包含眼睛，而該地區(qū)眼睛下面皮膚只 含有〕。區(qū)域是對(duì)試和對(duì)這一平眼睛面顯示。面積為含有眼中區(qū)域。用樣用小模板單，眼， 然后提只眼睛。這個(gè)模板眼睛方法，提供了相，但不能完眼睛區(qū)域。但是，能能和。眼睛是在，然后分兩些眼睛，和 些眼睛。以地，在平距離眼睛模板〔4-2〕，，該是，這現(xiàn)眼睛密切相眼睛模板， 如樣。然而，點(diǎn)在眼睛區(qū)域，這方面是不一 ，不于模板。 4-2對(duì)眼睛模板〔〕，于方和〔〕顯示 在〔〕，，鼻子，，背景用了假，并眼睛了平距離。點(diǎn)區(qū)包圍，一個(gè)配和鼻子和 地區(qū)相相。以，如圖4-3示。用到分在結(jié)誤，這個(gè)方提了出。4一 34.2相方法 方法稱為方法〔稱為模板利和〕，其中面。用'’，以涵蓋有技面臨，以沒有任何形式形象空 間分析，方或特征提。因此，不能推斷皮爾遜函相，為用相似能〔這種做法顯然會(huì)受到相義〕。用歐氏距離為結(jié)果〔負(fù)相，Pearson相，可以考慮為一 個(gè)規(guī)模和翻譯相敏形式〕， PAGEPAGE10 /12這還比照了后面章節(jié)空間和子空間圖像方 法。 首先，所有面部圖像必須保持一致，這樣使眼睛在兩個(gè)中心位于指定像素 坐標(biāo) 和裁剪，以消除任何背景中圖像信息。這些圖像存