The footprints of visual attention in the Posner cueing ...

An important paradigm for studying visual attention in the last two decades has been the Posner cueing paradigm (Posner, 1980). In this paradigm, a target can ... JumpTo... Introduction ClassificationImageSignatures Methods Results Discussion Conclusions Acknowledgments Footnotes AppendixA AppendixB References Free ResearchArticle  |  January2002 ThefootprintsofvisualattentioninthePosnercueingparadigmrevealedbyclassificationimages MiguelP.Eckstein;StevenS.Shimozaki;CraigK.Abbey AuthorAffiliations MiguelP.Eckstein DepartmentofPsychology,UniversityofCalifornia,SantaBarbara,CA,USAhttp://www.psych.ucsb.edu/~eckstein/lab/[email protected] StevenS.Shimozaki DepartmentofPsychology,UniversityofCalifornia,SantaBarbara,CA,USAhttp://www.psych.ucsb.edu/~eckstein/lab/[email protected] CraigK.Abbey Dept.ofBiomedicalEngineering,UniversityofCalifornia,Davis,CA,USAhttp://www.psych.ucsb.edu/~eckstein/lab/[email protected] JournalofVisionJanuary2002,Vol.2,3.doi:https://doi.org/10.1167/2.1.3 Views FullArticle Figures Tables PDF Share E-mail Facebook Twitter Google Digg Delicious Tumblr StumbleUpon Tools Alerts UserAlerts Youareaddinganalertfor: ThefootprintsofvisualattentioninthePosnercueingparadigmrevealedbyclassificationimages Youwillreceiveanemailwheneverthisarticleiscorrected,updated,orcitedintheliterature.YoucanmanagethisandallotheralertsinMyAccount Thealertwillbesentto: Confirm × Thisfeatureisavailabletoauthenticatedusersonly. SignIn or CreateanAccount × GetCitation Citation MiguelP.Eckstein,StevenS.Shimozaki,CraigK.Abbey;ThefootprintsofvisualattentioninthePosnercueingparadigmrevealedbyclassificationimages.JournalofVision2002;2(1):3.doi:https://doi.org/10.1167/2.1.3. Downloadcitationfile: Ris(Zotero) EndNote BibTex Medlars ProCite RefWorks ReferenceManager ©ARVO(1962-2015);TheAuthors(2016-present) × GetPermissions Supplements AbstractInthePosnercueingparadigm,observers’performanceindetectingatargetistypicallybetterintrialsinwhichthetargetispresentatthecuedlocationthanintrialsinwhichthetargetappearsattheuncuedlocation.ThiseffectcanbeexplainedintermsofaBayesianobserverwherevisualattentionsimplyweightstheinformationdifferentlyatthecued(attended)anduncued(unattended)locationswithoutachangeinthequalityofprocessingateachlocation.Alternatively,itcouldalsobeexplainedintermsofvisualattentionchangingtheshapeoftheperceptualfilteratthecuedlocation.Inthisstudy,weusetheclassificationimagetechniquetocomparethehumanperceptualfiltersatthecuedanduncuedlocationsinacontrastdiscriminationtask.Wedidnotfindstatisticallysignificantdifferencesbetweentheshapesoftheinferredperceptualfiltersacrossthetwolocations,nordidtheobserveddifferencesaccountforthemeasuredcueingeffectsinhumanobservers.Instead,wefoundadifferenceinthemagnitudeoftheclassificationimages,supportingtheideathatvisualattentionchangestheweightingofinformationatthecuedanduncuedlocation,butdoesnotchangethequalityofprocessingateachindividuallocation. Introduction AnimportantparadigmforstudyingvisualattentioninthelasttwodecadeshasbeenthePosnercueingparadigm(Posner,1980).Inthisparadigm,atargetcanappearinoneoftwolocations,andtheobserverreportswhetherthetargetispresent(yes/no).Priortothepresentationofthestimulus,acue(precue)indicatestheprobablelocationofthetarget(giventhatthetargetispresent)withsomevalidity(e.g.,80%ofthetrials).Thosetrialsinwhichthecuecorrectlyindicatesthelocationofthetargetareknownasthevalidcuetrials,whereasthetrialsinwhichthecueincorrectlyindicatesthelocationofthetargetarecalledtheinvalidcuetrials.Aclassicalresultisthatperformance(measuredwithresponsetimesortargetdetectionaccuracy)isbetterinthevalidcuetrialsversustheinvalidcuetrials.ThisresultledPosner(Posner,1980;Posner&Peterson,1990)andmanyresearchersinsubsequentstudiestoconcludethatthecueorientsvisualattention,whichenhancesprocessingatthatcued(attended)location.Ananalogousinterpretationoftheresultisthatvisualattentionhaslimitedresourcesthatcanbeallocatedatoneofthelocations.Whentheresourcesareallocatedatthecuedlocation,aperformancebenefitattheattendedlocationarises.  TheBayesianObserver:CueingEffectsWithoutCapacityLimitations/AttentionalEnhancement Recently,analternativeapproachhasbeenproposedforthecueingparadigmintermsofaBayesianobserver.Thismodelpredictsacueingeffectwithoutachangeinthequalityofprocessingattheattendedandunattendedlocations(i.e.,changesintheperceptualfilters,internalnoise,etc.).Inthismodel,theobservermonitorstheresponsesoftwoequivalentperceptualfilters1atthecuedanduncuedlocations.Eachoftheperceptualfilterslinearlyweightstheluminanceatthecuedanduncuedlocationsresultinginonescalarresponseforeachofthelocations.Thescalarresponsestothetwolocationsarestochasticvariablesthatvaryfromtrialtotrialduetointernalnoiseintheobserver(e.g.,neuralfiring)and/ortoluminancevariabilityintheimage(externalnoise).  TheBayesianobservercalculatesalikelihoodofthescalarfilterresponsesgiventargetpresenceforeachlocation.Themodelthenoptimallycombinesthetwolikelihoodsacrossthecuedanduncuedlocations.Thelikelihoodfromthecuedlocationisweighted(wc)bythepriorprobabilityofthetargetbeingpresentinthatlocation(precuevalidity).Thelikelihoodfromtheuncuedlocationisweighted(wu)byitscorrespondingpriorprobabilityoftargetpresence(1minusprecuevalidity).Theresultisanoveralllikelihoodofthefilterresponsesgiventargetpresenceacrossthetwolocations.TheBayesianobserverthencalculatesanoveralllikelihoodofthedatagiventargetabsence.Finally,themodelcomputesaratioofthelikelihoodsandmakesadecisionbycomparingthelikelihoodratiotoadecisioncriterionorthreshold.Figure1showsaschematicoftheBayesianobserverforataskinwhichthesignalisaGaussian“contrastincrement”embeddedinwhiteGaussiannoise.summarizesthemathematicalexpressionsdescribingtheBayesianobserverforthePosnerparadigm.  Figure1ViewOriginalDownloadSlide SchematicofaBayesianobserverinthePosnercueingparadigm.Stimuliareasimpleschematic(actualexperimentalimagescontainedaddedvisualnoise).Thetaskoftheobserveristodeterminewhetheracontrastincrementispresentatoneofthetwolocations(yes/notask).Inthisstudy,theprecueisvalid80%ofthetime.Figure1 SchematicofaBayesianobserverinthePosnercueingparadigm.Stimuliareasimpleschematic(actualexperimentalimagescontainedaddedvisualnoise).Thetaskoftheobserveristodeterminewhetheracontrastincrementispresentatoneofthetwolocations(yes/notask).Inthisstudy,theprecueisvalid80%ofthetime.ViewOriginalDownloadSlide Theoptimalweightingofthelikelihoodsfromthecuedanduncuedlocationsmaximizestheoverallhitrategivenafalsealarmrateacrossbothtypesofsignaltrials:validandinvalidcuetrials.Theconceptiseasiesttounderstandfortheextremecaseofacuethatis100%valid.Inthiscase,theobserverknowsapriorithathighevidence(likelihood)oftargetpresencearisingfromtheuncuedlocationisdueonlytonoise,andnottotargetpresence(giventhattheuncuedlocationnevercontainsthetarget).Therefore,evidenceoftargetpresencearisingfromtheuncuedlocationsonlycontributestogenerateerrors(falsealarmtrials).Asaresult,fortheparticularcaseofa100%validcue,theoptimalstrategyistocompletelyignoretheinformationfromtheuncuedlocation(wu=0inFigure1).Forthemoregeneralcasewherethecueisvalidacertainpercentofthetime(cuevalidity=80%),theBayesianobserversimplygivesmoreweighttoevidence(orinformation)arisingfromthecuedlocation.  AconsequenceofthehigherweightingofinformationatthecuedlocationisthattheBayesianobserverwillproducebetterperformance(hitrategivenaconstantfalsealarmrate)forvalidcuetrialsversusinvalidcuewithoutanydifferenceinthequalityofprocessing(e.g.,differenceinperceptualfilters,internalnoise,etc.)atthecuedanduncuedlocations.Recently,Shimozaki,Eckstein,andAbbey(2001)haveshownhowaBayesianobservercanpredictcuevalidityeffectsofthesameorlargermagnitudethanhumanobserversforaGaussianblobdetectiontaskinoneoftwolocations.  Inthisstudy,theBayesianmodelcanalsoquantitativelypredictthecueingeffectinataskwherethetargetisacontrastincrementinoneoftwoGaussianblobs.Theprobabilityoftargetpresenceis50%andthecuevalidityis80%.Figure2showshitrateinthistaskforaBayesianobserverdegradedwithGaussianinternalnoiseinordertomatchapproximatelythefalsealarmratesofthehumanobservers.ThedifferencebetweenthehitrateforthevalidandinvalidcuefortheBayesianobserverisclosetothatoffourhumanobservers.  Figure2ViewOriginalDownloadSlide Uppergraph:Hitrateforvalidcueandinvalidcuetrialsforfourhumanobservers(K.F.,A.H.,O.C.,K.C.).AlsoplottedareaBayesianobserver(triangles)thatsimplyoptimallyweightsthelikelihoodfromthecuedanduncuedlocationsandaTuningmodel(circles)inwhichvisualattentionchangesthetuningoftheperceptualfilter.Lowergraph:Falsealarmrateforvalidandinvalidtrialsforthesamefourhumanobserversandthetwomodels.Figure2 Uppergraph:Hitrateforvalidcueandinvalidcuetrialsforfourhumanobservers(K.F.,A.H.,O.C.,K.C.).AlsoplottedareaBayesianobserver(triangles)thatsimplyoptimallyweightsthelikelihoodfromthecuedanduncuedlocationsandaTuningmodel(circles)inwhichvisualattentionchangesthetuningoftheperceptualfilter.Lowergraph:Falsealarmrateforvalidandinvalidtrialsforthesamefourhumanobserversandthetwomodels.ViewOriginalDownloadSlide CueingEffectsWithAttentionalTuningofPerceptualFilters AlthoughtheBayesianobservercansuccessfullypredicthumanobservers’cueingeffects,thereareotherpossiblemodelsthatincludeattentionalchangesintheperceptualqualityoftheinformationateachlocationthatcouldalsopredictthehumancueingeffects.Forexample,somepreviousstudieshavesuggestedthatvisualattentionchangesthetuningorshapeoftheperceptualfilters.Inanotherexample,physiologicalstudieshavesuggestedthatattentionnarrowstheorientationtuningandcolortuningofcellsinV4(HaennyandSchiller,1988;Spitzer,Desimone,&Moran,1988).Also,psychophysicalstudiesusingtexturesegmentation(YeshurunandCarrasco,1998,1999)suggestthatattentionchangesthespatialresolutionofprocessing,whichmighttranslatetoachangeinthespatialfrequencytuningoftheperceptualfilters.LuandDosherhaveusedanextensionofthelinearamplifiermodel(theperceptualtemplatemodel)andexternalnoisewithacueingparadigmtoshowthatinanumberoftasks,attentionincreasestheoptimalityoftheperceptualfilter(Lu&Dosher,2000;Dosher&Lu,2000)2.  Figure2showsoneexampleofahypotheticalmodelwherevisualattentionatthecuedlocationimprovesthetuningoftheperceptualfilterproducingacueingeffectofthesamesizeasobservedinhumans.TheparticularshapesofthefiltersusedinthismodelareshowninFigure6(leftcolumn).TheperceptualfilterattheuncuedlocationisaDifferenceofGaussians(DOG)filter,andtheperceptualfilteratthecued(attended)locationisaGaussianthatmatchesthesignal.Thelikelihoodsareequallyweightedfromeachlocationtoreachadecision.IndependentGaussianinternalnoisefollowingtheperceptualfilterswasusedtodegradethemodeltomatchhumanperformancelevels.Forthismodel,thecueingeffectarisessolelybecausevisualattentionchangestheperceptualfilteratthecuedlocationtomakeitoptimal.Thelowerperformanceintheinvalidtrialsisduetothesuboptimalnatureoftheperceptualfilterattheuncuedlocation.Thisexampleillustratesthatamodelwithanattentionalchangeofperceptualfiltersattheattendedandunattendedlocationsalsocanexhibitcueingeffectssimilartothosemeasuredinhumans.  Figure6ViewOriginalDownloadSlide Toprow:Perceptualfiltersforthecuedanduncuedlocations.Bottomrow:Classificationimagesobtainedthroughsimulations.Left:PerceptualfilterattheuncuedlocationisasuboptimalDifferenceofGaussians,whereasthatforthecuedlocationisanoptimalGaussian.Right:PerceptualfilterattheuncuedlocationisasuboptimalwideGaussian,whereasthatforthecuedlocationisanoptimalGaussian.Figure6 Toprow:Perceptualfiltersforthecuedanduncuedlocations.Bottomrow:Classificationimagesobtainedthroughsimulations.Left:PerceptualfilterattheuncuedlocationisasuboptimalDifferenceofGaussians,whereasthatforthecuedlocationisanoptimalGaussian.Right:PerceptualfilterattheuncuedlocationisasuboptimalwideGaussian,whereasthatforthecuedlocationisanoptimalGaussian.ViewOriginalDownloadSlide Tuningversustaskperformance-basedtuningofperceptualfilters Althoughvisionscientistscommonlyrefertotheconceptofperceptualtuning,thetermisinterpretedindifferentways.Manyinvestigatorsusethetermtorefertothenarrowingofthesensitivity(inorientation,space,color,etc.)ofaninferredfilter,ameasuredcell,orapopulationofcells.Anothercommonuseistodefinetheperceptualtuningintermsofhowwellthefiltermatchesthesignaltobedetected.Ourviewisthatchangesintheperceptualfiltersshouldalsobejudgedintermsoftheimpacttheyhaveonperformanceinthetaskbeingstudied.Forexample,therearetasksinwhichattentionmightnarrowthetuningcharacteristicsoftheperceptualfilterbutmightnotenhanceormightevendegradeperformanceinthecuedattendedlocation.Ifso,thosechangesintheperceptualfilterwouldnotbeabletoaccountforastandardcueingeffectinhumanperformance.Inthiscontext,onecandefinethetuningoftheperceptualfilterintermsofperformanceintherelevanttask.  Forsimpletasksinexternalnoise,theoptimalfiltersareknownorcomputable.Inthesecases,onecandefinetheperceptualtuningofafilterintermsoftheratioofsignalenergy(toachieveagivenperformancelevel,e.g.,80%)fortheoptimalfilterandthatofthehumanperceptualfilter(Eidealfilter/Ehumanfilter).Thismeasureisknownastheefficiencyoftheperceptualfilter.ForsimplelineartasksinwhiteGaussiannoise,theefficiencycanbedirectlycalculatedbycomputingthesquaredcorrelation(match)betweentheperceptualfilterandtheoptimalfilter(whichisthesignal).However,whentheexternalnoisedoesnothaveequalpowerinallthefrequencies(nonwhitenoise),thenthedegreeofmatchbetweentheperceptualfilterandthesignalisnotthesolefactordeterminingtheperformanceofthefilter.Inthesecases,theoptimalfilterdoesnotmatchthesignal.FortaskssuchasthePosnerparadigmwherethedecisionisanonlinearfunctionofthedata,nosimplecalculationsareavailableandMonteCarlosimulationsand/ornumericalapproximationsarerequiredtocomputethetaskperformanceassociatedtoaperceptualfilter(Nolte&Jaarsma,1967).  ClassificationImagesasaTooltoEstimatePerceptualFilters Giventhattwodifferentmodelsofvisualattention(weightingofinformationwithidenticalperceptualfiltersvs.changeinperceptualfilters)canpredictcueingeffectsofthesizeobservedinhumans,thereisarationaletousemoreelaboratepsychophysicaltechniques(beyondcomparingmodelandhumanperformance)tobeabletodistinguishdifferentpossibleattentionalmodulationsthatmediatehumanvisualperformanceinthePosnercueingparadigm.Inthisstudy,weusethetechniqueknownasclassificationimagestodistinguishthetwodifferentmodelsofvisualattention.  Whatisaclassificationimage? Theclassificationimagetechniqueallowstheinvestigatortodirectlyestimatehowtheobserverweightstheinformationintheimagetoreachadecision.ArelatedtechniquebasedonmultiplelinearregressionwasfirstappliedbyAhumadaandLovell(1971)toaudition.Ahumada(1996)andBeardandAhumada(1998)usedtheclassificationimagetechniquetostudyhowobserversusedvisualinformationinavernieracuitytask.Ringach,Hawken,andShapley(1997)usedarelatedmethodtostudytheorientationtuninginthemonkeyprimaryvisualcortex.Othershaveusedthetechniquetolookatillusorycontours(Gold,Murray,Bennett,&Sekuler,2000),stereo(Neri,Parker,&Blakemore,1999),andoff-frequencylookinginnonwhitenoise(Abbey&Eckstein,2000)  Forsignalsvaryingonlyinluminance,themainmethodologicalrequirementistoaddrandomspatiallyuncorrelatedluminancenoisetotheimage.Theinvestigatorthenkeepstrackofthenoisystimulipresentedinthetrialscorrespondingtothedifferenthumanobserverdecisions:signalpresenttrialsinwhichtheobservercorrectlyresponded“signalpresent”(hittrials),signalpresenttrialsinwhichtheobserverincorrectlyresponded“signalabsent”(incorrectrejectionormisstrials),signalabsenttrialsinwhichtheobservercorrectlyresponded“signalabsent”(correctrejectiontrials),andsignalabsenttrialsinwhichtheobserverincorrectlyresponded“signalpresent”(falsealarmtrials).  Theintuitionbehindclassificationimagesisbestillustratedwiththefalsealarmtrials.Inthesetrials,theinvestigatorcollectsnoisesamplesthatdidnotcontainthesignalyetresultedintheobserverrespondingthatthesignalwaspresent.Itfollowsthattherandomluminanceperturbationsinthattrialmusthavecontainedsomeluminancepatternthatcorrespondedtowhattheobservertookasevidenceofsignalpresence.Thus,thesamplemeanofallthenoiseimagesfromthefalsealarmtrialswillrevealdeviationsinluminancethatledtheobservertorespondthatthetargetwaspresentwhenitwasnot.Forsimpletasks,onecanderiveclosedformexpressionstoshowthatthesamplemeanofthenoisyimageswillaccuratelyestimatealinearfilterortemplateusedtoweighttheinformationintheimagetoreachthedecision.Instatistics,onewouldrefertotheclassificationimageobtainedbycomputingthesamplemeanofthenoiseimagesfromfalsealarmtrialsasanunbiasedestimatorofthelineartemplateorperceptualfilter.Ofcourse,forayes/notask,therearefourgroupsofnoisesamplesthatarise,oneforeachofthefourtypesofdecisions(correctdetectionorhit,correctrejection,incorrectdetectionorfalsealarm,andincorrectrejectionormiss).Forsimpletasks,onecanderiveoptimalmethodstocombinethenoisesamplesarisingfromthesefourtypesoftrialstooptimallyestimateclassificationimages(Beard&Ahumada,1998;Abbey&Eckstein,2002,inthisspecialissue).Twoalternativeforcedchoicetasksrequiretakingthedifferencebetweenthetwonoiseimagespresentedineachtrialtocomputetheclassificationimage(seeAbbey&Ecksteininthisissuefordetailson2AFCclassificationimagetechnique).Iftheaddednoisedoesnothaveauniformpowerspectrum,thenamoreinvolvedintermediatestepisrequiredtoobtainanunbiasedestimationofthelinearfilter(Abbey,Eckstein,&Bochud,1999).Formorecomplextasksinwhichdecisionrulesareanonlinearfunctionoftheimagepixels,aderivationthatshowsthattheclassificationimageisanunbiasedestimatoroftheperceptuallinearfilterdoesnotyetexist(A.Ahumada,personalcommunication,1999).However,MonteCarlosimulationscanbeusedtodeterminewhethertheclassificationimagearisingfromthesignalabsenttrialsisanunbiasedestimator.  Assumptionsoftheclassificationimagetechnique Anunderlyingassumptionintheclassificationimagetechniqueisthattheobserverismonitoringasingleperceptualfiltertoreachadecision.Itisunderthesecircumstancesthattheobtainedclassificationimagecanbeinterpretedintermsofasingleperceptualfilter.Whentheobserverismonitoringanumberofperceptualfiltersandusesanonlinearcombinationtoreachadecision,cautionisneededintheinterpretation.A.Ahumada(personalcommunication,1999)firstnotedthattheclassificationimagesarisingfromthetargetpresenttrialsintasksinwhichtheobserverismonitoringanumberoffiltersperlocation(e.g.,positionalintrinsicuncertainty)maynotaccuratelyrepresentthelinearperceptualfilterorfiltersinthetask.Forthesetasks,classificationimagesfromsignalpresenttrialscanbemisleading.Inaddition,theclassificationimageobtainedfromsignalabsenttrialscannotbeinterpretedintermsofsingleperceptualfilterbutacompositeofmanyperceptualfiltersinfluencingthedecisioninsomenonlinearfashion.Oneinstanceinwhichhumanobserversmonitormorethanoneperceptualfilterperlocationiswhentheyareuncertainaboutsomeparameteraboutthesignal,suchasposition,spatialfrequency,phase,etc.(Pelli,1985).Thepresenceofeffectsofintrinsicuncertaintycanbediagnosedbymeasuringpsychometricfunctions(accuracyvs.signalcontrast)and/orbycomparingclassificationimagesarisingfromthesignalpresentandsignalabsenttrials(A.Ahumada,personalcommunication,1999).Adifferenceintheclassificationimagesfromsignalpresentandsignalabsenttrialspointstoadiagnosisofnonlinearityinsomecases(AbbeyandEckstein,2002,inthisspecialissue).Agoodapproachistochoosetasksthatareknowntoshowsmalleffectsofintrinsicuncertainty,suchascontrastandsizediscriminationtaskswherealinearobserverisagoodapproximationtohumanperformance(Burgess&Ghandeharian,1984;Ahumada,1987).Itisunderconditionsinwhichintrinsicuncertaintyhasnoeffectthattheclassificationimagetechniqueismostpowerfulintermsofinformationcontent(expressedasthesignaltonoiseratiooftheclassificationimage)andinterpretation.Ontheotherhand,taskssuchasthedetectionofspatialandtemporalperiodicsignalsinnoisetypicallyshownonlinearpsychometricfunctionreflectingintrinsicuncertaintyaboutphaseandwillnotapproximatetheassumptionsoftheclassificationimagetechnique.  ClassificationimagesforthePosnerparadigm ForthePosnerparadigm,theBayesianobservernonlinearlycombinestheresponseoftwoperceptualfilterstoreachadecision.Forthisreason,weusedonlythefalsealarmtrialsarisingfromsignalabsenttrialstoderiveclassificationimages.Toverifythattheobtainedclassificationimagesareunbiasedestimatorsofperceptualfilters,weimplementedextensiveMonteCarlosimulationswithdifferentversionsofoptimalandsuboptimalBayesianobservers.ThefollowingsectionshowstheresultsforthesesimulationsandverifiesthevalidityoftheuseofclassificationimagestoestimateperceptualfiltersforthecuedanduncuedlocationsofthePosnerparadigm.ThesimulationsalsoallowustoestablishhowthedifferentmodelsofvisualattentioninthePosnerparadigmgiverisetodistinctclassificationimagesignatures.Thesesignatureswillbeusedtoinferpropertiesaboutvisualattentionfromthehumanclassificationimagesdescribedlater.  ClassificationImageSignatures EachofthemodelsshownwasgeneratedbyusingimplementationofthegeneralmodelframeworkshowninFigure1.Thesimulationswerebasedon13,000trials,whichisapproximatelythesamenumberoftrialsperformedbythehumanobservers.Thetaskusedforthemodelsimulationswasidenticaltothatoneusedforthepsychophysicalexperimentsincludingthenoiselevel,Gaussianpedestals,contrastincrementoftheGaussiansignal,andthecuevalidity.Moredetailsaboutthetaskandsimulationsarediscussedin“Methods”and.  1.AttentionChangestheWeightingatCuedandUncuedLocations Thesemodelsassumethatattentiondoesnotchangetheshapeoftheperceptualfilter,butsimplychangestheweightingofinformationatthecuedanduncuedlocations.Weinvestigatedthreetypesofweightingofinformationatthecuedanduncuedlocationscorrespondingtodifferentattentionalsignatures:theoptimalattentionalweighting;attendbothlocationsequally(equivalentweightingofeachlocation);and,attendcuedlocationonly.Thesemodelsareobtainedbychangingtheweightsofthelikelihoods(wcandwu)inourBayesianmodel(seeFigure1and).  Figure3showstheperceptualfiltersusedinthesimulations(optimalGaussianfiltersforallconditions),theweightsforthelikelihoodsforthecuedanduncuedlocations,andthecorrespondingclassificationimagesobtained.Thesimulationsshowthattheshapeoftheclassificationimagesmatchtheshapeofthemodelinputperceptuallinearfilterscaledbyaconstant.  Figure3ViewOriginalDownloadSlide (a)Toprow:Twoequivalentperceptualfilters(Gaussianfiltersthatmatchthesignal)atthecuedanduncuedlocationsforallthreesimulations.(b)Bottomrow:Theclassificationimagesfromsimulationsassociatedtodifferentweightingsofthelikelihoodatthecuedanduncuedlocation.Inallofthesemodels,visualattentionchangestheweightingsofthelikelihoodfromthecuedanduncuedlocations.Theimagesshownherehavebeenreduced(byafactorof2usingbilinearinterpolation)fromtheactualimages.Figure3 (a)Toprow:Twoequivalentperceptualfilters(Gaussianfiltersthatmatchthesignal)atthecuedanduncuedlocationsforallthreesimulations.(b)Bottomrow:Theclassificationimagesfromsimulationsassociatedtodifferentweightingsofthelikelihoodatthecuedanduncuedlocation.Inallofthesemodels,visualattentionchangestheweightingsofthelikelihoodfromthecuedanduncuedlocations.Theimagesshownherehavebeenreduced(byafactorof2usingbilinearinterpolation)fromtheactualimages.ViewOriginalDownloadSlide Thispointbecomesmoreapparentifradialaveragesacrossanglesareplottedforeachclassificationimage(Figure4).Theradialaveragesoftheclassificationimagesarescaledversionsoftheperceptualfilterusedinthemodelsimulation(aGaussian).Inaddition,theinputweightingofthecuedanduncuedlocationusedinthemodelisreflectedbythemagnitude(oramplitude)oftheclassificationimages.Forexample,whentheweightingsofthetwolocationsinthemodelareequal(attendbothlocationsequally),thenthemagnitudesoftheclassificationimagesarethesame(middlecolumninFigure3;middlegraphinFigure4).Whenthemodelweightsthecuedlocationmoreheavily(andoptimally)thantheuncuedlocation,themagnitudeoftheassociatedclassificationimageforthecuedlocationisalsolargerthanthatoftheuncuedlocation(Figure3leftcolumn;topgraphinFigure4).Finally,whenthemodelsolelyweightstheinformationfromthecuedlocationandignoresthatfromtheuncuedlocation,thennoclassificationimageisobtainedattheuncuedlocation(rightcolumninFigure3;bottomgraphinFigure4).Inthisway,ifweobtainhumanobserverclassificationimages,wecanpotentiallyinfertheobservers’attentionalweightingstrategy.  Figure4ViewOriginalDownloadSlide Radialaveragesofclassificationimagesfromsimulationsforthreedifferentattentionalweightingsofthelikelihoodfromthecued(blue)anduncued(red)locations.Solidcurvesarescaledversionsoftheperceptualfilterusedinthesimulations.Top:Optimalweighting.Middle:Attendbothlocationsequally.Bottom:Attendonlycuedlocation.Errorbarsareomittedwhentheyaresmallerthanthesymbol.Figure4 Radialaveragesofclassificationimagesfromsimulationsforthreedifferentattentionalweightingsofthelikelihoodfromthecued(blue)anduncued(red)locations.Solidcurvesarescaledversionsoftheperceptualfilterusedinthesimulations.Top:Optimalweighting.Middle:Attendbothlocationsequally.Bottom:Attendonlycuedlocation.Errorbarsareomittedwhentheyaresmallerthanthesymbol.ViewOriginalDownloadSlide Inferringtheweightingacrosscuedanduncuedlocationsfromtheratioofclassificationimages Althoughtheprevioussectionshowsthattherelationshipbetweenthemagnitudeoftheclassificationimagesforthecuedanduncuedlocationsreflectstheattentionalweightingsassignedtoeachofthetwolocations,itwouldbedesirabletobeabletodirectlyrelatetheratioofthemagnitudeoftheclassificationimagestotheinputmodelweights(wcandwuinFigure1).BecauseofthenonlinearstageintheBayesianobserverinthePosnerparadigm,themathematicalrelationshipbetweentheweightsusedinthemodelforthelikelihoodforeachlocationandtheratioofmagnitudesoftheobtainedclassificationimagesisnoteasilyderivedanalytically.WethereforeperformedextensiveMonteCarlosimulationswiththeBayesianobserverwithtwoGaussianperceptualfilterstoempiricallymeasuretherelationshipbetweenthesetwo.Figure5showstheratioofmagnitudesoftheclassificationimagesandinputweightsusedinthemodel(see“Methods”fortechnicaldetailsaboutfittingroutineused)3.Thisrelationshipcanpotentiallybeusedtoinfertheunderlyingweightsusedbythehumanobserversforthecuedanduncuedlocationsfromtheobtainedhumanclassificationimages.  Figure5ViewOriginalDownloadSlide Relationshipbetweentheratioofmagnitudesofclassificationimagesandtheinputweightofthemodelforthecuedlocation.Figure5 Relationshipbetweentheratioofmagnitudesofclassificationimagesandtheinputweightofthemodelforthecuedlocation.ViewOriginalDownloadSlide 2.AttentionChangestheShapeofthePerceptualFilter Thesecondtypeofattentionalsignaturesweconsiderarethoseinwhichvisualattentionchangesthetuningoftheperceptualfilter.WithintheframeworkoftheBayesianmodel,onecanhypothesizethatattendingtothecuedlocationchangesthetuningoftheperceptualfilter.Forexample,Figure6showsasuboptimalDOGfilterusedattheunattendedlocationandanoptimalperceptualfilterusedattheattendedlocation.IncludedinFigure6aretheperceptualfiltersforanotherscenariowherethesuboptimalperceptualfilterattheuncued(unattended)locationiswiderthantheoptimalperceptualfilter.ThecorrespondencebetweentheoriginalfiltersandtheirresultingclassificationimagescanbeseeninFigure6.Figure7showstheFouriertransformoftheperceptualfiltersandtheclassificationimages.Theresultsshowthattheobtainedclassificationimagesforthecuedanduncuedlocationsmatchtheshapeoftheunderlyingperceptualfiltersusedinthemodelsimulations.Forexample,theDOGfiltergivesrisetoanoisyDOGfilterinitsassociatedclassificationimage.Thecorrespondencebetweenthemodel’sperceptualfilterandtheobtainedclassificationimagecanbeseenmoreeasilyintheplotsoftheradialaverages(Figure8).Thesimulationsdemonstratethatonecanpotentiallyinfertheshapeoftheobservers’perceptualfiltersfromtheirclassificationimages.  Figure7ViewOriginalDownloadSlide Toprow:Fouriertransformoftheperceptualfiltersforthecuedanduncuedlocations.Bottomrow:ClassificationimagesobtainedthroughMonteCarlosimulations.Radialdistancefromthecenterrepresentsspatialfrequencywiththezerofrequencyatthecenter.Left:PerceptualfilterattheuncuedlocationistheFouriertransformofasuboptimalDifferenceofGaussians,whereasthatforthecuedlocationisanoptimalGaussian.Right:PerceptualfilterattheuncuedlocationistheFouriertransformofsuboptimalspatiallywideGaussian(andthereforenarrowerthantheoptimalfilterintheFourierdomain),whereasthatforthecuedlocationisanoptimalGaussian.Figure7 Toprow:Fouriertransformoftheperceptualfiltersforthecuedanduncuedlocations.Bottomrow:ClassificationimagesobtainedthroughMonteCarlosimulations.Radialdistancefromthecenterrepresentsspatialfrequencywiththezerofrequencyatthecenter.Left:PerceptualfilterattheuncuedlocationistheFouriertransformofasuboptimalDifferenceofGaussians,whereasthatforthecuedlocationisanoptimalGaussian.Right:PerceptualfilterattheuncuedlocationistheFouriertransformofsuboptimalspatiallywideGaussian(andthereforenarrowerthantheoptimalfilterintheFourierdomain),whereasthatforthecuedlocationisanoptimalGaussian.ViewOriginalDownloadSlide Figure8ViewOriginalDownloadSlide Radialaveragesofclassificationimages(Figures6and7)forsimulationsfortwodifferentexamplesofmodelswherevisualattentionchangestheshapeoftheperceptualfilteratthecuedlocations.Bluesymbolscorrespondtoradialaveragesofclassificationimagesatthecuedlocation,whereastheredsymbolscorrespondtothosefromtheuncuedlocation.Solidlinescorrespondtothescaledradialaveragesoftheperceptualfiltersusedinthemodelsimulations.Leftcolumn:OptimalGaussianfilterforthecuedlocationandaDifferenceofGaussiansfilterfortheuncuedlocation.Rightcolumn:OptimalGaussianfilterforthecuedlocationandaspatiallywidersuboptimalGaussianfortheuncuedlocation.Toprow:Spatialdomain.Bottomrow:Fourierdomain.Figure8 Radialaveragesofclassificationimages(Figures6and7)forsimulationsfortwodifferentexamplesofmodelswherevisualattentionchangestheshapeoftheperceptualfilteratthecuedlocations.Bluesymbolscorrespondtoradialaveragesofclassificationimagesatthecuedlocation,whereastheredsymbolscorrespondtothosefromtheuncuedlocation.Solidlinescorrespondtothescaledradialaveragesoftheperceptualfiltersusedinthemodelsimulations.Leftcolumn:OptimalGaussianfilterforthecuedlocationandaDifferenceofGaussiansfilterfortheuncuedlocation.Rightcolumn:OptimalGaussianfilterforthecuedlocationandaspatiallywidersuboptimalGaussianfortheuncuedlocation.Toprow:Spatialdomain.Bottomrow:Fourierdomain.ViewOriginalDownloadSlide Methods PsychophysicalTask Theobservers’taskwastodecidewhetheracontrastincrement(4.69%)waspresent(yes/no)inoneoftwoGaussianpedestals(percentagerootmeansquare[RMS]contrast=6.25%).ThetwoGaussianpedestalswerelocatedtotherightandleftofafixationpointataneccentricityof2.5degrees.WhiteGaussianluminancenoisewithacontrastof0.117wasaddedtoeachimage.Everyimageineverytrialofthestudyhadindependentsamplesofnoise.Theviewingdistancewas50cm.Thesignalwaspresenton50%ofthetrials.Thevalidityoftheprecuewas80%(i.e.,thetargetwaspresentintheprecuelocationin80%ofthetargetpresenttrials).Fournaïveyettrainedobserversparticipatedinthestudy.Theobserversparticipatedin50sessionsof250trialsresultingin12,500trials.StimuliwerepresentedonanImageSystemsmonochromemonitor(ImageSystemsCorp.,Minnetonka,MN).Eachpixelsubtendedavisualangleof0.03degrees.TherelationshipbetweendigitalgraylevelandluminancewaslinearizedusingaDomeMd2board(ImagingSystems,Waltham,MA)andaluminancecalibrationsystem.  Procedure Observersstartedthetrialwithakeypress.Afixationimagewaspresentedfor1s.Observerswereinstructedtofixateacentralcrossatalltimes.Followingasquareprecue(lengthofside=2.5degrees)appearedfor150msaroundoneofthetwopossibletargetlocations.Thestimuluswasthendisplayedfor50ms.Theshortpresentationofprecueplusstimulus(200ms)waschosentoprecludeobserversfromexecutingasaccadiceyemovementtofixatethecuedlocation.AwhitenoisemaskwithhigherRMScontrastwasthenpresentedfor100ms(samemeanbackgroundluminance24.8cd/m2).Theobserversthenpressedoneoftwokeysonacomputerkeyboardtoselecttheirdecision(signalpresentorsignalabsent).Feedbackaboutthecorrectdecisionwasprovided,butnofeedbackaboutthesignallocationwasgiven.  HumanandModelPerformance Performanceforhumanobserverswasmeasuredintermsoftheproportionofsignalpresenttrialsinwhichtheobservercorrectlyresponded(hitrate).Hitratewasmeasuredseparatelyforthevalidcuetrialsandtheinvalidcuetrials.Inaddition,wedeterminedtheproportionofsignalabsenttrialsinwhichtheobserverincorrectlyresponded“signalpresent”(falsealarmrate).Performanceforthemodelswasquantifiedusingthesamemeasures.  ClassificationImages Classificationimageswereobtainedbycomputingthesamplemeanofthenoiseimagespresentedinthesignalabsenttrialsinwhichthehumanand/ormodelobserverincorrectlyresponded“signalpresent”(falsealarmtrials).Thenumberofimagesusedtocomputetheclassificationimageswasgivenbythenumberofsignalabsenttrials×falsealarmrate.Theactualnumberofimagesdependedonthefalsealarmrateofeachindividualobserverbutwasapproximately1,625(6,250×0.26).Radialaveragesacrossallangleswerecomputedforeachofthenoiseimages.Asamplemean,astandarddeviationforeachelementoftheradialaverages,wascomputed,aswellasthesamplecovariancebetweeneachelement.  StatisticalInferenceforClassificationImages Althoughclassificationimagescanshowtheshapeoftheunderlyingperceptualfilter,theimagesandradialaveragescontainalargeamountofnoise(statisticaluncertainty).Tomakemeaningfulinterpretations,statisticaltechniquesareneededtotestthedifferenthypotheses.TheHotellingT2statisticisageneralizationoftheunivariatetstatistictomultivariatevectors,andcanbeusedtotestfordifferencesbetweenasamplemultivariatevectorandapopulationvectororbetweentwo-samplemultivariatevectors.Weusedone-sampleandtwo-sampleHotellingT2statistics(Harris,1985)todohypothesistestingoftheradialaveragesoftheclassificationimages.TheHotellingT2statisticis    wherexisavectorcontainingtheobservedradialaverageoftheclassificationimage,andx0iseitherapopulationorahypothesizedradialaverageclassificationimage.K−1istheinverseofthecovariancematrixthatcontainsthesamplevarianceofeachoftheelementsoftheradialaverageclassificationimages,andthesamplecovariancebetweenthem.Totestforsignificance,theT2statisticcanbetransformedtoanFstatisticusingthefollowingrelationship:    wherepisthenumberofdependentvariables(numberofvectorelementsintheradialaverageoftheclassificationimages),andNisthenumberofobservations(numberoffalsealarmtrialsforourcase).TheobtainedFstatisticcanbecomparedtoanFcriticalwithpdegreesoffreedomforthenumeratorandN-pdegreesoffreedomforthedenominator.  Tocomparetwo-sampleclassificationimages,onecanusetheindependenttwo-sampleT2,whichisgivenbythefollowingexpression:    wherex1andx2arevectorscontainingtheobservedradialaveragesofthetwoclassificationimages;N1andN2refertothenumberofobservationsforthetwoclassificationimages.Forthetwo-sampletest,apooledcovarianceKiscomputedcombiningthesumofsquaredeviationsandsumofsquaredproductsfrombothsamples.Totestforsignificance,thetwo-sampleT2statisticcanbetransformedtoanFstatisticusingthefollowingrelationship:    wherep,N1,andN2aredefinedbefore.TheobtainedFstatisticcanbecomparedtoanFcriticalwithpdegreesoffreedomforthenumeratorandN1+N2−p−1degreesoffreedomforthedenominator.  Results HumanPerformanceforValidCueandInvalidCueConditions Table1showsthehitratesforvalidcueandinvalidcuetrials,aswellasthefalsealarmrateforthefourhumanobservers.Thelastcolumnshowsthesizeofthecueingeffectcomputedasthedifferenceofhitratesforthetwotypesofcuetrials.Forallobservers,wefoundastatisticallysignificantcueingeffect(p<.001 table1 andinvalidcuetrialsandfalsealarmratesforhumanobserversinthecontrast discriminationposnertask.table1 discriminationposnertask.observerhitrate humanclassificationimages figure9showstheclassificationimagesforfourhumanobserversobtainedfromthefalsealarmtrialsforthecuedand uncuedlocations.figure10showsthefouriertransformoftheclassificationimages.overall figure9vieworiginaldownloadslide figure10vieworiginaldownloadslide radialaverages radialaveragesacrossallanglesforeachnoiseimagefromeachfalsealarmtrialwerecomputed.samplemeanradialav erageswerethencalculatedforcuedanduncuedlocations figure11vieworiginaldownloadslide figure12vieworiginaldownloadslide radialaveragesofclassificationimageswerefitwithdogfunctionswithfourfittingparameters:oneamplitudefor eachofthetwogaussians p table2 fordifferenceofgaussianstoradialaveragesofhumanclassificationimages withfourfittingparameters.goodnessoffitandestimatedweightsarealso given.table2 given.observerperceptualfilteratthecuedlocationperceptualfilterattheuncuedlocationk1k2 scaledperceptualfilterstocomparetheshapeofthefilters tocomparetheshapeoftheperceptualfilters figure13showsthescaledperceptualfilterattheuncuedlocationtogivethebestfittotheunscaledperceptualfilt eratthecuedlocationforallfourobservers.errorbarsforobserversa.h.andk.f.arelargerduetothefactthatthem agnitudesoftheclassificationimagesfromtheuncuedlocationwerelower>.01).4  Figure13ViewOriginalDownloadSlide Radialaverages(spatialdomain)oftheuncuedlocationscaled(minimizingtheweightederror)tomatchtheradialaverageoftheclassificationimageforthecuedlocation.Topleft:O.C.Bottomleft:K.F.Topright:K.C.Bottomright:A.H.Bluesymbolscorrespondtothecuedlocationsandredsymbolscorrespondtotheuncuedlocations.Figure13 Radialaverages(spatialdomain)oftheuncuedlocationscaled(minimizingtheweightederror)tomatchtheradialaverageoftheclassificationimageforthecuedlocation.Topleft:O.C.Bottomleft:K.F.Topright:K.C.Bottomright:A.H.Bluesymbolscorrespondtothecuedlocationsandredsymbolscorrespondtotheuncuedlocations.ViewOriginalDownloadSlide PerformanceoftheHumanClassificationImages Althoughwedidnotfindstatisticallysignificantdifferencesacrosstheshapesoftheinferredperceptualfiltersatthecuedanduncuedlocations,weevaluatedthecueingeffectthatwouldarisefromtheobserveddifferencesinshapeofthehumanperceptualfilters.Todoso,weusedthebest-fitDOGforeachobserverforthecuedanduncuedlocationsandperformedcomputersimulationsintheframeworkofourBayesianmodelframework(Figure1).Toisolatecueingeffectsarisingfromthedifferenceinshapeofthefiltersfromdifferentialweightingofthecuedanduncuedlocations,thesimulationsincludedequalweightingofthelikelihoodateachlocation.Table3showstheobtainedhitratesandfalsealarmratesforthebest-fitDOGforeachobserverTable4showssimulationresultsforthebest-fitDOGforeachobserverforthecasewhereinternalnoise(independentadditiveGaussiannoiseaddedtotheoutputofeachfilter)wasaddedtomatchperformanceofthehumanobservers.Bothsimulationresultsshowthatthecueingeffectsthatarisefromtheobserveddifferencesintheshapeoftheperceptualfiltersareeithertoosmall(<0.02forK.C.andO.C.)orinthewrongdirection(A.H.andK.F.)toexplaintheobservedcueingeffectsinhumanobservers(Table1).Figure14plotsthecueingeffects(hitrateforvalidcuetrialsminushitrateforinvalidcuetrials)measuredforthehumanobserversandthosepredictedfromthedifferencesbetweentheinferredperceptualfiltersforthecuedanduncuedlocations.  Figure14ViewOriginalDownloadSlide Cueingeffect(hitrateforvalidtrialsminushitrateforinvalidtrials)measuredinhumanobservers(redsymbols).Greensymbolscorrespondtothecueingeffectpredictedbythedifferencesintheinferredperceptualfiltersfromthehumanclassificationimages.Figure14 Cueingeffect(hitrateforvalidtrialsminushitrateforinvalidtrials)measuredinhumanobservers(redsymbols).Greensymbolscorrespondtothecueingeffectpredictedbythedifferencesintheinferredperceptualfiltersfromthehumanclassificationimages.ViewOriginalDownloadSlide Table3 ViewTable Performanceofthebest-fitDifferenceofGaussianswithequalweightingofthe likelihoodofthecuedanduncuedlocations.Table3 Performanceofthebest-fitDifferenceofGaussianswithequalweightingofthe likelihoodofthecuedanduncuedlocations.ObserverEqualweightingHitrate(validtrials)Hitrate(invalidtrials)Falsealarmrate(alltrials)Cueingeffect(HRv–HRiv)O.C.0.9390.9190.0530.02K.F.0.9230.9430.059−0.02K.C.0.9300.9290.0710.001A.H.0.9300.9690.050−0.039 Table4 ViewTable Performanceofthe best-fitDifferenceofGaussianswithequalweightingofthecuedanduncued locations.Fortheseresults,internalnoisewasinjectedtomatchthehuman performancelevels.Table4 Performanceofthe best-fitDifferenceofGaussianswithequalweightingofthecuedanduncued locations.Fortheseresults,internalnoisewasinjectedtomatchthehuman performancelevels.ObserverEqualweightingHitRate(validtrials)HitRate(invalidtrials)Falsealarmrate(alltrials)Cueingeffect(HRv–HRiv)O.C.0.8190.7990.2310.02K.F.0.8210.8240.233−0.03K.C.0.8920.8830.2640.009A.H.0.8800.9240.229−0.043 InferringtheUnderlyingWeightsUsedbytheObserversFromtheRatioofMagnitudesoftheClassificationImages Thescalarusedtobestfittheuncuedhumanclassificationimagetothecuedhumanclassificationimagewastakenastheratioofthemagnitudesoftheclassificationimagesforthecuedanduncuedlocations.WethenusedcomputersimulationswiththeBayesianmodelvaryingtheinputweightsofthemodeltogeneratealookuptablebetweenweights(wcandwuinFigure1)andtheratioofthemagnitudeoftheclassificationimagesobtainedforthemodel(e.g.,Figure5).Fromthislookuptablewecouldtheninfertheweightsusedbytheobserversfromtheratioofthemagnitudeofthehumanclassificationimages.ThesimulationsfortheBayesianmodelwereperformedbyinjectinginternalnoiseandadjustingthecriterioninordertomatchthefalsealarmratesobservedinhumans.Theprocedurewasdoneseparatelyforeachhumanobserver.Theweightsinferredforthecuedlocationwere:0.76(O.C.),0.84(K.F.),0.8(K.C.),and0.88(A.H.).  Discussion HumanVersusOptimalPerceptualFilters Forthespecialcaseinwhichtheexternalnoiseisspatiallyuncorrelated(white)Gaussiannoise,theperceptualfiltersoftheidealBayesianobservermatchthesignal.Comparisonofthehumanclassificationimagestotheoptimalperceptualfilter(Figure3vs.Figure9)showsthatforallobserversthehumanperceptualfilterstendtobenarrowerinthespatialdomainthantheoptimalGaussianfilter,andalsohaveaninhibitorysurround.ThesurroundcanbeseenmoreclearlyintheradialaveragesinFigure11andcorrespondstoalowspatialfrequencysuppression.Thelowersensitivitytolowspatialfrequenciescanbeseenasadark“hole”intheFouriertransformationsoftheclassificationimages(Figure10).Thelow-frequencysuppressioncanalsobeseenasthedecreasedmagnitudeoftheradialaverageoftheFouriertransformationsoftheclassificationimages(Figure12).TheFouriertransformationoftheidealperceptualfiltercorrespondstoaGaussianthatismorecompactthanthehumanperceptualfilterinthefrequencydomain(andmoreextensiveinthespatialdomain;seeFigures11and12).TheinabilityofhumanobserverstomatchtheoptimalprofilewhenthesignalisaGaussianhasbeenobservedbeforebyAbbeyetal.(1999)forthedetectionofaGaussiansignal.Thelowfrequencysuppressionmightbeexplainedinpartbythedecreasedcontrastsensitivityofthehumanvisualsystemtolowfrequencies(i.e.,thecontrastsensitivityfunction).  ShapeofHumanPerceptualFiltersattheAttendedandUnattendedLocations Acommonexplanationforthecueingeffectisthatvisualattentionenhancesthequalityofprocessingattheattendedlocation.Onepossiblemechanismsuggestedbypreviousstudiesisthatattentionchangesthetuningoftheperceptualfilterattheattendedlocation(e.g.,Yeshurun&Carrasco,1999;Dosher&Lu,2000a,2000b)sothatitmatchesthesignalmoreoptimally.Ifso,theclassificationimagetechniqueshouldrevealadifferenceintheshapeoftheperceptualfiltersatthecuedanduncuedlocations(seeFigures6,7,and8forexamplesofpossibleclassificationimagesignaturesforthisscenario).Ourresultsdidnotfindstatisticalsignificancebetweentheshapeoftheperceptualfiltersatthecued(attended)anduncued(unattended)locationsforallfourobservers.Yetstatisticalsignificanceshouldnotbetheonlycriteriontojudgethedifferencesacrossperceptualfilters.Itisplausiblethatifthenumberoftrialswereincreasedbyafactorof10,thedifferencesinshapesacrossperceptualfilterswouldbecomestatisticallysignificant.Anotherimportantcriterionistodeterminehowmuchofacueingeffectwouldbeproducedbytheobserveddifferencesintheinferredshapeoftheperceptualfilters.MonteCarlosimulationsusingthebest-fitDOG(Table2)totheobservers’perceptualfiltersandequalweightingofinformationofbothlocationsresultedincueingeffectsrangingfrom−4%to+2%.TheperceptualfiltersforobserverA.H.resultedinahigherperformanceattheuncuedlocation(−4%negativecueingeffect).Thisresultisconsistentwithherclassificationimages(seeFigures9,10,and11)wheretheperceptualfilterattheunattendedlocationdidnothavethelow-frequencysuppression,and,therefore,bettermatchedtheoptimalfilterthantheperceptualfilterattheattendedlocation.Overall,thesefindingssuggestthatevenifthedifferencesinshapesacrosstheperceptualfilterswereassumedtobestatisticallysignificant,thesedifferencesbythemselveswouldnotbeabletoaccountforthelargecueingeffectsmeasuredonhumanobservers,whichareintheorderof10%to23%.Wethereforeconcludethatforthepresenttask,visualattentiondoesnotchangethetuningoftheperceptualfilteratthecuedlocationsufficientlytoaccountforthehumanobservercueingeffects.  VisualAttentionChangestheWeightingofInformationattheCuedandUncuedLocations Anotherexplanationofthecueingeffectisintermsofadifferentialweightingofinformationattheattendedandunattendedlocationswithoutresortingtoadifferentqualityofprocessingateachlocation.Kinchla,Chen,andEvert(1995)usedamodelthatlinearlyweightsinformationacrossbothlocationstofittohumandata.Shimozakietal.(2001)andthisstudyusedanoptimalBayesianobserverwithidenticalperceptualfiltersatbothlocationstopredictthehumancueingeffect.Thismodelpredictsthattheclassificationimagesforthecuedanduncuedlocationshoulddifferinmagnitudebutnotshape(Figures3and4).Wefoundthatthehumanclassificationfollowedthispattern(Figures10and12).Theseresultssupporttheideathatvisualattentiondoeschangetheweightingofinformationatthecuedanduncuedlocation.  Inaddition,weusedsimulationstoinfertheunderlyingweightingofinformationateachlocation(cuedanduncued)usedbythehumanobserversfromtheratiobetweenthemagnitudesofthehumanclassificationimages.Weobtainedarangeofweights(0.88,0.85,0.8,and0.76)thatwerescatteredaroundtheoptimalweighting(0.8).Notethattherankorderoftheweightsfortheobserversisinagreementwiththesizeoftheirobservedcueingeffect,aswewouldexpectfromthemodeldescribedinFigure1.Thehighertheweightassignedtothecuedlocation,thelargerthecueingeffect.Insummary,theclassificationimagessupporttheideathatvisualattentionactstomoreheavilyweighttheinformationatthecuedlocation.  AttentionalWeightingVersusAttentionalSwitching Analternativemodelthatisconsistentwithadifferenceinmagnitudesfortheclassificationimagesisoneinwhichtheobservermonitors(attends)onelocationpertrialandswitchesacrosstrialsbyattendingeitherthecuedlocationortheuncuedlocationwithsomeprobability.Werefertothismodelastheattentionalswitchingmodel.Acommonassumptionisthattheattentionalswitchingisdeterminedbythepriorprobabilitiesofsignalpresence.Therefore,forourtask,themodelattendsthecuedlocationon80%ofthetrialsandtheuncuedlocationon20%ofthetrials.Thismodelwillalsoyieldclassificationimageswithahighermagnitudeatthecuedlocationthantheuncuedlocation.However,themodelpredicts(see)cueingeffects(oftheorderof0.445),whicharesignificantlylargerthanthosemeasuredforhumanobserversandtheattentionalweightingmodel(Table2).Therefore,theattentionalswitchingmodel(asmanyotherlimitedcapacityattentionalmodels)canberejectedbecauseitpredictslargercueingeffectsthanthosepresentinhumanobservers.Nevertheless,thefactthattheattentionalswitchingmodelgeneratesclassificationimagesignaturesthataresimilartothoseoftheattentionalweightingmodelemphasizestheimportanceofconsideringboth—classificationimagesandtaskperformance—whenevaluatingmodels.  VisualAttention:SelectionandCombinationofInformation Overall,ourresultssupporttheideathatforthesimpletaskstudied,thecueingeffectisduetothedifferentialweightingofinformationatthecuedanduncuedlocation,andnotduetoachangeintheshapeoftheperceptualfiltersattheattendedandunattendedlocations.Theconceptthatvisualattentionallowstheobservertoselectand/ordifferentiallyweightinformationfromdifferentsourceshasbeenproposedbeforeforthecueingparadigm(Kinchlaetal.,1995).Shaw(1982),Palmer(1995),andothers(Sperling&Dosher,1986;Palmer,Verghese,&Pavel,2000;Verghese&Stone,1995;Eckstein,1998;Eckstein,Thomas,Palmer,&Shimozaki,2000;Verghese,2001)havealsoshownthathumanperformanceinsimplevisualsearchtaskscanbeaccountedforintermsofvisualattentionasaselectionmechanismandwithoutresortingtoachangeinthequalityofprocessing.Thesemodelshavebeensuccessfulinpredictingmanyeffectsinvisualsearchincludingset-sizeeffects,distractorvariability,searchasymmetries,andthefeature/conjunctionsearchdichotomy(seePalmeretal.,2000,forareview)  However,morecomplextasks(Poder,1999)orthoseinvolvingmemorystudieshaveshownthatattendingtoalocationwillnotsimplyallowtheobservertoselectrelevantinformationandignoreirrelevantinformation,butinsteadwillimprovethequalityofprocessingattheattendedlocationduetocapacitylimitations.Inaddition,thepresentresultscannotexplaincueingeffectsobtainedinparadigmsinwhicha100%validpostcue(whichcanbelocalizedbytheobserver)waspresentedinadditiontothepre-orsimultaneouscue(Luck,Hillyard,Mouloua,&Hawkins,1996;DosherandLu,2000a,2000b;LuandDosher,2000)andintasksinwhichanoninformativeprecuewaspresented(Henderson,1991).  AHypotheticalExperimentWhereAttentionWouldChangetheShapeofthePerceptualFiltersWithoutReflectingLimitedResources Itshouldbenotedthat,intheory,experimentscouldbedesignedsothatattentionhasaneffectontheshapeoftheperceptualfilterusedbythehumanobserver.Forexample,onesuchtaskmightbeadetectiontaskwherethesignalisahigh-frequencywindowedsinewavethatmightappearatoneoftwolocations.Letussupposethattheprecueisahigh-contrastcopyofthesignal,appearsdirectlybelowtheprobablesignallocation,andisinphasewiththesignal(whenthesignalispresent).Itiswidelyknownthathumanobservershaveintrinsicuncertainty(Pelli,1985)aboutthespatialphaseofperiodicsignals(Burgess&Ghanderharian,1984).Inthiscase,theprecuewouldprovidenotonlyinformationabouttheprobablesignallocation(rightvs.leftlocation),butalsoinformationabouttheexactphaseand/orpositionofthesignal.Therefore,forthisexample,onemightobtainaclassificationimagefortheuncuedlocationthatisnotphase-coherentbecausetheobserverhasintrinsicuncertaintyaboutthephaseofthesignal,andthereforemonitorsmanylocations.Ontheotherhand,fortheattendedlocation,thehighcontrastcuewouldprovidetheobserverwithinformationabouttheexactphaseorpositionofthesignal.Inthiscase,theobserverwouldmonitorasingleperceptualfilterwiththephaseorpositionmatchingthatofthereference.Asaresult,onewouldobtainaphase-coherentclassificationimageforthecued/attendedlocation.Infact,onecouldbuildaBayesianmodelwithintrinsicphaseuncertaintythatwouldpredictthechangeinperceptualfilters.  Thisexamplesimplyillustratesthatonemightfindtasksinwhichtheattendedlocationchangestheshapeoftheperceptualfilterattheattendedlocation.However,itshouldbeclearthatinthisexamplethecuenotonlygivesinformationaboutwhichofthetwolocations(rightimagevs.leftimage)hasahigherprobabilityofcontainingthetargetbutalsoprovidesinformationaboutthespecificphaseorpositionofthetargetwithinthecuedlocation.Therefore,thecuealsoallowstheobservertoselectoneofmanyfiltersdifferingslightlyinlocationshe/sheisuncertainaboutwithintherightorleftimage.Therefore,theobservedchangeintheperceptualfilterwouldnotbeassociatedwithacapacitylimitationinvisualattention,butinsteadthecueprovidesmore/furtherinformationfortheobservertoselectwhatisrelevantandignorewhatisirrelevant.  ClassificationImagesVersusOtherMethodstoInferPropertiesAboutPerceptualFilters Variationofenergythresholdswithexternalnoise Acommonlyusedmethodtoinfertheabilityofaperceptualfiltertomatchtheoptimalfilteristovarytheexternalnoiseandmeasurethesignalenergyrequiredbyahumanobservertodetectthesignalatagivenperformancelevel.Fromtheslopeofthevariationofenergywithexternalnoise(i.e.,noisespectraldensity),onecaninferwhatisknownasthesamplingefficiencyoftheperceptualfilter(Burgessetal.,1981;Pelli,1985).Thesamplingefficiencyisaquantitativemeasure(squaredcorrelation)ofthematchbetweenthehumanperceptualfilterandtheoptimalfilter.Aswiththeclassificationimagetechnique,typicallythereisanunderlyingassumptionthattheobserveriseffectivelymonitoringasinglefiltertoreachthedecision.Iftheobserverismonitoringmorethanonefilter(e.g.,thesamefilterbutatdifferentpositions;i.e.,spatialuncertainty)andcombiningtheresponsesofthefilternonlinearlyorwhenthefilterresponsegoesthroughatransducernonlinearity,thenamorecomplexanalysisisrequiredtoobtainthesamplingefficiency(Eckstein,Ahumada,&Watson,1997;Lu&Dosher,1999).Althoughthesamplingefficiencyisaveryusefulmeasure,ithasthelimitationthatitdoesnotprovideinformationabouttheshapeoftheperceptualfilter.Infact,perceptualfilterswithavarietyofdifferentshapescanhaveidenticalsamplingefficiencies.Inthisrespect,thesamplingefficiencyestimationtechniquecouldbecombinedwiththeclassificationimagetechniquetoprovidetheinvestigatorwithinformationabouttheshapeoftheperceptualfilter.  Bandpassnoise-maskingexperiments Anothermethodthathasbeenusedtoinfertheunderlyingtuningofthespatialfrequencyororientationoftheperceptualfiltershasbeenthebandpassnoise-maskingparadigm.Inthisparadigm,thefrequencycontentofthenoiseissystematicallyvariedsothatthenoisecontainspowerindifferentfrequencybandsineachparticularcondition.Theinvestigatorthenmeasurestheenergythresholdtodetectthesignalasafunctionforthedifferentnoisefrequencybands.Fromtheeffectofthedifferentnoisefrequencybandsonhumanobservers’thresholdelevation,theinvestigatorinfersthesensitivitytoagivenspatialfrequencyoftheperceptualfilterusedtoperformthetask.Thebasicideaisthatnoisefrequenciesthatdonotaffectperformancecorrespondtospatialfrequenciestowhichthehumanperceptualfilterisnotsensitive.Ontheotherhand,noisefrequencybandsthatdrasticallyelevatethethresholdenergyfordetectioncorrespondtospatialfrequenciestowhichthehumanperceptualfilterishighlysensitive.Thus,onecanderivemathematicalmethodstoderivethefrequencytuningoftheperceptualfilters(e.g.,Solomon&Pelli,1994).Themainlimitationofthebandpassnoise-maskingtechniqueisthatitassumesthattheobserveralwaysmonitorsthesameperceptualfilterinthedifferentbandpassnoiseconditions.AnoptimalBayesianobserverwouldchangetheperceptualfiltertoavoidregionsofhighnoisetooptimizeperformance.Theabilityofamodelorhumanobservertomodifytheperceptualfilterasafunctionofthefrequencycontentofthenoiseisreferredtoasprewhiteningand/oroff-frequencylooking.Ithasbeenshownthatinmanyinstanceshumanobserversareabletodooff-frequencylookingand/orprewhitening(Burgess,Li,&Abbey,1997;Burgess,1999;AbbeyandEckstein,2000;Solomon,2000).Inthesecases,useofthebandpassnoise-maskingtechniquetoderiveanunderlyingsinglefixedperceptualfiltercanresultinmisleadingresults.Becausetheclassificationimagetechniquedoesnotchangethefrequencycontentofthenoise,itdoesnotpresenttheproblemofoff-frequencylooking.  Conclusions WehaveappliedtheclassificationimagetechniquetodeterminehowattentionaffectstheprocessingofinformationattheattendedandunattendedlocationsinthePosnercueingparadigm.Ourresultsshowthat,forthecontrastdiscriminationtaskstudied,changesintheshapeoftheperceptualfilterswereneitherstatisticallysignificantnorwerethesmallchangesintheshapesoftheperceptualfiltersabletoaccountforthesizeofthecueingeffectmeasuredforhumanobservers.Ontheotherhand,thehumanclassificationimagesignaturescorrespondedtotheconceptthatvisualattentionweightstheinformationattheattendedlocationmoreheavily.TheBayesianmodelexploredhereisanalogoustotheBayesianorquasi-Bayesian(i.e.,approximationstoBayesianmodels)modelsusedpreviouslytoexplainvariousresultsinvisualsearch,suchasset-sizeeffectsandthedichotomybetweenfeatureandconjunctionsearches.Thusinthegreatercontext,ourfindingssuggestthatforsimpletasks,thePosnercueingparadigmnowjoinsanotherinfluentialattentionalparadigm,visualsearch,thatcanbeexplainedintermsofaBayesianobserver.Inthisframework,visualattentionallowstheobservertoselectordifferentiallyweightinformationatdifferentlocationsbutdoesnotchangetheperceptualqualityoftheprocessedinformationateachofthepossiblelocations.  Acknowledgments ThisworkwassupportedbyaNationalAeronauticsandSpaceAdministrationgrant(NASANAG-1157)andaNationalInstitutesofHealthgrant(NIH-HL53455).TheauthorswouldliketothankAlbertAhumadaJr.forinsightinthetopicofclassificationimagesandCharlieChubbforacarefulreviewandinsightfulcomments.TheauthorsalsothankKristineFazio,AudreyHill-Lindsey,OrianaChavez,andKathyChongforparticipatingasobserversinthestudy.SomeoftheresultsinthispaperwerepreviouslypresentedattheAnnualmeetingoftheVisionScienceSociety,Sarasota,FL,2001.CommercialRelationships:None.  Footnotes Footnotes1 Inthispaperweusethetermfiltertorefertoatemplatethatisappliedtoindividuallocationsoftheimageandnottoakernelthatisconvolvedwiththeimage. Footnotes2 Intheperceptualtemplatemodel(PTM)model,attentionchangeswhatisreferredtoastheexternalnoiseexclusion,whichisidenticaltowhattraditionallyisknownasthesamplingefficiencyinthelineartemplatemodel(Burgess,Wagner,Jennings,&Barlow,1981). Footnotes3 Oursimulationsshowthattherelationshipdependsonthedecisionthreshold(orcriterion)usedbythemodel.Itisthereforeimportantwheninferringthehumanweightstoadjustthemodelthresholdtomatchthemeasuredfalsealarmratesintheindividualhumanobservers. Footnotes4 ApotentialproblemisthatthetwosampleHotellingT2assumesequalcovariance.Thisisclearlynottrue,atleastforobserversA.H.andK.F.,wherethecovariancefortheuncuedlocationwasscaledbyaconstant,resultinginhighervariancethanforthecuedlocation.ItoandSchull(1964)haveshownthattheHotellingT2statisticisrobusttoviolationsoftheequalcovariancewhenNislarge.Webelieveourcase,Nofapproximately1,625,tobesufficientlylarge. AppendixA IdealandSuboptimalBayesianObserver TheperceptualfiltersatthecuedanduncuedlocationsaregivenbyFc(x.y)andFu(x,y)andarenormalizedtohaveunitlength.Theimageatthecuedanduncuedlocationsisgivenbygc,i(x,y)andgu,i(x,y).Thefirstsubscriptreferstothelocations(“c”forcuedand“u”foruncued),whereasthesecondsubscriptreferstotheithtrial.  Theimagesforsignal-presentvalidcuetrialsaregivenby    (A.1)wheres(x,y)isthesignalluminanceprofile,p(x,y)isthepedestalthathasthesamespatialprofileasthesignal,andnc,i(x,y)andnu,i(x,y)aretheexternalimagenoisesamplesatthecuedanduncuedlocations,whichareindependentlysampled.  Forsignal-presentinvalidcuetrialstheimagesaregivenby    (A.2).  Finallyforsignalabsenttrialstheimagesaregiven by    (A.3)  Theresponseofeachoftheperceptualfilters(λc,iandλu,i)tothestimuliintheithtrialisgivenby    (A.4)    (A.5)whereεc,iandεu,iisarandomscalarcorrespondingtointernalnoise,whichisindependentlysampledforeachtrialandlocation(cuedanduncued)fromaGaussiandistributionwithstandarddeviationσint.  TheBayesianmodelcalculatesthelikelihoodoftheresponses(λc,iandλu,i)giventhatthesignalispresentatthecuedlocation,L(λc,λu|sc,nu),andalikelihoodoftheresponsesgiventhatthesignalispresentattheuncuedlocationL(λc,λu|nc,su).Themodelthencomputesanoveralllikelihoodoftheresponsesgiventhatthesignalispresentbyweightingtheindividuallikelihoodfromeachlocationbyaweight(wcandwu):    (A.6)  Theoptimalweightsarethosethatmatchthepriorprobabilityofthesignalappearingatthelocationsgivenbytheprecuevalidity.Nextthemodelcomputesalikelihoodoftheresponsesgivensignalabsence,L(λc,λu|nc,nu).Finally,theBayesianmodelcomputestheratioofthelikelihoodforsignalpresenceandsignalabsence:    (A.7)  Themodelmakesadecisionbycomparingthelikelihoodratio(Lratio)toadecisionthresholdorcriterion:  IfLratio>threshold,thenrespond“signalpresent,”;otherwiserespond“signalabsent.”  ForthespecificcasewherethefilterresponsesateachlocationareGaussiandistributed,theindividuallikelihoodofthefilterresponsesgiventhesignalpresenceandabsenceisgivenby    (A.8)and,    (A.9)whered′uandd′caredefinedasthemeanresponseoftheperceptualfiltertothesignalpresentlocationminustheresponsetothesignalabsentlocationdividedbythestandarddeviationoftheresponse(includingtheeffectsofexternalandinternalnoise):    (A.10)where,istheexpectedvalueoftheseresponsesoftheperceptualfilteratthecuedlocationwhenthesignalispresent;istheexpectedvalueoftheresponseoftheperceptualfilteratthecuedlocationwhenthesignalisabsent;σλcisthestandarddeviationoftheresponseduetoexternalnoise;and,σintisthestandarddeviationoftheadditiveinternalnoise.Similarly,d′uisgivenby    (A.11)  Whenthenoiseiswhite,onecancalculated′candd′udirectlyfromtheperceptualfilter,F(x.y),thesignal,s(x,y),andexternalimagenoise(pixelstandarddeviationgivenbyσe):    (A.12)    (A.13)  ThisgeneralframeworkoftheBayesianobserverbecomestheidealobserverforthecaseofwhitenoisewhenthefiltersatthelocationsmatchtheoptimalfilter(thesignalforthecaseofwhitenoise),theweightingofthecuedanduncuedlikelihoodsaredeterminedbytheprecuevalidity(0.8forthecuedlocationand0.2fortheuncuedlocationinthepresentstudy),andthereisnointernalnoise.  MonteCarloSimulationsofModels ThemodeloutlinedwasimplementedinInteractiveDataLanguage(IDL).Inthecomputerimplementation,continuousintegralsintheaboveequationswerereplacedbysummations.ThedifferentmodelsofattentionalweightingswereimplementedbychangingtheweightsinEquationA.7.ThedifferentmodelsthatassumedthatattentionchangestheshapeoftheperceptualfiltersatthecuedlocationwereimplementedbychangingthefiltersinEquationsA.4andA.5.Thedecisionthresholdofthemodelwasalsoadjustedtomatchthefalsealarmrateofthehumanobservers.Theinternalnoisewasadjustedtomatchhumanperformance.  AppendixB SinglePerceptualFilterModelWithAttentionalSwitchingDeterminedbyPriorProbabilities Herewederivetheperformancepredictionsforamodelthatmonitorsasingleperceptualfilterthatisswitchedfromthecuedlocationtotheuncuedlocationfromtrialtotrial(attentionalswitching).Thefrequencywithwhichthemodelmonitorstheperceptualfilteratthecuedlocationismatchedtothepriorprobabilityofthesignalbeingpresent(0.8forthecuedlocationand0.2fortheuncuedlocation).Inthistreatment,theattentionalswitchingmodelisdevelopedinthecontextofsignaldetectiontheorywheretheresponsestoeachlocationarestochastic(duetotheexternalandinternalnoise).  ThefirststagesofthemodelremainthesameasthosedescribedfortheBayesianmodel.Theobserverisassumedtohavetwoperceptualfilters(EquationsA.4andA.5),andtheirresponsesareperturbedbyinternalnoise.ThedifferencebetweentheBayesianmodelandtheattentionalswitchingmodelisthatthelattermodelmonitorsonlyoneperceptualfilteroneachtrialtoreachadecision.Themodelcomputesthelikelihoodoftheresponseofasingleperceptualfiltergiventhatthesignalispresent,thelikelihoodgiventhatthesignalisabsent,andcomputesalikelihoodratio.Thisdecisionruleresultsinidenticalperformancetocomparingtheresponseofthesingleperceptualfiltertoadecisioncriterion(thelikelihoodisamonotonicfunctionofthefilterresponse).  Thehitrateforthemodelinthevalidcuetrialsiscalculatedbyconsideringthe0.8proportionofthevalidcuetrialsinwhichtheobserverwillcorrectlymonitorthecuedlocationandthe0.2proportionofthevalidcuetrialsinwhichtheobserverincorrectlymonitorstheuncuedlocation(i.e.,thesignalisatthecuedlocationbuthe/sheismonitoringtheresponsearisingfromtheuncuedlocation).  Thehitrateforthevalidcuetrialsisthereforegivenbytheprobabilitythatthefilterresponseexceedsthedecisioncriteria(th)inthesetwocircumstances:    (B.1)whereGisthecumulativeGaussian,d′istheindexofdetectability,whichisgivenbyEquationsA.11andA.12andthisthedecisioncriteria.  Similarly,thehitratefortheinvalidcuetrialsisgivenby    (B.2)  Thefalsealarmrateforbothtypesoftrialsissimplygivenbytheprobabilityoftheresponseexceedingthedecisioncriteriainsignalabsenttrials:    (B.3)  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(1998).Attentionimprovesorimpairsvisualperformancebyenhancingspatialresolution.Nature,396,72–76.[PubMed][CrossRef][PubMed] Figure1ViewOriginalDownloadSlide SchematicofaBayesianobserverinthePosnercueingparadigm.Stimuliareasimpleschematic(actualexperimentalimagescontainedaddedvisualnoise).Thetaskoftheobserveristodeterminewhetheracontrastincrementispresentatoneofthetwolocations(yes/notask).Inthisstudy,theprecueisvalid80%ofthetime.Figure1 SchematicofaBayesianobserverinthePosnercueingparadigm.Stimuliareasimpleschematic(actualexperimentalimagescontainedaddedvisualnoise).Thetaskoftheobserveristodeterminewhetheracontrastincrementispresentatoneofthetwolocations(yes/notask).Inthisstudy,theprecueisvalid80%ofthetime.ViewOriginalDownloadSlide Figure2ViewOriginalDownloadSlide Uppergraph:Hitrateforvalidcueandinvalidcuetrialsforfourhumanobservers(K.F.,A.H.,O.C.,K.C.).AlsoplottedareaBayesianobserver(triangles)thatsimplyoptimallyweightsthelikelihoodfromthecuedanduncuedlocationsandaTuningmodel(circles)inwhichvisualattentionchangesthetuningoftheperceptualfilter.Lowergraph:Falsealarmrateforvalidandinvalidtrialsforthesamefourhumanobserversandthetwomodels.Figure2 Uppergraph:Hitrateforvalidcueandinvalidcuetrialsforfourhumanobservers(K.F.,A.H.,O.C.,K.C.).AlsoplottedareaBayesianobserver(triangles)thatsimplyoptimallyweightsthelikelihoodfromthecuedanduncuedlocationsandaTuningmodel(circles)inwhichvisualattentionchangesthetuningoftheperceptualfilter.Lowergraph:Falsealarmrateforvalidandinvalidtrialsforthesamefourhumanobserversandthetwomodels.ViewOriginalDownloadSlide Figure6ViewOriginalDownloadSlide Toprow:Perceptualfiltersforthecuedanduncuedlocations.Bottomrow:Classificationimagesobtainedthroughsimulations.Left:PerceptualfilterattheuncuedlocationisasuboptimalDifferenceofGaussians,whereasthatforthecuedlocationisanoptimalGaussian.Right:PerceptualfilterattheuncuedlocationisasuboptimalwideGaussian,whereasthatforthecuedlocationisanoptimalGaussian.Figure6 Toprow:Perceptualfiltersforthecuedanduncuedlocations.Bottomrow:Classificationimagesobtainedthroughsimulations.Left:PerceptualfilterattheuncuedlocationisasuboptimalDifferenceofGaussians,whereasthatforthecuedlocationisanoptimalGaussian.Right:PerceptualfilterattheuncuedlocationisasuboptimalwideGaussian,whereasthatforthecuedlocationisanoptimalGaussian.ViewOriginalDownloadSlide Figure3ViewOriginalDownloadSlide (a)Toprow:Twoequivalentperceptualfilters(Gaussianfiltersthatmatchthesignal)atthecuedanduncuedlocationsforallthreesimulations.(b)Bottomrow:Theclassificationimagesfromsimulationsassociatedtodifferentweightingsofthelikelihoodatthecuedanduncuedlocation.Inallofthesemodels,visualattentionchangestheweightingsofthelikelihoodfromthecuedanduncuedlocations.Theimagesshownherehavebeenreduced(byafactorof2usingbilinearinterpolation)fromtheactualimages.Figure3 (a)Toprow:Twoequivalentperceptualfilters(Gaussianfiltersthatmatchthesignal)atthecuedanduncuedlocationsforallthreesimulations.(b)Bottomrow:Theclassificationimagesfromsimulationsassociatedtodifferentweightingsofthelikelihoodatthecuedanduncuedlocation.Inallofthesemodels,visualattentionchangestheweightingsofthelikelihoodfromthecuedanduncuedlocations.Theimagesshownherehavebeenreduced(byafactorof2usingbilinearinterpolation)fromtheactualimages.ViewOriginalDownloadSlide Figure4ViewOriginalDownloadSlide Radialaveragesofclassificationimagesfromsimulationsforthreedifferentattentionalweightingsofthelikelihoodfromthecued(blue)anduncued(red)locations.Solidcurvesarescaledversionsoftheperceptualfilterusedinthesimulations.Top:Optimalweighting.Middle:Attendbothlocationsequally.Bottom:Attendonlycuedlocation.Errorbarsareomittedwhentheyaresmallerthanthesymbol.Figure4 Radialaveragesofclassificationimagesfromsimulationsforthreedifferentattentionalweightingsofthelikelihoodfromthecued(blue)anduncued(red)locations.Solidcurvesarescaledversionsoftheperceptualfilterusedinthesimulations.Top:Optimalweighting.Middle:Attendbothlocationsequally.Bottom:Attendonlycuedlocation.Errorbarsareomittedwhentheyaresmallerthanthesymbol.ViewOriginalDownloadSlide Figure5ViewOriginalDownloadSlide Relationshipbetweentheratioofmagnitudesofclassificationimagesandtheinputweightofthemodelforthecuedlocation.Figure5 Relationshipbetweentheratioofmagnitudesofclassificationimagesandtheinputweightofthemodelforthecuedlocation.ViewOriginalDownloadSlide Figure7ViewOriginalDownloadSlide Toprow:Fouriertransformoftheperceptualfiltersforthecuedanduncuedlocations.Bottomrow:ClassificationimagesobtainedthroughMonteCarlosimulations.Radialdistancefromthecenterrepresentsspatialfrequencywiththezerofrequencyatthecenter.Left:PerceptualfilterattheuncuedlocationistheFouriertransformofasuboptimalDifferenceofGaussians,whereasthatforthecuedlocationisanoptimalGaussian.Right:PerceptualfilterattheuncuedlocationistheFouriertransformofsuboptimalspatiallywideGaussian(andthereforenarrowerthantheoptimalfilterintheFourierdomain),whereasthatforthecuedlocationisanoptimalGaussian.Figure7 Toprow:Fouriertransformoftheperceptualfiltersforthecuedanduncuedlocations.Bottomrow:ClassificationimagesobtainedthroughMonteCarlosimulations.Radialdistancefromthecenterrepresentsspatialfrequencywiththezerofrequencyatthecenter.Left:PerceptualfilterattheuncuedlocationistheFouriertransformofasuboptimalDifferenceofGaussians,whereasthatforthecuedlocationisanoptimalGaussian.Right:PerceptualfilterattheuncuedlocationistheFouriertransformofsuboptimalspatiallywideGaussian(andthereforenarrowerthantheoptimalfilterintheFourierdomain),whereasthatforthecuedlocationisanoptimalGaussian.ViewOriginalDownloadSlide Figure8ViewOriginalDownloadSlide Radialaveragesofclassificationimages(Figures6and7)forsimulationsfortwodifferentexamplesofmodelswherevisualattentionchangestheshapeoftheperceptualfilteratthecuedlocations.Bluesymbolscorrespondtoradialaveragesofclassificationimagesatthecuedlocation,whereastheredsymbolscorrespondtothosefromtheuncuedlocation.Solidlinescorrespondtothescaledradialaveragesoftheperceptualfiltersusedinthemodelsimulations.Leftcolumn:OptimalGaussianfilterforthecuedlocationandaDifferenceofGaussiansfilterfortheuncuedlocation.Rightcolumn:OptimalGaussianfilterforthecuedlocationandaspatiallywidersuboptimalGaussianfortheuncuedlocation.Toprow:Spatialdomain.Bottomrow:Fourierdomain.Figure8 Radialaveragesofclassificationimages(Figures6and7)forsimulationsfortwodifferentexamplesofmodelswherevisualattentionchangestheshapeoftheperceptualfilteratthecuedlocations.Bluesymbolscorrespondtoradialaveragesofclassificationimagesatthecuedlocation,whereastheredsymbolscorrespondtothosefromtheuncuedlocation.Solidlinescorrespondtothescaledradialaveragesoftheperceptualfiltersusedinthemodelsimulations.Leftcolumn:OptimalGaussianfilterforthecuedlocationandaDifferenceofGaussiansfilterfortheuncuedlocation.Rightcolumn:OptimalGaussianfilterforthecuedlocationandaspatiallywidersuboptimalGaussianfortheuncuedlocation.Toprow:Spatialdomain.Bottomrow:Fourierdomain.ViewOriginalDownloadSlide Figure9ViewOriginalDownloadSlide Humanobserverclassificationimagesforthecuedanduncuedlocations.Figure9 Humanobserverclassificationimagesforthecuedanduncuedlocations.ViewOriginalDownloadSlide Figure10ViewOriginalDownloadSlide HumanobserverclassificationimagesintheFourierdomain(imaginarypartdiscarded)computedseparatelyforthecuedanduncuedlocations.TheFourieroriginisplacedatthecenterofeachimage.Figure10 HumanobserverclassificationimagesintheFourierdomain(imaginarypartdiscarded)computedseparatelyforthecuedanduncuedlocations.TheFourieroriginisplacedatthecenterofeachimage.ViewOriginalDownloadSlide Figure11ViewOriginalDownloadSlide Radialaverages(spatialdomain)oftheclassificationimagesforthefourhumanobservers.Topleft:O.C.Bottomleft:K.F.Topright:K.C.Bottomright:A.H.Bluesymbolscorrespondtothecuedlocationsandredsymbolscorrespondtotheuncuedlocations.Blacksolidlinesarethebest-fitDifferenceofGaussianstothedata.Thedottedlinecorrespondstotheradialprofileoftheoptimalfilter.Figure11 Radialaverages(spatialdomain)oftheclassificationimagesforthefourhumanobservers.Topleft:O.C.Bottomleft:K.F.Topright:K.C.Bottomright:A.H.Bluesymbolscorrespondtothecuedlocationsandredsymbolscorrespondtotheuncuedlocations.Blacksolidlinesarethebest-fitDifferenceofGaussianstothedata.Thedottedlinecorrespondstotheradialprofileoftheoptimalfilter.ViewOriginalDownloadSlide Figure12ViewOriginalDownloadSlide Radialaverages(Fourierdomain)oftheclassificationimagesforthefourhumanobservers.Topleft:O.C.Bottomleft:K.F.Topright:K.C.Bottomright:A.H.Bluesymbolscorrespondtothecuedlocationsandredsymbolscorrespondtotheuncuedlocations.ThedottedlinecorrespondstotheFouriertransformoftheoptimalprofile.Figure12 Radialaverages(Fourierdomain)oftheclassificationimagesforthefourhumanobservers.Topleft:O.C.Bottomleft:K.F.Topright:K.C.Bottomright:A.H.Bluesymbolscorrespondtothecuedlocationsandredsymbolscorrespondtotheuncuedlocations.ThedottedlinecorrespondstotheFouriertransformoftheoptimalprofile.ViewOriginalDownloadSlide Figure13ViewOriginalDownloadSlide Radialaverages(spatialdomain)oftheuncuedlocationscaled(minimizingtheweightederror)tomatchtheradialaverageoftheclassificationimageforthecuedlocation.Topleft:O.C.Bottomleft:K.F.Topright:K.C.Bottomright:A.H.Bluesymbolscorrespondtothecuedlocationsandredsymbolscorrespondtotheuncuedlocations.Figure13 Radialaverages(spatialdomain)oftheuncuedlocationscaled(minimizingtheweightederror)tomatchtheradialaverageoftheclassificationimageforthecuedlocation.Topleft:O.C.Bottomleft:K.F.Topright:K.C.Bottomright:A.H.Bluesymbolscorrespondtothecuedlocationsandredsymbolscorrespondtotheuncuedlocations.ViewOriginalDownloadSlide Figure14ViewOriginalDownloadSlide Cueingeffect(hitrateforvalidtrialsminushitrateforinvalidtrials)measuredinhumanobservers(redsymbols).Greensymbolscorrespondtothecueingeffectpredictedbythedifferencesintheinferredperceptualfiltersfromthehumanclassificationimages.Figure14 Cueingeffect(hitrateforvalidtrialsminushitrateforinvalidtrials)measuredinhumanobservers(redsymbols).Greensymbolscorrespondtothecueingeffectpredictedbythedifferencesintheinferredperceptualfiltersfromthehumanclassificationimages.ViewOriginalDownloadSlide Table1 ViewTable Hitrateforvalid andinvalidcuetrialsandfalsealarmratesforhumanobserversinthecontrast discriminationPosnertask.Table1 Hitrateforvalid andinvalidcuetrialsandfalsealarmratesforhumanobserversinthecontrast discriminationPosnertask.ObserverHitrate(validtrials)Hitrate(invalidtrials)Falsealarmrate(alltrials)Cueingeffect(HRv–HRiv)O.C.0.8240.7160.2350.108K.F.0.8450.6550.1940.190K.C.0.8900.7290.2700.160A.H.0.8800.6490.2270.231 Table2 ViewTable Best-fitparameters forDifferenceofGaussianstoradialaveragesofhumanclassificationimages withfourfittingparameters.Goodnessoffitandestimatedweightsarealso given.Table2 Best-fitparameters forDifferenceofGaussianstoradialaveragesofhumanclassificationimages withfourfittingparameters.Goodnessoffitandestimatedweightsarealso given.ObserverPerceptualfilteratthecuedlocationPerceptualfilterattheuncuedlocationK1K2σ1σ2χ1w1K1K2σ1σ2χ2w2O.C.1.560.574.97.321.090.760.600.114.39.37.5980.24K.F.2.140.795.18.219.070.840.460.085.314.025.070.16K.C.1.20.164.311.839.250.800.650.114.38.918.80.20A.H.1.70.514.98.433.830.880.760.57.36.420.710.12 Table3 ViewTable Performanceofthebest-fitDifferenceofGaussianswithequalweightingofthe likelihoodofthecuedanduncuedlocations.Table3 Performanceofthebest-fitDifferenceofGaussianswithequalweightingofthe likelihoodofthecuedanduncuedlocations.ObserverEqualweightingHitrate(validtrials)Hitrate(invalidtrials)Falsealarmrate(alltrials)Cueingeffect(HRv–HRiv)O.C.0.9390.9190.0530.02K.F.0.9230.9430.059−0.02K.C.0.9300.9290.0710.001A.H.0.9300.9690.050−0.039 Table4 ViewTable Performanceofthe best-fitDifferenceofGaussianswithequalweightingofthecuedanduncued locations.Fortheseresults,internalnoisewasinjectedtomatchthehuman performancelevels.Table4 Performanceofthe best-fitDifferenceofGaussianswithequalweightingofthecuedanduncued locations.Fortheseresults,internalnoisewasinjectedtomatchthehuman performancelevels.ObserverEqualweightingHitRate(validtrials)HitRate(invalidtrials)Falsealarmrate(alltrials)Cueingeffect(HRv–HRiv)O.C.0.8190.7990.2310.02K.F.0.8210.8240.233−0.03K.C.0.8920.8830.2640.009A.H.0.8800.9240.229−0.043 ©2002ARVO 13,723 Views 105 Citations ViewMetrics × RelatedArticles Evidenceforchromaticedgedetectorsinhumanvisionusingclassificationimages Labeledlinesforimageblurandcontrast 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BaselineDetrendingforthePhotopicNegativeResponse EffectsofLong-WavelengthLightingonRefractiveDevelopmentinInfantRhesusMonkeys AssessmentofVisualandChromaticFunctionsinaRodentModelofRetinalDegeneration TheEffectofBangerterFiltersonBinocularFunctioninObserversWithAmblyopia RelatedTopics VisualPsychophysicsandPhysiologicalOptics Advertisement Copyright©2015AssociationforResearchinVisionandOphthalmology. Forgotpassword? ToViewMore... Purchasethisarticlewithanaccount. CreateanAccount or SubscribeNow × × ThisPDFisavailabletoSubscribersOnly Signinorpurchaseasubscriptiontoaccessthiscontent. × Youmustbesignedintoanindividualaccounttousethisfeature. × Thissiteusescookies.Bycontinuingtouseourwebsite,youareagreeingtoourprivacypolicy.Accept