PerceptionPsychophysics200163199114 - PDF document

Perception&Psychophysics2001,63(1),99-114 Illusionshavelongbeenconsideredtoprovideinsightsintonormalvisualprocessing.ThusRichardGregoryasked,Canitbethatillusionsarisefrominformation-processingmechanismsthatundernormalcircumstancesmakethevisibleworldeasiertocomprehend?Ž(Gregory,1968,p.66).Acriticalissuehasbeenwhichnormalinformation-processingmechanismsarereflectedbyspecificillusions.ThePonzoillusion,illustratedinFig-ure1,hasbeenclaimedtoreflectmanydifferentfunda-mentalvisualprocesses,fromspatialfrequencyfilteringincorticalareaV1tothelinearperspectiveandthein- Copyright2001PsychonomicSociety,Inc. ThisresearchwassupportedbyNIHGrantsMH48757andNS17778toA.P.S.andNSFGrantSBR-9319103toW.P.WethankEdwardHub-bard,DianeBeck,SusanRavizza,RolfNelson,GuhaJayachandran,andAbigailBautistafortheirhelpfulcommentsonthemanuscript.Corre-spondenceconcerningthisarticleshouldbesenttoW.Prinzmetal,De-partmentofPsychology,UniversityofCalifornia,Berkeley,CA94(e-mail:wprinz@socrates.berkeley.edu). 100PRINZMETAL,SHIMAMURA,ANDMIKOLINSKI shiftedtotheright,ascomparedwiththebottomdot.Figure3Csimplyputsthetwoillusionstogetherandcon-nectsthedotsinadifferentmanner.Theconsequenceofthemisperceptionofthelocationofthedotsisthatthetophorizontallinewillappearlongerthanthebottomhori-zontalline.InExperiment1,wetestwhetherthemisper-ceptionoforientationcausedbythetiltinductioneffect(illustratedinFigures3Aand3B)isofsufficientmag-nitudetoaccountforthePonzoillusion(Figure3C).Figure4illustratestherelationbetweenthePonzoandtheZöllnerillusions.IntheZöllnerillusion,thedistancebetweenthelonglinesappearslargerontheright,whereasinthePonzoillusiontheverticallineontherightappearslonger.ThelowerpanelsuperimposesthetwoillusionsandillustratesthatthePonzoillusionisimplicitintheZöllnerillusion.IntheZöllnerillusion,theobliquecon-textlinescausetherightendofthehorizontallinestoappearfartherapartthantheleftend.InthePonzoillu-sion,theobliquelinescausetheendsoftheverticallineontherighttoappearfartherapartthantheendsoftheverticallineontheleft.Theconsequenceofthisdistor-tioninthePonzoillusionisthattheverticallineontherightappearslongerthantheoneontheleft(seeFig-ure1).Describedinthismanner,therelationbetweentheZöllnerandthePonzoillusionscouldbeconsideredahidden-figurestask:OnecanseelittlePonzofigureshid-denintheZöllnerillusion.ThereareanumberofsimilaritiesbetweenthePonzoillusion,ontheonehand,andtheZöllnerandtiltinduc-tionillusions,ontheother.Forexample,Gibson(1937)showedthatthetiltinductioneffectwasstrongestwhenthecontestlinewasfrom15ºto20ºfromverticalorhor-izontal(seealsoAndriessen&Bouma,1976;Kramer,1978;Shimamura&Prinzmetal,2000).Similarly,theZöllnerillusionisgreatestwhentheanglebetweenthetestandthecontextlinesisinthissamerange(e.g.,Oyama,1975;Wallace&Moulden,1973).NotethatthePonzoillusionisgreatestwheneachoftheobliquelinesis15º…20ºfromverticalorhorizontal(Fisher,1968b,1973).Gibsonnotedthatthetiltinductioneffectisgreaterwhenthecontextlinesarenearverticalthanwhentheywerenearhorizontal.Similarly,boththeZöllnerandthePonzoillusionsaregreaterintheverticalthaninthehor-izontalorientation(Fisher,1968b,1973;Oyama,1975).Wedonotknowthecauseofthisdifference,butitmayberelatedtootheranisotrophiesinthevisualfield(Prinz-metal&Gettleman,1993).Ofcourse,thesesimilaritiesmaysimplybeacoincidence,andthemisperceptionof Figure1.Avarietyofvisualillusionsthatcanbeaccountedforbythemisperceptionoforientation. Figure2.Thetiltinductioneffect.(A)Theverticallineappearsslightlyslantedinacounterclockwisedirection.(B)Theverticallineappearsslightlyslantedinaclockwisedirection.ThefigureisdrawntosuggestarelationbetweenthetiltinductioneffectandtheZöllnerillusion. PONZOANDORIENTATIONPERCEPTION101 lengthinthePonzoillusionmightbeunrelatedtoorien-tationperception.ThegoalofthispaperistodirectlytestthisaccountofthePonzoillusion.OuraccountofthePonzoillusionispartofamoregeneraltheorythatwecallthetiltconstancytheory(seePrinzmetal&Beck,inpress;Shimamura&Prinzmetal,2000).WewillpresentthetheoryinmoredetailintheGeneralDi

scussionsection.Briefly,bytiltconstancy,wemeantheabilitytoperceiveverticalandhorizontalde-spitechangesinretinalorientation.Wehavealsocalledthisapproachtheorientationframingtheory(Shima-mura&Prinzmetal,2000),buthereweusethetermconstancytoemphasizetheadaptivesignificanceofthemechanismsthatunderlietheseillusions.Inthetiltin-ductioneffect,visualcues(theobliquelines)causeerrorsintheperceptionoforientation,butgenerallyvisualcuestoorientationprovideveridicalandstableinformationaboutverticalandhorizontal,despitechangesinretinalorientation.AlthoughthegoalofthepresentpaperistotestthetiltconstancytheoryofthePonzoillusion,wewillsuggestintheGeneralDiscussionsectionthatthetheorycanalsoaccountforanumberofotherillusions.InExperiment1,wecomparedthemagnitudeofthemisperceptionoforientationwiththemagnitudeofthePonzoillusion,usingthesameobserversandalmostiden-ticalstimuli.Thisexperimentillustratesthatthemisper-ceptionoforientationisoftheappropriatemagnitudetoaccountforthePonzoillusion.InExperiments2,3,and4,wecomparedourtiltcon-stancytheoryofthePonzoillusionwithprevioustheo-riesofthisillusion.Thetheoriesthatweconsideredinthispaperare(1)thelow-passfiltertheory(Ginsburg,1984),(2)theassimilationtheory(Pressey&Epp,1992),(3)asize-comparisontheorybasedontheworkofKün- Figure3.TherelationbetweenthetiltinductioneffectandthePonzoillusionisillustrated.InpanelA,thetiltinductioneffectcausesthetopdottoappearslightlytotheleftofthebottomdot.InpanelB,thetopdotappearsslightlytotherightofthebottomdot.PanelCcombinestheseeffectstocreatethePonzoillusion. Figure4.TherelationbetweentheZöllnerandthePonzoillusions.Thetoppanelillus-tratesthetwoillusionsseparately.Inthebottompanel,theillusionsaresuperimposed.Notethatthedirectionofthemisperceptionofspaceisthesameinbothillusions. 102PRINZMETAL,SHIMAMURA,ANDMIKOLINSKI napasandothers(Künnapas,1955),(4)thepool-and-storetheoryofGirgusandCoren(1982),and(5)afam-ilyoftheoriesthatmakereferencetolinearperspectiveandsizeconstancy(e.g.,Gillam,1980;Gregory,1963).Althoughthislistoftheoriesisnotcomplete,theymaybethemostprominenttheoriesofthePonzoillusion,andtheyarereasonablydiverse.Thepresentexperimentsweredesignedtocontrastpredictionsofeachofthesetheorieswithpredictionsbasedonthemisperceptionoforientation.Eachofthesetheorieswillbediscussedinmoredetailwithinthecontextoftheexperimentsthatfollow.EXPERIMENT1InFigure5A,thetophorizontallineappearslongerthanthebottomhorizontalline.Weproposethatthisisbecause,inmakinglengthjudgments,observers,tosomeextent,aremakingjudgmentsabouttheorientationoftwovirtuallinesconnectingtheendsofthehorizontallines.Ifthesevirtuallinesappearedvertical,thehori-zontallineswouldappeartobethesamelength.However,thesevirtuallinesdonotappearvertical,andthereforethehorizontallinesdonotappeartobethesamelength.Thesenseofverticalorientationofthevirtuallinesisaf-fectedbythenearestobliqueline.Theissueaddressedinthisexperimentiswhetherthemisperceptionofverticalalignmentisofsufficientmag-nitudetoaccountforthePonzoillusion.TomeasurethePonzoillusion,wepresentedobserverswithstimulilikethatinFigure5A.Theobserverstaskwastoadjustthelengthofthebottomhorizontallinetomatchthelengthofthetophorizontalline.(Astheobserversadjustedtheline,itchangedatbothends.)Mostoftheobserversoverestimatedthelengthofthetoplineandthusmadethelengthofthelineonthebottomtoolong.Indesigningatasktomeasureobserverssenseofalign-ment,wehadtwocriteria.First,wewantedthestimulitobesimilartothePonzostimuli(Figure5A).Second,wewantedtomakethetasksothatitwasimpossibleforob-serverstodothetaskbymatchinglinelength.Thesecri-teriaweremetwiththestimulusillustratedinFigure5B.Theobserversadjustedthelengthofthelineonthebot-tomsothatthefreeendofthelinewasverticallyalignedwiththeendofthetophorizontalline.Insummary,theclaimisthatwhenmakinglengthjudgmentsinFigure5A,observersareattemptingtoaligntheendofthelinesandthesenseofalignmentisaffectedbytheobliquecontextlines.Hence,themagnitudeoftheerrorfromthealignmenttask(Figure5B)shouldpredictthemagnitudeofthePonzoillusion.MethodProcedur

e.ThemethodofadjustmentwasusedforboththePonzoillusiontaskandthealignmenttask.TomeasurethePonzoillusion(Figure5A),oneachtrial,theobserversadjustedthelengthofthebottomhorizontallinetomatchthelengthofthetophori-zontalline,usingtheupanddownarrowkeysonacomputerkey-board.Eachtimetheobserverpressedtheuparrowkey,thebaselinegotlongerby1pixelbutwascenteredbetweenthecontextlines.Inasimilarmanner,thedownarrowkeymadethebottomlineshorter.Theobserverswereinstructedtotaketheirtime.Whentheyweresatisfiedwiththeiradjustment,theypressedthereturnkey.Eachsubjectwastestedfor24trials.Forthealignmenttask,theobserverswerepresentedwithstim-ulisimilartothatinFigure5B.Thetaskwastoadjustthefreeendofthebottomlinesothatitwasverticallyaligned,accordingtogravityŽwiththefreeendofthetopline.Onhalfofthetrials,thefreeendwasontherightsideofthefigure(asinFigure5B),andonhalfthetrials,thefreeendwasontheleftsideofthefigure.Eachsubjectwastestedforatotalof24trials,andtheorderoftheleft-andright-handversionswasrandomlydetermined.Theinitialsettingofthebottomlinewasrandomlychosenfromarectangulardistributionoflengthsfrom50%shorterthanthetophorizontallineto50%longerthanthisline.Eachobserverpartici-patedinbothtasks,withhalftheobserversbeginningwiththePonzotask.Theexperimenttookabout10min.Stimuli.Thestimuliwerepresentedona17-in.AppleMacintoshmonitorsetat832624pixels.Thestimuliweredrawninblackonawhitebackground.Theobserverssat40cmfromthemonitor, Figure5.ThestimuliusedinExperiment1.(A)InthePonzotask,observersad-justedthelengthofthebottomhorizontallinetomatchthelengthofthetopline.(B)Inthealignmenttask,observersadjustedthelengthofthebottomlinesothatitsendwasverticallyalignedwiththeendofthetopline.Inthisway,theyindicatedwhattheyperceivedasvertical.Thestimuliaredrawntoscale. PONZOANDORIENTATIONPERCEPTION103 withtheirheadrestrainedwithachinrest.ThestimuliinFigure5aredrawntoscale.Thehorizontallineswere4pixelswide.InthePonzotask,thetop(standard)linewas120pixelslong(4.2cm),subtendingavisualangleof6.1º.Theinitialsettingofthebottomlinewasrandomlydeterminedandwasfrom60to180pixels(from3.1ºto9.1ºofvisualangle).Inthealignmenttask,thetoplinewasalways128pixelsinlength,subtendingavisualangleof6.5º.Theinitialsettingofthelengthofthebottomlinewasrandomlydeter-minedoneachtrialandwasfrom64to192pixelsinlength(from3.3ºto9.7ºofvisualangle).Theobliquecontextlineswereslanted18.4ºfromvertical.Observers.Therewere20observersrecruitedfromamonggrad-uateandundergraduatestudentsintheUniversityofCalifornia,Berkeley,psychologydepartment.Theobserversagesrangedfrom22to41years.Acrosstheexperimentsreportedinthispaper,ap-proximatelyhalftheobserversweremale,andhalfwerefemale.ResultsInthePonzotask,theobserversadjustedthebottomlinetoolongbyanaverageof12.8pixels.Thiserrorcor-respondstoadjustingtheline10.7%toolong,whichistypicalforthePonzoillusion.(Notethat20pixelsequals1ºofvisualangle.)Eachofthe20observersexhibitedtheillusion(e.g.,Fisher,1968b,1973).Inthealignmenttask,whenthefreeendstoalignwereontheleft,theobserversadjustedthebottomlineanav-erageof5.7pixelstoofartotheleft.Whenthefreeendswereontheright,theyadjustedtheendofthelineanaverageof6.0pixelstoofartotheright.Thedifferencebetweentheleftandtherighterrorsdidnotapproachsignificance.IfthePonzoillusionisduetoamisperceptionofalign-ment,thePonzoillusionshouldbesimilartothetotalalignmentillusion(left+rightmisalignment).Themag-nitudeofthePonzoillusionwasindeedclosetothetotalalignmentillusion,12.8versus11.7(i.e.,5.7+6.0)pix-els.Thisdifferencewasnotreliablebyapaireddt(19)1.24].Thestandarddeviationofthe24settings,averagedoverthe20observers,was5.7and4.6pixelsforthePonzoandthealignmenttasks,respectively.Hence,thealignmenttaskgivesanillusionofamagni-tudethatalmostperfectlypredictsthePonzoillusion.Forthisgroupofobservers,ifweweretopredictthemagni-tudeofthePonzoillusionfromperformanceonthealign-menttask,wewoulderrbyamere1.1pixels(0.056ºofvisualangle).Wewereworriedthattheexperienceofperformingonetaskmightchangeobserversstrategyontheothertask.Forexample,havi

ngfirstperformedthealignmenttask,observersmighthaveadifferentstrategyindoingthePonzotaskthantheywouldiftheyhadnotperformedthealignmenttask.Hence,weseparatelyanalyzedonlythefirstblock,whichconstitutesabetween-groupscom-parison.ThedifferencebetweenthemagnitudeofthePonzoillusionandthatofthetotalalignmentillusionwasnotsignificant[0.83].TheaverageerrorforthePonzogroupwas11.8pixels,andtheaveragetotalerrorforthealignmentgroupwas13.7pixels.Finally,ifthecauseofthePonzoillusionisamisper-ceptionoforientation,observerswhoevincealargealign-mentillusionshouldalsohavealargePonzoillusion.Thecorrelationbetweentaskswasquitehigh(.71,.01).Therecouldbeotherreasonsforthecorrelationbe-tweentasks,butthehighcorrelationbetweenthesetwoillusionsisconsistentwiththeclaimthatthetwoillu-sionsarecausedbythesamemechanism.DiscussionThisexperimentdemonstratesthatthemisalignmentowingtotheobliquecontextlinescancauseanillusionofthesamemagnitudeasthePonzoillusion.Inasense,thealignmenttaskisaquantitativemodelforthePonzoillusionwithnofreeparameters.Weweresomewhatsur-prisedathowcloselytheillusionsmatchedinmagni-tude.Notethatinthealignmenttask(Figure5B),itisimpossibletouselengthtoperformthetasks,becausethebottomlinewillalwaysbelonger.Whenmakingthelengthjudgment(i.e.,thePonzoillusion,Figure5A),ob-serverscoulduselinelengthandasenseofverticaltomakethejudgment.Notethattherearetwointerpretationsofourexplana-tionofthePonzoillusionandtheclosecorrespondencebetweentheresultsofthetwotasks.Ontheonehand,observersmaybeliterallylininguptheendsofthelineswithwhattheyperceiveasvertical.Ontheotherhand,theobliquelinesmaybedistortingtherepresentationofspacesothatonewouldobtainaPonzoillusioneveniftheendsofthelinesdidnotlineup.Forexample,Post,Welch,andCaufield(1998)foundthattheMüller-LyerandJuddillusionsarecausedbytheexpansionand/orthecontrac-tionofspacenearthearrowheads.Onthisinterpretation,theobliquelinescauselocaldistortionsofspacesothattheendsofthelinesneednotbedirectlyinalignment.Ofcourse,thesimilarityinmagnitudebetweentheil-lusionscouldbeacoincidence.Furthermore,othertheo-riesmayalsobeabletoaccountforthemagnitudeofthePonzoillusion(e.g.,Pressey,Butchard,&Scrivner,1971).Demonstratingthatatheoryiscapableofgeneratinganillusionofthecorrectmagnitudeisonlyweakevidenceforthattheory.Abetterapproachistocomparedirectlythepredictionsofcompetingtheories.Intheremainingexperiments,wecomparepredictionsofourorientationaccountofthePonzoillusionwithprevioustheoriesofthisillusion.Note,however,thatifwecandemonstratethatothertheoriesdonotaccountforthePonzoillusions,itisunnecessarytopostulatemultiplecausesofthisil-lusion:ThemisperceptionoforientationisofsufficientmagnitudetoaccountfortheentirePonzoillusion.EXPERIMENT2AExperiments2Aand2Bcomparedthelow-passfiltertheory(Ginsburg,1984),thepool-and-storemodel(Gir-gus&Coren,1982),andasize-comparisontheorywiththetiltconstancytheory.Thelow-passfiltertheoryisbasedontheideathatearlyinvisualprocessing,thevi-sualsystemperformsoperationsakintoFourieranalysis(DeValois&DeValois,1990),creatingafunctionalsep- Figure6.ArepresentationofthelowspatialfrequenciesinthestandardPonzostimulus.Thetophorizontallineblursintoandincludespartofthecontextlines,makingitlongerthanthebot-tomhorizontalline. Figure7.ThestimuliusedinExperiments2Aand2B:(A)stan-dardPonzofigureusedinExperiment2A;(B)rectilinearversionusedinExperiment2A;(C)asymmetricalstandardPonzover-sionusedinExperiment2B;(D)asymmetricalrectilinearstimu-lususedinExperiment2B.Thestimuliaredrawntoscale.104PRINZMETAL,SHIMAMURA,ANDMIKOLINSKIarationofspatialfrequencies.Figure6representssomeofthelowpatialfrequenciesinthePonzofigure.Inthisrepresentation,thetophorizontallineblursintothecon-textlines.Measurementsofthelengthofthislinewouldthereforeincludepartofthecontextlines.Thebottomhorizontallinedoesnotblendintothecontextlines.Hence,thetoplinewouldbelongerthanthebaselineinthelow-frequencyrepresentation.Thecriticalstimulusfactoristhatthegapbetweenthetophorizontallineandthecontextissmallerthanthegapbetweenthebottomlineandthecontext.Hence,blu

rringintothecontextlinesonlyoccursatthetopofthefigure.Althoughthelow-passfiltertheoryhasbeentestedasacauseoftheMüller-LyerandPoggendorfftheories(e.g.,Carlson,Moeller,&An-derson,1984),wedonotknowofexplicittestsofthisthe-oryinregardtothePonzoillusion.Forthepool-and-storemodel(Girgus&Coren,1982),likethelow-passfiltertheory,thecriticalstimulusfac-toristhesizeofthegapbetweentheparallellinesandthecontext.Attheapexofthefigure,wherethisgapissmall,theparallellineandthecontextareapprehendedinasingleglance,whereasatthebottomendofthefigure,perceptionofthetestlineandthecontextre-quiresmorethanoneglance,accordingtothepool-and-storemodel.Objectsthatareapprehendedinasingleglanceexhibitassimilation(i.e.,arepooled),whereasthosethatareapprehendedindifferentglancesrequirethatinformationberetained(i.e.,stored)andresultinacontrasteffect.TheassimilationatthetopofthefigureisamechanismsimilartoPresseysassimilationmodel(discussedbelow),whereasthecontrastnotionisuniquetothistheory.Thesize-comparisontheoryisbasedonthefindingthatalineinasmallrectanglecanappearlongerthanthesamelineinalargerectangle(e.g.,Gogel&Sturm,1972;Künnapas,1955;Rock&Ebenholtz,1959).Theclaimisthatobserversaremakinganimplicitcomparisonbe-tweenthesizesofthegapsatthetopandthebottomofthefigure.InthePonzofigure,thegapbetweenthetophorizontallineandthecontextlineissmallerthanthegapbetweenthebottomhorizontallineandthecontext.Anyimplicitsizecomparisonwouldhavetheconse-quenceofmakingthetoplineappearlonger.Hence,thecriticalstimulusfactorforallthreetheoriesistherelativesizeofthegapbetweenthecontextandthetestlines.Totestthisclaim,wecomparedthestandardPonzofigure(Figure7A)withwhatwetermtherecti-linearversion(Figure7B).Thecriticalfactoristhatthesizesofthegapsbetweentheparallellinesandtheapexlinewerethesameinthetwofigures.Thelengthofthebaselinevaried,butthegapsizebetweenagivenbaselineandthecontextwasthesameinthestandardandtherectilinearversions.Becausethegapsizeisthesame,allthreetheoriespredictthatthestandardandtherectilin-earformsshouldyieldthesamesizeillusion.Notethatinseveralrespects,Experiment2AissimilartoworkbyFisher(1968b,1973).WewillreviewFishersresultsintheDiscussionsection.Thetiltconstancytheorymakesaverydifferentpre-diction.WeproposethattheobliquecontextlinesinthePonzofigurelocallyaffecttheperceptionofverticalandhorizontal.Therectilinearversion(Figure7B)doesnothaveanyobliquelines.Therefore,wedonotpredictanillusionintherectilinearversion. PONZOANDORIENTATIONPERCEPTION105 MethodProcedure.AsinExperiment1,themethodofadjustmentwasusedtomeasurethePonzoillusioninthestandardversion(Fig-ure7A)ortherectilinearversion(Figure7B).Oneachtrial,theob-serverswerepresentedwitheitherthestandardortherectilinearversion.Thetoplinewasthestandard,andthetaskwastoadjustthelengthofthebottomlinetomatchthelengthofthestandardline.TheobserversadjustedthelengthofthebottomlineasinExperiment1.Eachobserverwastestedfor12trialswiththestandardPonzoandfor12trialswiththerectilinearversion.Theorderoftrialswasrandomlydeterminedforeachobserver.Theinitialsettingofthebot-tomlinewasdeterminedasbefore.Theexperimenttookabout10min.Stimuli.TheapparatusandstimuliweresimilartothoseusedforExperiment1.ThedimensionsofthestandardPonzowereexactlythesameasthoseinExperiment1.Thelengthofthehorizontallineswasthesameforthestandardandtherectilinearstimuli.Thestim-uliinFigure7aredrawntoscalesothatoverall,thesizesofthestan-dardandtherectilinearPonzofigureswereverysimilar.Observers.Therewere24observersrecruitedfromtheUniver-sityofCalifornia,Berkeley,psychologydepartmentsubjectpool.Theyweregivencoursecreditfortheirparticipation.Eachobserverparticipatedinseveraldifferentdiverseexperimentsina1-hses-sion,includingExperiment3(describedbelow).Theobserversagesrangedfrom18to21years.ResultsandDiscussionCountertothepredictionsofthelow-passfilter,pool-and-store,andsize-comparisontheories,thestandardversionofthePonzoyieldedasignificantlygreaterillu-sionthandidtherectilinearversion[9.78%vs.0.16%;.01].Inthestandardversion,23of24observersadjustedthebo

ttomlinelongerthanthetopline(i.e.,anormalPonzoillusion),whereaswiththerecti-linearversion,12observersadjustedthebottomlinelongerthanthestandard,while12adjusteditshorter.Hence,withthestandardversion,weobtainedarobustillusion,whereaswiththerectilinearversion,theillusionvanished,aswaspredictedbythetiltconstancytheory.Beforediscussingtheseresults,wewantedtotestanalternativeexplanationofthefindings.Itispossiblethatthereisadditionalinformationintherectilinearversionthatassistsobserversinmakingmoreveridicalsettings.ConsiderFigure7B.Perhapsobserverscanmentallypro-jectthetopverticallinesofthecontexttowardthebaselines.Thisimaginedlinewouldprovideextrainforma-tiontohelpobserversmakemoreveridicalsettingsintherectilinearversionthaninthestandardversion.Consis-tentwiththisexplanation,theobserversexhibitedlessvariabilityintherectilinearversionthaninthestandardversion.Thestandarddeviationofthe12settings,aver-agedoverthe24observers,was4.6%and3.6%illusionforthestandardandtherectilinearversionsofthePonzo,respectively.Experiment2Btestedthishypothesis.EXPERIMENT2BExperiment2BwassimilartoExperiment2A,exceptthatthestimuliweremadeasymmetrical,asisshowninFigures7Cand7D.Thecontextinthestandardversion(Figure7C)includedoneobliquelineandoneverticalline.Fisher(1968a)hasdemonstratedthataPonzoillu-sioncanbeobtainedwithasingleobliquelineofabouthalfthestrengthofthetwo-linedversion.Withasingleobliquelineandaverticalline,wewouldalsoexpectanillusionofabouthalfthemagnitudeasthatwiththestan-dardversioninExperiment2A,becauselocalorienta-tionperceptionisonlyaffectedononesideofthefigure.Ontheotherhand,thelow-passfilter,pool-and-store,andthesize-comparisontheoriespredictnodifferencebetweenthestandardPonzoversionsinExperiments2Aand2B(Figures7Aand7C),becausethegapsareapproxi-matelythesamesize.Thecriticalprediction,however,isbetweentheasym-metricalrectilinearversion(Figure7D)andtheasym-metricalstandardversion(Figure7C).Thelow-passfil-ter,pool-and-store,andsize-comparisontheoriespredictthesameillusion,becausethegapsbetweenthecontextandtheparallellinesarethesameforthetophorizontalline.Ourtiltconstancytheorypredictsanillusionintheasymmetricalstandardversion(Figure7C),butnotintheasymmetricalrectilinearversion(Figure7D).Sincetheparallellineswereoffsetrelativetoeachother,thecriti-cismdiscussedabovedoesnotapply.MethodTheprocedurewasidenticaltothatinExperiment2A,exceptthatweusedasymmetricalversionsoftherectilinearandthenor-malPonzoillusions(seeFigures7Cand7D).Theapex(standard)andbase(adjustable)lineswerecenteredbetweenthecontextlines.Sixteenobserversparticipated.ResultsandDiscussionConsistentwiththetiltconstancytheory,theasym-metricalstandardversionofthePonzoyieldedasignif-icantlygreaterillusionthandidtheasymmetricalrecti-linearversion[4.67%vs.1.25%;(15).01].(Thenegativenumberindicatesthattheobserversadjustedthelineshorterthanthestandard.)Thestandarddevia-tionsofthe12settings,averagedoverthe16observers,were4.1%and7.0%illusionfortheasymmetricalstan-dardandtherectilinearversions,respectively.Intheasym-metricalstandardversion,14of16observersadjustedthebaselinelongerthantheapexline(i.e.,anormalPonzoillusion),whereaswiththeasymmetricalrectilin-earversion,8observersadjustedthebaselinelongerthanthestandard,while8adjusteditshorter.Comparingthestandardversion(Experiment2A,Figure7A)withtheasymmetricalstandardversion(Experiment2B,Fig-ure7C),weobtainedanillusionabouthalfthemagnitudeofthatforthestandardPonzoinExperiment2A(9.78%vs.4.67%),butneitherrectilinearversionyieldedanillusion.Althoughthetiltconstancytheorydidnotpredictanillusionintherectilinearfigures,wehavetoadmitsur-prisethatwedidnotobtainsomeillusionwiththesestim-uli.Sizeframinghasbeendemonstratedmanytimes,anditisareliable,robustfinding(e.g.,Gogel&Sturm,1972;Künnapas,1955;Rock&Ebenholtz,1959).Thus,onemighthaveexpectedthatwhereasboththemechanismof 106PRINZMETAL,SHIMAMURA,ANDMIKOLINSKI orientationandthatofsizeframingwouldoperateinthestandardPonzofigures,sizeframingwouldoperateintherectilinearversions.Hence,onemightreasonablyexpecttheill

usiontobereduced,noteliminated.Infact,Fisher(1968b)foundasmallframingeffectwithsimilarstim-uli.Note,however,thatFisher(1973)didnotreplicatethiseffect.Althoughwedonotknowwhywedidnotobtainasize-framingeffect,wesuggestthreepossiblefactors.Onepossibilityisthatincomparisonwiththesize-framingexperimentscitedabove,thegapbetweentheparallellinesandthecontext(particularlythetophorizontalline)inourexperimentwasmuchsmallerthaninpreviousex-periments.Thisfactorwouldsuggestapossibledissoci-ationbetweenthePonzoillusionandsizeframing.WhereasthePonzoisgreatestwhenthegapbetweentheapexlineandthecontextlinesissmall(see,e.g.,Fisher,1969;Jordan&Randall,1987),theoppositemightbetrueofsizeframing.Asecondpossibilityisthatinthetyp-icalsize-framingexperiment,thelargeandsmallframesformdifferentobjects,whereasinourfigure,theyformasingleobject(cf.Fisher,1968b).Finally,inFishers(1968b)experiment,thecontextlineswereverythickandprominent,ascomparedwiththetestlines.Perhapsinthatsituation,aprocesslikelow-passfilteringoperates.Finally,notethatthelow-passfiltertheory,thepool-and-storemodel,andasize-comparisontheoryallpredictnodifferenceinillusionmagnitudewiththerectilinearandthestandardversionsofthePonzoillusioninExperi-ments2Aand2B.Wearebynomeansarguingthatsizeframingdoesnottakeplace.NorarewearguingthatthevisualsystemdoesnotengageinprocessesakintoFourieranalysis(De-Valois&DeValois,1990).WearearguingthatneitherexplanationisnecessaryorsufficienttoaccountforthePonzoillusion.EXPERIMENT3Presseyandhiscolleagues(Presseyetal.,1971;Pressey&Epp,1992)proposedthatthePonzoillusioniscausedbythesamemechanismthatcausestheMüller-Lyeril-lusion(seeFigure8A).IntheMüller-Lyerillusion,thehorizontalshaftconnectingthewingsout(topofFig-ure8A)appearslongerthanthehorizontalshaftcon-nectingthewingsin(bottom,Figure8A).AccordingtoPressey,theMüller-LyerillusioniscausedbyaprocessthatassimilatesthewingsŽoftheMüller-Lyerfigurewiththeshaft.PresseypointedoutthatthePonzofigurecontainscomponentsoftheMüller-Lyerfigure.ThesecomponentsareshownwithsolidlinesinFigure8B.TotheextentthatthecomponentsconsistentwiththeMüller-LyerillusionaffectperceptioninthePonzofig-ure,thetophorizontallineshouldappearlongerthanthebottomline.ThePonzofigurealsocontainscomponentsthatareinconsistentwiththeMüller-Lyerillusion,however.InFigure8B,thesecomponentsaredrawnwithdashedlines.ThelinesegmentsinconsistentwiththeMüller-LyerillusionwouldtendtoworkagainstthePonzoillu-sion.ThereasonthattheMüller-Lyer-consistentlinesegmentshaveagreatereffectonperception,accordingtoPressey,isthatwhileengagedinanexperiment,ob-serversareattendingtothecenterofthefigure.Ob-serversfieldofattentionisillustratedwithagraycircleinFigure8B.Observersprocessmoreinformationinthe Wingout Wingin Figure8.(A)TheMüller-Lyerillusion.Theshaftconnectingthewingsout(top)isperceivedaslongerthantheshaftconnectingthewingsin(bottom).(B)TheassimilationtheoryofthePonzoil-lusion.ThepartsofthefigurethatareconsistentwiththeMüller-Lyerfigureareshowninbold.Ob-serversattendtothecenterofthefigureandthusprocessmoreoftheMüller-Lyer-consistentin-formationthanoftheinconsistentinformation. PONZOANDORIENTATIONPERCEPTION107 centerofthefigure,andhencetheMüller-Lyer-consistentlinesegmentshaveagreaterinfluencethandotheincon-sistentsegments(dashedlines).WetestedtheassimilationtheoryofthePonzoillusionbycomparingthenormalPonzofigure(Figure9A)withaversionthatcontainedonlyMüller-Lyerconsistentlinesegments(Figure9B).Regardlessofthestateofatten-tion,PresseystheorypredictsthattheversionwithonlyMüller-Lyer-consistentlinesegmentsshouldhaveanil-lusionasgreatasorgreaterthanthestandardversion(whichcontainsbothconsistentandinconsistentlineseg-ments).Thetiltconstancytheorywouldmaketheoppo-siteprediction:ThestandardPonzofigureshouldhaveagreaterillusionthantheMüller-Lyer-consistentversion.Thereasonforthispredictionisthatinthestandardver-sion,thereareclearcontoursontheleftandrighttolo-callyperturborientationperception.IntheMüller-Lyer-consistentversion,thesecontoursha

vebeendistorted.Hence,wewereabletocreateasituationinwhichthetwotheoriesmadeoppositepredictions.MethodTheprocedurewasidenticaltothatinthepreviousexperiments,exceptforthefollowing.Theobserversweretestedfor12trialswiththestandardPonzoversion,andfor12trialswiththeMüller-Lyerversion.Theorderoftrialswasrandomlydeterminedforeachobserver.Thesame16observersparticipatedinthisexperimentasinExperiment2B.HalfparticipatedinExperiment3first,andhalfinExperiment2Bfirst.ThedimensionsofthestandardPonzowereidenticaltothoseinthepreviousexperiments,andthestimuliinFigure9aredrawntoscale.ResultsandDiscussionThenormalPonzofigureexhibitedasignificantlylargerillusionthandidtheMüller-Lyerversion(9.34%vs.6.63%illusion,respectively).Thisdifferencewasre-liable[(15).01].Thevariabilityofsettingwassimilarwiththetwofigures.Thestandarddeviationofthe12settings,averagedoverthe16observers,was4.0%and3.3%forthestandardandtheMüller-Lyerver-sionsofthePonzo,respectively.Inthisexperiment,theassimilationtheoryandthetiltconstancytheorymadedifferentpredictions.Theassim-ilationtheoryclaimsthatthePonzoillusioniscausedbythesamemechanismastheMüller-Lyerillusion.Hence,aversionofthePonzoillusionthatismoresimilartotheMüller-Lyerillusionshouldexhibitagreaterillusion.Thetiltconstancytheorymadetheoppositeprediction.Thenormalversionhasconsistentobliquecontourswithwtoaffectorientationperception,whereasintheMüller-Lyerversion,thecontoursarenotasclear.Theresultsfa-voredthetiltconstancytheoryovertheassimilationtheory.OnemightobjectthattheMüller-Lyerversion(Fig-ure9B)isnotafairtestofPresseystheory,becausetheMüller-Lyerillusionitselfwouldbereducediftherewereagapbetweenthewingsoutandtheshaft.Note,however,thatthePonzoisnormallydwithagapbe-tweenthetoplineandthecontextlines.Inthisregard,itisinterestingtonotethatthePonzoŽstimuliusedbyPresseyandhiscolleaguesdonotcontainagapbetweenthecontextlinesandthetophorizontalline(e.g.,Presseyetal.,1971;Pressey&Epp,1992).Thus,bothourstan-dardandourMüller-LyerversionsaremoresimilartothePonzoillusion,asitisnormallydepicted,thanisthatusedbyPresseyandhiscolleagues.ItmaybepossibletodrawaversionofthePonzofigurethatismoresimilartotheMüller-Lyerillusion.ForthetypicalPonzofigure,however,makingitsimilartotheMüller-Lyerfiguredoesnotincreasetheillusion;rather,itdecreasesit.Ofcourse,theMüller-Lyerillusion,whateveritscause,isanextremelyrobustillusion.However,Experiment3demonstratedthatanexplanationofthePonzoillusionintermsofthemechanismsthatcausetheMüller-Lyerillu-sionisneithernecessarynorsufficient.WefranklyhavenoideaofthecauseoftheMüller-Lyerillusion.Thatil-lusionmaybeduetosomeformofassimilation,aswassuggestedbyPresseyandhiscolleagues.Alternatively,itmaybecausedbytheinappropriateapplicationofasize-constancymechanism(Gregory&Harris,1975).What-everitscause,webelievethatitisnotrelatedtothePillusion,forthreereasons.First,inafactor-analyticstudy,Coren,Girgus,Erlichman,andHakstian(1976)foundthattheMüller-LyerillusionandthePonzoillusionwerenotclassifiedtogether:ObserverswhoshowalargePonzoillusionarenotthesameobserversasthosewhoshowalargeMüller-Lyerillusion(cf.ourfindingsinEx-periment1).Second,althoughboththeMüller-Lyerillu-sion(Coren&Girgus,1978,p.31)andthePonzoillusion(Fisher,1968b,1973)varyinstrengthasafunctionoftheanglebetweenthecomponents,therearefundamentaldifferences.TheMüller-Lyerillusiongenerallyincreasesmonotonicallyastheanglebecomesmoreacute(aslongastheshaftlinesarenottoolong),whereasthestrengthofthePonzoillusionfirstincreases,thendecreaseswiththeangle.Finally,Coren(1986)hasshownthatitisnottheanglebetweentheshaftandthearrowheadsthatiscritical,buthowfarfromtheshaftthearrowheadsex-tend.LongerarrowheadsandmoreacuteanglesareequivalentintheireffectontheMüller-Lyerillusion.Infact,ithasbeenlongknownthatanyblobsattheendsoftheshaftcancauseaMüller-Lyer-likeillusion.Thus, Figure9.StandardandMüller-LyerversionsofthePonzoillu-sionusedinExperiment3. 108PRINZMETAL,SHIMAMURA,ANDMIKOLINSKIthereareampleempiricalgroundsforbelievingthatthePonzandtheMÃ

¼ller-Lyerillusionsarecausedbydif-ferentmechanisms.Inretrospect,Experiment3couldalsobeconsideredatestcomparingourtiltconstancytheorywiththelow-passfiltertheoryandthepool-and-storetheory.Inthepresentexperiment,weemphasizedtheassimilationthe-ory.TheassimilationtheorypredictedalargerillusionintheMüller-Lyerversion(Figure9B),whereaswepre-dictedalargerillusioninthestandardversion(Figure9A).Low-passfilteringisonepossiblemechanismtoaccountforassimilation.Indeed,dependingontheparametersofthemodel,low-passfilteringmightpredictalargerillu-sionintheMüller-Lyerversion(Figure9B)thaninthestandardversion(Figure9A),becauseinafilteredrep-resentation,thecenterofmassoftheblobformedbytheapexlineandthecontextlineswouldbefartherfromthecenterofthefigure.Theresultswereconsistentwiththetiltconstancytheoryandinconsistentwiththelow-frequency,pool-and-store,andassimilationtheories.EXPERIMENT4ProbablythemostpopularandinfluentialtheoriesofthePonzoillusionmakereferencetodepthperception,linearperspective,and/orsizeconstancy.Thereareactu-allyfourorfiverelatedtheories(Green&Hoyle,1963),butwewillmentiononlytwo.Accordingtooneversion,aPonzostimulustriggersalinearperspectivemecha-nismsothattheapexofthefigureisperceivedasbeingfartherfromtheobserverthanisthebaseofthefigure.Inappropriateapplicationofsizeconstancythereforemakestheapexline(usuallyahorizontallineonthetop)appearlonger(Gregory,1963,1968).Alternatively,theapplicationofthelinearperspectivemechanism,with-outperceiveddepth,couldberesponsiblefortheillusion(Gillam,1980).Accordingtothisview,theforeshorten-ingcausedbylinearperspectivecausestheillusion(Gil-lam,1973).ForthepurposesofExperiment4,allofthetheoriesthatmakereferencetodepthperceptionand/orlinearperspectivemakethesameprediction,sowewillsimplycallthemtheperspectivefamilyoftheories.ThepredictionsoftheperspectivefamilycanbeseeninreferencetoFigure10,Condition1.ThefigureincludesthePonzofigure(verticallinesontheleft),anditalsocouldbeinterpretedintermsoflinearperspective.Onecouldimaginelookingdownalonghallway,withthesmallrectangleinthecenterasthedistantendofthehallway.Therightverticallinecouldbeinterpretedasbeingfar-therfromtheobserverthantheleftverticalline.Sincethetwoverticallinessubtendthesamevisualangleinthefigure,theapexline(rightverticalline)shouldappearlonger,accordingtotheperspectivefamilyoftheories.Mostobserverswillperceivetherightlinetobelongerthantheleftline,consistentwiththePonzoillusion.ThetiltconstancytheorymakesthesamepredictionforFigure10,Condition1.Whenjudgingtheheightofthetopsofthelines,localcontext(theobliqueline)willmakethetopoftherightlineappearhigher.Whenjudg-ingthebottomsofthelines,localcontext(theobliqueline)willmakethebottomoftherightlineappearlower.SinceboththeoriesmakethesamepredictionforCondi-tion1(andthePonzoillusioningeneral),wecreatedstim-uliforwhicheachtheorywouldmakeauniqueprediction.InjudgingthelengthofthetwoverticallinesinCon-dition2(Figure10)thetiltconstancytheoryreversesitsprediction.Becauseoflocalcontext,thetopoftheleftlinewillbeperceivedashigher,andthereforetheleftlinewillbeperceivedaslonger.Furthermore,thestrengthoftheeffectshouldbeabouthalfofthatforCondition1,becausethereisonlyoneobliquelinetoaffecttheob-serversperception.Itisunclearwhattheperspectivetheorieswouldpredict.Perhapsthesimplestpredictionisthatsincethetwolinesareatequalheightinthepicture,theyareatthesamedistancefromtheobserverand,there-fore,shouldbeperceivedasequalinlength.ThepredictionsoftheperspectivefamilyoftheoriesareclearinCondition3,however.Thelineontherightshouldbeperceivedasfartherfromtheobserver,becauseoflinearperspectiveandtheadjacencyprinciple(Gogel, Figure10.ThestimuliusedinExperiment4. PONZOANDORIENTATIONPERCEPTION1091978).Theadjacencyprinciplestatesthattheperceiveddistanceofanatanunknowndistancewillbethesameasthatofobjectsnearit.Hence,thelineontherightshouldbeperceivedaslonger(seeFigure10,Condition3).Furthermore,themagnitudeoftheillusionshouldbethesameasthatinCondition1,becausethedistancebetweenthelinesisidenticaltothatinCondition1.Thetiltc

on-stancytheorypredictsnodifferencebetweentheper-ceivedlengthsofthelines,sincetheeffectoflocalcon-textwillbeidentical.MethodEachobserverwasrunforasingleblockof24trials.Therewere8trialsofeachconditionrandomlyintermixedwithintheblock.Thetaskwastoadjustthelengthoftheverticallineonthelefttomatchthelengthofthelineontheright,usingthearrowkeysonthekeyboard,asinthepreviousexperiments.Note,however,thatun-likethepreviousexperiments,thebaseline(leftverticalline)wasfixedinlength,andtheobserverstaskwastoadjustthelengthofthelineontheright.Also,ineachcondition,thetopoftheadjustablelinewasfixed,andthebottomofthelineontherightbecamelongerorshorterastheobserverpressedthearrowkeysonthekeyboard.ThestimuluspatternswereplacedonthemonitorinthepositionshowninFigure10.Thefigureisaccuratelydrawntoscale;theout-lineofthepanelsrepresentstheedgeoftheviewableareaofthemonitor.Thestandardline(verticallineontheleft)subtendedavi-sualangleofapproximately4.6º(120pixels).Thelengthofthead-justablelinewasrandomlysetatthebeginningofeachtrial,asbe-fore.Twenty-fourobserversparticipated.Inallotherrespects,theexperimentwasidenticaltothepreviousexperiments.ResultsInCondition1,inwhichthelinesareobjectivelythesamelength,boththeoriespredictthatobserverswillperceivetheleftlineaslonger.Therefore,observersshouldadjustthelinetooshort.Indeed,eachof24ob-serversadjustedtherightlinetooshort.Themeanmag-nitudeoftheillusionwas4.94%(thesignindicatingthatthelinewasadjustedtooshort).InCondition2,theorientationtheorypredictedthatobserversshouldmaketheoppositeerror;theyshouldadjustthelinetoolong.Twentyof24observersadjustedthelinetoolong.Themeanillusionerrorwas+2.38%,aswouldbepredictedbythetiltconstancytheory;thisil-lusionwasabouthalfoftheillusioninCondition1,butitwassignificantlygreaterthanzero[(23)4.96,.05].Finally,thelinearperspectivefamilyoftheoriespre-dictedthesameillusioninCondition3asinCondition1;theobserversshouldhaveadjustedthelinetooshort.Only8of24observersadjustedthelinetooshort.Theaver-agemagnitudeoftheillusionwas+0.881%,notsignifi-cantlydifferentfromzero[(23)Byanalysisofvariance,theillusionmagnitudesignif-icantlydifferedbycondition[(2,46)71.34,.01].Thestandarddeviationoftheeightsettings(percondi-tion),averagedoverthe24observers,was1.9%,1.9%,and3.6%forConditions1…3,respectively.Insummary,boththeoriespredictedtheresultsinCondition1.ThepredictionofthetiltconstancytheoryforCondition2wassupported,whereasthepredictionofthelinearperspectivefamilyoftheoriesforCondition3wasnotsupported.DiscussionExperiment4demonstratesthatanexplanationintermsoflinearperspectiveandsizeconstancyisneithernec-essarynorsufficienttoaccountforthePonzoillusion.Ofcourse,wearenotarguingthatthemechanismsrespon-siblefortheprocessingoflinearperspectiveand/orsizeconstancydonotplayaroleinperception.Indeed,percep-tualerrorsinducedbythemisapplicationofsizeconstancycanbepowerful.Furthermore,theseothermechanismsmay,underspecialcircumstances,affectorcontributetotheperceptionofPonzo-likestimuli.Forexample,elabo-ratingaPonzostimulussothatitappearsthree-dimensional(with,e.g.,additionalperspectivecues)canenhancetheillusion.However,asNewmanandNewman(1974)cor-rectlypointout,increasingthesizeoftheillusionbyadd-ingafactordoesnotlogicallymeanthatthatfactoristhecauseoftheillusion;itsimplyaddsanothereffect.Thefactthatanotherfactor,suchasperceiveddepth,mayaffectthePonzoillusionwithoutcausingthebasicillusionisillustratedinFigure11(seeRock,1984,p.156).IfFigure11isperceivedasapyramidfromabove,theupperlineappearslonger,eventhoughitisperceivedasbeingcloserthanthelowerline.Thus,thereissomefac-toroperatinginoppositiontoperceiveddepth.Webe-lievethatfactorinvolveslocalorientationcues.Ofcourse,Figure11isambiguous,andthelowerlinemaybeper-ceivedascloserthanthetopline.Perceiveddepth,oper-atingwithorientation,canincreasetheeffect.ThefactthatperceiveddepthdoesnotreversetheeffectwhenthefigureisperceivedasapyramiddemonstratesthatitisnotasufficientexplanationforthePonzoillusion.Figure11alsoillustratesaninterestingqualificationtothelinearpersp

ectivefamilyoftheories.NoneoftheobserversinExperiment4spontaneouslyremarkedthatthestimuli(Figure10)lookedthree-dimensional(theywerenotasked).However,severalvisualscientists,uponseeingthestimuliinFigure10,commentedthattheyareambiguous(likeFigure11).Theymaybeperceivedasiflookingdownalonghallwayorasapyramidviewedfrom Figure11.Whenviewedasatruncatedpyramidfromabove,thetoplinestillappearslongerthanthebottomline. 110PRINZMETAL,SHIMAMURA,ANDMIKOLINSKIabove.TheillusioninFigure10(Condition1)remains,regardlesshowthefigureisinterpreted.IfthedepthrelationsinFigure10areambiguous,thedepthrelationsinthebasicPonzoillusionmustalsobeambiguous,andthelinearperspectivefamilyoftheoriesshouldspecifywhyoneinterpretationisfavored.Theabovediscussionhighlightsafundamentaldiffer-encebetweentheorientationandtheperspectiveap-proachestothePonzoillusion.Forthetiltconstancythe-ory,themostimportantstimuluscomponentistheobliquecontournearestthestimulus.Asingleobliquelinecanaffectorientationperception(e.g.,Andriessen&Bouma,1976)andthuscanexplainwhyaPonzoillusioncanoccurwithjustasingleobliqueline(Fisher,1968a).Lin-earperspective,ontheotherhand,requiresatleasttwolines.Intermsofperspective,asingleobliquelineisam-biguous.WecouldhaveperformedExperiment4withlesselaboratestimuli,butaminimumoftwocontextlineswouldberequiredtorepresentperspective.Thus,thelin-earperspectivetheorycannotexplainaPonzoillusioncreatedwithasingleline(Fisher,1968a).Thereare,ofcourse,otherproblemswiththesize-constancyaccountofthePonzoillusion.Ifthetestlinesarerotated90º,theillusiondisappears(e.g.,Gillam,1980).Thatis,forexample,iftheverticalbarsinFigure1arereplacedbyhorizontalbars,thereisnoPonzoillusion.TheseproblemsledGillam(1973)toproposethatitisnotsizescalingthatcausesthePonzoillusion,butfore-shorteningscaling.However,foreshorteningscalingmakesthesamepredictionsassizescalingforExperi-ment4and,therefore,isalsoinconsistentwiththere-sultsofExperiment4.GENERALDISCUSSIONOfthesixtheoriesofthePonzoillusiontestedinthisinvestigation,thetiltconstancytheoryprovidedthebestaccountofthefindings.Experiment1demonstratedthatthemisperceptionofverticalalignmentcausedanillu-sionofthesamemagnitudeasthePonzoillusion.Fur-thermore,performanceonthetiltinductiontaskwashighlycorrelatedwiththemagnitudeofthePonzoillu-sion.Experiments2Aand2Bcomparedpredictionsofthetiltconstancytheorywiththelowspatialfrequencytheory,asize-comparisontheory,andthepool-and-storemodel.Forthesealternativetheories,theorientationofthecontextlinesisnotimportant.Theonlyimportantstimulusfeatureisthesizeofthegapbetweenthecon-textlinesandthetestlines.Inthisexperiment,however,thepresentationofobliquecontextlines„thatis,thosethatdistortorientation„wasnecessarytoproduceaPonzoillusion.InExperiment3,wetestedpredictionsoftheas-similationmodelbycomparingthestandardPonzofig-urewithoneconsistentwiththeMüller-Lyerillusion.AstandardPonzofigurewithobliquecontextlinespro-ducedalargerillusionthandidastimulusthatwascon-sistentwiththeMüller-Lyerillusion.Inthefinalexper-iment,wecomparedpredictionsofthetiltconstancytheorywiththoseofthelinearperspectivefamilyofthe-ories.Inthisexperiment,thestimuliweredrawninac-cordancewiththerulesoflinearperspective.Theonlytheorythatwasconsistentwiththeentiresetofexperi-mentswasthetiltconstancytheory.Undoubtedly,therearetheoriesthatwehavenotexplicitlymentioned.How-ever,thepresentresultsprovideconstraintsforallexist-ingandfuturetheoriesofthePonzoillusion.Thereareanumberofotherillusionsthatcanbeex-plainedinasimilarmanner.TherelationbetweenthetiltinductioneffectandthePoggendorffillusioncanbeseeninFigure12.Figure12Adepictsthetiltinductionef-fectinwhichaverticalline,surroundedbyobliquelines,isperceivedastiltedinaclockwisedirection.Gibson(1937)alsoreportedthesameillusionforanobliquelinesurroundedbyverticallines:Theobliquelinewasper-ceivedashavingagreatertiltthanitactuallyhad(Fig-ure12B).ThedirectionoftheillusionisindicatedwitharrowsinFigure12C.Finally,inFigure12D,thecenterportionoftheobliquelinehasbeenoccluded.Ifthecen-terportionofth

eobliquelineisoccludedandtheorien-tationofthevisiblepartsismisperceived,theresultisthePoggendorffillusion„theobliquelinesegmentswillnotbeperceivedascollinear.Inseveralways,thePoggendorffillusionbehavessim-ilarlytothetiltinduction,Zöllner,andPonzoillusions.Liketheseotherillusions,itsmagnitudeisgreaterwhenitispresentedinaverticalratherthanhorizontalorien-tation(e.g.,Leibowitz&Toffey,1966),anditisalsogreaterwhentheanglebetweenthecontextlinesandthetestlinesareinthesamerangeastheZöllnerillusion(e.g.,Green&Hoyle,1964;Greene&Pavlow,1989;Velinsky,1925).ManyotherillusionsappeartoberelatedtotheZöll-nerfigure(seeFisher,1968b,forotherexamplesthatmightfitthisclassofillusion).Thebendingofthehori-zontallinesintheWündt…Heringillusion(Figure1)il-lustratestwopropertiesofthetiltinductioneffect(andtheZöllnerillusion).First,thedegreeofdistortionisre-Figure12.ThefiguredemonstratestherelationbetweenthetiltinductioneffectandthePoggendorffillusion.Inthetiltin-ductioneffect,(A)averticallineappearsslantedinthedirectionoppositethecontextlines(i.e.,clockwise);(B)aslantedlineap-pearstobetiltedtoagreaterextentthanitactuallyis;(C)thear-rowsindicatethedirectionofthemisperceptionoforientationinpanelB;(D)thePoggendorffillusionresultsineachoftheobliquelinesegmentsappearingtobetiltedtoagreaterextentthantheyare,causingthemtoappearmisaligned. PONZOANDORIENTATIONPERCEPTION111 latedtotheanglebetweenthecontextlinesandthehor-izontallines,yieldingtheperceptionofcurvature.NotethatlinearperspectivemakesthewrongpredictionfortheWündt…Heringillusion.Ifthepointatwhichtheobliquelinesmeetisthevanishingpoint,horizontallinesshouldappearhorizontal.Second,theeffectsarelocal,sothattheextentofbendismostlydeterminedbytheclosestcontextline.Speculatively,wewouldliketoaddthepos-sibilitythatthecafewallillusioncouldbeconsideredanexampleoftheZöllnerillusion.Thispossibilityisillus-tratedinFigure13,inwhichthedarkbricksmayprovidetheobliquelines.OnecouldalsoincludeinthegroupofillusionsrelatedtotheZöllnerillusiontheFraserspiral.TheFrasertwistedcord,however,probablyhasadiffer-entorigin(seeTyler&Nakayama,1984).ItshouldbenotedthatouraccountoftheZöllnerandPoggendorffillusionsisnotatheoryofthemisperceptionofanglesbut,rather,atheoryofthemisperceptionofori-entation.By,wemeanastimulusthatcontainsac-tuallinesthatmeetatapointornearlymeetatapoint.In1861,Heringproposedthatacuteanglesarealwaysoverestimated(Hering,1861).Althoughthistheorycan-notaccountforthePonzoillusion,ithasbeenusedtoex-plaintheZöllner,Poggendorff,andrelatedillusions.Inmodernphysiologicalterms,similarorientation-tunedneuralunitsmutuallyinhibiteachother,resultinginalargerperceivedangle(Blakemore,Carpenter,&George-son,1970).ThistheorycannotbecorrectfortheZöllnerorPoggendorffillusions,becausebothoftheseillusionscanbeobtainedwithoutintersectinglinesorevenlinesthatcomeclosetointersecting(e.g.,Pressey&Sweeney,1972;Tyler&Nakayama,1984;Wilson&Pressey,1976).Wehypothesizethattheseillusionsareduetoamisper-ceptionoforientation,andthusourexplanationdoesnotrequirethatthestimuluscontainexplicitangles.Thetiltconstancytheoryclaimsthattheseillusionsareduetothemisperceptionoforientationowingtovi-sualcontext.Theeffectofvisualcontextonthepercep-tionofverticalandhorizontalisdemonstratedbythetiltinductioneffect.Therelevanceofvisualcontexttothesenseoforientationinanaturalisticsettingwasdramat-icallyillustratedbyAschandWitkin(1948).Observerslookedintoaroomthatwasrotated22º.Observersper-ceptionwasinfluencedbytheroomsothatthepercep-tionofverticalandhorizontalwasdistortedinthedirec-tionofthetiltedenvironment.Thisillusion,calledthetiltedroomillusion,canbeexperiencedatseveralroad-sideattractionsandamusementparks(Banta,1995;Knight,1999;Shimamura&Prinzmetal,2000;seealsowww.illusionworks.com).Howardhasrecentlydemon-stratedthatthatthevisualcontextcanoverrideshiftsingravityrelativetobodyposition(Howard,1998;Howard&Childerson,1994).Thetiltedroomillusionmaybere-latedtothepitch-boxeffect(Kleinhans,1970;Matin&Li,1995;Stoper&Cohen,1986).Witki

nandAsch(1948)obtainedasimilareffectwithasimpleluminousrodandframe(i.e.,therod-and-frameeffect).CorenandHoy(1986)showedthatarod-and-frameeffectcouldbeobtainedwithstimulinearlyiden-ticaltothoseusedbyGibson(1937).Notethatthisac-countofvisualillusionsreferstoanormallyadaptiveprocess.Visualcontextnormallyprovidesveridicalandstableinformationaboutorientationsintheenvironment.Wehavesuggestedthatthemechanismsresponsibleforthetiltedroomillusionarethesameasthoserespon-sibleforotherillusionsoforientation(includingthePonzoillusion).Thisclaimiscontroversial.Ontheonehand,Day(1972)suggestedthatthetiltinductioneffect,theZöllnerillusion,andthetiltedroomillusionofAschandWitkin(1948)wereallcausedbythesamemechanism.Ontheotherhand,HowardproposedthatalthoughtheZöllnerillusionandthetiltinductioneffectwerecausedbyonemechanism,contextillusionsthatinvolvedlargestimuli(therod-and-frameeffectandthetiltedroomil-lusion)werecausedbyadifferentmechanism.FourofthereasonsgivenbyHowardforbelievingthatthelargeandthesmallcontextillusionsarecausedbydifferentmechanismsarediscussedbelow(Howard,1982,pp.155…156).Afterconsideringthesereasons,wehavecometotheconclusionthateithertheevidencesupportsDaysclaimthatthesamemechanismsareinvolvedortheev-idenceisequivocal.First,Howard(1982)assertsthatthelarge-scaleillu-sions(tiltedroom,rod-and-frameeffect)givemuchlargereffectsthanthesmall-scaleillusions(e.g.,Zöllnerillu-sion,tiltinductioneffect).HecitesthefindingofAschandWitkin(1948)ofa20ºerrorinsettingarodtover-tical(orhorizontal)inthetilted-roomillusion.Thetiltinductioneffectismuchsmaller.However,the20ºerrorcitedbyHowardwasfoundinveryparticularcircum- ab Figure13.Thecafewallillusioncouldbeconsideredanexam-pleoftheZöllnerillusion.(A)Inthecafewallillusion,themor-tarlinesbetweenthebricksdonotappeartobestraight.(B)ThepatternofthedarkbricksmayhavethesameeffectastheobliquelinesintheZöllnerillusion. A B 112PRINZMETAL,SHIMAMURA,ANDMIKOLINSKI stances(seeAsch&Witkin,1948).Forexample,theob-serverwasseatedinachairthatwastilted24º.Theob-serverswentthroughanelaborate7-minindoctrinationperiodsothattheywouldaccepttheroomasupright.Underlessunusualcircumstances,AschandWitkinre-portedamuchsmallerillusion.Indeed,Wenderoth(1974)hasshownthatthemagnitudeoftherod-and-frameef-fectisoftenoverestimated.Whenestimatedcorrectly,itissimilartothetiltinductioneffect.Wehavemeasuredthetiltedroomillusioninanaturalisticcontextandfoundthatitcanbesimilarinmagnitudetothetiltinductionef-fectinthelaboratory(Shimamura&Prinzmetal,2000).Forthetiltinductioneffect,thelargerthecontext,thelargertheillusion(Johnstone&Wenderoth,1989;Shima-mura&Prinzmetal,1999;Wenderoth&Johnstone,1988).Theonlygeneralizationthatemergesisthatthegreatertheamountofcontextastimuluscontains,thelargertheorientationillusion.ThesecondreasonthatHowardgivesforbelievingthatthelargeandthesmallcontexteffectsaredifferentisthatthelargecontexteffectsshowaspecialroleofpe-ripheralpresentation.TheevidenceforthisassertionisacomprehensiveseriesofexperimentsbyEbenholtzandhiscolleagues,demonstratingthatthemagnitudeoftherod-and-frameeffectincreasesasthestimulusgetsreti-nallylarger(e.g.,Ebenholtz,1977,1985;Ebenholtz&Callan,1980).Asthestimulusgetslarger,theframefallsmoreintheperiphery.Incontrast,MuirandOver(1970)foundthatthetilt-aftereffectdidnotvarywitheccen-tricity.However,thiscomparisonisflawed.MuirandOverusedthesamestimuluspresentedatdifferenteccentric-ities,whereaswiththerod-and-frametask,increasingthesizeoftheframeincreaseitseccentricityitssize.Aswasmentionedabove,increasingthesizeofthetiltin-ductionstimulusincreasesthemagnitudeoftheillusion.Third,Howardarguesthatthetiltinductioneffect(andtheZöllnerillusion)isgreatlydiminishedwhenthecon-textisseparatedfromthetestline(e.g.,Johnstone&Wen-deroth,1989),whereaswiththerod-and-frametask,con-text(theframe)canhaveaninfluenceoverlargedistances.Note,however,thattherod-and-frametaskbehavesinex-actlythesamemannerasthetiltinductioneffect:Asthegapbetweentherodandtheframeincreases,theeffectdi-minishes(Coren&Hoy,19

86;Zoccolotti,Antonucci,&Spinelli,1993).Clearly,quantitativecomparisonsaboutthemagnitudeoftheeffectofdistancearedifficulttomake,becauseasmallgapbetweenthecontextandthetestlineinthefoveamayhavealargereffectthanalargegapintheperiphery.Notethatincreasingthedistancebe-tweenthecontextandthetestportionsofthestimulusre-ducesthemagnitudeofboththeZöllner(Oyama,1975;Wallace,1969)andthePonzo(Fisher,1968b)illusions.Finally,Howardarguesthatthetilted-roomillusionin-volvescognitivefactors,suchasthedegreeofrealisminthetiltedscene.However,hepointsoutthatthetiltin-ductioneffectdoesnotinvolvefamiliarobjects.(Notethat,bythisargument,therod-and-frameeffectwouldbecausedbyadifferentmechanismthanthetiltedroomillusion.)Howardhaspersuasivelyarguedelsewherethatcognitivevariablescomeintoplaywhentheorientationofthestimulusbecomesambiguous(Howard&Childer-son,1994).Thus,whentherotationofaroom,frame,orgratingapproaches45º,directions(e.g.,top,bottom,left,right)becomeambiguous.Cognitivefactors,suchastheintrinsicorientationofreal-worldobjects,maydisam-biguateorientation.Wesimplydonotknowwhethercog-nitivefactorswouldsimilarlyinfluencethetiltinductioneffectasthestimulusorientationapproaches45º.Thishypothesishasnotbeentested.Recently,PrinzmetalandBeck(inpress)havetestedthenotionthatthePonzo,Zöllner,Poggendorff,andtiltinductionillusionsarecausedbythesamemechanismasthetiltedroomillusionandtherod-and-frameeffect.Theyreasonedthatifthesamemechanismsarerespon-sibleforthesmall-scaleillusionsasforthetiltedroomil-lusion,variablesthataffectthetiltedroomillusionsimilarlyaffecttheseotherillusions.AschandWitkindiscoveredthattiltingtheobserverincreasedboththetiltedroomillusionandtherod-and-frameeffect(Asch&Witkin,1948;Witkin&Asch,1948;seealsoDiLor-enzo&Rock,1982).Presumably,tiltingobserversmakesrelymoreonvisualcuestoorientationandlessongravity-basedcues.PrinzmetalandBeckdiscoveredthattiltingobserversincreasedthePonzo,Zöllner,Poggen-dorff,andtiltinductionillusionsbutdidnotaffectacon-trolcondition(theMüller-Lyerillusion).Thus,acriticalvariablethatinfluencesthetiltedroomillusionaffectsotherorientationillusions,suggestingthatacommonmechanismmayunderliebothtypesofphenomena.OtheraccountsofthePonzoillusionwouldnotpredictthisresult.Notethat,liketheoristsbeforeus,weattributetheseorientationillusionstonormallyadaptiveprocesses.Nor-mally,visualcuestoorientationsintheworldhelpusmaintainastablerepresentationoforientation,despitechangesinretinalorientation.Itisonlyinthetiltedroom„asdemonstratedintheantigravityhouse„thatthesenor-mallyadaptivecuestoorientationleadusastray.Thesesameprocessescanuselocalinformationtodetermineorientation,anditisthelocalcuestoorientationthatcausethePonzoillusion.REFERENCESAndriessen,J.J.,&Bouma,H.(1976).Eccentricvision:Adversein-teractionsbetweenlinesegments.VisionResearch,71-78.Asch,S.E.,&Witkin,H.A.(1948).Studiesinspaceorientation:II.Perceptionoftheuprightwithdisplacedvisualfieldsandwithbodytilted.JournalofExperimentalPsychology,455-475.Banta,C.(1995).Seeingisbelieving:Hauntedshacks,mysteryspots,andotherdelightfulphenomena.AgouraHills,CA:FunhousePBlakemore,C.,Carpenter,R.H.,&Georgeson,M.A.(1970).Lat-eralinhibitionbetweenorientationdetectorsinthehumanvisualsys-tem.Nature,37-39.Boring,E.G.(1942).Sensationandperceptioninthehistoryofex-perimentalpsychology.NewYork:Appleton-Century-Crofts.Carlson,C.R.,Moeller,J.R.,&Anderson,C.H.(1984).Visualillusionswithoutlowspatialfrequencies.VisionResearch,1407- PONZOANDORIENTATIONPERCEPTION113 Coren,S.(1986).Anefferentcomponentinthevisualperceptionofdirectionandextent.PsychologicalReview,391-410.Coren,S.,&Girgus,J.S.(1978).Seeingisdeceiving:Thepsychologyofvisualillusions.Hillsdale:NJ:Erlbaum.Coren,S.,Girgus,J.S.,Erlichman,H.,&Hakstian,A.R.(1976).Anempiricaltaxonomyofvisualillusions.Perception&Psycho-physics,129-137.Coren,S.,&Hoy,V.S.(1986).Anorientationillusionanalogtotherodandframe:Relationaleffectsinthemagnitudeofthedistortion.Per-ception&Psychophysics,159-163.Day,R.H.(1972).Visualspatialillusions:Ageneralexplanat

ion.Sci-ence175,1335-1340.DeValois,R.L.,&DeValois,K.K.(1990).SpatialVision.NewYork:OxfordUniversityPress.DiLorenzo,J.,&Rock,I.(1982).Therod-and-frameeffectasafunc-tionoftherightingoftheframe.JournalofExperimentalPsychol-ogy:HumanPerception&Performance,536-546.Ebenholtz,S.M.(1977).Determinantsoftherod-and-frameeffect:Theroleofretinalsize.Perception&Psychophysics,531-538.Ebenholtz,S.M.(1985).Absenceofrelationaldeterminationintherod-and-frameeffect.Perception&Psychophysics,303-306.Ebenholtz,S.M.,&Callan,J.W.(1980).Modulationoftherod-and-frameeffect:Retinalsizevs.apparentsize.PsychologicalRe-search,327-334.Fisher,G.H.(1968a).Anexperimentalcomparisonofrectilinearandcurvilinearillusions.BritishJournalofPsychology,23-28.Fisher,G.H.(1968b).GradientsofdistortionseeninthecontextofthePonzoillusionandothercontours.QuarterlyJournalofExperimen-talPsychology,212-217.Fisher,G.H.(1969).Towardsanewexplanationofcontourswhichin-duceillusorydistortion.BritishJournalofPsychology,179-185.Fisher,G.H.(1973).Towardanewexplanationforthegeometricalil-lusions:II.Apparentdepthorcontourproximity.JournalofPsychology,607-621.Gibson,J.J.(1937).Adaptation,after-effect,andcontrastinthepercep-tionoftiltedlines:II.Simultaneouscontrastandthearealrestrictionoftheafter-effect.JournalofExperimentalPsychology,553-569.Gibson,J.J.,&Radner,M.(1937).Adaptation,after-effectandcon-trastintheperceptionoftiltedlines:I.Quantitativestudies.JournalofExperimentalPsychology,453-467.Gillam,B.(1973).ThenatureofsizescalinginthePonzoandrelatedillusions.Perception&Psychophysics,353-357.Gillam,B.(1980,January).Geometricalillusions.ScientificAmeri-can242,102-111.Ginsburg,A.P.(1984).Visualformperceptionbasedonbiologicalfil-tering.InL.Spillmann&B.R.Wotten(Eds.),Visualformperceptionbasedonbiologicalfiltering(pp.53-72).Hillsdale,NJ:Erlbaum.Girgus,J.S.,&Coren,S.(1982).Assimilationandcontrastillusions:Differencesinplasticity.Perception&Psychophysics,555-561.Gogel,W.C.(1978,May).Theadjacencyprincipleinvisualpercep-tion.ScientificAmerican,126-139.Gogel,W.C.,&Sturm,R.D.(1972).Atestoftherelationalhypoth-esisofperceivedsize.AmericanJournalofPsychology,201-216.Green,R.T.,&Hoyle,E.M.(1963).ThePoggendorffillusionasaconstancyphenomeNature,611-612.Green,R.T.,&Hoyle,E.M.(1964).Theinfluenceofspatialorienta-tiononthePoggendorffillusion.ActaPsychologica,348-366.Greene,E.,&Pavlow,G.(1989).Angularinductionasafunctionofcontactandtargetorientation.Perception,143-154.Gregory,R.L.(1963).Distortionofvisualspaceasinappropriatecon-stancyscaling.Nature678-680.ory,R.L.(1968,November).Visualillusions.ScientificAmeri-can219,66-76.Gregory,R.L.,&Harris,J.P.(1975).Illusion-destructionbyappro-priatescaling.Perception,203-220.Hering,E.(1861).Beitragezurpsychologie[Contributionstopsy-chology].Leipzig:Engleman.Howard,I.P.(1982).Humanvisualorientation.NewYork:Wiley.Howard,I.P.(1998,December).Knowingwhichwayisup.Presenta-tionattheVisionScienceSymposium,UniversityofCalifornia,Berkeley,December15,1Howard,I.P.,&Childerson,L.(1994).Thecontributionofmotion,thevisualframe,andvisualpolaritytosensationsofbodytilt.Percep-tion,753-762.Johnstone,S.,&Wenderoth,P.(1989).Spatialandorientationspe-cificintegrationinthetiltillusion.Perception,5-23.Jordan,K.,&Randall,J.(1987).TheeffectsofframingratioandobliquelengthinthePonzoillusionmagnitude.Perception&Psycho-physics,435-439.Kleinhans,J.L.(1970).Perceptionofspatialorientationinsloped,slanted,andtiltedvisualfield.Unpublisheddoctoraldissertation,RutgersUniversity,NewBrunswick,NJ.Knight,J.(1999).Theworldturnedupsidedown.NewScientist34-42.Kramer,K.S.(1978).Inhibitoryinteractionsasanexplanationofvi-sualorientationillusions.Unpublisheddoctoraldissertation,UCLA.Künnapas,T.M.(1955).Influenceofframesizeonapparentlengthofaline.JournalofExperimentalPsychology,168-170.Leibowitz,H.,&Toffey,S.(1966).TheeffectofrotationandtiltonthemagnitudeofthePoggendorfillusion.VisionResearch,101-103.Matin,L.,&Li,W.(1995).Multimodalbasisforegocentricspatiallo-calizationandorientation.JournalofVestibularResearch,499-518.Muir,D

.,&Over,R.970).aftereffectincentralandperipheralvision.JournalofExperimentalPsychology,165-170.Newman,C.V.,&Newman,B.M.(1974).ThePonzoillusioninpic-tureswithandwithoutsuggesteddepth.AmericanJournalofPsy-chology,511-516.Oyama,T.(1975).DeterminantsoftheZöllnerillusion.PsychologicalResearch,261-280.Post,R.B.,Welch,R.B.,&Caufield,K.(1998).Relativespatialex-pansionandcontractionwithintheMüller-LyerandJuddillusions.Perception,827-838.Pressey,A.W.,Butchard,N.,&Scrivner,L.(1971).AssimilationtheoryandthePonzoillusion:Quantitativepredictions.CanadianJournalofPsychology,486-497.Pressey,A.W.,&Epp,D.(1992).SpatialattentioninPonzo-likepat-terns.Perception&Psychophysics,211-221.Pressey,A.W.,&Sweeney,O.(1972).AcuteanglesandthePoggen-dorffillusion.QuarterlyJournalofExperimentalPsychology169-174.Prinzmetal,W.,&Beck,D.M.(inpress).Tilt-constancytheoryofvi-sualillusions.JournalofExperimentalPsychology:HumanPercep-tion&PerformancePrinzmetal,W.,&Gettleman,L.(1993).Vertical…horizontalillusion:Oneeyeisbetterthantwo.Perception&Psychophysics,81-88.Rock,I.(1984).Perception.NewYork:ScientificAmericanLibrary.Rock,I.(1995).Perception.NewYork:ScientificAmericanLibrary.Rock,I.,&Ebenholtz,S.(1959).Therelationaldeterminationofper-ceivedsize.PsychologicalReview,387-401.Shimamura,A.P.,&Prinzmetal,W.(1999).Themysteryspotillu-sionanditsrelationtoothervisualillusions.PsychologicalScience,501-507.Stoper,A.E.,&Cohen,M.M.(1986).Judgmentsofeyelevelinlightandindarkness.Perception&Psychophysics,311-316.Tyler,C.W.,&Nakayama,K.(1984).Sizeintsintheper-ceptionoforientation.InL.Spillman&B.R.Wooten(Eds.),Sensoryexperience,adaptation,andperception:FestschriftforIvoKohler(pp.529-546).Hillsdale,NJ:Erlbaum.Velinsky,S.(1925).ExplicationphysiologiquedelillusiondePoggen-dorff[PhysiologicalexplanationofthePoggendorffillusion].AnnéePsychologique,107-116.Wallace,G.K.(1969).ThecriticaldistanceofinteractionintheZöll-nerillusion.Perception&Psychophysics,261-264.Wallace,G.K.,&Moulden,B.(1973).TheeffectofbodytiltontheZöllnerillusion.QuarterlyJournalofExperimentalPsychology10-21.Wenderoth,P.M.(1974).Thedistinctionbetweentherod-and-fillusionandtherod-and-frametest.Perception,205-212.Wenderoth,P.{M.},&Johnstone,S.(1988).Themechanismofthedirectandindirecttiltillusions.VisionResearch,301-312.Wilson,A.E.,&Pressey,A.W.(1976).TheroleofapparentdistanceinthePoggendorffillusion.Perception&Psychophysics,309-316. 114PRINZMETAL,SHIMAMURA,ANDMIKOLINSKI Witkin,H.A.,&Asch,S.E.(1948).Studiesinspaceorientation:IV.Furtherexperimentsoftheuprightwithdisplacedvisualfields.JournalofExperimentalPsychology,762-782.Zoccolotti,P.,Antonucci,G.,&Spinelli,D.(1993).Thegapbe-tweenrodandframeinfluencestherod-and-frameeffectwithsmallandlargeinducingdisplays.Perception&Psychophysics,14-19.NOTES1.Inordertoobtainthefinestresolution,eachkeyboardresponsecausedthelinetogroworshrinkby1pixel.Hence,forthePonzotask,oneveryotherresponse,thebaselinewas1pixeloff-center.2.Becausetheshapeofthegapbetweenthecontextandthehori-zontallinesisdifferentforthetwofigures,itwasdifficulttopreciselyequatethetwo.Tobeconservative,wemadethegapatthetopsmallerintherectilinearversionthaninthestandardversion.Thus,therewouldbemoreblurringintothecontextintherectilinearversion.Inthestan-dardversion,therewere30whitepixelsinthegaponeachend;intherectilinearversion,therewere24pixels.3.Gregorystheorydoesnotnecessarilyrequiretheconsciousper-ceptionofdepth(personalcommunication,July,1999).Experiment4addressesalltheoriesthatmakereferencetolinearperspective,regard-lessofwhetherornottheymakereferencetotheexplicitperceptionofdepthtriggeredbylinearperspective.4.Wealsorananexperimentinwhichthetopandbottomofthead-justablelinemoved,asinthepreviousexperiments.Theresultswereidentical.5.Historically,theZöllnerandPoggendorffillusionsarerelated.In1860,Zöllnersubmittedhisillusionforpublication.Thejournaleditor,Poggendorff,noticedthattheobliquelinesdidnotappeartobecollinear(Boring,1942,p.260).(ManuscriptreceivedAugust31,revisionacceptedforpublicationFebruary25,20