primarieswhenpresentedwitharedteststimulus.Similarly, - PDF document

primarieswhenpresentedwitharedteststimulus.Similarly, intheuniquecondition,subjectsassignedratingsofaboutfive toeachoftheredandyellowprimarieswhenpresentedwith anorangeteststimulus.Ifred,green,blue,andyellowreally canbedistinguishedasunique,weshouldexpectthatwhen theyarepresentedasteststimuliintheintermediatecondition theywouldbegivennear-zeroratings[Fig. 1(b) ].Thiswas clearlynotevidentintheresults. Isitpossiblethatindividualdifferencesinuniquehuesaf- fectourresults?Individualsvaryreliablyintheirsettingsof uniquehues[ 21 , 30 , 32 ],though within-subject variabilityin huesettingsaccountsforasubstantialportionofthetotalvari- abilityobserved[ 29 ].Weusedgroupmeanuniqueandinter- mediatehueselectionsasprimariesforourhuescalingtask. ThepredictionsshowninFig. 1(a) assumedthattheprimaries providedareunique,butthismightnotbetrueforparticular observerswhohaveuniquehuesettingsdifferentfromthe mean.If,foraparticularobserver,theprimariesprovided inthe “ unique ” conditionwerenotunique,wewouldexpect thepatternofresultstoresemblemorethepredictionforin- termediateprimariesshowninFig. 1(b) .Sinceresultsforthe majorityofobserversinbothconditionsmatchedthepredic- tionsforuniqueprimaries[Fig. 1(a) ],individualvariabilityin huesettingscannotundermineourconclusionthatthetypical patternofhuescalingresultsreportedintheliteraturecanbe achievedwithnon-uniqueprimaries. SternheimandBoynton[ 15 ]assessedfromtheirhuescaling resultswhetheragivenhuewasuniquebyapplyingthreecri- teria:(a)thatthecolorcategoryshouldbeusedreliably; (b)thattheratingfunctionforaprimaryshouldreachamaxi- muminaregionwherefunctionsforneighboringprimaries areataminimum;and(c)thataparticularuniquehueshould notberepresentedinratingsassignedtootherprimaries whentheprimaryassociatedwiththatuniquehueisnotper- mitted.Alltheprimariesweusedinbothuniqueandinter- mediateconditionssatisfiedSternheimandBoynton ’ s[ 15 ] firsttwocriteria(seeFig. 3 ).Takethefunctionfororange asanexample:thecategorywasusedreliablyasevidenced bysmallconfidenceintervalsandconsensusacrosssubjects, andthefunctionreachedamaximuminaregionwherefunc- tionsforneighboringhues(violetandlime)wereatamini- mum.Noprimariesfromeitherconditionfulfilled SternheimandBoynton ’ s[ 15 ]thirdcriterion.Theprimaries “ red, ”“ green, ”“ blue, ” and “ yellow ” werenotpermittedin theintermediatecondition.Yetwhenred,green,blue,oryel- lowteststimuliwerepresented,subjectswereabletomake responsesusingtheintermediateprimariestheywerepro- videdwith. “ Unique ” yellow,forexample,wasdescribedby assigningratingsofaboutfivetoeachofthepermittedprimar- iesoforangeandlime. Aminorityofcolorscientistshavequestionedtheassumed specialstatusofuniquehues.Jameson[ 32 ]hasdonesoby consideringthevariableresponsesofparticipantsinthe WorldColorSurvey[ 33 ].ApaperbySaundersandvanBrakel [ 34 ]questioningthelinguistic,neurophysiological,andpsy- chophysicalevidenceforuniquehuestriggeredmanyener- geticresponses.Theywereaccusedof “ throwingthebaby outwiththebathwater ” [ 35 ]and “ selectivevision ” [ 36 ].They madeavaluablepoint,however,thatsolidbehavioralevi- dencefortheexistenceofuniquehuesislacking.Huescaling resultswereputforwardbyseveralrespondentsasevidence supportingthedistinctionbetweenuniqueandintermediate hues[ 13 , 35 – 37 ].Resultsfromthepresentstudyundermine thisevidence.Broakes[ 38 ],alsoinresponsetoSaunders andvanBrakel,challengedcolorscientiststoperformexperi- mentsusinglime,purple,orange,andteal,andsuggestedthat “ ThefearsofSaundersandvanBrakelwillbejustifiedifpeo- plecanprovetodoaswellwithlime,purple,orange,andteal aswedowithred,yellow,green,andblue. ” Forhuescaling, surprisingly,thisturnsouttobethecase. Whatcanexplainthebehaviorofsubjectsinourhuescal- ingexperiment?Onepossibilityisthattheassumptionthat thereisconsensusforthesubjectiveuniquenessofred,green, blue,andyellowismisguided.Butanotherpossibility,which isimpossibletoruleoutinasubjectivetaskofthisnature,is thatsubjectsignoredormisinterpretedtheinstructionsand insteadperformedacolorsimilaritytask,ratingthesimilarity oftheprimaryandthetesthue.Butifthiscouldexplainthe resultsofthepresentstudy,itcouldalsoexplaintheformof allotherresultsfromhuescalingwhereuniquehuesaregiven asprimaries.Conclusionsfromhuescaling,oneofthemain linesofevidencethathasbeenadvancedinsupportofthe specialstatusofuniquehues,areunsound. B.Experiment2:EffectofInstructionsonSettingsof UniqueHues Wehavefoundthatsubstitutingintermediatecolortermsinto theinstructionsaltersmeansettingsofuniquehues.Ifsub- jectswereaskedforauniqueredthatwasneitherpurplish noryellowish,theyidentifiedamuchmoreorangeshadeof redthaniftheywereaskedforauniqueredthatwasneither bluishnoryellowish.Oursampleofnaïvesubjects,despitein mostcasesproducingcleanpsychometricfunctions[e.g., Fig. 5(b) ],didnotreliablyidentifyaparticularhueassubjec- tivelypure.Ourresultsallowforthepossibilitythatunique huesdonotexist,andthatsettingsofuniquehuesmightsim- plyreflectaperceptualintermediatebetweenthealternatives givenintheinstructions.However,wecannotexcludethe possibilitythatoursubjectsweresimplybiasedbythecon- tentsoftheinstructions.Whatwe can concludeisthatdecid- ingwhetheraparticularhueisneither “ toored ” nor “ too green ” tobeuniqueisnotasimpleenoughorsalientenough taskthatsubjectscanescapebias.Wecanalsoconcludethat thefactthatsubjectsareabletoidentifyaparticularblueas neithergreenishnorreddishisnotevidencethattheblueis unique. C.GeneralDiscussion Ourresultsundermineexistingbehavioralevidenceforthe specialstatusofuniquehues.Butourexperiments,andmost othersthathaveattemptedtoestablishtheuniquenessof uniquehuesempirically,employBrindleyclassBobserva- tions[ 39 ],wheresubjectsarerequiredtodescribethequality oftheirsensations.Onerecentandparticularlyinterestingex- ampleofaclassBmethodofinvestigatinguniquehuesis par- tialhuematching byLogvinenkoandBeattie[ 40 ],where subjectsarerequiredtoidentifythesetofhuesthatshares acomponentcolorqualitywithatesthue. Chromaticity classes (thelargestsetofstimulithatallpartiallymatch) areextractedfrommatricesofpartialhuematches,andfor about50%ofobserversfour “ unique ” huesthatbelongtoonly onechromaticityclassemerged.However,therewereseveral J.M.BostenandA.E.BoehmVol.31,No.4/April2014/J.Opt.Soc.Am.AA391 minorityphenotypes,includingsubjectswhoseemtohave morethanfouruniquehues,orwhohavenouniquehues. Thedifficultyofinterpretingthepossiblealternativestrategies ofsubjectswithatypicalresultshasledLogvinenko[ 41 ]to suggestthat “ thisproblemisfartooinvolvedtobelefttoinex- periencedobservers. ” However,itseemsequallylikelythat observerswhoareexperiencedinmakingcolorintrospec- tionsmightgiveinvalidorunrepresentativeresults.Even thosewhoarenotversedincolorsciencemayadoptanintro- spectivestrategyofbasingsubjectivejudgmentsonthe “ primary ” colorsthattheyareculturallyfamiliarwith. Giventhelimitationsofmethodsinvolvingintrospection, couldanypsychophysicalexperimenteitherproveordis- provetheexistenceofuniquehues?Whataboutperformance measuresorclassAobservations? Subjects ’ reliabilityatsettinguniquehuesisnoteasilycat- egorizedeitherasaclassBorasaclassAobservation.Inthe methodofaverageerror (whichconstitutesaclassAobser- vation),subjectsarerequiredtomakeamatchmanytimes, andthevarianceofmatchesistakenasameasureofperfor- mance.Measurementofthereliabilityofsettingsofunique huesusesthemethodofaverageerror,butthestandardto whichsubjectsaremakinga “ match ” isinternalratherthan external,sosubjectsarerequiredtojudgethequalityoftheir sensations.Ineithercase,itmightbethoughtreasonableto assumethatsubjectscansetuniquehuesmorereliablythan theycansetintermediatehues.However,Malkoc etal. [ 30 ] foundthattest – retestreliabilityisashighforbinary(inter- mediate)huesasitisforuniquehues.BostenandLawrance- Owen[ 29 ]haveindependentlyreplicatedthefindingsof Malkoc etal. [ 30 ]andhavefoundthatintra-subjectvariability (aswellasinter-subjectvariability)foridentifyinguniquehues isnodifferenttothatforidentifyingintermediatehues. AlthoughitisperhapstellingthatpureclassAobservations thatdistinguishtheuniquehueshave,untilrecently,been lacking(somestudieshavereportednegatively,thatunique huesarenotdistinguishedfromotherhuesusingclassAob- servations[ 29 , 42 – 46 ]),DanilovaandMollon[ 47 ]havefound thatthelocusofuniqueblueanduniqueyellowcorresponds tominimainthresholdsforcolordiscrimination.The correlationbetweenthelociofuniquehues,measuredusing subjectivejudgments,andapeakindiscriminationperfor- manceisinteresting.Suchfindingsdo,however,needtoac- countforthewiderangeofsettingsofuniquehuesfound acrossindividualsandacrossstudies[ 48 ].Acorrelationbe- tweenindividualdifferencesinthepositionsofcolordiscrimi- nationminimaandindividualdifferencesinsettingsofunique hueswouldbeprovocative. DanilovaandMollon ’ s[ 47 ]carefulmeasurements,and otherBrindleyclassAobservations,mightbeabletoestablish thepresenceorabsenceofchannelstunedtoparticularchro- maticities,buttheycannomoreestablishtheuniquenessof uniquehuesthanthemorewidespreadclassBobservations. Uniquenessisdefinedsubjectively,andthereforecannotbe proven.Perhapsitistimeforcolorscientiststoputunique huesaside,andknowthemsimplyasred,green,blue,and yellow. ACKNOWLEDGMENTS ThisworkwassupportedbyaResearchFellowshipfrom GonvilleandCaiusCollege,andbygrantEY011711 fromtheNationalInstitutesofHealthawardedtoDonald MacLeod. 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J.M.Bosten 1,2, *andA.E.Boehm 1,3,4 1 DepartmentofPsychology,UniversityofCalifornia,SanDiego,McGillHall,LaJolla,California92093,USA 2 DepartmentofExperimentalPsychology,UniversityofCambridge,DowningStreet,CambridgeCB23EB,UK 3 VisionScienceGraduateGroup,UniversityofCalifornia,Berkeley,380MinorHall,Berkeley,California94720,USA 4 SchoolofOptometry,UniversityofCalifornia,Berkeley,380MinorHall,Berkeley,California94720,USA *Correspondingauthor:jmb97@cantab.net ReceivedOctober3,2013;revisedDecember22,2013;acceptedDecember27,2013; postedJanuary13,2014(Doc.ID198752);publishedMarch11,2014 Red,green,blue,yellow,andwhitehavebeendistinguishedfromotherhuesasunique.Wepresentresultsfrom twoexperimentsthatundermineexistingbehavioralevidencetoseparatetheuniquehuesfromothercolors.In Experiment1weusedhuescaling,whichhasoftenbeenusedtosupporttheexistenceofuniquehues,buthas neverbeenattemptedwithasetofnon-uniqueprimaries.Subjectswereassignedtooneoftwoexperimental conditions.Inthe “ unique ” condition,theyratedtheproportionsofred,yellow,blue,andgreenthattheyper- ceivedineachofaseriesofteststimuli.Inthe “ intermediate ” condition,theyratedtheproportionsofteal, purple,orange,andlime.Wefound,surprisingly,thatresultsfromthetwoconditionswerelargelyequivalent. InExperiment2,weinvestigatedtheeffectofinstructiononsubjects ’ settingsofuniquehues.Wefoundthat alteringthecolortermsgivenintheinstructionstoincludeintermediatehuesledtosignificantshiftsinthehue thatsubjectsidentifiedasunique.Theresultsofbothexperimentsquestionsubjects ’ abilitiestoidentifycertain huesasunique.©2014OpticalSocietyofAmerica OCIScodes: (330.1690)Color;(330.1720)Colorvision;(330.5510)Psychophysics;(330.5020)Perception psychology. http://dx.doi.org/10.1364/JOSAA.31.00A385 1.INTRODUCTION Fivehues:red,green,blue,yellow,andwhite,havebeengiven specialstatusbycolorscientistsas “ unique. ” Theuniquehues aresaidtobephenomenologicallypure,whileallotherhues aresaidtobephenomenologicallymixed,containingvarious proportionsofthefiveuniquehues. Uniquehueshavealonghistoryinpsychology.Itwasthe beliefthatuniquehuesmusthavespecialstatusincolorrep- resentationthatledHering[ 1 ]toproposered,green,blue,and yellowasthepolesofhisopponentmechanisms.Following thetraditionestablishedbyHering[ 1 ],andlaterbyHurvich andJameson[ 2 ],whencoloropponentcellswerediscovered intheprimatelateralgeniculatenucleus,theyweredescribed asbeingselectiveforredandgreen,andblueandyellow[ 3 ]. Althoughitisnowclearthatthechromatictuningofcolor- opponentmechanismsrevealedpsychophysicallydoesnot mapontotheHeringprimaries[ 4 ],andthatthecolor-sensitive cellsinthelateralgeniculatenucleusencodeintermediate colordirections[ 5 , 6 ],theconvictionthatuniquehuesmust haveprominenceinneuralcolorsignalshasledtopersistence oftheideathatcolor-opponentcellsencodetheHeringpri- maries,andtoasearchforhigher-ordercolormechanisms thatareselectiveforred,green,blue,andyellow[ 7 – 10 ]. A.HueScaling Despitebroadconsensusamongcolorscientiststhatred, green,blue,andyellowshouldbeconsideredunique,solid behavioralevidencetosupportthisviewhasbeenhardto comeby.Onesourceofevidencethatisoftencitedtojustify thespecialstatusofuniquehues[ 11 – 13 ],ishuescaling.Hue scalingasamethodisbasedonsensoryscalingofmultiple stimulusattributes,introducedbyJamesonandHurvich [ 14 ].Thesubjectispresentedwithcoloredstimuliandasked toconsiderhowmuchofvariousgiven “ primary ” colorseach stimuluscontains.Thesubjectassignsanumericalratingto eachprimarythatreflectshisjudgmentofhowmuchofthat primaryiscontainedinhisperceptionofthestimulusthatis presentedtohimonaparticulartrial.Theideaisthatifahue isunique,itwillcontainoneprimary,butnotanyother. Resultsfromhuescalingexperimentstypicallyshowthat therearefourpointsaroundthehuecirclewheresubjectsre- portseeingonlyoneprimary.Forexample,at “ unique ” green, subjectsreportseeinggreen,butnotblue,yellow,orred. However,sincetheprimariestowhichsubjectsareasked toassignratingsaretypicallythemselvestheuniquehues, itisperhapsunsurprisingthatratingspeakforred,green, blue,andyellowinregionswhereneighboringhuesapproach thezerolevel.Red,yellow,green,andbluearesetapart roughly90°aroundthehuecircle,soitmaybesimplytheper- ceptualdistancebetweenthemthatresultsinonenotbeing seeninanother. SternheimandBoynton[ 15 ]didhuescalingformonochro- maticlightsbetween530and620nm.Theyintroducedorange asanavailableprimaryinsomeoftheirconditions,andcon- cludedthattheyhadevidencetoseparateyellow,green,and red,butnotorange,asunique.Infourconditionssubjectswere given(i)red,green,andblue,(ii)red,yellow,andgreen,(iii)red, orange,andgreen,and(iv)red,orange,yellow,andgreen,touse asprimaries.Whenyellowwasunavailableasaprimary,there werecertainwavelengthsthatSternheimandBoynton ’ s[ 15 ] subjectswereunabletoadequatelydescribebymixturesof red,green,andblue.Incontrast,whenorangewasunavailable, J.M.BostenandA.E.BoehmVol.31,No.4/April2014/J.Opt.Soc.Am.AA385 1084-7529/14/04A385-09$15.00/0©2014OpticalSocietyofAmerica lightofwavelengthsinthe “ orange ” partofthespectrumcould beadequatelydescribedasmixturesofredandyellow. WebelievethatSternheimandBoynton ’ s[ 15 ]comparison betweenconditionswasnotentirelybalanced.Inconditions whereorangewasunavailableasaprimary,twocloselyneigh- boringhues,redandyellow,wereavailable.Butinconditions whereyellowwasmissing,atleastoneofthetwoalternative primariesprovidedwasfurtherfromyellowonthehuecircle thaneitherredoryellowfromorange.Itcouldsimplybethe spacingoftheprimariesincolorsimilarity,ratherthantheir uniqueness,thatallowsadequatedescriptionofotherhues. NeitherSternheimandBoynton[ 15 ]norotherswhohave sinceusedhuescalingtoinvestigatecolorappearance [ 16 – 20 ],haveintroducedatruecontrolcondition.Inorder toconcludethathuescalingresultsdemonstratetheunique- nessofuniquehues,itisnecessarytoshowthatthesamere- sultscannotbeobtainedusingonlynon-uniqueprimaries roughlyevenlydistributedaroundthehuecircle.InExperi- ment1,wereporttheresultsofhuescalingundertwodiffer- entconditions:astandard “ unique ” conditionwherethefour uniquehuesaregivenasprimaries,andacontrol “ intermedi- ate ” conditionwherefourintermediatehues(purple,orange, lime,andteal)aregiven. B.EffectofInstructiononSettingsofUniqueHues Inexperimentswheresubjectsarerequiredtoidentifyorpro- videsettingsofuniquehues,otheruniquehuesareinvariably givenintheinstructions[ 21 – 26 ].Asubjectmaybeaskedtoset ayellowthatisneitherreddishnorgreenish[ 27 ],orformea- surementsofuniquegreen,todecidewhetheragivencoloris toobluishortooyellowish[ 17 ]. Subjectsarerequiredtoidentifyauniquehuebyconsider- ationofother(typicallyunique)huesspecifiedintheinstruc- tions.Thetwootheruniquehuescontainedinstandard instructionsaresituatedroughlyorthogonallyaroundthe huecirclefromtheuniquehuetobeidentified.Thissuggests possibleartifacts.Redmaybeidentifiedasneitherbluishnor yellowishsimplybecauseblueandyellowareeachsuffi- cientlydistantfromred.Alternatively,redmaybeidentified asneitherbluenoryellowbecauseitisperceptuallyhalfway betweenblueandyellow,ratherthanbecauseitissubjectively pure.OurExperiment2controlsforthesepotentialexperi- mentalartifactsbysubstitutingnon-uniquecolortermsinto theinstructions.Insteadofbeingaskedtoidentifyaunique redthatisneitherbluishnoryellowish,subjectsmightbe askedtoidentifyauniqueredthatisneitherbluishnororang- ish.Ifsubjectsidentifyuniqueredasasinglesubjectivelypure color,thechangeininstructionshouldhavenoeffectontheir “ unique ” huesettings. 2.EXPERIMENT1:HUESCALING A.Predictions Ifuniquehuesaresubjectivelypureandotherhuesaresub- jectivelymixed,whatshouldtheresultsofhuescalingbefor ouruniqueandintermediateconditions?Predictionsare showninFig. 1 .Fortheuniqueprimariesweexpectfunctions likethosethathavebeenobtainedbymanyotherresearchers. Thefunctionforeachprimaryshouldpeakatthehueangle ofitsassociateduniquehue,wherethefunctionsforthe threeotherprimariesshouldbeatzero.Atthepositionsof intermediatehues,twoprimariesshouldbereported.The predictionfortheintermediateprimariesisverydifferent. Functionsforeachintermediateprimaryshouldpeakatthe hueangleofthatprimary.Butatthepositionsofthe(subjec- tivelyunitary)uniquehues,allfunctionsshouldbeatzero. B.Stimuli ArepresentationofaparticulartrialisgiveninFig. 2(a) .The teststimuluswasadiskof4°diameterpresentedintheupper halfofthescreen.Thechromaticityoftheteststimuluswas randomlyselectedoneachtrialfrom36chromaticitycoordi- natesdistributedinacircleinMacLeod – Boynton[ 28 ]chroma- ticityspacearoundapointmetamericwithilluminantD65 [Fig. 2(b) ].Intheresultssection,thechromaticitiesofthe 36stimuliwillbegivenby “ hueangles. ” Wedefinedhueangle inMacLeod – Boyntonchromaticityspaceclockwise,withzero atthevertical(S

L  M  )axis[Fig. 2(b) ].Conversionfrom hueangletoMacLeod – Boyntonchromaticitycoordinates canbeachievedbythefollowingformulas,where
isthe hueangle: S

L  M  0 . 0167  0 . 013 cos
; L

L  M  0 . 6552  0 . 0364 sin
. Thebackgroundonwhichthestimuliwerepresentedwas metamericwithD65.Allteststimuliwereisoluminantwitha luminanceof 28 cdm  2 ,andtheluminanceofthebackground was 14 cdm  2 .Inthelowerpartofthescreen,disksof2° diameterwerepresentedthatcontainedfourprimaries [Fig. 2(b) ],whichwereeithertheuniquehuesortheinter- mediatehuesdependingonthecondition.Theluminance oftheprimarieswas 28 cdm  2 .Aboveeachprimarywasa boxinwhichthesubjectenteredanumbercorresponding tohisperceptionofhowmuchofthatprimarywascontained intheteststimulus.Theboxesweredelimitedwithablack line,onepixelwide.Thesubjectusedthearrowkeystomove betweenboxes,andthecurrentlyselectedboxwasindicated byreplacingtheblackborderwithawhiteborder,metameric Fig.1.Predictionsforhuescalingwithuniqueprimaries[panel(a)], andwithintermediateprimaries[panel(b)].Alongthe x axishuean- glesareplottedaroundthehuecircle,andonthe y axisthepredicted numericalratingsfrom0to9areshown.Thedashedverticallines indicatetheuniqueandbinaryhueprimaries,whicharelabeledwith uppercaseletters:purple(P),red(R),orange(O),yellow(Y),lime(L), green(G),teal(T),andblue(B).Predictedfunctionsforratingsfor eachprimaryasafunctionofthehueangleoftheteststimulus areindicatedbythesolidcurves,whicharelabeledwithlowercase letters. A386J.Opt.Soc.Am.A/Vol.31,No.4/April2014J.M.BostenandA.E.Boehm withD65andwithaluminanceof 28 cdm  2 .Subjectsentered aratingintoeachboxusinganumericalkeypad,andthe numberwasshownintheboxinwhite,alsometamericwith D65andwithaluminanceof 28 cdm  2 . C.SelectionofPrimaries Theprimariesusedinthehuescalingexperimentwerebased onselectionsofuniqueandintermediatehuesmadeby58sub- jects[ 29 ].Subjectswerepresentedwithannuliofselectable segmentscontainingaprogressionofhuesonaCRTmonitor coveredwithatouch-sensitivescreen.Thesegmentscontain- ingthehueswereisoluminantwithaluminanceof 28 cdm  2 . ThebackgroundwasmetamericwithD65andhadalumi- nanceof 17 cdm  2 .Oneachtrialacircleof90segmentscon- taining90discretehueswaspresented[Fig. 2(c) ].Thecircle wasrotatedrandomlyfromtrialtotrial.Accordingtothe block,subjectswereaskedtochoose,forexample, “ aredthat isneithertooorangenortoopurple ” or “ anorangethatisnei- thertoorednortooyellow ” [ 30 ].Thesubjectselectedthe segmenthethoughtbestmatchedtheinstruction,andasmall achromaticdiskappearedbesidethatsegment.Heconfirmed hisselectionbytappingachecksymbolpresentedinthelower leftpartofthescreen. Therewere16blocks,eachof15trials.Ineachblockoneof thefouruniquehues(red,green,blue,oryellow),oroneofthe fourintermediatehues(orange,purple,teal,orlime)was tested.Inthefirsteightblocks,alleighthuesweretested inarandomorder,andtheyweretestedagaininadifferent randomorderinthesecondeightblocks.Fifty-eightsubjects tookpartintheexperiment.Allhadnormalcolorvision assessedusingtheIshiharaplatespresentedunderMacBeth IlluminantC. Togatherresponsesofsubjects,weusedaKeytecMagic TouchProE-Xtouchscreen(modelnumberET2032C) attachedtoaCRTmonitor.Stimuliwerepresentedona DiamondPro2070SBCRTmonitor(Mitsubishi,Tokyo, Japan)calibratedusingaUDTphotometer(UnitedDetector Technology,Hawthorne,California)andaSpectraScan PR650spectroradiometer(PhotoResearchInc.,Chatsworth, California).ExperimentswereruninMatlab(TheMathWorks, Natick,Massachusetts)usingaVSG2/4graphicscard (CambridgeResearchSystems,Rochester,UK). Theprimariesusedinthehuescalingexperimentwere basedonthemeanhuesettingsforthe58subjects.These settingsareshowninFig. 2(d) alongwith95%confidence intervals. D.ProcedureforHueScaling Beforebeginningtheexperiment,subjectsweretoldthattheir taskwastomakesubjectivedecisionsaboutthecolorsofthe testdisks.Writteninstructionsfortheintermediatecondition wereasfollows: “ Youwillbeshownaseriesofcolors.For eachcoloryoumustdecidehowmuchoffourothercolors yoursubjectiveexperienceofthatcolorcontains.Youmust decidehowmuchorange,lime,purple,andtealyourexperi- enceofthecoloryouarepresentedwithcontains.Youmust ratethequantityofeachcolorinyourexperiencebyanumber from0to9.Enteryourratingsintotheboxesprovided.You cannavigatebetweenboxeswiththearrowkeys.Acceptall yourratingsforatrialbypressingReturn. ” Equivalentinstruc- tionsweregivenfortheuniquecondition,exceptthatthelist ofcolortermswas “ red,yellow,blue,andgreen. ” Subjectsweregivenadditionalinstructionsorally.They wereremindedthatthetaskwassubjective,thattherewas norightorwronganswerandthattheymustrespondinwhat- everwaytheyfeltwasmostappropriate.Theywereinstructed thattheratingstheyassigneddidnothavetoadduptoany particularnumberandthatanypossibleresponsewasaccept- able,includinggivingallfourprimariesascoreofzero. Oneachtrialasubjectenteredhisratingsintothefour boxes[Fig. 2(a) ].Hewasabletochangehisresponsesby overwritingthem.Whenhewassatisfiedwithallfourratings, hepressedtheReturnkeytomoveontothenexttrial.The36 testchromaticitieswerepresentedinarandomorderthree times,sothatall36teststimuliwerepresentedonceinaran- domorder,andthentwicemoreindifferentrandomorders. Fig.2.Stimuliusedinthehuescalingexperiment.Panel(a)repre- sentsthestimuluspresentedononetrial.Theupperdiskisthetest stimulus,andthefourlowerdisksaretheprimaries(lefttoright:red, yellow,green,andblue).Thesubjectwasinstructedtoassigna numericalratingtoeachprimaryaccordingtohowmuchofthatpri- maryheperceivedintheteststimulus.Theselectedboxwasindicated withawhiteborder.Thestimulusrepresentedherewasfortheunique condition:thestimulusfortheintermediateconditionwasequivalent, exceptthatthefourprimarieswereteal,lime,orange,andpurple. Panel(b)showsthechromaticitiesofthestimuliinMacLeod – Boynton chromaticityspace.Thetestchromaticitiesareshownbythedisks, andtheprimariesbythegraycrosses,labeled.Theblackdotin thecenterofthefigureindicatesthechromaticityofD65.Thehue angle(
)foranexampleredteststimulusisindicatedinthepanel. Panel(c)representsthestimulususedformeasuringuniqueandin- termediatehues.Eachof90segmentscontainedahuefromarange linearlyspacedaroundacirclecenteredatthecoordinatesofD65in MacLeod – Boyntonchromaticityspace.Instructionswerepresented intheupperpartofthescreen — fortheparticulartrialrepresented inthefigure,theinstructionsread “ pickanorangethatisneither toorednortooyellow. ” Thesubjectusedastylustoselectasegment, andanachromaticdiskappearedbesidetheselectedsegment.The selectionwasconfirmedbytappingthechecksign.Panel(d)shows meanselectionsofuniqueandintermediatehuesmadeby58subjects. Datapointsforeachprimaryarelabeled:purple(P),red(R),orange (O),yellow(Y),lime(L),green(G),teal(T),andblue(B).Errorbars (linesinsidedatapoints)indicate95%confidenceintervalsonthe mean.Themeanselectionswereusedastheprimariesinthehue scalingexperiment. J.M.BostenandA.E.BoehmVol.31,No.4/April2014/J.Opt.Soc.Am.AA387 Asubject ’ sratingforeachteststimuluswasbasedonthe meanofthethreetrials.Theexperimenttookmostsubjects between10and30minutestocomplete. E.Subjects Thirty-sixsubjectstookpartintheexperiment.Allhadnormal colorvisionassessedusingtheIshiharaplates.Subjectswere assignedrandomlyeithertothe “ unique ” ortothe “ intermedi- ate ” conditionsothat18subjectsparticipatedineachcondi- tion.ThesubjectswereUniversityofCalifornia,SanDiego undergraduatestudentswhoparticipatedinexchangefor coursecredit.Theystudiedarangeofsubjects,including statistics,psychology,biology,andlinguistics.Allsubjects werenaïvetothepurposesofthehuescalingexperiment andhadnottakenpartintheexperimenttoselectthe chromaticitiesoftheprimaries. F.Equipment StimuliwerepresentedonaMitsubishiDiamondPro2070SB CRTmonitor.Thegammafunctionswerelinearizedusing measurementsmadewithaUDTphotometercalibratedfor luminanceusingaSpectrascanPR560spectroradiometer. Thecolorcalibration,whichallowedforconversionfrom MacLeod – BoyntonchromaticitycoordinatestoRGBvalues, wasachievedbymeasuringthespectraofthethreephosphors oftheCRTmonitorusingtheSpectrascanPR650. G.Results Resultsaveragedacrosssubjectsarepresentedin Figs. 3(a) – 3(b) .Thefigureshowsthemeanratingsforhow muchofeachprimarywasjudgedtobecontainedineachtest stimulus.Resultsfromtheuniqueconditionarepresentedin panel(a),andresultsfromtheintermediateconditionarepre- sentedinpanel(b).Inbothpanels,thehueanglesoftheeight primariesusedinthetwoconditionsareindicatedbythever- ticaldashedlines. Resultsfortheuniqueconditionweresimilartothoseob- tainedbySternheimandBoynton[ 15 ].AsSternheimand Boynton[ 15 ]found,peakratingsareatthehueanglesof theuniquehues.Attheangleofeachuniquehue,ratings forthethreeotheruniquehueswereverylow.Attheangles ofintermediateprimaries,twouniqueprimariesweregiven mediumratings. Surprisingly,theresultsoftheintermediateconditionwere verysimilartothoseoftheuniquecondition.Peakratingsfor eachintermediateprimarywerefoundatthehueangleofthat primary.Attheangleofeachintermediateprimary,ratingsfor thethreeotherintermediateprimarieswerelow.Attheangles Fig.3.Resultsofthehuescalingexperiment.Ineachpanel,thehueangles(indegrees)oftheteststimulishowninFig. 2(b) areplottedalongthe x axesandratingsareplottedupthe y axes.Eachfunctionshowsratingsforhowmuchofaparticularprimarysubjectsjudgedtobepresentinthe teststimuli.Eachpanelshowsfourfunctionsdescribingtheresultsforthefourprimariesprovidedinthatcondition,coloredaccordingtothe primary.Dashedverticallinesindicatethehueanglesoftheeightprimariesusedacrossthetwoconditions,alsocoloredaccordingtotheprimary. Panel(a)showsgroupmeanresultsfortheuniquecondition( n  18 ),andpanel(b)showsgroupmeanresultsfromtheintermediatecondition ( n  18 ).Errorbarsinpanels(a)and(b)are95%confidenceintervalsforeachmeanrating.Panels(c) – (h)showexamplesofresultsfromindi- vidualsubjects,withthengivenforeachcaseindicatingthenumberofsubjectswhoproducedaresultsimilartotheoneshown.Panels(c) – (e)are fromtheuniquecondition,andpanels(f) – (h)arefromtheintermediatecondition. A388J.Opt.Soc.Am.A/Vol.31,No.4/April2014J.M.BostenandA.E.Boehm oftheuniqueprimaries,twointermediateprimarieswere givenmediumratings. Therewereothernotablefeaturesofthedata.Ineachcon- dition,theintersectionoftwodescendingfunctionsoccurred verynearthehueangleofaprimarynotusedinthatcondition. Forexample,intheuniquecondition,thefunctionsforthered andyellowprimariescrossedatabout125°,whichwas veryclosetothehueangleoftheorangeprimarythatwas notprovidedintheuniquecondition.Intheintermediate condition,thefunctionsforthelimeandorangeprimaries crossedatabout160°,whichwasclosetothehueangle fortheyellowprimarythatwasnotprovidedintheintermedi- atecondition. Themoststrikingfeatureoftheresultsisthesimilaritybe- tweenthetwoconditions.Differencesbetweenconditions,by comparison,arerelativelyminor.However,the “ baseline ” rat- ings(ratingsforprimariesatteststimuluspositions180°re- movedfromthepositionwhereratingspeak)arealittlehigher intheintermediateconditionthanintheuniquecondition. Thissmalldifferencebetweenconditionsmaybedrivenby individualdifferences.Aminorityofsubjectsperformed unusuallyonthistask,anditmaybethatinthetwoconditions thereweredifferentnumbersofsubjectswhofollowedminor- itystrategies. H.IndividualDifferences Resultsfromsixindividualsubjectsareshownin Figs. 3(c) – 3(h) .Resultsoftheuniqueconditionarepre- sentedinpanels(c) – (e),andresultsoftheintermediatecon- ditionarepresentedinpanels(f) – (h).Ineachpanel,n indicatesthenumberofsubjectswhoproducedresultssim- ilartotheexampleshown.Mostsubjectsassignedhighrat- ingstooneortwoprimariesforeachteststimulus,andzero ornearzeroratingstotheotherprimaries[panels(c)and (f)].Othersubjects,tovaryingdegrees,assignednon-zero ratingstomorethantwoprimariesforagiventeststimulus [panels(d)and(g)].Twosubjects[panels(e)and(h)]gave resultsthatresembledthepredictionsforintermediatehues [Fig. 1(b) ],butoneofthesewasgivenuniqueprimaries. Theaveragevariabilityinaratingwasgreaterforthe intermediatethanfortheuniquecondition.Specifically, themeanstandarddeviationofratingswas1.59forthein- termediateconditionand1.29fortheuniquecondition ( T  5 . 9 , p 0 . 01 ).However,ratingvariabilityonlydiffered betweenconditionsforlowmeanratings(Fig. 4 ).At mediumandhighmeanratings,thedistributionsofvariabil- ityinratingsoverlapped.Thisshowsthatthegreatervari- abilityintheintermediateconditionwasonlynearthe “ baseline ” levelofrating.Thisgreatervariationinbaseline ratingsindicatesthattheslightlyhigherbaselineratingsin theintermediateconditionarecausedbyindividual differences.Figures 3(c) – 3(h) bearthisout:moresubjects assignednon-zeroratingstomorethantwoprimariesfor agiventeststimulusintheintermediateconditionthan intheuniquecondition. Thesmalldifferenceinresultsbetweenthetwoconditions appearstobedrivenbyindividualdifferencesintaskstrategy. Therewereclearexamplesofthreedifferentstrategiesinboth conditions[Figs. 3(c) – 3(h) ],soweconcludethatprovidingin- termediateratherthanuniqueprimariesforhuescalingcan leadtoequivalentresults. 3.EXPERIMENT2:EFFECTOF INSTRUCTIONONSETTINGSOFUNIQUE HUES A.Stimuli Thestimuluswasadiskofapproximately2°presentedinthe centerofthedisplay.Theluminanceofthediskwas 28 cdm  2 .Itschromaticityvariedaccordingtoastaircasepro- ceduretrackingthesubject ’ sresponses.Thestartingpositions ofthestaircaseswereathueanglesof0°(L

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L  M  0 . 00675 )whenuniquered wasmeasured.ThebackgroundwasmetamericwithD65 andhadaluminanceof 21 cdm  2 .Stimuliwerepresented onthesamecalibratedMitsubishiDiamondProCRTmonitor asinExperiment1. B.Procedure Subjectswereassignedrandomlytooneofthreeconditions foruniqueblueandtooneofthreeconditionsforuniquered. Subjectswereinstructedthattheirtaskwastomakesubjec- tivedecisionsaboutthecolorofthetestdisk.Foruniqueblue theyweretheninstructed(dependingontheconditionto whichtheywereassigned)asfollows: “ Inthisblockyou arelookingforapurecolorthatis ” b(i) “ neithergreenishnorreddish, ” b(ii) “ neithertealishnorreddish, ” b(iii) “ neithergreenishnorpurplish. ” Theywereinstructedtopressonebuttononakeypadif,for example,thediskwas “ toogreen, ” andanotherbuttonifit was,forexample, “ toopurple. ” Foruniquered,subjectswere givenequivalentinstructions,exceptthecolorwordsgivenin thethreeconditionswere: r(i)blueandyellow, r(ii)blueandorange, r(iii)purpleandyellow. Bothuniqueblueanduniqueredweremeasuredforeach subjectinseparateblocksinarandomorder. 0 2 4 6 8 10 0 0.5 1 1.5 2 2.5 3 Mean rating Standard deviation of ratings Fig.4.Distributionsofratingvariabilitywithmeanrating.Standard deviationsofratingsfortheintermediateconditionareshownbythe graysquaresandfortheuniqueconditionbytheblackcircles.The distributionsofvariabilityinratingslargelyoverlap.However,lowrat- ingsshowlowervariabilityintheuniqueconditionthanintheinter- mediatecondition. J.M.BostenandA.E.BoehmVol.31,No.4/April2014/J.Opt.Soc.Am.AA389 Ineachblock,fourrandomlyinterleavedstaircases convergedonasubject ’ suniquehue.Theinitialstepsize wasahueangleof10°,andthiswasreducedto5°oncea pairofstaircaseshadcrossed[seeFig. 5(a) ].Eachstair- caseterminatedafter60trials.Therewere240trialsper block. C.Subjects Onehundredfifteensubjectstookpartintheexperiment. NonehadtakenpartinExperiment1.Allhadnormalcolor visionassessedusingtheIshiharaplates.Allsubjectswere naïvetothepurposesoftheexperiment.TheywereUniversity ofCalifornia,SanDiegoundergraduateswhoparticipatedin exchangeforcoursecredit. D.Results ResultsofExperiment2areshowninFig. 5 .Panel(a)shows examplesofstaircasesforuniqueblue.Thesubjectwhose dataareshowninthepanelwasgiveninstructionsb(ii),to identify “ abluethatisneithertealishnorreddish. ” Panel (b)showsapsychometricfunctionfittothedatashownin panel(a).WefitcumulativeWeibullpsychometricfunctions using modelfreev1.1 [ 31 ].Uniquehuesettingsweredefinedas the50%pointonthepsychometricfunction,wheresubjects wereequallylikelytogiveeachofthetwoalternativere- sponses.Panel(c)showsgroupresultsplottedinthecontext ofthefullhuecircle.Whitelinesshowgroupmeanhue settings,andthelightgrayareasindicate95%confidence intervals.Hueanglesofthehuesettingsareshowninpanel (d)foruniqueredandpanel(e)foruniqueblue. Thedatashowthatmeansettingsofuniquehuesareshifted bychangesintheinstructionsthatweregiventosubjects. Therewasasignificanteffectofinstructionbothforunique red( F  22 . 7 , p  5 . 6 × 10  9 )andforuniqueblue( F  64 , p 1 × 10  16 ).Inbothcases,huesettingsforthestandardin- structionswereintermediatebetweenthosefortheothertwo conditions.Comparedtosettingsresultingfromthestandard instructions, “ abluethatisneithergreenishnorreddish, ” set- tingsof “ abluethatisneithergreenishnorpurplish ” were shiftedawayfrompurpleandsettingsof “ abluethatisneither tealishnorreddish ” wereshiftedawayfromteal.Thepattern ofresultsforuniqueredwasanalogoustothatforuniqueblue. 4.DISCUSSION A.Experiment1:HueScaling Wehavefoundthat,surprisingly,whenasetofintermediate huesaresubstitutedfortheuniquehuesasprimariesinhue scaling,resultsremainbroadlythesame.Ourresultsare clearlyagainstpredictionsofwhatshouldhappengiventhe prevailingviewthatuniquehuescanbedistinguishedfrom otherhuesassubjectivelypure(compareFigs. 1 and 3 ).Sub- jectsreportedseeingintermediateprimariesin “ unique ” hues inthesamewayastheyreportedseeinguniqueprimariesin intermediatehues.Intheintermediatecondition,subjectsas- signedratingsofaboutfivetoeachofthepurpleandorange Fig.5.ResultsofExperiment2.(a)Examplesofstaircasesforonesubjectinconditionb(ii): “ Neithertealishnorreddish. ” (b)CumulativeWeibull psychometricfunctionfittothedatashownin(a).Theareaofeachdatapointisproportionaltothenumberoftimestheparticularstimuluswas presented.(c)Groupresults.Whitebarsindicategroupmeansforeachcondition,andlightgrayareasindicate95%confidenceintervals.Ineach case,the ‘ standard ’ versionofthequestion(conditioni)producesintermediateresults,withalterationsinthecolorwordsgivenintheinstructions predictablyshiftingthemeansettingsofuniquehues(conditionsiiandiii).(d)Resultsforuniqueredshownasafunctionofhueangle.Errorbars are95%confidenceintervals.(e)Resultsforuniqueblueshownasafunctionofhueangle.Errorbarsare95%confidenceintervals. A390J.Opt.Soc.Am.A/Vol.31,No.4/April2014J.M.BostenandA.E.Boehm