Cumming BG, Parker AJ

17 Pages·1999·0.3 MB·English

TheJournalofNeuroscience,July1,1999,19(13):5602–5618
Binocular Neurons in V1 of Awake Monkeys Are Selective for
Absolute, Not Relative, Disparity
B.G. Cumming and A.J. Parker
UniversityLaboratoryofPhysiology,Oxford,OX13PT,UnitedKingdom
Most neurophysiological accounts of disparity selectivity in neural responses to unchanged external stimuli, which were
neurons of the primary visual cortex (V1) imply that they are wellpredictedbythemeasuredchangeinabsolutedisparity:in
selectiveforabsoluteretinaldisparities.Bycontrast,anumber 45/53cases,theneuronmaintainedaconsistentfiringpattern
ofpsychophysicalobservationsindicatethatrelativedisparities with respect to absolute disparity so that the manipulation
playamoreimportantroleindepthperception.Duringrecord- creatednosignificantchangeintheabsolutedisparitypreferred
ings from disparity selective neurons in area V1 of awake by the neuron. No neuron in V1 maintained a consistent rela-
behaving monkeys, we used a disparity feedback loop (Rash- tionship with relative disparity. We conclude that the relative
bass and Westheimer, 1961) to add controlled amounts of disparity signals used in primate depth perception are con-
absolute disparity to a display containing both absolute and structedoutsideareaV1.
relative disparities. This manipulation changed the absolute
disparity of all the visible features in the display but left un- Key words: primary visual cortex; binocular disparity; stere-
changedtherelativedisparitiessignalledbythesefeatures.The opsis; vergence eye movements; depth perception; receptive
addition of absolute disparities produced clear changes in the field
Sincethediscoveryofdisparityselectiveneuronsintheprimary gence). More strikingly, Erkelens and Collewijn (1985) and
visualcortex(V1)threedecadesago(Barlowetal.,1967;Nikara Regan et al. (1986) found that large changes in the absolute
etal.,1968),ithasbeenwidelyassumedthattheseneuronsmay disparityofawide-fielddisplayproducednosensationofmotion-
form the physiological substrate for stereopsis. To provide a in-depth. The use of relative rather than absolute disparities in
critical evaluation of this hypothesis, it is essential to perform the representation of depth has been compared with the use of
detailed comparisons between the psychophysical properties of contrast rather than luminance in the representation of spatial
stereopsisandthepropertiesofdisparityselectiveneurons. structure(RogersandGraham,1982;BrookesandStevens,1989;
A striking psychophysical feature of stereopsis is its de- HowardandRogers,1995).
pendence on relative, rather than absolute, disparity (Westhei- Theselinesofevidencehaveresultedinawidelyheldviewthat
mer, 1979). The difference between these terms is illustrated in human stereopsis depends primarily on relative disparities. On
Figure 1. Absolute disparity is simply an angular measure of the theotherhand,itiswidelybelievedthatdisparity-selectiveneu-
differenceinthetworetinallocationsoftheprojectionofasingle rons,atleastinprimaryvisualcortex,areselectiveforabsolute,
point (sometimes also called retinal disparity). The relative dis- ratherthanrelative,disparities(JoshuaandBishop,1970;Bishop
paritybetweentwopointsisalsoanangularmeasure,givenbythe and Henry, 1971). Nearly all existing physiological data can be
difference between their respective absolute disparities. As Fig- explainedonthebasisofabsolutedisparities(Barlowetal.,1967;
ure1shows,changesinthevergenceangleoftheeyeswillcause Nikaraetal.,1968;JoshuaandBishop,1970;BishopandHenry,
changesintheabsolutedisparityofapoint,whereastherelative 1971;PoggioandFisher,1977;PoggioandTalbot,1981;Ohzawa
disparitybetweentwopointsisunaffected. etal.,1990;Ohzawa,1998),anditissimpletoenvisageamech-
Thegeometricfactthatrelativedisparityisindependentofeye anism that generates selectivity for absolute disparities (by re-
positionmaybeonereasonwhyitisexploitedbythevisualsystem ceiving equivalent input from different locations on the two
to support so many psychophysical judgements. For example,
retinae).
Westheimer (1979) found that stereoacuity was approximately
Although almost all physiological data in V1 are compatible
five times poorer when two isolated targets were presented se-
with a representation of absolute disparity, only two studies
quentiallyasopposedtosimultaneously.Simultaneouspresenta-
(Motter and Poggio, 1984, 1990) have attempted to distinguish
tionallowstheuseofrelativedisparitysignals,whereassequential
between representations based on absolute or relative disparity.
presentation forces a reliance on absolute disparity (when per-
They examined this issue by analyzing the effect of errors in
formance may be limited by uncertainty about the state of ver-
convergence (fixation disparities) in awake monkeys. If neurons
areselectiveforabsolutedisparities,variationinvergenceshould
ReceivedDec.23,1998;revisedApril12,1999;acceptedApril14,1999. causevariationinneuronalfiringrates.MotterandPoggio(1984)
ThisworkwassupportedbytheWellcomeTrust.B.C.isaRoyalSocietyUniver-
foundthatvergenceerrorswerelargecomparedwiththewidthof
sityResearchFellow.WethankOwenThomas,AndrewGlennerster,HollyBridge,
JonDodd,SimonPrince,GregDeAngelis,andFredMilesforacriticalevaluation disparitytuningfunctions.Theysuggestedthatthenarrownessof
ofthispaper. observed disparity tuning results from a process that adjusts
Correspondence should be addressed to Dr. Bruce G. Cumming, University
LaboratoryofPhysiology,ParksRoad,Oxford,OX13PT,UK. dynamically for changes in vergence. Motter and Poggio (1990)
Copyright©1999SocietyforNeuroscience 0270-6474/99/195602-17$05.00/0 showedresponsesfromanexamplecellforwhichtheinfluenceof
CummingandParker•AbsoluteDisparityinV1 J.Neurosci.,July1,1999,19(13):5602–5618 5603
rate convergence when the mirrors of the haploscope were rotated,
changingthevergencestimulus.Initiallyanimalsdidnotfollowchanges
inthevergencestimulusaccurately;whenconvergence(towithin0.25°)
wasrequiredtoearnrewards,theanimalsachievedasatisfactorydegree
ofaccuracy.Afterthistraining,wefoundthattheanimalscontinuedto
convergeaccurately,evenwhenthiswasnotrequiredtoearnrewards.
Stimulus presentation. Stimuli were generated on a Silicon Graphics
IndigoComputeranddisplayedontwomonochromemonitors(Tektro-
nix GMA 201). Gamma correction was applied to produce a linear
relationship between luminance and the gray level specified by the
computer.Themeanluminancewas188cd/m2,themaximumcontrast
was 99%, and the frame rate was 72 Hz. Each eye viewed a separate
monochromemonitorthroughasmallcircularmirror(18mmdiameter)
placed approximately 2 cm in front of the eye to form a stereoscope
(Wheatstone,1832).Attheviewingdistanceused(89cm),eachpixelon
the128031024displaysubtended0.98arcmin.The“red”videosignal
Figure 1. Diagram illustrating relative and absolute disparities of two wasusedtocontroloneofthemonochromemonitorsviewedbytheleft
points in different depth planes. If the vergence angle changes, the eye,andthe“blue”signalwasusedtocontroltheothermonitorviewed
absolute disparity associated with each point changes. On the left, the by the right eye. Because the display monitors were monochrome, this
moredistantdotisfixatedandhasanabsolutedisparityofzero.Thenear allowedthepresentationofdifferentblackandwhiteimagestoeacheye,
dotthenprojectstononcorrespondingretinallocationsandthushasan while the operator viewed simultaneously an anaglyphic version of the
absolutedisparity,arbitrarilyassigned1unithere.Ifthedepthoffixation stimulusonacolormonitor.
changes(right),theabsolutedisparityofbothdotschanges(to61⁄2here). Eachmirrorofthehaploscopewasmountedonagalvanometerservo-
Thedifferenceinabsolutedisparitybetweenthedotsisunchangedandis motor(GeneralScanningG325DP),sothatthevergenceanglerequired
termedtheirrelativedisparity. for bifoveation could be manipulated by rotating the mirrors about a
vertical axis. The viewing distance of 89 cm required convergence of
2.25°inmonkeyRband2.32°inmonkeyHg.Below,vergenceanglesare
fixation disparity on firing appears to be smaller than would be described relative to these values: negative angles indicate fixation be-
predicted on the basis of selectivity for absolute disparity. Both hind the plane of the monitors and positive angles indicate fixation in
front. Similarly, positive disparities are crossed (near), and negative
studies concluded that disparity-selective neurons in V1 do not
disparitiesareuncrossed(far).Themirrorstook6msectocompletea
simply encode the absolute disparity of the stimulus within the step change in position, much faster than the associated changes in
receptive field. However, this approach relies heavily on the convergence.
accuracyofbinoculareyepositionrecordings(seeDiscussion). Stimuliconsistedofbars,sinewavegratings,orrandomdotpatterns,
all presented against a mid-gray background. Bar stimuli were used to
To summarize, a wealth of psychophysical data indicate that
mapoutreceptivefields.Orientationtuningcurveswerefirstconstructed
relative, rather than absolute, disparities are important for the
with moving bars, then the extent of the minimum response field was
perception of stereoscopic depth. The great majority of physio- delineated with flashing bars at the preferred orientation. Quantitative
logical data in V1 are compatible either with selectivity for data on disparity selectivity were then collected with random dot pat-
absolute disparity or with selectivity for relative disparity. Only terns.Thesewereallconstructedwithequalnumbersofwhitedotsand
black dots against a gray background. The dot size was usually 0.08°,
twostudieshaveattemptedtodistinguishthesepossibilities.Both
andthedensitywas25%.(Forafewcells,theseparameterswerealtered
suggest that disparity-selective neurons in primate V1 neurons
to increase response rates). An example of a stereogram is shown in
mayencoderelativedisparity.Acceptingthisconclusionwouldbe Figure2.
amajordeparturefromthewelldevelopedexperimentalcharac- The random dot stereograms (RDSs) always consisted of a central
terizationandmodelsofdisparity-selectiveneuronsrecordedin circularregion,whosedisparityvariedfromtrialtotrial,andasurround-
ingannulus(usually0.5°wide),whosedisparitywasalwayszero(hence
the anesthetized visual cortex (Ohzawa et al., 1990; Ohzawa,
changesinbinoculardisparitywerenotassociatedwithanymonocularly
1998). We therefore decided to use a disparity feedback loop detectable changes in the stimulus). The disparities of the center and
(Rashbass and Westheimer, 1961) (see Materials and Methods) annulusalwaysremainedthesamethroughoutatrial,althoughanewset
to apply controlled changes to the absolute disparities of visual ofrandomdotswasusedoneachvideoframe(i.e.,theseweredynamic
RDSs). The horizontal dimension of the central region was chosen so
stimuliwhilerecordingtheactivityfromneuronsinV1ofawake
thatatthelargestdisparitytestedthesizeofthecentralregioncovered
primates. This draws a clear distinction between selectivity for
theminimumresponsefieldinbotheyes:thesizeofthecentralregion
absolutedisparityorrelativedisparity. wasthusatleastaslargeasthemonocularminimumresponsefieldplus
the value of the largest disparity to be tested. This precaution was
MATERIALS AND METHODS
necessarytoavoidthepossibilitythattheneuron’sreceptivefieldmight
Training.Datawereobtainedfromtwoadultmonkeys(Macacamulatta), be incorrectly stimulated with a mixture of the central region and the
onefemale(Rb)andonemale(Hg).Alloftheprocedurescarriedouton surroundannulusatthelargestdisparitiesundertest.
theanimalscompliedwiththeU.K.HomeOfficeregulationsonanimal Duringthemeasurementofadisparitytuningfunctionforaneuron,
experimentation. thedisparitywasvariedfromtrialtotrialinapseudorandomorder,but
Animals were trained initially according to the method of Wurtz theorderwasconstrainedsuchthateachdisparityinthesetwasshown
(1969):pressingaleverilluminatedasmallspot;afteravariableinterval oncebeforeanydisparityvaluewasrepeated.
thespotdimmed,andthemonkeyswererewardedwithadropofwater A small number of neurons (four) did not respond vigorously to
iftheleverwasreleasedpromptly.Afterthisinitialtraining,eachmonkey random dot stereograms at any disparity, so they were tested with
was implanted (under general anesthesia) with scleral magnetic search circular patches of sinusoidal grating stimuli. Spatial and temporal fre-
coils (Judge et al., 1980) in both eyes and a head restraining device quencytuningcurveswereconstructed,andtheorientationtuningwas
[modifiedafterMountcastleetal.(1975)].Afterarecoveryperiodofat checkedwithastimulusoftheoptimalspatialandtemporalfrequency.
least 7 d, animals were further trained to maintain fixation during When disparities were applied, the monocular location of the circular
haploscopic presentation of visual stimuli. The positions of both eyes windowmovedwiththegrating.Thisensuredthattherewasnomatching
weremonitored,andanimalsearnedfluidrewardsforkeepingthemean ambiguityinthestimulus,althoughithadthedisadvantagethatchanges
conjugateeyepositionwithin0.4°ofthecenterofthefixationtarget(a in disparity were associated with detectable changes in the monocular
brightdot,0.2°indiameter),forperiodsof2sec.Atthisstage,theuseof stimulus. When absolute and relative disparities were compared, the
theleverwasdiscontinued,andtheonlyrewardcriterionwasthemain- stimulus was surrounded by another sinewave grating that remained at
tenanceoffixation.Finally,theanimalsweretrainedtomaintainaccu- zerodisparitythroughout,providingagoodsignalforrelativedisparity
5604 J.Neurosci.,July1,1999,19(13):5602–5618 CummingandParker•AbsoluteDisparityinV1
Figure2. Exampleofrandomdotstimulusshownforfreefusion.
inthevicinityofthereceptivefield.Theresultsforthesefourneurons of conjugate movements; no assumptions about the vergence perfor-
closelyresembledthosefortherestofthepopulation. manceoftheanimalsweremade.
It would have been possible to manipulate the relative disparity be- Thehorizontalandverticalpositionsofbotheyes,andthepositionsof
tween the foreground and background of the RDS simply by changing thehaploscopemirrors,weredigitizedandsampledat587Hz,allowing
thedisparityofthebackgroundregion.However,insuchanexperiment, vergence angle to be computed on-line. The measured vergence angle
theabsenceofaneffectofrelativedisparitywouldbehardtointerpret. was then used to control the position of the haploscope mirrors in a
Itisalwayspossiblethattheneuronsaresensitivetothedisparityrelative feedbackloop.Thesequenceofevents,illustratedbytheeyemovement
tosomevisiblefeature(suchasthefixationmarker)otherthantheone recordsinFigure4,wasasfollows:(1)Forthefirstsecondofatrial,the
thatwasmanipulated. animalmaintainedsteadyfixationatafixedvergenceangle.(2)Att51.0
Itisbettertoaltertheabsolutedisparityoftheentirebinocularfield secthemirrorsweresteppedtoanewpositionintroducinganabsolute
while leaving all relative disparities unchanged, including those gener- disparityofeither0.15or0.2°.Fromthismoment,thevergencestimulus
atedbythefixationmarker.Thisisexactlywhathappenswhenasubject wassettobethesumofthemeasuredvergenceresponseandthedesired
converges at a different distance from the fixation marker (Fig. 3). absolute disparity. This led to a smooth vergence movement of nearly
Unfortunately,thereisnosimplewayofexploitinganynaturallyoccur- constant velocity, as the animal attempted to regain binocular fixation.
ring convergence errors as an experimental manipulation of absolute (Inpractice,delaysinthefeedbackloopmeantthattheabsolutedisparity
disparity because (1) if the change in absolute disparity is significant, producedwassmallerthanthenominalvalue,butbecausethepositions
subjectsusuallyrespondwithavergencemovement,and(2)ifthechange ofbotheyesandbothmirrorswererecorded,itwaspossibletocalculate
inabsolutedisparityissmall,itishardtomeasureaccurately. therealvalueoftheabsolutedisparityimposed.)(3)Attheendofthe2
An alternative is to manipulate the absolute disparity of a fixation sectrial,thefeedbackloopwasstopped,andthemirrorpositionwasset
markerusingafeedbackloop(RashbassandWestheimer,1961).Here,a to a fixed value. This value was set approximately to the mean of the
smalldisparityisaddedtothefixationmarker(byrotatingthemirrorsof vergenceanglesreachedattheendofsuchrampsduringtraining.The
ahaploscope).Assubjectsattempttoconvergeonthedisplacedtarget, nexttrialbeganwith1secofsteadyfixationatthisnewvergenceangle.
the measured vergence changes are counteracted by additional mirror (4)Finally,duringthenextsecondofthistrial,thevalueoftheabsolute
rotations,clampingthefixationmarkeratafixedabsolutedisparity.This disparityclampwasofthesamemagnitude,butofoppositesign,asthe
producesacontinuousrampinvergenceinbothhumans(Rashbassand precedingtrial.Thusthevergencemovementwasintheoppositedirec-
Westheimer,1961)andmonkeys(CummingandJudge,1986).Theuseof tion and returned the vergence angle to its value at the start of the
a feedback loop allows much greater confidence to be placed in the previous trial. (5) The entire sequence was then repeated, so that the
measureddisparityofthefixationmarker.Ifameasuredfixationdispar- valueoftheabsolutedisparityclampalternatedbetweentrials.However,
ity is purely instrumental, no vergence movement will result. Further- the relative disparity of the stimulus was in general different on these
more,becausetherateofthevergencemovementisproportionaltothe sequentialtrials,becausethestimulusorderwaspseudorandom.
size of the clamped disparity (Rashbass and Westheimer, 1961; Cum- ThevergencemovementshowninFigure4indicatesthatadisparity
mingandJudge,1986),thevergencemovementitselfprovidesanaddi- hasbeensuccessfullyappliedtothefixationmarker.Earlierwork(Rash-
tionalcheckontheabsolutedisparityofthefixationmarker. bassandWestheimer,1961;CummingandJudge,1986)hasshownthat
Eyemovementrecordingandmanipulation.Thehorizontalandvertical thespeedofsuchvergencemovementsisproportionaltothesizeofthe
positions of both eyes were monitored by means of a magnetic scleral clampeddisparity.Thefactthatthespeedofthevergencemovementis
searchcoilsystem(C-N-CEngineering)withthedetectortimeconstant nearlyconstantintheserecordsindicatesthatthedisparityofthefixation
set to 0.5 msec. The high-frequency noise level was no more than 61 markerhasremainedconstantduringthefeedbackloop.Thisprovidesa
analog-to-digital bit, (0.6 arcmin). However, there also appeared to be usefulsafeguardagainstcalibrationerrors:ifthespeedofthevergence
some slow drift in the signals over longer periods. The system was movementisnotconstantorismuchdifferentfromtheaverageresponse
calibrated by presenting targets at 2° either side of straight ahead and toaparticularabsolutedisparity,itsuggeststhattheremaybeanerror
adjustingthegaincontrolsuntiladeflectionof62°wasrecordedforeach intherecordedvergencesignal.Togiveaspecificexample,ifforsome
eye. The signal from one eye in one monkey (Hg) showed a clear reason the recorded vergence is 0.15° greater than the true vergence
asymmetrywithrespecttostraightahead,sothesignalforthiseyewas position,thenanattempttoclampthedisparityat10.15°willresultina
calibratedovertheactualrangeofeyemovementsused.(Thisasymmetry trueabsolutedisparityof10.3°andavergencemovementofdoublethe
was most likely caused by the coil in this eye being aligned out of the normalvelocity,whereasanattempttoclampthevergenceat20.15°will
fronto-parallelplanewhentheeyewasinitsprimaryposition,afeature resultinnovergencemovementatall.
thatwasevidentonvisualinspectionoftheeye.)Notethatthecalibration Inpractice,theaveragevergencespeedsacrosstheentiredatasetfor
forthegainoftheeyepositionsignalswasperformedpurelyonthebasis the two animals studied here were comparable with values reported
CummingandParker•AbsoluteDisparityinV1 J.Neurosci.,July1,1999,19(13):5602–5618 5605
this saturation. First, the vergence stimulus is changing without any
change to the accommodative stimulus, so that as the vergence move-
mentproceedstheneurallinkbetweenvergenceandaccommodationis
likelytodefocusthestimulus.Second,therecordedvergencesignalmay
go outside the region in which it is well calibrated. Third, when the
vergenceanglereachedavaluethattheanimalusuallyassociateswiththe
end of the trial, there may be a change in the animal’s attention to
binocularfixation.
Whateverthereason,thechangeintherateofthevergenceresponse
indicates that it would be unsafe to rely on the accuracy of the clamp
during this period. Consequently, when constructing tuning curves,
spikes were only counted from a time 50 msec after the clamp was
introducedtoatime750msecaftertheclampwasintroduced,sothatthe
last250msecofeachclampperiodwasexcluded.Separatetuningcurves
wereconstructedforpositiveandnegativeclamps.
Twoadditionaldisparitytuningcurveswereconstructedfortheperi-
odsofsteadyfixation(oneforeachstaticvergenceangle).Spikeswere
counted from a period 50 msec after the first frame of a stimulus
appeareduntil50msecaftertheclampwasapplied.Forthiscondition
therewasnodifficultyinusingspikesfromthelast250msec.Reanalysis
ofthedatausingonlythefirst750msecofthesteadyfixationperiodsdid
notaffectthepatternofresults.Thusfourdisparitytuningcurveswere
constructedforeachneuron.
Unit recording and analysis. Once animals were fully trained on bin-
ocularfixation,asecondoperationwasperformed(undergeneralanes-
thesia) to implant a recording chamber (Narishige) over the occipital
cortex.Afterarecoveryperiodofatleast1week,unitrecordingexper-
imentscommenced.Tungsten-in-glassrecordingelectrodes(Merrilland
Ainsworth, 1972) were advanced through the dura. The electrode was
thenusuallywithdrawnuntilitsoundedasifitwereleavinggraymatter
andallowedtorestforafewminutesbeforeadvancingoncemoreand
Figure3. Diagramillustratingtheeffectofanabsolutedisparityclamp searchingforunits.Thepatternofreceptivefieldlocationsrecordedat
ontwostimulusconfigurations.Eachpanelshowsaplanviewofthetwo differentlocationsfromthechamberconfirmedthatwewererecording
eyesofasubjectwhoisrequiredtofixatethecrosswhilearandomdot fromprimaryvisualcortex.Neuronswithreceptivefieldstooclosetothe
stereogram(RDS)ispresentedtotheleftofthefixationpoint.TheRDS verticalmeridianwerenotincludedbecauseitwasimpossibletobesure
isdepictedasthesetofthicklinesparalleltotheinterocularaxis.Note these were not in V2. Receptive fields were all in the lower right
thatthebackgroundoftheRDSisalwaysatthesamelocationindepthas quadrant,ateccentricitiesfrom1to4°.
thebinocularfixationmarker,whereasthecentralregionoftheRDSmay Signals from the electrode were amplified (Bak Electronics) and fil-
be altered in disparity. The ellipse shows the position of an idealized tered(200Hzto5kHz)beforebeingdigitized(32kHz)andstoredto
neuronalreceptivefield,shownatafixedabsolutedisparityof0°.Note disk. The timing of spikes was recorded to the nearest 0.1 msec. The
that therefore the receptive field is always depicted at the convergence storageofspiketraces,eye-positionsignals,andmirror-positionsignals
pointoftheeyes,notatafixedthree-dimensionallocationrelativetothe wasperformedbytheDatawaveDiscoverySystem,whichalsoprovided
head. Each panel shows a different combination of absolute disparity, a system for on-line classification of spikes. Subsequently, all the spike
either zero or crossed (near), and relative disparity, also either zero or traceswereinspectedoff-lineandreclassifiedusingsoftwaredeveloped
crossed.InAandC,theRDSshowsasingleplanarsurfaceatthesame inourlaboratory.
depthasthefixationmarker,butinCtheclamphasplacedthecentral Much of the quantitative analysis relied on fitting curves to the dis-
regionoftheRDSatacrossedabsolutedisparity.InBandD,thecentral paritytuningdata.Gaborfunctionswereusedforthisforthreereasons.
regionoftheRDSisdistinguishedbyadisparityrelativetothesurround First,manymodelsofdisparityselectivityproducetuningfunctionsthat
region,andrelativetothefixationmarker,butinDtheclamphasplaced areGabor;second,manyoftheparametersofthefittedGabor(suchas
thiscentralregionatanabsolutedisparityofzero.Soaneuronselective thephaseandspatialfrequency)haveanintuitivesignificance;andthird,
for zero absolute disparity would respond to configurations A and D, theyprovidedagoodfittothevastmajorityofthedata.Thefittingwas
whereasaneuronrespondingtozerodisparityrelativetotheothervisible performedbynonlinearregression(NumericalAlgorithmsGroup).One
featureswouldrespondtoconfigurationsAandC. disadvantage of Gabor functions is that there are frequently multiple
localminima,sotheresultingfitcanbesensitivetothechoiceofinitial
parameters. We therefore started the fitting procedure from a large
previouslyintheliterature(RashbassandWestheimer,1961;Cumming
numberofdifferentinitialconditionsandselectedthesolutionwiththe
and Judge, 1986). To minimize the effect of any calibration errors,
lowest residual variance. However, in some cases a solution had a low
individualtrialswereexcludedfromfurtheranalysisifthespeedofthe
residual, although it was clearly an inadequate description of the data.
vergence movement on that trial was 60% greater or smaller than the
Forexample,insomecasesthefittedspatialperiodwassmallerthanthe
mean speed for that clamp size and that animal. Note that this mean
spacing between the stimuli used, so the fitted curve had peaks and
speedwascalculatedovertheentiredataset,notjustforanysingleday,
troughsthatfellbetweentherealdatapoints.Toavoidthis,fitswitha
sotheexclusioncriteriondependsontheabsoluteerroroftheimposed
spatialperiodsmallerthantwicethespacingbetweendatasampleswere
clamp.Thecriterionof60%waschosenarbitrarily,mainlybecausemore
notpermitted.
restrictivecriteriacausedlargenumbersoftrialstobeexcludedforafew
cells.Inpractice,removingthiscriterionaltogetherhadnoeffectonthe
overallpatternofresults,butweapplieditnonethelessbecauseitallowed RESULTS
us to place more confidence in the values of the measured absolute
Asawhole,251neuronswerestudied(149fromMonkeyRb,102
disparities. Figure 5 shows three vergence eye movement traces in
frommonkeyHg).Ofthese,53neurons(28fromRb,25fromHg)
responsetoanabsolutedisparityclampof0.2°.Themiddletraceillus-
tratesaspeedclosetotheaverageforthisanimalandthisclampsize, yielded useful quantitative data on the effects of absolute and
whereas the two outer traces show trials that were excluded from the relative disparities. Most of these cells (51/53) were recorded at
analysisbytheabovecriterion. eccentricities between 1 and 4°, and the mean receptive field
ThevergencetracesinFigures4and5showatendencyforthespeed
width (estimated by hand plotting, with no corrections for eye
ofthevergencemovementtoslowdowntowardtheendofthetrial.This
effect tended to be larger on those trials in which the initial vergence movements)was0.46°(60.20°SD).Cellswereclassifiedassimple
movementwasfasterthanaverage.Thereareseveralpossiblereasonsfor or complex on the basis of the modulation in their firing to
5606 J.Neurosci.,July1,1999,19(13):5602–5618 CummingandParker•AbsoluteDisparityinV1
Figure4. Eyemovementrecordsduringaperiodofsteadybinocularfixationfollowedbyaperiodinwhichanadditionalabsolutedisparitywasimposed
byafeedbackloopbasedonmeasuredvergenceangle(twosequentialtrialstakenwhilerecordingthedatashowninFigs.6–9below).Thedashedline
showsthevergencestimuluscalculatedfromtherecordedpositionsofthetwohaploscopemirrorservos;thesolidlinesshowthemeasuredvergence
response.Forthefirst1secofeachtrial,thevergencestimulusisconstant.Intheleftpanel,thisvergencestimulusisatarelativelydivergedposition.
After1sec,themirrorsofthehaploscoperotate,placingthefixationmarkerinfrontofthepointofconvergence(by0.2°inthiscase).Afterareaction
time,theanimalbeginstoconvergetoregainbinocularfixation,butthemeasuredvergencepositionisusedtorotatethemirrorsfurther,tomaintain
theadditionalabsolutedisparityofthefixationmarker.Thusthedisparityofthefixationmarkerisclampedtothepreselectedvalueforaperiodof1
sec.Throughoutthewholeofthe2sectrial,thesamestimulusispresentedontheCRTmonitors.Notethatthereisachangeinvergencewithno
systematicchangeintheconjugateeyeposition(dottedline,positivevaluesindicateleftwardmovement,scaleatright-handsideoffigure).Also,small
changesinconjugateeyepositionarenotassociatedwithchangesinvergence.Spikeswerecountedfrom50msecafterthebeginningofeachperiod,
anddisparitytuningcurveswereconstructedseparatelyforfourconditions:(1)FarFixation,(2)Crossedclamp,(3)NearFixation,(4)Uncrossedclamp.
drifting gratings (Skottun et al., 1991), after taking into account tuning functions constructed for each cell, and neurons were
eye movements. Of 37 neurons classified in this way, 9 were includedonlyiftheyshowedasignificanteffectofdisparity(p,
simpleand28werecomplex.(Theuseofrandomdotstimulimay 0.05) independently in all four cases. In practice, our informal
havebiasedthesampletowardcomplexcells.)Oftheninesimple criteriaappliedatthetimeofrecordingusuallyensuredthatthis
cells,fiverespondedtotherandomdotpatternsweusedhere,and was true: only three units were excluded from the study by this
four were tested with grating stimuli. All other neurons were finalcriterion.
testedwithrandomdotstereograms.All53neuronsshowedsome
degree of orientation selectivity, and the majority were well Effects of adding absolutedisparities
tuned.Quantitativedataonorientationtuningwerestoredfor44
Theeffectofanabsolutedisparityclamponvergenceeyemove-
units, and this group had a mean orientation bandwidth (half-
ments has been described in Materials and Methods. A clamp
widthathalf-height)of34°.Thedistributionofpreferredorien-
addsafixedabsolutedisparitytotheentiredisplay(includingthe
tationsshowedaslightbiastowardverticalorientations(34units
fixation marker and any visible part of the CRT monitors them-
had preferred orientations within 45° of vertical; 19 units had
selves), and leaves the entire pattern of relative disparities be-
preferred orientations within 45° of horizontal). No histology is
tween all visible elements unchanged. The effects on neural
availabletoconfirmthelayersfromwhichtheserecordingswere
activity are illustrated for one neuron in Figures 6–9. Figure 6
taken, but based on physiological identification of layer IVc, we
were able to classify 19 units as infragranular and 29 units as showstheresponsetoastimulusatthepreferreddisparity(0.2°,
supragranular. averageoffivetrials).Alloftherelativedisparitiesareunchanged
Unitsthatdidnotfireatarategreaterthan10spikes/sectoany during the 2 sec trial because the same stimulus is presented on
stimulus were excluded from the quantitative analysis. We also the display screens throughout. Nonetheless, there is a dramatic
tended to select strongly disparity-selective neurons for this changeinfiringratewhenthemovementofthemirrorsaddsan
study.Ifthemodulationattributabletodisparitywasweak,albeit additional absolute disparity to the retinal stimulus. Changes in
statisticallysignificant,theneuronwasusuallyexcluded.Finally,a absolute disparity change the mean firing rate (calculated over
one-way ANOVA was performed on each of the four disparity- the first 750 msec; see Materials and Methods) to a constant
CummingandParker•AbsoluteDisparityinV1 J.Neurosci.,July1,1999,19(13):5602–5618 5607
Figure 5. Vergence eye movements from three individual trials with a
nominaldisparityclampof0.2°.Thetopandbottomtracesshowexamples
oftrialsinwhichthevelocityofthevergencemovementcausedthetrial
tobeexcludedfromtheanalysis.Thecentraltraceshowsatrialinwhich
thevergencevelocitywasnearthemeanforthisanimalandthisclamp
size.Inthebottomtrial,theanimalappearstobeunderconvergedduring
thefixationperiod,andthisisfollowedbyarelativelyslowconvergence
ramp. This is to be expected if the measured underconvergence is an
instrumental artifact. If convergence is underestimated, the real clamp Figure 6. Effects of the feedback loop on activity of one disparity-
appliedwillbesmallerthanthatmeasured.Similarly,thetoptraceshows selectiveneuron.Thestimulusthroughoutwaspresentedatadisparityof
initialoverconvergenceandarelativelyfastramp. 0.2° relative to the fixation marker, the preferred disparity when tested
duringsteadyfixation.Whentheabsolutedisparityofthefixationmarker
ischanged(by0.172°createdbysettingatargetdisparityclampof0.2°;
external stimulus. This indicates that the neuron is not simply seeMaterialsandMethodsandFig.7),sothattheabsolutedisparityof
selectiveforrelativedisparities. the stimulus is 0.372°, the firing rate drops immediately, although the
relativedisparityisunchanged.Averageoffivetrials.
Figure7showshowadditionalabsolutedisparitieschangedthe
neuron’s responses to a range of relative disparities. The left
panel shows disparity tuning plotted as a function of relative
disparity(relativetothefixationmarker).Thus,identicalstimuli
on the CRT monitors are plotted in the same positions on the identicalforthetwoclampconditions.Thisoccurredbecausethe
abscissa. The right-hand graph plots the same responses as a measured value of the clamp differed slightly from the value
functionofabsolutedisparity.Foreachstimulus,themeanofthe designated in the feedback loop (see Materials and Methods).
measured disparity clamp was used to calculate the additional Thus, in Figure 7 the disparity tuning curve was measured at
absolute disparity imposed on the stimulus by the clamp proce- intervalsof0.2°.Thevalueoftheabsolutedisparityclampwasset
dure. These additional absolute disparities were added to the to60.2°,butthemeasuredclampsizewasactually60.17°.Thus
relative disparities already present on the CRT monitors to cal- thedatapointsfromthetwoclampconditionsinFigure7areat
culate the absolute disparity of the stimulus on the retina. The slightlydifferentpositionsalongtheabscissa.
right-hand panel of Figure 7 shows that this neuron gives a Hence, we require an alternative way of testing whether the
consistent pattern of behavior with respect to absolute disparity responses to absolute disparity are consistent. Ideally, the same
rather than relative disparity. The magnitude of the change in testshouldalsobeapplicabletotheresponsestorelativedispar-
firing rate to a fixed physical stimulus is well predicted by the ity.WeapproachedthisbyfittingGaborfunctionstothedisparity
measured absolute disparity of the clamp. Figure 8 shows the tuningdata,asillustratedinFigure9.Asinglecurvewasfittedto
responseoffourotherneurons,twofromeachmonkey,plottedas the combined data sets from the two clamp conditions. This
afunctionofabsolutedisparity.Allfourcasesshowaconsistent procedure was applied separately to tuning curves expressed in
relationshipwithabsolutedisparity. terms of relative disparity and absolute disparity. If the neuron
weretomaintainaconsistentresponsetorelativedisparity,then
the residual variance around a single curve fitted to the relative
Are the responses of the population better described by absolute disparities should be smaller than for a curve fitted to absolute
or relativedisparity? disparities. On the other hand, if the neuron were to behave
Thefactthatadditionalabsolutedisparitiesaltertheresponsesto consistently with respect to absolute disparity, then the reverse
relative disparity can be confirmed by a two-way ANOVA: for should be true. Figure 10 plots the residual variance around a
51/53 cells, the interaction between relative disparity and clamp single Gabor fitted to the mean firing rates for each cell. This
condition was significant (p , 0.05). One might expect that the Gaborwasfittedtothedataexpressedintermsofeitherrelative
same approach could be used to detect any interaction between disparity or absolute disparity. For all 53 cells, the fit to the
absolutedisparitytuningandclampcondition.Unfortunately,an absolutedisparitydatahadalowerresidualvariancethanthefit
ANOVA on the absolute disparity responses cannot be per- totherelativedisparitydata.
formed because the absolute disparities of the stimuli were not Thisanalysisindicatesthatforall53cellstheresponsesbeara
5608 J.Neurosci.,July1,1999,19(13):5602–5618 CummingandParker•AbsoluteDisparityinV1
Figure7. DisparitytuningcurvesforthecellillustratedinFigure6.Thedatawerecollectedduringtheimpositionoftwodifferent,additionalabsolute
disparities.Theleftpanelshowsthedataplottedintermsofrelativedisparity(thedisparityofthestimuluswithinthereceptivefieldrelativetothe
fixationmarker).Afrequencyhistogramisalsoshownforthemeasuredabsolutedisparityofthefixationmarkerduringeachclamp.Therightpanelshows
theneuraldatareplottedintermsofabsolutedisparity(thedisparityofthestimuluswithrespecttoretinallandmarkssuchasthefovea).Eachtuning
curvefromtheleftpanelhassimplybeenmovedhorizontallybythemeanmeasuredabsolutedisparityvaluefortherespectiveclampcondition.
closerrelationshiptotheabsolutedisparityofthestimuluswithin paritydifferencebetweenthetwoconditions.Ontheotherhand,
the receptive field than to the relative disparities between the for a neuron that is selective for relative disparity, the opposite
receptivefieldandtherestofthevisiblescene. patternshouldhold:theshiftshouldbesmallwhenthedataare
expressedintermsofrelativedisparityandequaltothechangein
How accurately can the tuning curves be described by absolutedisparitywhenthedataareexpressedintermsofabso-
absolutedisparity? lutedisparity.
The previous analysis does not by itself establish that the re- Thestatisticalsignificanceoftheseshiftscanbeassessedwith
sponsesofV1corticalneuronsareaccuratelydescribedinterms a sequential F test (Draper and Smith, 1966), in which the vari-
ofabsolutedisparity.Itcouldbethattheresponsesareinterme- ance accounted for by adding the shift term is divided by the
diatebetweenthetwoextremesbutlieclosertoabsolutethanto residual variance around the fit that includes the shift. This test
relative disparities. To evaluate this possibility, an additional wasappliedseparatelytoeachunit,andineverycasetherewasa
parameter was introduced to the fits. This allowed separate Ga- significant shift (p , 0.05) in the tuning to relative disparities
bor functions to be fitted to the tuning data for the two clamp underthetwodifferentclampconditions.Thismeansthatadding
conditions.AlltheparametersofthetwoGaborfitswereidenti- an absolute disparity always significantly alters the responses of
cal,exceptforahorizontaldisplacement.Thisfittingprocedure V1 neurons to relative disparity stimuli. Conversely, when the
wasagainappliedtodataexpressedintermsofbothrelativeand fittingprocedurewasappliedtoabsolutedisparities,asignificant
absolutedisparity.ExamplesoftheseGabor1Shiftfitsareshown shift was present in only 8/53 cells. For the majority of cells
inFigure9. (85%),absolutedisparitybyitselfgaveacompletelysatisfactory
Foraneuronthatmaintainsaconsistentrelationshiptoabso- descriptionofthedisparitytuningfunctionsunderthetwoclamp
lute disparity, the value of this fitted shift should be small when conditions.
the data are expressed in terms of absolute disparity. When the Thesizesofthefittedshiftsinthetuningfunctionsarehighly
samedataareexpressedintermsofrelativedisparity,thevalueof informative. They are shown in Figure 11A, where a frequency
the shift should be equal to the magnitude of the absolute dis- histogramforthe53cellsisshown.Thisisaunimodaldistribu-
CummingandParker•AbsoluteDisparityinV1 J.Neurosci.,July1,1999,19(13):5602–5618 5609
Figure8. Disparitytuningfunctionsforfourunits,plottedasafunctionofabsolutedisparity.Twounitsfromeachmonkeyareshown.Varioustuning
types[asidentifiedbyPoggioandFisher(1977);Poggio(1995)]arerepresented:TE/T0cells(toprow,showingamaximalresponsetodisparitiesnear
zero),aNearcell(bottomleft,showingastrongerresponsetoneardisparitiesthantofardisparities),andaTIcell(bottomright,suppressedbynear-zero
disparities).Thesolidbarineachgraphindicatesthesizeoftheabsolutedisparityshiftproducedbytheclamp.Shiftingthesolidsymbolsbythisdistance
totheleftwouldaligntheresponsesintermsofrelativedisparity.Inallcases,thereisaconsistentrelationshiptoabsolute,notrelative,disparity.
tionwithamean(20.011°)notsignificantlydifferentfromzero(t showninFigure11C.Again,thisisaunimodaldistributionwith
test,p.0.05).Theclampprocedureinducedadifferenceinthe amean(20.03260.184SD)notsignificantlydifferentfromzero
added absolute disparities of between 0.2 and 0.4° for the two (ttest,p.0.05).Notethatvaluesofexactlyzeroindicatethatthe
clampconditions,dependingontheexperimentalconditionsthat fitted shift in tuning exactly matched the measured size of the
appliedforeachneuronalrecording.Itisevidentthatthereisno absolutedisparityclamp.
tendencyfortheshiftstoclusterinthisregionalongtheabscissa. It appears that disparity-selective neurons in V1 represent a
To account for the differences in the clamp size between homogeneous group that are selective for absolute, not relative,
experiments,wecalculatedascaledshiftforeachcell.Thisisthe disparity. There are neurons that show a statistically significant
shiftfittedtotheabsolutedisparitydatadividedbythedifference shift,butasFigure11Cshows,theyarefoundatbothtailsofthe
in the additional absolute disparity created by the two clamp unimodal distribution. If these neurons with significant shifts
conditions. For an ideal neuron selective only for absolute dis- represented a subpopulation with a degree of selectivity for
parity,thisscaledshiftshouldbe0.0(noshiftintuningexpressed relativedisparity,thentheyshouldfallontheright-handsideof
in absolute disparity). For an ideal neuron selective only for thedistribution(nearertoascaledshiftof1.0,whichcorresponds
relativedisparity,thescaledshiftshouldbe1.0;thatis,thetuning to selectivity for relative disparity). In fact, there are more neg-
curves should be separated by an amount equal to the added ative shifts (six) than positive shifts (two), arguing against any
absolute disparity. The frequency histogram for the 53 cells is representationofrelativedisparityinV1.
5610 J.Neurosci.,July1,1999,19(13):5602–5618 CummingandParker•AbsoluteDisparityinV1
Figure9. GaborfunctionsfittedtothetuningdatashowninFigure7.Tobegin,twoGaborfunctionsarefitted,onetoeachclampcondition;thatis,
oneGaborfortheadditionalabsolutedisparitywithapositivevalueandanotherGaborfortheonewithanegativevalue.Theparametersofthetwo
Gaborfunctionsareidentical,exceptforahorizontaltranslation.Themagnitudeofthehorizontaltranslationthengivesameasureofhowconsistently
theneuronrelatestoagivenexperimentalvariable.Clearly,therelationshiptorelativedisparity(left)isnotconsistent,becausethereisasubstantial
horizontal shift in the curve when the absolute disparity is changed. Furthermore, the size of the horizontal shift measured from the fitted curves
(20.363°)isverysimilartothemeasureddifferenceinadditionalabsolutedisparitybetweenthetwoconditions(20.339°).Consequently,whenthedata
areexpressedintermsofabsolutedisparityandthesamecomparisonsaremade,thefittedshiftisverysmall(0.024°).Thesignificanceoftheseshifts
canbeassessedbycomparingthegoodnessoffitofthelinkedpairofGaborfunctionswithasingleGaborthatattemptstodescribethecombineddata
set.Addingthehorizontalshiftincreasesthenumberofparametersbyone.Ontheleft,thesingleGaborisclearlyapoorfit(dottedline);theaddition
ofthehorizontalshifttocreateapairoflinkedGaborfunctionsimprovesthefit(F 5408,p,0.00001).Ontheright,usingthepairoflinkedGabor
functionsdoesnotsignificantlyimprovethefit(F 53.0,p.0.05)comparedw(1i,t8h6)asingleGabor.(Infact,thefitwithasingleGaborissosimilar
(1,86)
tothetwoillustratedcurvesthatitisnotshownseparately.)Itcanbeconcludedthatthefiringratebearsaconsistentrelationshiptoabsolutedisparity
regardlessoftheaddeddisparityclamp.
How good is the model used to assess shifts in the disparity Gabor1Shift fit, and this figure was 96% for the fit with two
tuningfunctions? independent Gabors. (This also confirms that the Gabor func-
Sofar,theanalysishasassumedthatthedisparitytuningdatacan tionsprovidedgoodfitstothetuningfunctions.)Thesedeviations
be well described by the Gabor1Shift curves. This assumes that therefore do not raise any substantial difficulties for the main
theshapeofthetuningcurveremainsconstantwhentheabsolute conclusion that disparity-selective neurons in primate V1 are
disparityofthedisplayisaltered,allowingonlyforchangesinthe selective for absolute, not relative, disparities. Possible reasons
neurons’ preferred disparity. To assess the possibility that there why the responses of a minority of neurons appear not to be
wereotherchangesproducedbytheabsolutedisparityclamps,we simply described by absolute disparity will be considered in the
also fitted two completely independent Gabor functions to the nextsection.
tuningcurvesforthetwoconditionsandperformedasequential
F test to determine whether there was a significant reduction in Effects of changes in vergencealone
the variance around the fit. Two independent Gabor fits were a Thevergencemovementsproducedbyabsolutedisparityclamps
significant improvement on the linked Gabor1Shift fit in only serveasausefultoolformanipulatingabsolutedisparitiesinde-
10/53cases.Indeed,whentwoindependentGaborswithasingle pendently of relative disparities. However, the changes in ver-
Gabor (no shift) fitted to the absolute disparity tuning were genceanglealsoraiseapotentialcomplicatingfactor:changesin
compared,only14/53neuronsshowedasignificantimprovement vergence angle by themselves may have a significant effect on
in the fit. Thus the responses of 39/53 neurons (74%) are well disparity tuning. An interaction of this type has been reported
describedsolelybytheirresponsetotheabsolutedisparityofthe (Trotteretal.,1992,1997).Itwasimportanttodeterminewhether
stimuluswithinthereceptivefield. similar interactions were present in this study. For this reason,
Even for the cells that appear to deviate from a consistent data were collected at two different vergence angles, covering
relationshiptoabsolutedisparity,themagnitudeofthedeviation approximately the range of movement produced by the clamps
wasgenerallysmall.ThecellshowninFigure9is1ofthe10cells (seeMaterialsandMethods)andinterleavedwiththeclampdata.
thatshowsasignificantimprovementwhenafitisperformedby It should be pointed out at once that it will be impossible to
twoindependentGabors,yetitisclearthatthedataarequitewell make a direct comparison between our results and those of
describedbyasingleGabor.Toquantifythesizeoftheimprove- Trotter et al. (1992, 1997) because there are several critical
mentproducedbytwoindependentGaborfits,thefractionofthe differencesintheexperimentalconditions.Notably,Trotteretal.
variance that was explained by the two fits was calculated. On (1992, 1997) changed vergence by changing the physical viewing
average, 88% of the variance was accounted for by the distance over a wide range (from 80 to 20 cm, corresponding to
CummingandParker•AbsoluteDisparityinV1 J.Neurosci.,July1,1999,19(13):5602–5618 5611
Figure 10. Comparison of goodness of fit of a single Gabor function
fitted to relative disparity or absolute disparity tuning functions. The
fractionofthetotalvarianceaccountedforbyasingleGaborfittothe
meanfiringratesasafunctionofdisparitywascalculated.Notethatboth
fits have the same number of free parameters. Cells shown with open
symbolsarethoseforwhichtuningcurvesareshownelsewhere.Forall53
cells, fitting a Gabor to the absolute disparity data produces a better
descriptionthanafittotherelativedisparitydata:allcellsmaintaineda
moreconsistentrelationshiptoabsolutedisparitythantorelativedispar-
ity.Forpointsfarawayfromtheidentityline(solidline),thisdifference
waslarge.Pointsmightfallclosetotheidentitylineforseveralreasons.
(1)Iftheshiftinabsolutedisparityissmallcomparedwiththedisparity
bandwidthofthecell(seerb073,Fig.8,bottomright),thenbothfitswill
begood.(2)ForNear/Farcells,ifonlyoneortwodatapointsfallonthe
sharplychangingregionofthetuningfunction(theonlyregionaffectedby
theclamp),neitherfitneedbeverypoor(seerb077,Fig.8;hg197,Fig.16).
(3)Ifthereisashiftinpreferredrelativedisparity,butthisshiftisnot
equal to the absolute disparity measured from eye and mirror position
records, then the fit to both relative and absolute disparities will be Figure11. Frequencyhistogramsshowingthedistributionof(A)shifts
imperfect (rb073 in Fig. 8 is an example where the shift in the tuning inpreferredabsolutedisparity,(B)shiftsinmeasuredabsolutedisparity
curvesappearsslightlylessthanthemeasuredshift).(4)IfasingleGabor of the fixation marker (fixation disparity), and (C) the ratio of these
functionisapoordescriptionofthedisparitytuningcurve,bothfitswill measures, termed scaled shift. For each neuron, the tuning to absolute
bepoor,typicallybecauseeithertheneuronsareonlyweaklymodulated disparities was fitted with a pair of Gabors differing only in their hori-
bydisparityorthereisachangeintheshapeoftuningcurvebetweenthe zontalposition,andtheshiftbetweenthetwoGaborswascalculated(the
twoclampconditions(hg178,Fig.17). shift in absolute disparity preference). For the same set of trials, the
actualsizeoftheabsolutedisparityclampwascalculatedfromrecordsof
mirror and eye position, and the difference between the two clamp
conditionswascalculated(shiftinfixationdisparity).Theratioofthese
vergenceanglesof2–10°foramonkeywithaninterocularsepa- measures(scaledshift)givesameasureoftheextenttowhichdisparity
ration of 3.5 cm). This was larger than the range of 1.0–3.5° preferencewasinfluencedbytheclamp.Valuesofzerocorrespondtoa
studied here with the mirror haploscope. For this reason, any consistentrelationshipwithabsolutedisparity.Ifaneuronmaintaineda
consistentrelationshiptorelativedisparity,thenthetuningwhenplotted
interactions between disparity tuning and vergence may be
intermsofabsolutedisparityshouldshiftbyadisparityexactlyequalto
smaller in our results. Also, in the work presented here, the the change in absolute disparity, giving a scaled shift of 1.0. The eight
positionsofbotheyesweremonitored,andaccuratevergencewas units shown in white had significant alterations in their selectivity for
required behaviorally of the animal, whereas vergence was not absolutedisparityunderthetwoclampconditions.Notethatvaluesof0
donotarisesimplybecausethereisnomeasurablechangeindisparity
monitoredinthestudiesofTrotteretal.(1992,1997).
selectivity;rather,theyarisewhenthechangeinresponsetoastimulusof
Themainaimofthefollowinganalysisistoestablishtheextent
fixed relative disparity is exactly explained by the measured change in
towhichanyvergence-relatedchangesinthedisparitytuningof absolutedisparityproducedbytheclamp.
corticalneuronscanbeidentifiedwithinthepresentdataset.As
will become apparent, small but significant changes are identifi- the conclusions from the disparity-clamp data, which point to
able in some of our data, so the second aim is to examine the absolute disparity being the critical parameter for disparity-
underlyingcausesofthesechanges.Inparticularweexaminethe selectiveneuronsinV1.
importance of fixation disparity during static vergence and the
significance of careful measurement of the receptive field char- Disparity selectivity at different vergenceangles
acteristicsbeforeexaminationoftheneuronunderdifferentver- SomeofthemostextremechangesfoundbyTrotteretal.(1992,
gencestates.Forourdataset,theresultscanbereconciledwith 1997)atdifferentviewingdistancesinvolvewhatisessentiallythe