J. Phyeiol. (1977), 264, pp. 621-640 621With 12 text-figurewPrinted in Great Britain

ANOMALIES OF DISPARITY DETECTION IN THEHUMAN VISUAL SYSTEM

BY RONALD JONESFrom the Ohio State Univer8ity, College of Optometry,

Columbu8, Ohio 43210, U.S.A.

(Received 5 January 1976)

SUMMARY

1. Oculomotor and psychophysical depth responses were investigatedin thirty individuals by use of briefly exposed disparities in the rangefrom 0-6 to 4-6 degrees (1-8 centrads).

2. The results substantiate a previous finding which reported the com-mon occurrence of specific types of stereoanomalies within a sample fromthe normal population. However, arguments are presented to suggestthat these forms of stereoanomalies are limited to coarse stereopsis andspare mechanisms concerned with fine disparity, high resolution stereopsis.

3. A relatively high proportion of individuals were found to manifestdeficiencies of vergence eye movement under these stimulus conditions.These vergence-anomalies are characterized by a marked reduction, orabsence, of either convergent or divergent eye movements to brieflyexposed stimuli.

4. The vergence-anomaly is not detrimental under normal seeing con-ditions since it can be present in persons with adequate binocular visionand normal fine stereopsis.

5. The presence of vergence-anomaly was always associated with theoccurrence of stereoanomaly; however, the converse was not true.

6. The results are taken as evidence to show how disparity informationis organized prior to its influence upon the processes of coarse stereopsisand vergence initiation.

INTRODUCTION

Richards (1970, 1971) has investigated individual differences in stereop-sis for the range of disparity from jO to 40 (coarse stereopsis). His subjectswere required to report the depth of targets in a psychophysical procedurewhich permitted separate evaluation of sensitivity to each of crossed,zero, and uncrossed disparity. He found that individuals may havediscrete anomalies of stereopsis limited to one or more of these classes;for example, a person may be 'blind' to crossed disparity while still

21-2

maintaining normal ability to perceive uncrossed and zero disparity. Allcombinations of stereoanomaly were found and the frequency of occurrenceof loss of one or more classes was relatively high (30 %).

Since disparity is the stimulus to both fusional vergence and stereopsis,Richard's discovery of stereoanomaly raises the possibility that theremay exist congruous anomalies of vergence eye movement. The purposeof this study was twofold: to attempt to replicate the important resultsof Richards and, simultaneously, to investigate vergence eye movementsin order to disclose the nature and extent of the variations existing inhuman vergence-responses to disparity. It is hoped that a study of suchanomalies would provide insight about the processes of disparity detectionin a manner analogous to the role that colour deficiency has played in theunderstanding of colour vision mechanisms.

METHODSApparatus

Disparate stimuli consisting of luminous vertical lines, subtending 3 x 0-2 centrads(a centrad is i4 radian or O057 degree; symbol, V), viewed against a dark back-ground were presented independently to each eye by means of a mirror haploscope.In between stimulus exposures, small circular fixation targets (0 4V diam.) occupiedthe field of view. At 5 sec intervals the fixation point was removed and one of threerandomly selected stimulus conditions (crossed, uncrossed disparity or monocularstimulus) was exposed for 200 ms. Disparate stimuli were created by displacing theline target to the right of the fovea of the right eye and to the left ofthe fovea in theleft eye to obtain an uncrossed disparity and vice versa for crossed disparities. Fourdisplacements were employed (j, 1, 2 or 4 centrads) so that a total of eight disparitysizes resulted: 1, 2, 4, 8 centrads, crossed and uncrossed. This corresponds to arange of from 0-6 to 4.60. The monocular stimulus conditions were the same in allrespects as the disparate stimulus conditions except that both the vertical lines werepresented to the same eye. The monocular stimuli simulated the appearance ofphysiological diplopia but contained no depth information and thus served as a'catch' category in the psychophysical method employed (see below).

All targets were photographically produced. The random sequence was estab-lished by rotary stepping motors controlled by a timer. The details of this arrange-ment have been described elsewhere (Jones & Kerr, 1971, 1972).The horizontal eye movements of each eye were monitored photoelectrically by

a method which senses the motion of the irido-scleral boundary (Biometrics,Model SGVH-2). Any anterior pole movement is detected by this method, includingtranslation; but since the limbus is about twice as far from the centre of rotationas is the centre of the curvature of the cornea, the method is only about half assensitive to this artifact as are corneal reflexion methods. The output is reasonablylinear over ranges of + 150. The irradiating diodes are pulsed at a frequency of5 kHz and the amplifiers are locked to this frequency. This essentially eliminatesany effects of changes in ambient illumination on the eye monitor.The movement of each eye was not recorded directly; rather, for convenience of

interpreting the results and to allow greater sensitivity in measuring the vergenceresponses, the signals were manipulated so that the conjugate component wasrecorded on one channel and the vergence component on the other channel of a two-

622 R. JONES

HUMAN DISPARITY DETECTIONchannel rectilinear pen-recorder (Beckman Type RS Dynograph with Type 9806Acouplers). Signal processing was accomplished by use of operational amplifiers tosum the two eye signals and feed this to one channel and to subtract the two eyesignals and feed this to the other channel of the recorder. This yields the conjugateand vergence responses respectively. The difference or vergence signal was moni-tored by an oscilloscope to facilitate balancing of the gains of the two eye signalsas required for calibration. As used, the eye monitor-recording system had anapproximate rise time of 16 ms.

Subjects indicated the depth appearance of the disparate stimulus as 'in front','behind', or 'equal to' plane of fixation point by use of a three position 'joy stick'.This response was coded on to the strip-recorder adjacent to the oculomotorresponse.Each subject was positioned in the haploscope by means of a chin and forehead

rest. The eye movement monitor was attached to the subject's head by a modifiedspectacle trial frame secured by an elastic head-band. The targets were adjusted tolie at optical infinity for emmetropes or at the subject's punctum remotum if theywere ametropic. The vergence position of the haploscope 'arms' was adjusted so thatthe fixation points had a vergence demand equal to the subject's lateral phoria.Under these conditions if all stimuli are removed, the eyes should maintain thisvergence position known as the 'physiological position of rest'. The disparatestimuli required relative divergence (uncrossed disparity) or relative convergence(crossed disparity) with respect to this 'rest' position of the eyes.Once the initial positioning in the haploscope was achieved, additional fixation

points to the right and left of the single customary fixation point were inserted. Thesubject was instructed to fixate back and forth between these right and left fixationpoints and the gains of each eye monitor were adjusted to equality as determined byan absence of a vergence component on the oscilloscope monitor. A sample right andleft saccade was also recorded on the conjugate channel of the recorder to providea permanent record for calibration purposes. Such calibrations were repeated afterevery tenth stimulus during the experimental sessions.

Before obtaining data, the subject was practiced in the use of the 'joy stick'response indicator. He was told to move the stick in the direction that the flashedtargets appeared with respect to the fixation point. A 'behind' response was signalledby pushing the stick away, 'in front' by pulling the stick forward and if the targetappeared at the same distance the stick was pushed to one side. At least ten practicestimuli were presented in order for the subject to familiarize himself with the re-sponse key. The subjects were also instructed in the meaning ofphysiological diplopiaand cautioned not to use this doubling as a cue to depth. They were warned thatstimuli at the same distance as the fixation point could be made to look double(the monocular stimuli); their only criterion should be the appearance of depth.The subjects were not given information about their response accuracy.

SubjectsSubjects were students and faculty of the Ohio State University. It must be

stressed that all subjects had normal binocular vision as determined by thestandard clinical tests and each had stereoacuity better than 20 s of arc asmeasured on a Brewster stereoscope (Keystone Multistereo Slide Sequence). Thirtysubjects were used in this sample.

Scoring of p8ychophy8ical depth judgmentA two-category method of response, as has been employed in most ofthe studies of

stereopsis (Mitchell, 1968, 1969; Ogle, 1952; Westheimer & Tanzman, 1956), does

623

not permit detection of individuals with deficiencies limited to only one class ofdisparity: crossed or uncrossed. Clearly, if the subject saw only one of these stimulus

categories he could by inference report the presence of the other in a two-category

choice. The use of a monocular stimulus category as a catch stimulus overcomes this

difficulty and permits the determination of a criterion-free index of sensitivity, d'

(Egan & Clarke, 1966). The d' index is based upon the theory of statistical decisions

(Green & Swets, 1966). In this psychophysical method the proportion of correct

responses to the stimulus is not used to determine a threshold value as is the case

in the classical psychophysical procedures. Rather, the proportion of correct re-

sponses, which is referred to as the 'hit-rate', is compared to the proportion of the

same class of response to the catch-stimulus (the 'false-alarm' rate). If the hit-rate

exceeds the false-alarm rate, detection is evidenced. The d' index is obtained

through a non-linear transformation of these proportions and is essentially a stan-

dardized score having a value greater than zero in the case of detection. The Tables

and detailed procedures for its determination are provided elsewhere (Swets, 1964).

The chief advantages of this method are its high sensitivity and freedom from

adverse influence from the subject's judgment criterion.Ad' for sensitivity to crossed disparity(do) was determined from its hit-rate, which

is the proportion of 'in front' responses obtained to crossed disparity stimuli and its

false-alarm rate, which is the proportion of 'in front' responses to the catch stimuli.

Additionally, a second d' for crossed disparity was determined by pooling the 'in

front' responses to the monocular stimuli and the uncrossed stimuli and using this

proportion as a second estimate of the false-alarm rate. This second index of sensitivity

is designated d,. If only crossed disparities are detected,d' should equal d' since

both monocular and uncrossed stimuli would appear without depth. On the other

hand, if uncrossed disparities are detected, inclusion of an uncrossed disparity

group into the catch stimulus group should result in arelative decrease in the num-

ber of 'in front' responses so that d' would be greater thand. A similar analysis

was applied to the detection of uncrossed disparity: d' and d'. The rules used todetermine detection of either one or both classes of disparity are summarized as

follows:

(1) if d' >df > 0 andd'> db > 0 both crossed and uncrossed disparities aredetected;

(2) if d- >db anddf< df then only the crossed disparity condition is detected;(3) if df' > df and dZ< d, then only the uncrossed disparity condition is

detected.

RESULTS

Examples of disparity-induced responses to each of the eight experi-mental stimulus magnitudes are shown in Fig. 1. In general, the responsesare less in amplitude than that required by the stimulus and the dis-crepancy is greater for the larger stimuli. There are no marked dif-ferences between the amplitudes of convergence and divergence. Responsesobtained to the same disparity stimulus throughout the random sequencewere generally similar (Fig. 2). There is a tendency for the amplitude to'wax and wane' but no habituation of the response. Mitchell (1968)reported habituation of responses to repetitive stimuli as did Rashbass &Westheimer (1961). However, this was not observed in these experimentsin which the size and direction of the disparity was randomly varied. The

624 R.JONES

HUMAN DISPARITY DETECTIONpeak response-amplitude for each disparity size has been plotted in theupper graph of Fig. 3 (vergence-disparity profile). Each point on the graphis an average of from five or more individual vergence responses. Since the

1

2

4

8

I

2

4

8

Con. Div.

Fig. 1. Sample vergence response tracings for each of the disparity magni-tudes employed in these experiments. Units are centrads (-- radian=0.57°; symbol, v). Beneath each response is a calibration trace showingthe time coarse of the stimulus (width = 200 ms) and its relative amplitude(height corresponds to the indicated number of centrads).

stimulus duration was only 200 ms, these vergence responses are incom-plete. Complete eye movements would be described by a straight linethrough zero as indicated by the dashed diagonal line in the upper graph ofFig. 3. The vergence-disparity profile shown in Fig. 3 is characteristic of

625

the results obtained in the majority (80 %) of subjects and is consistentwith the expectations for normals.The psychophysical depth judgments made by the subject F.A.W. for

the session during which the eye movements were recorded are shown in

Fig. 2. Five divergence responses obtained to a 21 uncrossed disparity.These are consecutive responses taken out of a random presentationsequence and indicate the consistency of the response amplitudes (calibra-tion traces; as in Fig. 1).

Legend to Fig. 3

Fig. 3. Vergence-di-8parity profile (upper graph) obtained by determination ofthe average peak-vergence-amplitude for each disparity size and alsomonocular stimulation (M). The (dashed) diagonal line indicates theamplitude of vergence required for complete responses. The responses areincomplete except for the I' uncrossed disparity condition. The subjectgave divergent responses (+) to the monocular stimulus conditions(see text). The lower graph is a frequency polygon of the psychophysicalresponses that were obtained during the experimental session in which theseeye movements (upper graph) were recorded: 'in front', filled circles; 'onplane', open circles; 'behind', open squares. The number of responses ateach point on the graph, from which each proportion was calculated, is5 or greater for this and all subsequent graphs (generally a larger sample

[Continued on facing page,

B..JONES626

HUMAN DISPARITY DETECTIONDegrees

0

10co

I-E(_0U

10

0.

1.0C00

0.0

12 0-50

00L.0

0

8 4 2 M 2 4 8Con. Div.

627

0A00

0

4 2 M 2 4Crossed Uncrossed

Disparity (centrads)Fig. 3

was taken when discrimination was questionable). Values of d' werecalculated as follows: the number of 'behind' responses were totalled for alluncroswed stimuli (16) and divided by the total number of such stimuli (20)to find the hit-rate = 0-80 for uncrossed disparity detection. Two false-alarm rates were then determined for the 'behind' responses; the first bydividing the number of 'behind' responses to the monocular stimuli by itstotal, i.e. 5 by 10 = 0-5 (the total number of monocular stimuli was half thenumber for the other disparity classes). From these values of the hit-rateand the false-alarm rate d' = 0-84 was obtained from published tables(Swets, 1964). The second estimate of the false-alarm rate was determinedby finding the proportion of 'behind' responses to both the monocular andcrossed stimulus categories (5/30 = 0.17) which yields d' = 1-79. SincedZ' > d > 0 (at least) cro88ed disparities are discriminated. This subjectmade 100% correct 'in front' responses so that d' and d' are indeter-minately high. The analysis must be modified in this special case. Sinceno 'in front' responses were ever obtained to either the monocular or un-crossed stimuli, for purpose of analysis, the crossed category may bedeleted and the uncrossed disparity discrimination may be regarded as atwo-category test. It then follows that uncrossed disparities are detectedsince d' > 0.

628 R. JONESthe lower graph of Fig. 3. The proportion of responses for each category(in front, on plane, and behind) is plotted at each of the disparity valuesused in the presentation sequence. The responses to the monocular 'catch'stimuli are plotted at the zero-disparity position (M) on the graph.According to the d' analysis, F.A.W. detects both crossed and uncrosseddisparities, but even without such analysis, one is easily convinced of thisfrom examination on F.A.W.'s raw responses (Fig. 3). However, suchdeterminations by inspection are not always obvious in the case of thestereoanomalous (below) who may adopt complicated response strategiesas a result of their deficiency.

I--

'+

CVta-.. +1

E- 1.to 0

Eco _ I

>

UCV -2a,0

C

0

0

0.a-c

0

0.VI

Degrees4 3 2 1 0 1 2I I I I I I / I I

E.M. /

/

///

a i I

8 4 2 M 2 4Con. Div.

Crosse(

3 4

+1*0

+05

0

-05

-10

VI

a,

4 2 M 2 4d UncrossedDisparity (centrads)

Fig. 4. Vergenwe-diparity profile of convergence-anomalous subject E.M.(upper graph). There is a complete absence of convergence, yet the diver-gent responses are of normal amplitude. The d' analysis of the psycho-physical responses (lower graph, each point represents seven or more

responses) indicated that only the depth associated with uncrossed dis-parities is correctly appreciated (despite his 'in front' responses bias):d, = 0 45, d' = 1.01, d' = 1-31, d' = 1-22.

I

HUMAN DISPARITY DETECTION

Vergence-anomalyThe vergence responses of subject F.A.W. are typical of the majority

of the subjects in that the amplitudes of convergence and divergence areapproximately equal giving the vergence-di8parity profile a symmetric,S-shaped appearance. However, in a number of the subjects either theconvergence or the divergence response amplitudes were much reduced inamplitude. The vergence-disparity profile of subject E.M. (Fig. 4), for

1 Con. I Div.

I -

2 Con. *2 Div.

4 Con. 4 Div.

8 Con. 8 Div.

Fig. 5. Sample vergence responses of convergence-anomalous subject E.M.(units are centrads). No responses occur for crossed disparities whereasthe divergent responses to uncrossed disparities are apparently normal(calibration traces as in Fig. 1).

629

630 R. JONES

example, indicates that he was unable to converge under the conditionsof the experiment. Typical individual responses are shown in Fig. 5. Thedivergent responses of this subject were not distinguishable from those ofthe previous normal subject (F.A.W., Fig. 3) in terms of their latency andmagnitude. A total of five subjects exhibited this type of responsedeficiency. There was a tendency, in some of these subjects, for crosseddisparities to elicit small amplitude eye movements in the inappropriatedirection, i.e. divergence instead of convergence (subject A.K., Fig. 6).

Degrees

4. +1-

bo0. ~~~~~~~~~~~~~~~~~~~~~~~~~~~41

E0

8 42 2-1240

Con. Div.

Fig. 6. Vergence-di~parity profile of convergence-anomalous subject A.K.All responses are in the direction of divergence, however, the amplitudeof divergence is a function of disparity. The response to monocular stimuliwas also divergent for these 200 ms exposure durations. The subject has acrossed stereoanomaly: d' = 0-14, df' = 0-48, d' = 0-30, d' = 0-23.

In addition, the monocular stimulus condition also elicited a divergentresponse. The procedure used to obtain these responses was expected toresult in no eye movement response to the monocular stimuli, since thevergence position of the haploscope arms was equated to the subject's.lateral-phoria position (the arm position required to meet this criterionwas close to parallelism for all subjects and no clear association was foundbetween this angle and the presence or absence of vergence or stereo-anomaly). Nevertheless, since this adjustment required the cooperation ofthe subject, there was always the possibility that the subject habituallymisadjusted the haploscope arm position. To test this explanation, thefollowing control experiment was undertaken. The vergence position ofthe haploscope arms was purposely under-converaged by 2v with respectto the subject's setting of his own phoria position. Ocular responses werethen recorded for 200 ms presentations of the monocular stimuli. The

HUMAN DISPARITY DETECTION 631

response was still divergence (Fig. 7); convergence would be expected ifthe eyes were simply returning to their physiological position of rest.However, if the monocular stimuli were presented for longer periods (e.g.4*5 s) convergence responses were obtained, as would be predicted from

4 5 sec

Con. 6

Posn.

A

- 4 5 sec

Div.

Posn. v6

B

Fig. 7. A comparison of the vergence responses obtained for 200 msexposures of a monocular stimulus to those obtained to a 4-5 s exposure tothe same stimulus (a downward deflexion indicates divergence, the calibra-tion trace applies to both response durations); eyes converged 2' withrespect to the lateral phoria position (A); eyes diverged 2V with respectto the lateral phoria position (B); the response to short durationstimulation is opposite in direction to the response to the 4-5 s exposure(subject A.K.).

the phoria position. It is apparent from these results, that stimulus durationhas a non-linear effect on the vergence responses since there was no initialresponse in the wrong direction.Although displacement of the arm position by 2V did not influence the

R. JONESresults, since larger angles were not employed, broad conclusions cannotbe drawn about the possible influence of this variable.The vergence responses obtained from monocular stimulation of short

duration were not limited in occurrence to those individuals with extremeattenuation of convergence or divergence. The tendency was present even

Degrees1 0 1

+1 *0

+050

bo

4)-05 t

-1 0

Con. Div.

I

I %A .-, I I I-_ L

8 4 2 M 2 4 8Crossed Uncrossed

Disparity (centrads)

Fig. 8. Vergence-disparity profile of divergence-anomalous subject F.D.(upper graph). The amplitudes of the divergent responses are extremelyattentuated with respect to the convergent amplitudes. The d' analysis ofthe psychophysical responses (lower graph) indicated that this individualappreciates the depth associated with crossed disparities only (db = 0*034,d' = 1-07, d' = 1 15, d' = 1.05).

when the imbalance between the convergence and divergence amplitudewas slight (note the 'M' responses of F.A.W., Fig. 3). The direction ofthe vergence responses to monocular stimuli were always in the directionof the vergence of greater peak-amplitude.

632

.-I

'+Mlis +2a

J0I-

+1

0.cV

4)

MO -2

100-

0

0.0

Q

C

0

o

0.

ah

0

HUMAN DISPARITY DETECTION63Only one subject out of the thirty investigated had a marked attenuation

of divergence (Fig. 8). As in the cases of 'convergence-anomaly', the non-attenuated responses were apparently normal in terms of their responselatency and amplitude. In addition, small amplitude convergenceresponses were obtained to monocular stimulation.

Relative attenuation of convergence or divergence was the major dif-ference between the eye movements of individuals. The vergence responsecurves always approximately 'butted' the demand line (diagonal line inthe vergence-di8parity proftle-8). There were no systematic shifts of thecurves either laterally along the disparity axis or vertically along theamplitude axis. For each individual the ratio of the maximum amplitudeof convergence to the maximum amplitude of divergence was calculated.

5

4-UC 3-

<-0-8 -0-6 -0-4 -0.2 0 0.2 0-4 0-6 >0-8

log convergence/divergence

Fig. 9. Frequency histogram of the distribution of the log of the ratios -maximum amplitude of convergence to the maximum amplitude ofdivergence - for each of the thirty subjects investigated. The arrows onthe abscissa indicate the limits used to define the condition of vergence-anomaly. There are six individuals who fall outside these limits since theirconvergence and divergent amplitudes differ by more than 3 to 1.

A frequency histogram of these ratios (Fig. 9) reveals that the distributionis skewed. Most individuals tend to have slightly greater amplitudes ofdivergence than convergence. In six out of the thirty subjects, the attenua-tion of convergence or divergence was either complete or extreme. Theterm vergence-anomaly will be used to describe those individuals in whichthe 'opposing' vergences differ by more than 3 times.

StereoanomalyAnalysis of the psychophysical responses of the subjects revealed that

this was not a homogeneous group but included individuals who exhibited-qualitatively distinct forms of stereo-deficiencies. In confirmation of the

633

634 R. JONES

TABIE 1. Contingency table showing the number of individuals in each categorybased on the adequacy of their sensory and motor responses to disparity

Psychophysical responses,~~~~~~

Vergenceresponse

Convergence-anomalyDivergence-anomalyNormal vergence

Crossed Uncrossedstereo- stereo- Asym-anomaly anomaly metric

20

2

0

14

20

4

report ofRichards (1970, 1971) subjects having defects of stereopsis limitedto either crossed or uncrossed disparity targets were identified. Conver-gence-anomalous subjects E.M. (Fig. 4) and A.K. (Fig. 6) failed to correctlydiscriminate crossed disparities and divergence-anomalous subject F.D.(Fig. 8) had a stereoanomaly of uncrossed disparity. The sensory andmotor anomalies were not always present concurrently. Six cases ofstereoanomaly were found in the absence of an apparent vergence de-ficiency and of three subjects who failed to discriminate the depth of any

r 1-0-NuI 0

o _0

O-S0~~~~~~~

a,< 8 4 2 M 4 8Crossed Uncrossed

Disparity

R.K.

(centrads).°1 0 -

01*

CL LXL.

os~ ~~~~b

8 4 2 M 24 8Crossed Uncrossed

Disparity(centrads)

?_ B.G.1-0

o

c 8 4 2 M 2 4 8Crossed Uncrossed

Disparity

° 10 ~~(centrads)0 -

@ ~ ~' ' gS 'Ba 42 M 24 8

Crossed Uncrossed

Disparity

(centrads)

0

~0

C ~ ~ ~

Fig. 10. The psychophysical responses of four asymmetric-stereoanomaloussubjects having normal vergence responses. Subject N.I. and B.G. indi-cated that no stimuli appeared to lie 'behind' the plane of fixation andR.K. had only two 'behind' responses. Filled circles 'in front', open

squares 'behind', open circles 'on plane'.

Stereo-blind

102

Normal

0012

HUMAN DISPARITY DETECTION 635

disparity (stereoblindness) only one was vergence-anomalous. However,none of the vergence-anomalous individuals had normal stereopsis. Theseresults are summarized in Table 1.Another form of stereoanomaly was identified and was present in a

total of six of the group; two of these were convergence-anomalous. Thecharacteristics of this class of stereo defect were apparent from examina-tion of the psychophysical response curves (therefore the d' analysis was

Degrees 1 Degrees43 21 0 12 34 43 21 0 123 4

+2 L.S. / 1 .. +2 -D.L./ +1

+0.5~-+1 -/05W0 ------ 0 bo 0-

U -1-0.5 0 E -.CIV - / -

-2 / 2-1-8 4 2 M24 8 8 4 2 M24 8

Con. Div. > Con. Div.1*0 /P 1.0

0 0o 'o O-0.m.'C"

0 0~~~~~~~~~~~~.0a8 42 M 24 8 8 4 2 M24 8Crossed Uncrossed Crossed Uncrossed

Disparity Disparity(centrads) (centrads)

Fig. 11. Vergence-disparity profiles for two convergence-anomalous subjects(vergence-disparity profiles, uppcr graphs). The psychophysical responses(lower graphs) identify these individuals as asymmetric-stereoanomalous;the maximum for 'on plane' responses (open circles) is shifted toward theregion of uncrossed disparity and there is an accompanying shift of the'in front' (filled circles) and 'behind' (open squares) responses.

not used to diagnose these cases). All reported that some value of un-crossed disparity most often appeared to lie at a distance equal to theplane of fixation. Concomitantly, the monocular stimuli usually appearedin front of the plane of fixation. Two of the subjects did not give any'behind' responses; targets which should have been seen behind the planeof zero depth were seen either in front (B.G., Fig. 10) or were confused(N.J., Fig. 10). The results for the two convergence-anomalous subjectsare similar and are shown in Fig. 11. I have classified these subjects ashaving 'asymmetric' stereoanomaly since the major characteristic is afailure of the ability to correctly localize the plane of fixation.

It is apparent from the responses of the asymmetric stereoanomalousthat the depth induced by a continuously viewed object (the fixationpoint), having zero disparity, is not equivalent to the depth from atransient (200 ms) zero-disparity stimulus. Rather, a short exposurecrossed-disparity is equivalent to a continuously exposed zero dis-parity. The duration of the disparity, as well as the sign and magnitude,determines the appearance of depth.

DISCUSSION

Stimuli employed in these experiments were symmetric about thefixation point, thus these are a special case of disparity detection involvingthe mid line of the visual field. However, the results likely are not specific tothis case; Richards (1970) determined that stereoanomaly may be presentwhen disparate images project to the same hemisphere and preliminarymeasurements of vergence eye movements (Jones & Kerr, 1971) concurfor vergence-anomaly.

Disparity-induced eye movements permit normal, single, binocularvision and are referred to as fusional eye movements. It has been shown(Mitchell, 1969, 1970; Jones & Kerr, 1971, 1972) that transient vergenceresponses are elicited by large disparities from binocular images toodissimilar to permit sensory fusion (e.g. a vertical line presented to oneeye and a horizontal line to the other) but fusional vergence is sustainedonly if the binocular images are similar enough to allow sensory fusion(Ogle, 1950). There is a basis, therefore, for separating vergencemechanisms into two phases: (1) a transient process of vergence initiation,and (2) a sustained or tonic phase which is truly fusional in nature, i.e.allows fixation to 'lock-on' binocularly similar images. Transient responseswere isolated in these experiments by use of short-duration disparatestimuli. The results showed that vergence-anomalies were of relatively highincidence (20 %) in individuals whose sustained fusional vergence wasadequate (as attested by the fact that none was strabismic). Thus ver-gence-anomaly reflects a defect limited to a phasic response of disparitydetection and its presence is further evidence in support of the hypothesisthat two functionally distinct vergence processes are present in the visualsystem.Two forms of vergence-anomaly were demonstrated, either convergence

or divergence responses could be absent (or extremely attenuated) whilethe retained vergence appeared normal in all respects. This suggests thatconvergence and divergence are normally initiated independently andvergence-anomaly is the result of a functional deficit in one component.Given this 'reduction-hypothesis' about the origin of vergence-anomaly,the disparity sensitivity of the convergence and divergence initiation

B. JONES636

HUMAN DISPARITY DETECTION63processes of normals may be inferred from the responses obtained indivergence-anomaly and convergence-anomaly. The data of the diver-gence-anomalous, subject F.D. and convergence-anomalous subject E.Mare taken to represent the sensitivities of the fundamental receptivesystems of normals and are illustrated in Fig. 12A. A model of vergenceinitiation emerges: if the velocity of convergence and divergence depends.

F.D

E

-8 -4-2 0 2 4 8Disparity

A

U0

-8 -4- 2 4 8

BFig. 12. The sensitivities of the two hypothetical 'pools' of disparitydetectors derived from the vergence-di8parityj profileB of a convergence-anomalous and a divergence-anomalous subject (A) (the curves have beennormalized and adjusted to cross at zero). It is proposed that each 'pooi'contributes activity of opposite sign to an operator responsible for theinitiation of vergence. The net activity determines the velocity of theresponse (magnitude of convergence and divergence) and may be predictedby taking the difference between the amplitude of the pool sensitivities ateach point (B).

637

upon the activity that disparate stimuli elicit in their respective receptivesystems or disparity 'pools', the resultant vergence velocity will be pro-portional to the difference between these curves. The difference-curve isillustrated in Fig. 12B and predicts that the vergence velocity will beapproximately linearly related to disparity near zero and will becomeattenuated for large disparity values. This is in satisfactory agreementwith actual measurements of vergence velocity made under open-loopconditions by Rashbass & Westheimer (1961).The derived response function of Fig. 12B does not accurately represent

the vergence-disparity profiles of all subjects who have been classified ashaving normal vergence. Many subjects tended to give small divergentresponses to zero disparity and had slightly greater peak-amplitudes ofdivergence than convergence. A wide range of such response asymmetryoccurred (Fig. 9) and indicates that the relative sensitivities of the twopools in Fig. 12A is often not equal and the neutral-point may occur atother than zero disparity. The term vergence-anomaly denotes an arbi-trary extreme of asymmetry close to the limiting case, which is charac-terized by responses that distinguish disparity only by variations inamplitude, not direction.

Bishop & Henry (1971) have reviewed the evidence in support of ahypothesis that stereopsis is a dual process consisting of fine and coarseneural mechanisms of disparity detection. The present psychophysicalresults and those of Richards (1970, 1971) provide further evidence insupport of this notion since anomalies of coarse stereopsis were found inpersons with normal fine stereopsis (all subjects had normal stereoacuity).Moreover, the characteristics of stereoanomaly illustrate that the coarsemechanism is not a homogeneous class but is comprised of at least twosub-processes having sensitivities roughly corresponding to the region ofuncrossed and crossed disparities. The results also emphasize that a dis-tinction between the fine and coarse mechanisms may be made on thebasis of their temporal properties. The temporal differences between thespatially dichotomized classes is clear in asymmetric-stereoanomaly.These individuals perceived the depth of a briefly exposed non-zero dis-parity as identical to that of the fixation point, which had zero disparitybut was present for much longer durations. The literature agrees onnormals: Langlands (1926), Ogle & Weil (1958), showed that fine stereopsisis improved as the exposure duration is increased; maximum stereoacuityis achieved at about 3 s exposure. On the other hand, for large disparitiesobservers as early as Hering have noted that depth judgments are mostcritical for short viewing durations (Ogle, 1962). Coarse stereopsis thusappears to rely on transient processes while appreciation of fine disparitieshas a graded, sustained nature.

638 R. JONES

HUMAN DISPARITY DETECTIONThe functional similarities between stereopsis and fusional vergence is

circumstantial evidence that the model proposed for vergence initiationalso describes the behaviour of coarse stereopsis. This contention is sup-ported by the degree to which the model accounts for stereoanomaly.Crossed and uncrossed stereoanomaly can be reasonably attributed to thecomplete loss of one of the pools, whereas, asymmetric stereoanomaly isconsistent with the presence of sensitivity imbalance between the pools.The latter would move the neutral-point away from zero disparity tocause the observed shift in the plane of apparent zero-depth. Althoughthe model may apply to both the sensory and motor systems, the questionas to whether these systems actually share disparity pools cannot be easilyresolved by the data. The occurrence of all types of stereoanomaly un-accompanied by congruous forms of vergence-anomaly (but not theconverse) is notproofofthe segregation ofthe pools, but rather, may indicateonly that there is a difference in sensitivity at some subsequent stage inthe visual system. This conclusion is not unreasonable since the motorresponse is reflexive while the psychophysical response requires a consciousdiscrimination.One may only speculate about the possible clinical significance of these

motor and sensory anomalies. An intriguing possibility, for which there issome circumstantial evidence (Richards, 1970), is that these 'subclinical'entities may reflect genetic information that would be useful in predictingthe inheritance of strabismus or other binocular disorders.

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