Perception & Psychophysics

1992, 52 (6), 705-713

The interaction of perceived distance withthe perceived direction of visual motion

during movements of the eyes and the head

MICHAEL T. SWANSTONDundee Institute of Technology, Dundee, Scotland

NICHOLAS J. WADEDundee University, Dundee, Scotland

HIROSHI ONOYork University, Toronto, Canada

and

KOICHI SHIBUTAKagoshima Women’s College, Kagoshima, Japan

A horizontally moving target was followed by rotation of the eyes alone or by a lateral move-ment of the head. These movements resulted in the retinal displacement of a vertically movingtarget from its perceived path, the amplitude of which was determined by the phase and ampli-tude of the object motion and of the eye or head movements. In two experiments, we tested theprediction from our model of spatial motion (Swanston, Wade, & Day, 1987) that perceiveddis-tance interacts withcompensation for head movements, but notwith compensationlor eye move-ments with respect toa stationary head. In bothexperiments, when the vertically moving targetwas seen at a distance different from its physical distance, its perceived path was displaced rela-tive to that seen when there was no error in pereived distance, or when it was pursued by eyemovements alone. In a third experiment, simultaneous measurements of eye and head positionduring lateral headmovements showed that errors in fixation were not sufficient-to require -modifi-cation of the retinal paths determined by the geometry of the observation conditions in Experi-ments 1 and 2.

A moving target may be fixated and pursued by move-ments of the eyes in a stationary head, by movements ofthe head with the eyes stationary, or by some combina-tion of the two. If an observer judges the direction of mo-tion of a second target moving in a different direction tothe one that is pursued, the perceived direction of motionof the second target is nonveridical and is displaced towardthe direction of its motion on the retina (Becklen, Wal-lach, & Nitzberg, 1984; Festinger, Sedgwick, & Holtz-man, 1976; Swanston & Wade, 1988; Wallach, Becklen,& Nitzberg, 1985). Compensation for the effects of eyemovements on the path of retinal motion is better thanthat for headmovements, but in bothcases there is a par-tial failure of the processes that relate self-motion to reti-nal motion (Swanston & Wade, 1988).

The outcome of such undercompensation is a perceivedtilt in the path of a vertically moving target observed dur-ing a horizontal eye or head movement. A similar per-

ceptual outcome with lateral head movements canalso becaused by an error in the target’s perceived distance(Gogel, 1980). In this paradigm, fixation is normallymaintained on the single target during the head move-ments. As a result, its path of retinal motion is approxi-mately the same as its physical motion, eliminating theeffectsof undercompensation described above. If the tar-get appears farther than its physical distance, it will ap-pear to move in the opposite direction to the head. If itappears nearer than its physical distance, it will appearto move with the head. The extent and direction of suchperceived movements are predictable from the perceiveddistance of the target and the extent of head movement(see Gogel, 1990, for a review). In effect, an error in per-ceived distance acts as if the target were undergoing areal physical motion, and such perceived motions can beshown to add as vectors to real motions (Gogel, 1979,1982). Depending on the phase relationships of verticalobject motion and horizontal head motion, it is possibleeither to increase or decrease the apparent tilt of a verti-cally moving target by altering its apparent distance(Gogel, 1979). Thus, perceived distance may contributeto perceived target motion during concomitant headmovements.

This work was supported by NATO Grant RG 0067/89 and NSERCGrant A0296. Correspondenceshould be addressed to M. T. Swanston,Dundee Institute of Technology, Bell Street, Dundee DD1 1HG, Scot-land (e-mail:bstmts@vaxb.cc.dct.ac.uk).

705 Copyright 1992 Psychonomic Society, Inc.

706 SWANSTON, WADE, ONO, AND SHIBUTA

In previous studies of compensation for the effects onretinal motion of eye or head movements, the tracked andjudged targets have beenpresented, and perceived, in thesame depth plane. Since the perceived distance of bothtargets was approximately veridical (Swanston & Wade,1988), the perceived motion path during eye and headmovements would not have been differentially affected.In addition, studies of motion perceived during lateralhead movements have not involved differences betweenthe directions of retinal and physical motion of a secondtarget. Since both undercompensation and perceived dis-tance canbe shown independently todetermine perceivedtarget motion, it is of interest to establish the extent ofany interaction between the two.

A theoretical basis for predicting the form of this inter-action is provided by the model that we have proposed

(see Figure 1) for the recovery of information about po-sition and motion relative to the environment (the geo-centric representation) from the changing patterns ofstimulation available to the eyes of a moving observer(Swanston, Wade, & Day, 1987; Swanston, Wade, &Ono, 1990; Wade & Swanston, 1987). This model de-scribes the information necessary to obtain geocentric per-ceptions, when the eyes move relative to the head andwhen the head, together with the eyes, moves relative tothe environment. The initial representation of motion iswith respect to the coordinates of each retina (retinocen-tric). Combination of the left and right monocular repre-sentations leads to a single cyclopean motion signal. Ifthis is added to an appropriately signed signal for eyemovements, a representation of motion is obtained thatis relative to the head (egocentric) and is independent of

Frame of Reference:

INFORMATION FORSELF MOVEMENT

MONOCULAR RETINAL DISPLACEMENTS

SINGLE BINOCULAR DISPLACEMENT

>, ,

ANGULAR DISPLACEMENT

WITH RESPECT TO HEAD

INFORMATION FOREYE MOVEMENTS

Monocular Retinocentric

Cyclopean Retinocentnc

Egocentric

Geocentric

INFORMATION FOROBJECT DISTANCE

REPRESENTATION OF OBJECT MOTION

IN 3-D SPACE, IRRESPECTIVE OF

OBSERVER MOVEMENTS

Figure 1. Outline of the model of geocentric motion perception proposed by Swanston, Wade, and Ono (1990).See text for details.

VISUAL MOTION DURING EYE AND HEAD MOVEMENTS 707

movements of the eyes in the head. If the eyes move asthe result of head movements, then such egocentric mo-tion cannot be interpreted unambiguously unless the dis-tance of objects from the observer is available as well.Egocentric motion can be scaled by egocentric distanceto correspond to a particular extent in three-dimensionalspace. This scaled information is then in a form suitablefor compensation for the extent of headmovement, whichalso consists of a displacement in three-dimensional space.The model therefore predicts an interaction of perceiveddistance with compensation for lateral head movements,but notwith compensation for eye movements. By specify-ing the form and sequence of the combination of varioussources of spatial information, it allows prediction of theconsequencesof errors in the values of these. The modelessentially constitutes a description of an “ideal per-ceiver”; the extent to which the human visual systemac-tually achieves the necessary integration of informationrequired for veridical perception needs to be establishedby experiment.

EXPERIMENT 1

The purpose of Experiment 1 was to test the predic-tion that the perceived path of a vertically moving targetwould depend on its perceived distance during head pur-suit, but that this would not occur with eyepursuit. Thus,the judged target was seen as either equidistant with thepursued target or farther away. The phase relationshipsof the target movements were such that the apparent pathwith head pursuit was predicted to be more tilted whenthe targets appeared at different distances. In addition tothe four main experimental conditions (head and eye pur-suit, with targets equidistant or separated in depth), therewere three control conditions. These provided measuresof the perceived path without pursuit movements orchanges in perceived distance, the perceived path pro-duced during headmovements while fixating a single tar-get whose perceived distance was greater than its physi-cal distance, and the influence of any interaction betweenthe simultaneous motions of the two targets.

MethodObservers. Twelve paid observers took part in the experiment.

All had normal or corrected-to-normal vision.Apparatus. Stimuli were generated by an Amiga 2000 computer

and were displayed with a pixel resolution of 640 (width) x 250(height) on a 35-cm-diagonal video monitor (Philips 8833). Theviewing distance was 114 cm. Observations were made in an other-wise dark room. The targets were small rectangles, 2 pixels widex 1 pixel high, subtending approximately 0.04°on a side. In con-ditions in which there was a horizontally moving target, it movedback and forth along a path subtending 4.1°,with a velocity of2.73°/sec.A single motion from left to right, or vice versa, tookapproximately 1.5 sec, and there was a pause of approximately0.5 sec when the target reached either end of its range. In Condi-tions 1 and 2, this target remained stationary in the midpoint ofthe horizontal path and in the median plane. In Condition 3, an ad-ditional stationary target was present, 0.25°below the center of

the horizontal path. The judged target moved on a vertical path lo-cated to the left of the horizontal target at a velocity of 0.8°/sec.The vertical path subtended 1.2°,with its midpoint located 3°fromthe leftmost position of horizontal path. To produce changes in theperceived distance of the judged target, two strips of oppositelyoriented polaroid were applied to the surface of the screen. Thesingle vertically moving target was replaced by two targets, mov-ing in unison over the same path, but with an uncrossed disparityof 0.5°.When viewed through polaroid filters in front ofeach eye,this corresponded approximately to an increase in distance of20.7 cm, relative to the pursued target at the viewing distance of114 cm, and with an assumed interoculardistance of 6.5 cm. Thedisplay was viewed with the head placed on a rest, which wasmounted on a track, and could be moved easily from side to side.The lateral excursion of the head was set by stops separated by8.2 cm and aligned with the horizontal motion of the pursued tar-get. A linear transducer was attached to the rest, which providedposition signals during movements of thehead. These signals weredigitized and interpreted in real time by the software that gener-ated the display. The experimenter’s screen showed a cross thatmoved synchronously with the observer’s head, and it provided avisual indication of theaccuracy of pursuit. In addition, the signeddifference between the horizontal position of the pursued target andof the observer’s head was measured at 10 points approximately0.8 cm apart, whenever observations were being made. Aftera trial,the mean difference between head and target positions was com-puted for each point. For conditions in which the head was notmoved, the rest was locked in the center point of its travel. Thejudged target moved upwards synchronously with the rightward mo-tion of thepursued target. Thus, pursuit with either the eyes or thehead resulted in aretinal path tilted counterclockwise from the ver-tical. Given the relative extent of the vertical and horizontal mo-tions, and assuming accurate pursuit, the retinal path wasat an an-gle of 73.7°from the vertical.

Procedure. There were seven experimental conditions (see Fig-ure 2), each of which was seen four times by each observer, in arandom order. In all conditions, the observer’s task was to reportthe direction of motion of the left (judged) target, which alwaysmoved vertically along the same path. Initially, the different ob-servationconditions were explained, and practice wasgiven in theuseof the chinrest for lateral head movements. Two practice trialswere performed, one with eye and one with head pursuit, and arandom choice of the two distances of the judged target. A checkwas made that observers saw the judged target as more distant whena disparity was present between the two targets. The duration ofobservation in each trial wasdetermined by the observer, but wasnormally between 8 and 10 excursions ofthe judged target. On averbal signal from the observer, a light was switchedon in the ob-server’s booth. Theobserver then adjusted the position of a metalrod attached to apotentiometer mounted on the vertical surface ofthe front of the apparatus. The angularsetting was read by the ex-perimenter from a digital voltmeter. Once this was recorded, theobserver rotated the metal rod randomly away from the verticalin preparation for the next trial. For Condition 1, the headand eyeswere kept stationary, fixating the stationary target, which wasstraight ahead and to the right ofthe vertically moving target. ForCondition 2, the right target was again stationary, but the judgedtarget was presented with astereo disparity and seen as farther away.Lateral head movements were made in synchrony with the verticalmovements of the judged target, and fixation was maintained onthe right target. The purpose of this condition was to obtain an es-timate of the perceived tilt produced only by the change in per-ceived distance. For Condition 3, three targets were presenton thedisplay. Two ofthese corresponded to the left and right targets ofthe other conditions. These moved vertically and horizontally,respectively. The third target was located 0.5° below the center

708 SWANSTON, WADE, ONO, AND SHIBUTA

Figure 2. Schematic representation of the physical and retinal paths for each condition in Experiment 1. In Condi-tions 2, 5, and 7, the vertically moving left-hand target was presented with a stereo disparity such that itwas seenas more distant than the right-hand target.

of the horizontal path ofthe right target, and observers maintainedfixation on this point, keeping their heads stationary. This condi-tion was designed to check for any interaction between the appar-ent motions of the left and right targets, which might have influ-enced the perceived paths independently of perceived distance orcompensation for pursuit. For Conditions 4 and 5, the chinrest wasstationary in the central position, and observers pursued the hori-zontal motion of the right target with eye movements. For Condi-tions 6 and 7, the motion of the right target was followed by lat-eral head movements. At the start of a trial, the target and theheadrest were positioned at the left of their ranges. The observerthen made lateral movements synchronously with the target’s hor-izontal motion, so as to keep the pursued target straight ahead. InConditions 5 and 7, the left target was presented with a stereo dis-parity. Figure 2 shows diagramatically the physical and retinalcharacteristics of the stimuli in each condition.

ResultsThe results of the experiment are summarized in Table 1.

The values shown are the means and standard errors ofthe perceivedpaths of the judged target. The meansettingin Condition 1 was 1.00 clockwise, so any bias in thejudged vertical with stationary observation was slight. InCondition 3, there was a perceived counterclockwise tiltof 0.80, indicating that there was no effect of interactionbetween the motions of the two targets. This was muchless than the counterclockwise tilts observed inother con-ditions and also less than typical values for such interactionsreported in other studies (e.g., Gogel, 1974). Swanstonand Wade (1988) found no effect of this type in a similarcontrol experiment, and it is unlikely to have played a

significant part in these results. In Condition 2, there wasa perceived counterclockwise tilt of 8.4°, as a result ofthe increasedperceived distance ofthe judged target. Thistilt corresponded to a horizontal motion of 0.35 cm, rel-ative to the vertical motion of 2.4 cm. The perceiveddis-tance corresponding to such an apparent horizontal mo-tion canbe found from the expression (Swanston & Gogel,1986):

D’ = D(K—W’)/K, (1)

where D’ is the perceived distance, D is the physical dis-tance, K is the extent of lateral head motion, and W’ isthe signed perceived concomitant target motion (negative

Table 1Means and Standard Errors of Perceived Motion

Paths in Experiment 1

Condition Target Distance M SE123

EqualFarEqual

1.0—8.4—0.8

1.11.41.4

Eye Pursuit45

EqualFar

—28.9—27.4

4.94.9

Head Pursuit67

EqualFar

—31.7—38.6

4.15.0

Note—Values shown are degrees of tilt from thevertical (negative valueindicates counterclockwise tilt).

CONDITIONS

2 3

AS.

AI 5o

(far)

AIe

AS

AS

•A

.

PHYSICALPATH

RETINALPATH

PHYSICALPATH

RETINALPATH

4 5 6 7

A5- ~.

A5- ~.

(far)

A5- ~.

A5- 4,.

(far)

•—--5

~—--- • ~---.--~ • ~-~--.- S~_--.

VISUAL MOTION DURING EYE AND HEAD MOVEMENTS 709

when opposite to the direction of head movement). Thevalue obtained for Condition 2 was 119.0 cm (i.e., an in-crease in perceived distance of 5.0 cm, relative to thephysical distance of 114 cm). This was approximately25% of the distance appropriate to the stereo disparityemployed, and it indicates that under these conditions dis-parity was not a fully effective cue or that the perceivedtilt was not wholly determined by perceiveddistance. Theperceived distance of the judged target was neverthelessincreased, as shown by the change in its perceived mo-tion path during concomitant head movements. Thiscouldin part have been due to a difference in compensation forretinal displacements due to eye and head movements. Al-though in Condition 2 there was no significant tilt in theretinal path of the target, the head was moved laterallywhile the eyes turned so as to maintain fixation on thecentral stationary point. Thus, the perceived path of thetarget depended on compensation for both eye and headmovements, independently of its perceiveddistance. Wedid not find perceived tilts from this cause in our earlierwork (Swanston & Wade, 1988), but this may have beenbecause the effect was not large enough to be measuredunder the conditions of that study.

The four conditions involving pursuitdiffered in the pre-dicted manner. In general, as found in our earlier study(Swanston & Wade, 1988), the perceived path during eyemovements was closer to the physical path than was thecase with head movements, indicating a greater degreeof compensation for self-produced retinal motion in theformer case. When both targets were seen as equidistant,the path with eye movements was tilted by 28.9°(Condi-tion 4), and the path with head movements was tilted by31.7° (Condition 6), both counterclockwise. However,when the stereodisparity was present, and the judged tar-get appeared more distant, the path with eye movementsremained the same (Condition 5, 27.40), while that withhead movements was significantly more tilted [Condi-tion 7,38.6°,t(11) = 6.34,p < .01]. Although the mag-nitude of the difference varied, all subjects reported amore tilted path in Condition 7 than in Condition 6. Themain prediction from the model described above wastherefore confirmed. Although the difference in the tiltsduring head movement with and without disparity (Con-dition 6-Condition 7) was less than the tilt obtained inCondition 2 (6.90 and 9.4°,respectively), this differencewas not significant [t(1 1) = 1.0].

In addition, data were obtained regarding the accuracyof pursuit head movements during trials in which thesewere required. Each observer completed eight such trials(four with Condition 6 and four with Condition 7). Aftereach trial, data were available for the mean signed dif-ference between the positions of the observer’s head andthe pursued target at each of 10 locations across the hori-zontal path. Figure 3 shows the mean data for all sub-jects, as the error in degrees between head and target po-sition at each location, combined for both left-to-right andright-to-left movements. The maximum error, in the mid-dle part ofthe movement, was around 0.10, with the head

,~ I—. ~0:25 065 1.05 1.45 1.85 2.25

DISTANCE MOVED BY HEAD (deg)

FIgure 3. Mean error in head position relative to thepursued targetin Experiment 1, at 10 points in the movement of the head. Left-ward and rightward motions are combined. Vertical bars representthe standard error of each mean and are shown in one directiononly for diagrammatic clarity.

being in advance of the target. A lag error was found onlyat the ends of the movement, following or preceding astationary pause. No systematic effects on the retinal pathof the judged target would be produced by such headmovements, assuming that the eyes remained approxi-mately stationary in the head. Data presented below (Ex-periment 3) address the issue of what, if any, eye move-ments may take place during such head movements. Here,subjects accelerated from rest to be somewhat ahead ofthe pursued target at the midpoint and then began to slowdown. The pattern suggests that once the observer has be-come accustomed to the timing of the rhythmic headmovements, they are launched ballistically from the leftor right stop points rather than continuously controlledby the monitoring of visual feedback from positional er-rors. The pattern of errors was very similar for Condi-tions 6 and 7. There was perhaps a slight tendency forthe head to lead the target by less in Condition 6 (equidis-tant targets) than in Condition 7, but the difference wason average less than 0.02°,and could not haveproducedthe difference in the perceived tilts of the judged target.

EXPERIMENT 2

Experiment 1 demonstrated that the horizontal vectorsof perceived motion produced by inadequate compensa-tion for head movements and by an increase in perceiveddistance can combine additively to give a perceived mo-tion path more tilted than that obtained witheither ofthesefactors in isolation. The perceived distance of the targetwas larger than the physical distance, so its perceived hor-izontal motion was against the direction of head move-ments. Undercompensation for head movements also re-sults in a perceived motion against the direction of headmovement, and thus the combined effect of bothprocesseswas an increased perceived tilt. By contrast, if the per-ceived distance of the target is less than its physical dis-tance, the perceived horizontal motion should be in thesame direction as the head movement. With a similar un-dercompensation for head movements, the combined re-sult should be a less tilted motion path; that is, it shouldbe more vertical and therefore closer to the physical path.Accordingly, measurements were made in Experiment 2with the same procedure as in Experiment 1, but with

0.20-a 0.15.~ lead 0.10

~ 0.050

~ lag -0.05-0.10

0

• Condition 6

I Condition 7

¶-‘I

2.65 3.05 3.45 3.85

710 SWANSTON, WADE, ONO, AND SHIBUTA

crossed rather than uncrossed disparity in the critical con-ditions. As before, the perceived path during pursuit eyemovements was expected to be unchanged by altering theperceived distance of the pursued target.

MethodObservers. Ten observers, who were paid volunteers, took part

in the experiment. All had normal or corrected-to-normal vision.Eight of the observers had participated in Experiment 1.

Apparatus. The apparatus was the same as that described forExperiment 1. The polaroid filters mounted in front of each eyewere reversed in orientation to give a crossed disparity when re-quired.

Procedure. The same seven conditions were employed as for Ex-periment 1. However, the judged target appeared closer than thepursued target in Conditions 2, 5, and 7. Thecrosseddisparity was0.5°, which corresponded to an equivalent target distance of98.8 cm, or 15.2 cm nearer than the display screen. The observerswere tested according to the same procedure, and they completedthe same number of trials.

ResultsTable 2 shows the results of Experiment 2. As in Ta-

ble I, the values shown are the means and standard er-rors of the perceived motion paths. The results of Condi-tions 3, 4, and 6 broadly replicated those for Experiment 1.There was no effect of simultaneous motion interaction(Condition 3). When the pursued and judged targets werepresented in the same depth plane, the perceived tilt waslarger with head movements (36.6°counterclockwise inCondition 6) than with eye movements (26.6°counter-clockwise in Condition 4). These values were close tothose obtained before and indicated similar undercompen-sations. In Condition 2, the perceived tilt was 5.0°clock-wise, as was expected for a perceived distance less thanthe physical distance. From Equation 1, this correspondedto a perceived distance of 111.1 cm, or 2.9 cm in frontof the display surface. As with the uncrossed disparityin Experiment 1, the perceived separation of the two tar-gets was less than 25% of that simulated by the dispar-ity. The reduced perceived distance of the judged targethad no significant effect on the perceived path of thejudged target during ocular pursuit in Conditions 4 and5. However, during head pursuit with the judged target

Condition M SE

12

EqualNear

—0.65.0

0.61.8

3 Equal —0.9 0.9

Eye Pursuit45

EqualNear

—26.6—26.1

5.95.1

Head Pursuit67

EqualNear

—36.6—25.5

6.65.0

nearer than the pursued target, the perceived path was25.5° counterclockwise, a significantly less tilted paththan that perceived with both targets equidistant [t(9) =3.58, p < .011. Thus, by reversing the direction of thedifference between physical and perceived distance, theeffect on the perceived motion path was also reversed.Takentogether, these results provide confirmation for thepredictions made from our model for the perception ofgeocentric motion. As in Experiment 1, the tilt in Con-dition 2 was not equivalent to that given by the differ-ence between Conditions 6 and 7, although in principleboth were indirect measures ofperceived distance. Whilethe difference between these measures did not reach sig-nificance [t(9) = 1.511, the discrepancy found inbothex-periments suggests caution in generalizing measures ofperceived distance from concomitant head movementacross displays withdifferent numbers of visible elements.

Data were also obtained for the accuracy of head pur-suit. The pattern of results was almost identical to thatfor Experiment 1. An apparently ballistic movementresulted ina lag at either end of the horizontal range, fol-lowed by a period in which the head led the target in themiddle section. The positional error was within ±0.150.

EXPERIMENT 3

Data obtained in Experiments 1 and 2 showed that theposition of the head during pursuit of a horizontally mov-ing target was close to the position of the target. How-ever, eye position was not measured at the same time,so it remained possible that the observers’ eyes might havemoved in such a way as to invalidate the assumptions madeabout the path of retinal motion. For example, the eyesmight have turned so as to maintain fixation on the pointbeing fixated before the head movement began. If so, adifferent explanation would be required for the perceivedpath of a vertically moving target. Under other conditions,such a turning of the eyeswould be expected, in the formof the vestibulo-ocular reflex (VOR). The VOR is typi-cally obtained following rotation, rather than lateral dis-placement, of the head (Howard, 1982), and a movingtarget would not be present. However, the possibility thatsome effect of this type might occur was considered suffi-ciently important to warrant an attempt to make simulta-neous measurements of head and eye position during head

MethodObservers. Three observers, all of whom were authors (M.T.S.,

N.J.W., and K.S.), took part in the experiment.Apparatus. The apparatus was located in a different laboratory,

but was set up to match as closely as possible the apparatus em-ployed in Experiments 1 and 2. Stimuli were generated by a Com-modore Amiga 2500 and presented on a Commodore 1084 videomonitor. There were two stimulus patterns. One, for calibrationpurposes, consisted ofthree stationary points, 2.05°apart horizon-tally, in positions corresponding to the left, right, and center posi-tions of the path ofthe pursued target. For the other, a single pointmoved back and forth along a horizontal path subtending 4.1°,ata velocity of 1.75°/sec.This was somewhat less than the velocity

Table 2Means and Standard Errors of Perceived Motion

Paths in Experiment 2

Target Distance

pursuit.

Note—Values shownare degrees oftilt from thevertical (negative valueindicates counterclockwise tilt).

VISUAL MOTION DURING EYE AND HEAD MOVEMENTS 711

employed previously. The observers viewed the display from114 cm. A headrest with a bite board was mounted on a track, andit activated apotentiometer as it was moved from left to right througha distance of 8.2 cm. An eye-position sensor (Biometrics SGH/V-2) was mounted on a rigid frameattached to the headrest. Thesen-sor was adjustedfor maximum sensitivity when theobserver grippedthe bite board with his head on the rest. Signals from the eye-positionsensor and from the potentiometer were recorded on an FM taperecorder and displayed on a Beckman Type R Dynograph. In addi-tion, the computer generated a marker signal at the start and endof a target movement, and this was also recorded. The apparatuswas constructed so that observations were made from a standingposition.

Procedure. Each observer completed a session oftesting that con-sisted of calibration, followed by head pursuit and a final calibra-tion. Calibration was obtained by presenting the three stationarytargets, with the headrest in the central position. The observer fix-ated the central, left, central, and right targets in turn, twice. Forheadpursuit, the target moved repeatedly from left to right and back,and the observer followed this movement by lateral movements ofhis head, while maintaining fixation on the target. Ten cycles oftarget movement were pursued.

ResultsThe main purpose of Experiment 3 was to establish

whether there was any tendency to move the eyes duringa head movement, which would result in maintaining fix-ation on the point in the straight-ahead position before thestart of the head movement. The first three pursuit cy-cles were discarded to allow for practice. Data were ex-amined from the following three pursuit cycles, which foreach subject provided stable measurements. Head posi-tion with respect to the target was found by plotting a linerepresenting target position over the record for head po-sition. At each of 12 positions in the cycle, approximately0.5 secapart(equivalentto 1.6 cmor0.8°oflinearmove-ment), a measurement was made of the extent to whichthe observer’s head was to the left or right of the target.For left-to-right target movements, a leftward position ofthe head represented a lag error, and vice versa. Eye po-sition was recorded with respect to the head. For thesedata, the deviation to the left or rightof the straight ahead(obtained from calibration trials) was found at the sametwelve locations. This procedure effectively eliminatedsaccadic eye movements from the mean data. These pro-vided a measure of the direction of gaze over the courseof a headmovement, as was required to establish whethereye movements could have altered the retinal path of thejudged target from that expected from the extent of thehead movement. The mean data for the 3 subjects for headand eye position are plotted in Figure 4. The actual mea-surements of eye position obtained in the experiment cor-respond to the separation of the head and eyedata points.Head pursuit errors were somewhat larger in Experi-ment 3 than in Experiments 1 and 2, but were still withinabout 0.25° of the target. There was a tendency for theobservers to undershoot the rightmost target location, butto be close to the correct position at the leftmost point.The data indicate that the head was typically ahead of thetarget, by approximately 0.2°on average. Eye positionwith respect to the target clearly follows that of the head

0~0

z0

TIME FROM START OF PURSUIT CYCLE (secs)

Figure 4. Mean position of the head and gaze relative to the pur-sued target in Experiment 3. Head movements were rightward ini-tially, followed by a 0.5-sec pause, and a leftward return tothe ini-tial position. Vertical bars represent the standard error ofeach meanand are shown in one direction only for diagranunatic clarity.

and generally seems to reflect overcorrection of errorsinhead position. There is no indication of eyemovementsto maintain fixation on the initial location of the targetbefore the start of a target movement. Within the limitsof this experiment, it can be concluded that eye move-ments during head pursuit did not produce a nonlinearretinal path of target motion. Ideally, eye-movement datawould have beenobtained from naive subjects during thecourse of Experiments 1 and 2. However, this would havebeen impracticable, given the demands imposed on ob-servers in recording eyemovements. These data can there-fore only be applied to the interpretation of the earlierexperiments with caution. However, head-movement re-cordings were available from the earlier experiments, andthey showed smaller tracking errors than those obtainedhere. It is therefore likely that any eyemovements by ob-servers would also have been smaller, since their func-tion during head movements appears to be to maintain fix-ation on the pursued target.

One issue raised by these data concerns the differencein the tilt of the path of the judged target with head andeye pursuit found in Experiments 1 and 2. The eyes ro-tated by about 0.6°to the right during a left-to-right headmovement, and the reverse (0.6°to the left) as the headmoved back to the left. This would have produced a moretilted retinal path for a vertically moving target than wouldbe expected if the eyes had remained stationary. In ef-fect, a further horizontal vector was addedto the motion.An eye rotation of 0.6°during head movement wouldhave produced a retinal path for the judged target in Ex-periments 1 and 2 of 75.4°rather than 73.7°,a differ-ence of 1.70. The difference in perceived tilt for eye andhead pursuit was however between 5°and 10°,so eyerotation of the magnitude observed here would not havebeen sufficient to account for the result. In addition, thedata for head-pursuitaccuracy in Experiments 1 and 2 didnot indicate a tendency to undershoot the rightmost tar-get position, which may have been caused in Experiment 3

• Gaze• Head

Target

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5

712 SWANSTON, WADE, ONO, AND SHIBUTA

by the greater difficulty of making head movements whileusing a bite board and with the eye position sensors inplace.

DISCUSSION

The results of these experimentsconfirm previous find-ings that a target that moves in a different direction fromthe eyes is perceived to move in a direction displacedtoward the retinal path of motion. We interpret this asa consequence of undercompensation for the effectof eyemovements on the retinal motion of objects. Such under-compensation is greater when the eyes move as result ofa lateral motion of the head, relative to their rotation withrespect to a stationary head. In addition, Experiments 1and 2 provide information regarding the role of perceiveddistance in the perception of motion with a moving head.Objects viewedduring concomitant lateralhead movementsappear to move themselves if their perceived distancediffers from their physical distance (Gogel, 1980). The ex-tent of this perceived object motion is proportional to themagnitude of the error in perceived distance. It is oppo-site to the direction of head movement when perceiveddistance is larger than the physical distance, and in thesame direction as the head movement when the perceiveddistance is less than the physical distance. In effect, it con-stitutes a perceived motion vector that adds to any physi-cal motion (Gogel, 1982). Our experiments demonstratethat the perceived path of motion of a target moving ina different direction to the head is determined both by un-dercompensation for effects of head movements on thetarget’s retinal path and by the target’s perceived distance.These two factors contribute vectors to the perceived mo-tion path, which increased the apparent tilt in Experi-ment 1 and decreased it in Experiment 2, as the result ofchanging the perceived distance from farther to nearerthan the physical display. Perceived distance had no ef-fect on the perceivedpath of motion when the eyes wererotated in a stationary head. This pattern of results is pre-dicted by our model of motion perception (Swanstonet al., 1987), which identifies the sources of informationrequired for veridical motion perception, and the man-ner of their combination. Wehave argued that observers’reports are based on the geocentric representation. Thus,a given retinal path is interpreted in terms of the avail-able information regarding eye movements, head move-ments, and perceived distance. In the conditions involv-ing eye movements, the perceivedpath of the target wasnot determined by perceiveddistance, because this wouldhave influenced both the vertical and the horizontal com-ponents of the motion equally.

In Experiments 1 and 2, the perceived distance of thejudged target as measured by its concomitant motion dur-ing head movements was considerably less than that sim-ulated by the disparity present in the display. It could beargued that the perception of the disparity as a small depthinterval indicated that the perceived distance of the dis-play was markedly less than its physical distance, since

the perceptual effect of a given disparity is scaled by per-ceived distance. If this were so, it could also account fora difference between the perceived tilts with eye and headpursuit, even in the absence of disparity. However, Swan-ston and Wade (1988) found a similar difference in per-ceived tilt with the two types of pursuit and demonstratedby a head-movement procedurethat physical distance andperceived distance were the same in an equivalent dis-play. More probably, the relative ineffectiveness of thedisparity was due to the off-center observation of the tar-get and to its having been viewed during lateral headmovements.

Experiment 3 showed that the movements of the eyesand/or head were not systematically different from themotion of the pursued target. While errors of pursuit werepresent, these were not such as to give a retinal path ofthe judged target either more or less similar to the per-ceived path. It appears reasonable to assess the extent ofcompensation for eye or head movements on the basis ofa retinal path derived from accurate pursuit, at least toa first approximation. Data for the accuracy of head move-mentsobtained in Experiments 1 and 2 support this con-clusion, as does the comparison of these results with thoseof our previous study (Swanston & Wade, 1988). In theexperiments described here, a pursuit procedure was em-ployed in which observers followed the horizontal move-ments of the pursued target in the same manner for bothhead and eye movements. In our previous study, the mo-tion of the judged target was linked to the motion of thehead, but this was not the case for pursuiteye movements.In part, this was intended to ensure that the retinal pathduring head movements was predictable in the absenceof information for the accuracy of head movements. Sincethe outcome in comparable conditions was the same inboth studies, it is likely that head movements are the sameboth when the target is locked to head position and whenit is followed voluntarily.

In general, the data reported here add to evidence forthe “phenomenal geometry” advanced by Gogel (1990).From this viewpoint, the perceived characteristics of ob-jects (e.g., size, shape, and motion) are determined byinternal values for retinal extents, the movements of theeyes with respect to the head, the distance of the object,and motion of the self in three-dimensional space. Thecombination of these values follows rules that reflect thegeometry of Euclidean space, and the outcome is a per-ceptual representation that can act as a reliable guide toaction. Errors in these internal values give rise to pre-dictable and interrelated errors in perception.

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(Manuscript received September 12, 1991;revision accepted for publication June 4, 1992.)