gibson (1959) motion parallax as a determinant of

Journal of Experimental PsychologyVol. 58, No. 1, 1959

MOTION PARALLAX AS A DETERMINANT OFPERCEIVED DEPTH1

ELEANOR J. GIBSON, JAMES J. GIBSON, OLIN W. SMITH,AND HOWARD FLOCK

Cornell University

Motion parallax is the opticalchange of the visual field of an ob-server which results from a change ofhis viewing position. It is oftendenned as the set of "apparent mo-tions" of stationary objects whicharise during locomotion. Psycholo-gists assert that it is a "cue" forperceiving the depth of the objects,but the optical fact of motion paral-lax must be distinguished from itscapacity to induce perceptions. Ithas not been experimentally demon-strated that motions in the field ofview will actually yield correspondingjudgments of depth. This is a purelypsychological problem. The opticsof motion parallax, on the other hand,is a problem for geometry and ecology.

Recently, the suggestion has beenmade that a continuous gradient ofmotions in the field of view will inducethe perception of slant-depth (J. J.Gibson, Olum, •& Rosenblatt, 1955)inasmuch as the perception of depthis intimately connected with the per-ception of surfaces (J. J. Gibson,^950). This statement also needs ex-perimental test. The purpose of thepresent study is to investigate whatkinds of motion in the light enteringan eye do in fact consistently arousecertain judgments of depth, and whatdo not.

The experiments must be carriedout with artificial motions in a fieldof view rather than those obtained

1 This work was supported by the Office ofNaval Research under Contract NONR 401(14) with Cornell University. Reproductionin whole or in part is permitted for any pur-pose of the U. S. Government.

in a natural environment if we wishto study the effect of motion parallaxin isolation from other cues or stimulifor depth. The variables of size,density, linear perspective, differen-tial blur, and binocular parallaxshould be eliminated or so reducedas to be ineffective in the array oflight entering O's eye. A method ofachieving this result has been devised,and a suitable control employed.

The experimental method shouldalso preclude actual movement orlocomotion of 0. If the cue of motionparallax is so defined as to requireactive head movement or locomotion,proprioceptive and vestibular stimu-lation is also present. This definitionis unjustified, since passive locomo-tion in trains and airplanes should beadmitted as circumstances when mo-tion parallax occurs. Certain pat-terns of motion in the field of view of0 do induce impressions of beingmoved through space if we acceptas evidence the illusions of locomo-tion obtained in viewing a panoramicmotion picture, or in a training devicefor simulating aerial flight.

Perception of absolute distance and ofrelative depth.—The apparent displace-ments of the sensations of objects aresaid to be cues for perceptions of theirdepth. What kind of depth? The ques-tion arises whether their distances fromthe perceiver can be judged or whetherthey will only appear to be separatedin the third dimension. Helmholtz, inhis description of motion parallax, as-serted both hypotheses. On one pagehe described the appearance of objects"gliding past us" as we walk through

40

MOTION PARALLAX IN PERCEIVED DEPTH 41

the countryside, and asserted that "evi-dently under these circumstances theapparent angular velocities of objectsin the field of view will be inverselyproportional to their real distances away;and consequently safe conclusions canbe drawn as to the real distance of thebody from its apparent angular velocity"(Helmholtz, 1925, p. 295). On the nextpage he described the appearance of anindistinguishable tangle of foliage andbranches in a thick woods as a manstands motionless, but noted that "themoment he begins to move forward,everything disentangles itself and im-mediately he gets an apperception of thematerial contents of the woods and theirrelations to each other in space, justas if he were looking at a good stereo-scopic view of it" (Helmholtz, 1925p. 296).

In the first quotation Helmholtz saysthat angular velocity is a cue for theperception of absolute distance. In thesecond, he suggests that a difference inangular velocity is a cue for the percep-tion of separation in depth, or of relativedistance only. These two hypothesesare by no means the same, and theyshould be considered separately andtested separately. We will be concernedhere primarily with the second.

Two-velocity motion parallax and flow-velocity motion parallax.—Although mo-tion parallax has been said to apply tothe whole array of objects in an environ-ment and a large array of apparentmotions in the field, the experimentsperformed have in the past been con-fined to two objects and two velocitiesin a restricted field of view.

Bourdon (1902) reported experimentsin which O looked with one eye at a pairof luminous spots in a dark corridor.The sources were at different distancesbut the spots were of the same angularsize. When the head was fixed with abiting-board, 0 "could not judge at allaccurately" which light was the nearer,but with the slightest movement of thehead from side to side "it was easy tojudge" the relative depth of the two.But the absolute distance of neitherlight was detectable.

Tschermak-Seysenegg (1939) improvedon this arrangement with what he calleda "parallactoscope," by analogy with thestereoscope. He defined motion parallaxas arising from movement either of agroup of visible objects on the one hand,or the position of O's eye on the other,emphasizing the relativity of the situa-tion. But, he studied only the detectionof depth of two objects with voluntaryhead movement. His apparatus was amodification of the familiar two-pinssetup used to obtain the threshold forbinocular depth perception. It per-mitted O to move one eye from side toside, with a sliding headrest, so as toobtain successive impressions equivalentto the simultaneous impressions obtainedwith both eyes open. The average errorof equating the distance of the verticalwires was small under these conditions,although not as small as the error withboth eyes open. When only one eyewith a fixed head was used, the errorwas very large.

Graham, Baker, Hecht, and Lloyd(1948; see also Graham, 1951) obtainedthe threshold for separation in depth oftwo needles pointing toward one another,as seen on a uniform field through awindow. The needles moved from sideto side on a common carriage. Theyappeared to be aligned at the center oftheir motion cycle and offset at the ex-tremes of the cycle unless the adjustableneedle had been set into the same frontalplane as the fixed needle. Graham thuseliminated for the first time in this typeof experiment the additional sensoryinformation produced by voluntary headmovement.

More exactly, what Graham obtainedwas the just noticeable difference be-tween two angular velocities in a fieldof view, under probably optimal condi-tions. The threshold was extremelylow—about 30 sec. of arc per second oftime. It is notable that the reports ofwhat Os perceived, however, were notunanimous. Some saw the separationin depth as such; others perceived eitherthe difference in velocity of the twoneedles or noticed the change of align-ment or offset of the needles. Although

42 E. J. GIBSON, J. J. GIBSON, O. VV. SMITH, AND H. FLOCK

the latter impressions may be cues forthe former, the experiment was notconcerned with the effectiveness of suchcues for producing depth impressions.

Somewhat later, a case of motionparallax different from the two-velocitycase was defined mathematically byGibson, Olum, and Rosenblatt (1955).This is the array of angular velocitiesof the optical elements projected froma surface to a moving station point.There is a flow of velocities rather thana pair of velocities in such an array, andthe phenomenon was named motionperspective to distinguish it from motionparallax as it had been studied up to thattime.

For the study of the perceptions in-duced by, flow-velocity in a field of view,including gradients of velocity, skewmotions, and transformations, a differentsort of apparatus is required from thatpreviously employed. The two-velocityexperimenters used a pair of real objectsat real distances to produce the opticalmotions. More freedom is achieved byusing a projection screen or some otheroptical means to produce them. Theexperiments to be described used shadowson a translucent screen. Accommoda-tion is thereby controlled.

Several exploratory experiments havebeen published on flowing motion. Theyare of various types, and they have beenproduced in various ways. J. J. Gibsonand Carel (1952) attempted to inducethe perception of a receding surface in adarkroom with a bank of luminous pointswhich carried a gradient of velocities.This stimulus failed to arouse the per-ception of a surface, however, and thedepth judgments were ambiguous. O. W.Smith and P. C. Smith (1957) investi-gated the perception of convexity orcurvature of a textured surface withvarious combinations of depth cues,including the flow-velocity type of mo-tion parallax. Although motion in thefield contributed to the judgment ofconvexity, in no case did motion causea surface otherwise judged as flat to bejudged as curved. Hochberg and 0. W.Smith (1955) studied the perception ofdepth induced by the centrifugal flow

of luminous pattern elements in the dark,the expansion phenomenon. J. J. Gib-son and E. J. Gibson (1957) investigatedthe perception of the rigid rotation ofan apparent surface elicited by thecontinuous perspective transformationof regular and irregular patterns or forms.

These experiments differed in thestructure of the optic array used to"carry" the motion in question, and theyalso differed in the degree to which per-ceptions of space were aroused. Theyled to the choice of the kind of randomtexture employed in the present experi-ments, which is intended to yield theexperience of a plane surface.

What is now needed is an experimentalcomparison of the judgments obtainedwith two velocities in a field of view andthose obtained with many velocities ina field of view. Although no clear linecan be drawn between them, the two-velocity type of motion parallax appliesto the problem of perceiving a group ofobjects in otherwise empty space, whilethe flow-velocity type of motion parallaxapplies to the perceiving of a backgroundsurface such as a wall (or substratum).These are not the same problem forperception even though it may be dif-ficult to distinguish sharply betweentheir respective kinds of stimulation.

Optical geometry of motion parallax.—•The environmental situation which leadsto an array of different motions in avisual field should be defined more care-fully. This is the optical geometry ofmotion parallax, as distinguished fromthe visual appearance of motion parallax.Graham (1951, pp. 878 ff.) has given thegeometry of certain special cases of thissituation. J. J. Gibson et al. (1955)have analysed the case of an extendedsurface such as the ground. What willbe discussed here is the case of an en-vironment of discrete objects.

When light rays from permanentobjects of an environment converge to apoint, they constitute what may becalled an optic array, and the elementsof this array constitute a pattern. Aneye or a camera at the station pointcan register this pattern of luminouselements. If the point moves, the


pattern is altered in a way which de-pends on both the displacement of thepoint and the layout of the objects.How the eye responds to this alterationof pattern is our problem.

The first question is how to specifymathematically the change of patternin a way that is relevant for vision. Bychoosing a coordinate system for thearray, one can specify the absolute posi-tion of each element and the displace-ment of each element per unit of time,that is, its absolute angular velocity.It would then be true in a certain sense,as Helmholtz (1925, p. 295) said, that"the apparent angular velocities ofobjects in the field of view will be in-versely proportional to their real dis-tances away." But more exactly, itwould be true only if the linear velocityof the station point were constant (J. J.Gibson et al., 1955). A given angularvelocity is a cue for distance, or permitsa "safe conclusion" about distance, onlyif the speed and direction of one's locomo-tion is known.

The trouble with positions and angularvelocities of elements in a field is thedifficulty of understanding how an eyecan register them. As the Gestalttheorists have emphasized, what the eyeseems to pick up is the mutual separationof elements, their pattern, rather thantheir position or directions. And, ac-cordingly, it is easier to suppose that theeye responds to changes of separation,or change of pattern, rather than toabsolute displacements or velocities.Helmholtz might better have assertedthat a difference between the angularvelocities of two elements in the fieldwill be directly related to the differencein distance between the correspondingobjects in space. Such relative veloci-ties involve a transformation of pattern,and this may be what the eye is primarilysensitive to. It is not immediately evi-dent what the best method is for speci-fying the information about objects in anarray of light projected to an eye.

But one fact should be clear. Onlyif there is an eye at the point of projec-tion and only if it is sensitive to themotions in the optic array, relative or

absolute, does a psychological questionarise. Will the possessor of the eye seemerely the change of pattern of the array ?Or will he see moving objects in thefield of view? Or will he see stationaryobjects at different distances? In orderto show that motion parallax is effectivefor the perception of depth it must bedemonstrated experimentally that dif-ferential motions in an array of light toan eye will yield differential judgmentsof depth. And the array should be suchthat when the motion is eliminated thejudgments of depth will cease, for onlythen will motion parallax have beenisolated from other cues for depth.

EXPERIMENT I : MOTION PARALLAXWITH Two VELOCITIES

Problem and Method

The two-velocity experiments were re-peated with (a) two spots in a field to carrythe motions, and (6) two superimposed tex-tures filling the field to carry them. In bothcases the velocity difference was taken to bethe essential cue for possible judgments ofdepth, not the absolute velocities. In thisexperiment, reports were obtained for a largevelocity difference, a small velocity difference,and no velocity difference, that is, a motion-less field. The last was a control.

Apparatus and stimuli.—The light enter-ing O's eye came from the translucent screenof a point source shadow-projector (J. J.Gibson, 19S7; J. J. Gibson & E. J. Gibson,1957). He saw only a luminous rectangularfield in which dark circles or textures could bemade to appear and to move. These wereactually the shadows of opaque substancesattached to a transparent mount behind thescreen. This was a large sheet of glass orplastic whose edges were never visible. Dif-ferential translatory velocity of the shadowswas produced with two mounts, one behindthe other, which could be made to move paral-lel to the screen on a common carriage. Thearray of light to the eye was simply the re-verse of the array projected to the screen,since the eye and the point source were sym-metrically located equidistant from the screen(Fig. 1). The window was 32.2 X 36 cm. ata distance of 126 cm. from the eye, subtendingan array 14.5° high and 16.2° wide. Thewindow was viewed through an aperture by aseated 0.

44 K. J. GIBSON", J. J. GIBSON, O. W. SMITH, AND H. FLOCK

STANDARDMOUNT. ,MOUNT

FRANSLUCENT WINDOW

FIG. 1. The shadow projector viewedfrom above. In a unit of time, the shadow ofa spot at the center of the standard mountsweeps through a certain angle and that of acorresponding spot on the variable mountsweeps through a lesser angle, as shown. Thetwo mounts roll on the same carriage. If theyare close together, there is no difference inangular velocity, but as the variable mount ispositioned farther from the point source andcloser to the screen, the angular velocity of itsshadow decreases. With this apparatus, itcan decrease to about one half of the angularvelocity of the standard. By trigonometry,the ratio of the lesser (V) to the greater (S)angular velocity is equal to the inverse of theratio of the distances of their respectivemounts from the point source. In the dia-gram above, it is about 0.7.

The carriage which bore the two mountsrolled silently on tracks and could be pulledfrom side to side through an excursion of 45cm. It was operated by hand to produce amotion cycle in about 8 sec. A small shutterclose to the point source enabled E to elimin-ate the shadow between trials, leaving thescreen illuminated by diffuse light.

The two adjacent spots in the field wereproduced by attaching small paper circles toeach mount, at different elevations so thattheir shadows did not pass through one an-other as they moved across the field. Thefaster spot was above the slower spot. Thediameter of both was 5.2°, one paper circlebeing compensated in size to match theshadow of the other.

The superimposed random textures wereproduced by a technique of sprinkling talcumpowder over the surfaces of the two transpar-ent mounts. This yields an optical texturewith indefinite contours and indefinite ele-ments. When the two were superimposedbut motionless, they constituted a singletexture with no cue for superposition, andgave the appearance of a single surface, some-thing like that of a cloud. This apparentsurface filled the whole window and appearedat an indefinite distance from 0.

As noted, the two angular velocities as

such were not uniform, decreasing to zero ateither end of a motion cycle, and changingdirection alternately. Minor variations invelocity also occurred as a consequence ofmoving the carriage by hand. The inde-pendent variable of this experiment was thedifference in velocity between the twoshadows. It was expressed as the ratio ofthe slower (the variable) velocity to that ofthe faster (the standard) velocity, or V/S.

Procedure.—Each 0 was seated at theapparatus, asked to apply his preferred eyeto the aperture, and instructed simply to "de-scribe what he saw in the window." He wasfirst presented with a motionless field for aslong as he needed to make a report, which wasrecorded. He was then presented with con-tinuous cycles of motion at the maximum vel-ocity difference (V/S = .51) until his reportwas completed. Finally he was given theminimum velocity-difference (V/S = .97).The E made no comment at any time, sincewholly spontaneous reports were desired.The order of presentation was intended tominimize the effect of suggestion on the per-ceiving of depth.

A group of 26 Os went through this pro-cedure with the spot field and another groupof 46 with the textured field. Formal judg-ments and answers to questions were obtainedafterwards from some Os, which will be de-scribed when relevant. They were requestedin the terms used spontaneously by the 0.

Results

The words used by the Os todescribe what they saw varied widely,and the effect to identify things wasreminiscent of descriptions of cogni-tive inference (Vernon, 1957). Butthe reports could later be classifiedeasily with respect to depth or dis-tance. The motionless textured fieldwas unanimously reported to be asingle surface without any differencein depth. The motionless spots, how-ever, were reported at different dis-tances by 4 of the 26 Os. The spots,therefore, did not wholly satisfy therequirement that impressions of depthbe absent in the absence of motion,although the combined textures did.

A large velocity difference (.51) forthe textured field always gave a


perception of two surfaces separatedin depth, as evidenced by the reportsof all 46 Os. For the spot field, thereports were not unanimous, but 22out of 26 Os did describe a differencein depth of the two objects.

The small velocity difference (.97)was evidently close to the threshold.None of the Os reported two sepa-rated surfaces for the textured field,and only 7 out of 26 reported differentdistances for the spots.

The direction of the difference indepth reported was not unanimousfor either the spots or the textures.Insofar as two-velocity parallax is areliable and effective indicator ofrelative depth, the faster velocityshould correspond to the nearer ob-ject or surface. But 7 out of 26 Ossaw the slower spot as the nearerobject instead of the reverse, and 10out of 46 Os saw the slower textureas the nearer surface. Some degreeof ambiguity as to the depth-differ-ence is also indicated by the fact that7 Os reported spontaneous reversalsof the front-back relationship betweenthe two surfaces at one time or an-other.

The amount of separation in depthbetween the two objects or the twosurfaces was estimated on formalrequest by a sample of these Os, afterthe main procedure. The estimateswere highly variable. For the spotsthey ranged from zero to 5 ft. Forthe textures they ranged from 2 in.to 3 ft. Some Os were unwilling tojudge, saying, "It depends on whatit is," or "It could be infinity."Evidently the impression of how farapart these entities were was in-definite, as also was the impressionof how far away they were.

Figure 2 represents an ideal theo-retical possibility of what the Osmight have seen in this experiment,but it cannot be asserted that this

FIG. 2. The two angular velocities ofFig. 1, with a pair of virtual objects at differ-ent distances moving in apparent space. Thetwo apparent objects (or surfaces) are shownas if seen behind the translucent window.The nearer (N) is shown close to the window;the farther (F) is shown at the distance itwould have to be if the two were taken to be inrigid translation (if the two vectors wereequal). In the diagram ON/OF = V/S, bytrigonometry. That is, the distances aresuch that the optical velocities are inverselyproportional to them. (Note that N corre-sponds to S, and F to V.) But this relationdepends entirely on the assumption of rigid-ity. The absolute distances of N and F mayvary, but the ratio of ON/OF will remainconstant on that assumption. If rigidity isnot assumed, however, there is no rationalefor predicting any relation of distance ordepth or even which object will be seen infront of the other.

is what they did see. The reportsindicated that they perceived twothings of some kind in some kind ofspace behind the screen, but neitherthe direction nor the amount of theirseparation in the third dimension wasdefinite.

DiscussionThe significant result of this two-

velocity experiment is not so much theeffect of motion on depth perception asits effect in separating one surface intotwo. With the textures, all Os saw asingle frontal surface when there wasno differential motion, and all Os sawtwo frontal surfaces when there was asufficient degree of differential motion.This separation is not what is ordinarilymeant by depth, since it was not alwaysclear which surface appeared in frontand which behind.

The phenomenon is similar to the

46 E. J. GIBSON, J. J. GIBSON, O. \V. SMITH, AND H. FLOCK

' 'disentanglement'' of foliage and brancheswhich Helmholtz noted when he beganto move in the thick woods. But thisis not the same as his "apperception ofdepth." The separation is probably re-lated to Wertheimer's (1923) demonstra-tion that a group of spots interspersedamong others will be unified by what hecalled their "common fate" if theymoved together. Other conditions forthe seeing of one thing in front of another,for transparency and superposition, havebeen discussed by Koffka (1935). Al-though the phenomenon may not seemrelevant for some kinds of space percep-tion it is certainly relevant for objectperception.

How can this result be explained?Instead of appealing to a process oforganization, or a law of "common fate,"one might look for its basis in the geom-etry of the optical stimulus. Geometrydistinguishes between (a) perspectivetransformation of forms, (6) topologicaltransformations of forms, and (c) dis-ruptions. These correspond roughly withthe distinctions in physics between rigidmotions of bodies, elastic motions ofbodies, and the motions of breaking,tearing, or splitting. In this experi-ment, the motion of one set of texturalelements relative to the other was a dis-ruption, geometrically speaking. Whensufficiently different velocities were im-posed on them, the adjacent order ofelements in the textures was destroyed.More exactly, there was a permutationof this order. It was a particular sortof permutation, to be sure, for each oftwo sets of elements retained an adjacentorder, but the disruption of order asbetween these sets broke the originalcontinuity. And this produced the per-ception of different surfaces with separa-tion between. The detection by the eyeof continuity or solidity as comparedwith discontinuity, disruption, or separa-tion, is probably a fundamental kindof perception. The continuity of asingle surface in two dimensions may begiven by a static optical texture. Butthe continuity of a solid object in threedimensions probably depends on thekind of optical motion presented to

the eye. Perhaps it was this lack ofsolid continuity or rigid connectednessbetween the nearer and farther surfacein our experiment which prevented theideal possibility represented in Fig. 2from having been realized.

The earlier investigators of motionparallax were willing to assume that aneye was sensitive to the stimulus of mo-tion, but they did not seem to realizethat differential motion necessarily en-tails a change of pattern. In our experi-ment there were motions of the elementsrelative to the window but there werealso motions of one set of elements rela-tive to the other. For example, whenboth sets of elements were moving to theleft, relative to the window, and onemoved faster than the other, the slowerwas moving to the right, relative to thefaster. Spontaneous reports of this ap-pearance were given by several Os. Whyshould not a differential velocity be per-ceived just as directly as the two com-ponent velocities? When two movingelements are far apart in the field, onemight suppose the slower and the fastervelocity might have to be compared inorder to detect a difference betweenthem. But when the elements areadjacent in the field the difference isgiven by the change of pattern. Permu-tation of order is one type of change ofpattern. In order to study the sensi-tivity of the eye to form, to change ofform, and to the forms of change of form,a taxonomy of these variables is desirable.

EXPERIMENT II : MOTION PARALLAXWITH A FLOW OF VELOCITIES

Problem and Method

If a two-velocity field does not arouse con-sistent perceptions of depth, will a flow-veloc-ity field do so? In order to make this com-parison, the apparatus already described wasmodified so as to present to the eye a texturein which the horizontal velocities of the ele-ments varied from slow to fast from the topto the bottom of the field, that is, a gradient.As before, the field could also be motionless.

Apparatus.—The shadows on the screenwere produced by spattering paint on a trans-parent sheet interposed between the point


source and the screen. This mount wasslanted toward the screen at an angle of 45°(Fig. 3). By the principle of mirror reversal,the gradient at the eye should yield an ap-parent slant away from the screen.

If this texture had been composed of ele-ments regularly spaced in a grid or pattern,then the gradients of size and spacing wouldhave been effective in producing the impres-sion of a slanted surface even when the texturewas motionless, as previous research hasdemonstrated (J. J. Gibson, 1955). But asit was, the brightness-transitions which com-posed the texture were not sharp, the elementshad indefinite sizes and shapes, and the staticgradients, if present, were not effective inproducing a perception of slant. This texturewas nevertheless sufficient to produce theperception of a continuous surface.

As before, 0 looked through an aperturewhich prevented his seeing either the edgesof the window or any other part of the appara-tus. The field was 82° wide by 52° high.The eye and the point source were each 75 cm.from the window.

Procedure.—All Os were naive. Each wastold that when he applied his eye to the aper-ture he would see a gray field of view, and wasasked to report what he saw. They weredivided into two groups, one of which waspresented with the moving texture withoutever seeing it static (Group I), and the otherwith the moving texture after having seen itstatic (Group II) . > Their spontaneous de-scriptions were recorded and later classified.Questions were asked only after these reports,and in the same terminology used by 0.

r I

Resultsi

Nineteen out of 21 Os (Group 1)reported a rigid moving plane surfaceof some kind slanting away from themat the top of the field. The inclina-tion of the surface was estimatedwithout difficulty, and they judgedit to be receding upward. Of the2 remaining Os, one's report was unin-terpretable, and the other's was of asurface perpendicular to his line ofsight.

With the static texture, 25 Os outof 28 (Group II) reported somethingwhich could be classed as surface-like,'but which was in no case slantedbackward into space. Of the re-

FIG. 3. The shadow projector giving agradient of angular velocities, viewed fromthe side. The carriage and mount move backand forth parallel to the translucent window.The angular velocity is greatest at the bottomof the window, where the mount is closest tothe point source, and least at the top, wherethe mount is farthest from the point source.At an inclination of 45°, this yielded a ratioof the minimum to the maximum velocity of3 to 1. The apparent surface should appear toslant backward at the top.

maining 3 Os, 2 saw a surface whoselower part was perpendicular butwhose upper part was slanted back,and one saw the surface slanting backinto space. When these 28 Os werelater presented with the moving field,26 saw it unambiguously to be areceding rigid surface at a fixedinclination. Of the remaining two,one saw it perpendicular to the lineof sight; the other's report was unin-terpretable.

Estimates of the slant of the ap-parent moving surface were obtainedfrom each 0 in terms of degrees ofinclination backward from the frontalplane. For Group I, the 19 judg-ments varied from 20° to 60° witha median of 40°. For Group II,the 26 judgments varied from 12J°to 55° with a median at 37|°. Thetheoretical value based on the gradientof velocities alone would be 45 °. Themedians show a constant error ofunderestimation. The surface neverappeared to be at 90°, that is, it neverlooked like a ground on which 0 mightbe standing.

Estimates were requested of how

48 E. J. GIBSON, J. J. GIBSON, O. W. SMITH, AND H. FLOCK

far away the apparent moving surfaceseemed to be from 0, but these judg-ments, in contrast to those of slant,could not as easily be made. Forthe total of 49 Os, they varied from3 in. to 5 miles. Some of these Osreported that it was possible to seethemselves moving with respect tothe surface instead of the surfacemoving with respect to them.

Discussion

These results indicate that motionparallax with a continuous gradient ofvelocities does induce consistent judg-ments of slant. This is the property ofreceding in depth in a certain direction.It is combined with the experience of acontinuous rigid surface. The secondexperiment was like the first in mostrespects except that continuity of dif-ferential motion was introduced. Toput it another way, permutation of tex-tural elements was absent, but a skewof the pattern of elements was present.Judgments of distance in this experimentwere highly variable and were made withreluctance, as they were in the firstexperiment.

There is evidently more than one kindof "depth" and more than one kind ofmotion parallax. The two experimentalsituations so far described were sufficientfor judgments by naive Os of two kindsof spatial perception, (a) the phenomenonof separation in the third dimension and(b) the phenomenon of recession in thethird dimension. Neither situation, how-ever, was sufficient for absolute judg-ments of distance. This may be con-nected with the fact that no perceptionof a level ground was induced.

EXPERIMENT I I I : CORRESPONDENCEBETWEEN VELOCITY-PAIRS AND

JUDGMENTS OF DEPTHUNDER VARIOUS

INSTRUCTIONS

Problem and Method

In Exp. I, a difference in optical velocitydid not induce the perception of a difference

in visual distance with any great consistency.An explanation of this result has been sug-gested in terms of the absence of continuitybetween the two velocities. Another possibleexplanation however, in the spirit of Helm-holtz, would be that the expected perceptiondid not occur because 0 did not interpret thetwo motions as a difference in distance, or hadnot learned to perceive differential velocity asa difference in distance. On this theory, thesuggestion that there was always an elementof depth between the objects, with instruc-tions about the limits of this separation, wouldbe expected to alter the perceptions and leadto consistent judgments of depth. This pre-diction was tested in Exp. Ill , using thetextures and spots of Exp. I.

Naive Os were given one of three degreesof suggestion or verbal information aboutdepth, and were asked to reproduce on anadjustable but unmarked scale 1 m. in lengththe separation between the nearer and thefarther apparent surface. The degree of ve-locity difference, the V/S ratio, was systemati-cally varied so that judgments could be corre-lated with it.

Procedure.—All Os, as previously de-scribed, initially made spontaneous observa-tions to the request "Describe what you see,"in response to the motionless stimulus, thegreatest velocity difference (V/S = .51), andthe least velocity difference (V/S = .97).The apparatus was that of Exp. I. Each 0then made 20 judgments of amount of sepa-ration for both the textures and the spots.The variable transparent mount was so setas to produce 10 velocity ratios of .51, .54,.57, .61, .65, .70, .76, .83, .90, and .97. Eachratio was presented twice, in random order, inthe texture series and the spot series. Halfthe Os began with one series and half with theother. An 0 was assigned to one of threegroups, and then instructed as follows:

Group I (Least information): The 0 wasshown the sliding scale beside his chair andwas told that it could be used to indicate thedistance between the nearer and farther of thetwo (surfaces, spots). If 0 had used otherterms instead of "nearer" and "farther," theseterms were employed. He was then told thathe would be shown a number of different set-tings of the apparatus, and that each time hewould be asked to make a judgment (degree ofseparation, distance between, etc.). Noother information was given. The 0 wasencouraged to report as he went along but nocomments were made on his performance.There were 16 Os.

Group II (Maximum and minimum):After the adjustable scale had been demon-


TABLE 1

MEDIANS AND RANGES OF CORRELATIONS BETWEEN VELOCITYRATIOS AND JUDGMENTS OF DEPTH

Measure

Median r

Range

Number r's significantat <.05

Stimuli

SurfacesSpots

SurfacesSpots

SurfacesSpots

Group I(AT =16)

+.72+ .57

-.23 to +.95-.52 to + .94

12/1614/16

Group II(,V = 17)

+ .67+ .51

+ .34 to +.85-.14 to +.85

15/178/17

Group III(]V =20)

+ .83+ .84

-.18 to +.96-.45 to +.99

19/2019/20

strated, these Os were given another demon-stration of the greatest and the least velocity-difference and were told which one was themaximum and which the minimum. Theprocedure thereafter was the same as forGroup I. There were 17 Os.

Group III (Most information): After thepreliminaries described, these Os were told:"These are shadows of two (surfaces, objects)which are actually at different distances fromyou. One is farther away from you than theother. This is what they look like at theirmaximum separation, which is 18 in. (The0 was shown 18 in. on the adjustable scale.)This is what they look like at their minimumseparation, which is $ in. (The 0 was shown1 in. on the scale.) Each time I will ask youto estimate how far apart the (surfaces, ob-jects) making the shadows are." The proced-ure was thereafter the same as for the othergroups. There were 20 Os.

When each O had finished his judgments,he was questioned by E as to how he had madethem unless he had already made this clear.The questions were: How did you make yourjudgments? Did you go by appearance ofdepth, or did you try to use some other cue?If some other cue, what was it? Did you eversee the front and back (surfaces, spots) changeplaces or fluctuate? Did the two (surfaces,spots) ever appear to be connected, like partsof a rigid object?

Results

For each 0 a rank order correlationwas run between his 20 judgmentsof separation and the correspondingvelocity-ratios. Table 1 summarizesthe median coefficients for the threekinds of instruction and for the twokinds of apparent objects, surfaces

and spots. They range from .51 to.84. Eighty-seven of the 106 corre-lations were significant at the 5%level (r > .44). The data thus dem-onstrate some correlation betweenamount of differential velocity anddegree of depth judged. The spreadof the individual correlations was verygreat, however, ranging from —.52to +.99.

Group III, which was given themost information, had higher correla-tions (medians of .83 and .84) thanthe other two groups. If individualcorrelations are considered, 19 out of20 were significant for both the sur-faces and the spots. The correlationsof Groups I and II do not differ fromone another. The demonstrating ofthe maximum and minimum stimuluspresentations at the ends of the scaledid not, therefore, improve the order-ing of the estimates. But telling 0that he was seeing shadows of twothings separated by a given amountof space did so.

When the instructions were given,they seemed to make 0 begin search-ing at once, and quite deliberately,for cues which he could put into someorder. Only a minority of the Osreported that they had depended onany "appearance of depth" in makingtheir estimates. Considering all Os,70% reported that they had used

50 E. .J. GIBSON, J. J. GIBSON, O. W. SMITH, AND H. FLOCK

the "relative motion," or the "dif-ference in speed," or "how far onepasses the other" as the basis forjudgment. Evidently, most of themsaw motions of some kind of entitiesbut did not clearly see the amountof space separating them.

The appearance of a connectionbetween the two surfaces or spots"like parts of a rigid object" was al-most never reported in answer to thequestion. The appearance of ex-changing place or fluctuating in depthwas reported by 17 out of 53 Os.

Because the more specific instructionsraised the correlations, two Os (both psychol-ogists and familiar with the apparatus and theproblem) were run on consecutive days withreinforcement, to see how high the correlationsmight go and how stable they might become.The spots were not used in this experiment.The first 20 trials on each day were run with-out comment. But on the next 10 trials Owas corrected after each judgment. The Edid so by marking off on the scale the actualdistance which separated the standard andvariable mounts behind the translucent screen.This procedure of 20 uncorrected and 10 cor-rected trials was repeated for 9 days with one0 and 7 days with the other.

The correlations improved rapidly fromcoefficients of .20 and .30 to ones of .90 ormore. The introduction of new and unfami-liar textures had little effect on the correlation.Neither did the requiring of one 0 to use averbal rating scale of 1 to 10 instead of theadjustable sliding scale.

These Os definitely took a problem-solvingapproach to the task and checked their meth-ods of judging against the corrections given byE. One estimated the ratio of the two veloci-ties and tried to express this numerically eachtime. The other said, after a few days, thatthe task had become similar to memorizingparied associates; he was trying to link upordered "cues" with particular scale positions.The training did not have the effect of produc-ing or enhancing an immediate appearance ofdepth.

Discussion

After verbal suggestion, information,or training concerning separation indepth, a correlation was present between

the degree of velocity-difference and thedegree of separation judged. It wasraised by information and correctedtraining. But the reports indicatedthat the Os generally saw motions ratherthan depths, and that the appearance ofdepth was not induced by informationor training. They were led to look forand use cues for the required judgmentsof depth, but not to report that theyperceived it. They could interpret avelocity-difference as a depth-differenceif given instructions, and they couldimprove the consistency of their estimatesif given reinforcement. They couldlearn to perceive in one sense of theterm, but they did not learn to see adifferential velocity as a difference indepth.

This result does not support the theoryof "unconscious inference" or point toany process for the conversion of bi-dimensional impressions into perceptions.It should be remembered, of course, thatin these experiments motion has beenisolated from other determinants ofperception. This does not occur ineveryday life. Motion usually comesin conjunction with size, shape, density,and disparity. But it might be supposedthat the fact of this conjunction overyears of past experience would havegiven an associative cue value to themotions in our experiment. In thatcase the velocity-pairs should have pro-duced spontaneous judgments at once.Since they did not, this particular theoryof cue learning is not supported by ourresults.

SUMMARY

The common assertion that motion paral-lax is a cue for depth perception is vague.The optics of differential velocities of the ele-ments in a field of view were examined andtwo cases were distinguished: that of two ve-locities in the field and that of a gradient ofvelocities in the filed. The two-velocity caseyielded consistent perceptions of the separa-tion of one surface into two. The flow-gradi-ent case (motion perspective) yielded con-sistent perceptions of slant, or rate of recessionin depth. In neither case were there consist-ent judgments of distance from 0. Still an-other case, that of two different velocities of


two different spots in an otherwise emptyfield, did not yield consistent space percep-tions of any kind. Evidently Helmholtz waswrong about an "immediate apperception"of the distances of bodies or the depth betweenthem solely from an impression of the veloci-ties of spots in the field of view. The onlyconsistent or "immediate" impressions ob-tained were those of separation in depth (inresponse to a permutation of adjacent orderof texture), and recession in depth (in responseto a transformation of the texture).

These were spontaneous perceptions in thesense that no other information was given 0than that carried in the optical stimulation.When he was given verbal information aboutdepth in the two-velocity situation he wasable to correlate a judgment of depth with animpression of motion. But the correlationswere not perfect, and a minority of Os "saw"the depth. One might conclude from thesefacts that there are two kinds of optical stim-ulation for experiences of space: a kind whichrequires additional information to yield con-sistent judgments, and another kind whichdoes not require it—which is compelling orcoercive. The facts also suggest that thereare two kinds of experience of space: "empty"depth, as exemplified by one surface in frontof another, and "filled" depth, as exemplifiedby the slant or recession of a surface. Thedepth of a surface is perceived more consist-ently than is the depth of the space betweensurfaces, in our situation.

As regards the perception of absolute dis-tances, this probably depends on the percep-tion of a terrain or ground surface, the condi-tions for which were not reproduced in thepresent experiments. For the investigationof this problem, a very large field of view isrequired.

REFERENCESBOURDON, B. La perception visuette de

I'espace. Paris: Schleicher, 1906.GIBSON, J. J. The perception of visual sur-

faces. Amer. J. Psychol, 1950, 63, 367-384.

GIBSON, J. J. Optical motions and trans-formations as stimuli for visual perception.Psychol. Rev., 1957, 64, 288-295.

GIBSON, J. J., & CAREL, W. Does motionperspective independently produce the im-pression of a receding surface? J. exp.Psychol, 1952, 44, 16-18.

GIBSON, J. J., & GIBSON, E. J. Continuousperspective transformations and the per-ception of rigid motion. J. exp. Psychol.,1957, 54, 129-138.

GIBSON, J. J., OLUM, P., & ROSENBLATT, F.Parallax and perspective during aircraftlandings. Amer. J. Psychol., 1955, 68, 372-385.

GRAHAM, C. H. Visual perception. In S. S.Stevens (Ed.), Handbook of experimentalpsychology. New York: Wiley, 1951, 868-920.

GRAHAM, C. H,, BAKER, K. E., HECHT, M.,& LLOYD, V. V. Factors influencingthresholds for monocular movement paral-lax. J. exp. Psychol, 1948, 38, 205-223.

HELMHOLTZ, H. Physiological optics. Vol.III. J. P. Southall, Ed., Optical Soc.America, 1925.

HOCHBERG, J., & SMITH, O. W. Landing stripmarkings and the "expansion pattern": I.Program, preliminary analysis, and ap-paratus. Percpt. mot. Skills, 1955,2, 81-92.

KOFFKA, K. Principles of Gestalt psychology.New York: Harcourt, Brace, 1935.

SMITH, O. W., & SMITH, P. C. Interaction ofthe effects of cues involved in judgments ofcurvature. Amer, J. Psychol, 1957, 70,361-375.

TSCHERMAK-SEYSENEGG, A. Uber Paral-laktoskopie. Pfliig. Arch. ges. Physiol,1939, 241, 454-469.

VERNON, M. D. Cognitive inference in per-ceptual activity. Brit. J. Psychol., 1957,48, 35-47.

WERTHEIMER, M. Untersuchungen zurLehre von der Gestalt. II. Psychol.Forsch., 1923, 4, 301-350.

(Received July 24, 1958)

gibson (1959) motion parallax as a determinant of

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