Journal of

Experimental Psychology

VOL. 45, No. 4 APRIL, 1953

THE KINETIC DEPTH EFFECT

HANS WALLACH AND D. N. O'CONNELU

Swarthmore College

The problem of how three-dimen-sional form is perceived in spite of thefact that pertinent stimulation consistsonly in two-dimensional retinal imageshas been only partly solved. Much isknown about the impressive effective-ness of binocular disparity. How-ever, the excellent perception of three-dimensional form in monocular visionhas remained essentially unexplained.

It has been proposed that some pat-terns of stimulation on the retina giverise to three-dimensional experiences,because visual processes differ in thespontaneous organization that resultsfrom certain properties of the retinalpattern. Rules of organization aresupposed to exist according to whichmost retinal projections of three-di-mensional forms happen to producethree-dimensional percepts and mostretinal images of flat forms lead toflat forms in experience also. Thisview has been held mainly by gestaltpsychologists.

Another approach to this problemmaintains that the projected stimuluspatterns are interpreted on the basisof previous experience, either visual

1 Most of the work reported in this and thefollowing paper was done while the senior authorwas holder of a John Simon Guggenheim Me-morial fellowship.

or kinesthetic. However, such empiri-cistic assumptions do not explainmuch, unless it is made clear how thoseprevious experiences come about whoseinfluence is supposed to account forthe current perception. Kinestheticform perception itself presents far morecomplex problems than does three-dimensionality in vision, and recourseto kinesthesis appears at present quitefutile. Retinal disparity can of courseaccount for that previous visual expe-rience insofar as Ss with binocularvision are concerned. Whether in theabsence of binocular vision, e.g., incongenitally monocular Ss, head move-ment parallex can fully play the role ofbinocular parallex appears doubtful.It seems that all we have left to ac-count for an original experience ofthree-dimensional form in monocularSs is the assumption that certain pat-terns of retinal stimulation will natu-rally produce experience of solid form.However, once it is assumed that per-ception of three-dimensional form canfollow directly from retinal stimula-tion because of spontaneous organiza-tion of visual processes alone, there isno point in postulating an influence ofpast experience.

Unfortunately it appears that no onehas succeeded in formulating rules of

205

206 HANS WALLACH AND D. N. O'CONNELL

spontaneous organization adequate topredict which pattern of retinal stim-ulation will lead to perceived flatfigures and which one will producethree-dimensional forms. We havemade a vain attempt of our own andhave become convinced that the three-dimensional forms perceived in per-spective drawings, photographs, etc.are indeed a matter of previous expe-rience.2 In this situation the searchfor a visual process which can accountfor an original perception of three-dimensional form in monocular visionbecomes imperative. Such a processwill be described in this paper.

When one moves about, the retinalimage of solid objects lying to the sideof one's path not only expands but alsodistorts, because the objects are seensuccessively from different directions.More specifically, a retinal image dis-torts under these conditions as if thecorresponding object were rotatedthrough a certain angle in front of theeye of a stationary observer.

This fact suggests a simple techniquefor the investigation of the perceptualresults of these distortions. An objectis placed between a punctiform lightsource and a translucent screen and isrotated or turned back and forth. Itsshadow is observed from the other sideof the screen. The shadow-castingobject is placed as close to the screenas possible, whereas the distance be-tween the light source and the objectis made large. Owing to this arrange-ment isometric projection is closelyapproximated. The shadows of agreat number of three-dimensionalforms, solid or wire-edged, will be per-ceived as three-dimensional underthese circumstances. The shadows ofsome forms will look three-dimensionalonly in such a moving presentation;that is, in none of the positions through

5 Evidence supporting this point of view willbe reported in a subsequent paper.

which such a form passes during rota-tion will it cast a stationary shadowwhich looks three-dimensional. Withsuch forms one can study this effect inisolation. I t will be referred to by theterm "kinetic depth effect." I t isimportant because it answers ourproblem: It appears that the kineticdepth effect can cause a genuine per-ception of three-dimensional form in amonocular S whenever he moves andkeeps looking at an object which doesnot lie directly in his path.

Similar set-ups have been used before by Miles(3) and Metzger (2). Miles presented to Ss theshadow of a two-bladed fan wheel in rotation,the shaft of which was parallel to the screen onwhich the shadow was formed. His Ss reporteda large number of different motion patterns,most of them involving depth, but no attemptwas made to find out whether the object thatwas seen in motion was a good representation ofthe fan wheel whose shadow was presented.Metzger also was not primarily concerned withthe perception of three-dimensional form whichsuch a set-up can yield. In fact, he investigatedwith great thoroughness the effects of a veryspecial kind of arrangement which is not favor-able to the emergence of stable three-dimensionalforms. He had arrangements of vertical rodsrotate about a vertical axis and showed theirshadows in a low oblong aperture which hid theends of the rod shadowsfromview. AsinMiles'sexperiment the motion patterns seen by a givenS during an extended period of inspection werevery changeable. Moreover, naive Ss mostlydiffer among each other as to whether the firstmovement process which they perceive is inthree dimensions or takes place in a plane.Suggestion has a strong influence, in the courseof longer observation as well as initially. Weshall see below that the patterns of line shadowswhich Metzger presented to his Ss do not containthe condition essential for the kinetic deptheffect.

The depth observed in Lissajous figures (1, 4)is the result of complex effects and will be dis-cussed in a later paper.

EXPERIMENTS TO DEFINE CONDITIONSOF KINETIC DEPTH PERCEPTION

Experiment 1: Rotation of solids.—One of the figures which we presentedto many Ss was a solid block in the

KINETIC DEPTH EFFECT 207

FIG. 1. Solid form (A) used in Exp. 1, and twosamples (B, C) of its shadows

shape of a roof with sloping gables, asshown in Fig. 1A. This was rotatedcontinually about its longest axis.Figures IB and 1C show two of theforms of the shadow during rotation.When any one of the three figures isshown stationary to a naive S, it isdescribed as a two-dimensional figure.When the solid is slowly rotated sothat the shadow undergoes continuousdeformation, S sees a three-dimen-sional solid in rotation. The directionof the seen rotation may or may notcoincide with that of the object be-hind the screen, and this is in agree-ment with the conditions of stimulationwhich give no clue of the object's realdirection of rotation. Which one ofthe two directions of rotation is seenseems entirely a matter of chance, andwith prolonged observation S usuallyexperiences a number of spontaneousreversals of the direction of rotation.Occasionally an S sees for long periodsreversals after each rotation of 180°.

In experiments like this the impression ofthree-dimensional form is so natural that manySs who are not psychologists are not astonishedby their observations. They correctly assumethat behind the screen is just such an object asthey see. Only after reversals of the direction ofrotation have occurred do they begin to wonder.

Where the kinetic depth effect takes place, arigid three-dimensional form in rotation is seeninstead of the distorted two-dimensional figuregiven on the shadow screen. The distorting two-dimensional shape may occasionally be seen afterprolonged exposure of the same kinetic presen-

tation, or when one looks from a sharply obliquedirection'at the screen. The S's experience of acontinuously flowing form seems to him abnor-mal or unusual although this is exactly what isgiven on the retina.

The essential difference between this two-dimensional experience and the three-dimen-sional form which is usually seen seems to be thatthe latter is unchanging and rigid instead of everchanging and flowing. The changes in the shapeof the retinal image are accounted for by aperceived rotation of the three-dimensionalobject, whereas in the two-dimensional processthe seen movement distorts the form itself. Asfar as we can see, the distortions of the perceivedtwo-dimensional form agree closely with thechanges of the retinal image. But the perceivedthree-dimensional form is not determined merelyby what is presented on the retina at a givenmoment. A single one of the projections of theshadow-casting object which make up the chang-ing shapes of the shadow does not look three-dimensional. Only the sequence of changingshapes gives rise to the seen three-dimensionalform. In other words, a single projection causesa three-dimensional form to be seen only becauseit was preceded by a number of other projections.By itself, it simply does not convey enough dataabout the three-dimensional form which it repre-sents. The seen three-dimensional form is richerin structure than any single projection and it isbuilt up in a temporally extended process. Theindividual retinal image determines only whichaspect of the turning three-dimensional formappears to be given at the moment. Thus, per-ceptual experience far surpasses what one shouldexpect of a process determined by momentarystimulation and seems to a higher degree a prod-uct of the immediate past than of stimulationoccurring at a given moment.

Experiment 2: Partial rotation ofwire figures.—Experiments of the kindjust reported differ in two ways fromthe realistic situations in which thekinetic depth effect occurs. In thefirst place, a shadow-casting object isput through a complete rotation andproduces a pattern of distortion on thescreen which corresponds to that ob-tained when under natural viewingconditions an S moves completelyaround an object, which is hardly everdone. In the second place, in theshadow of a solid object an edge of thethree-dimensional form is visible only

208 HANS WALLACH AND D. N. O'CONNELL

FIG. 2. The wire "parallelogram" used in Exp. 2

for a comparatively short period,namely as long as it forms a contourof the shadow, whereas in the realisticsituation it usually can also be seenwhen it passes across the front of thefigure. We therefore performed quan-titative experiments with wire figureswhich of course show all edges con-tinuously, and had them turn back andforth through an angle of only 42°.

Figures 2 and 3 each show projections of twoof the wire figures used. The figure representedin Fig. 2 can best be described as a parallelogramcontaining one diagonal, which was bent alongthis diagonal so that the planes of the upper andthe lower half formed an angle of 110° with eachother. The other figure (Fig. 3A) consisted of apiece of wire twice bent to form part of whatmight be described as a triangular helix. Figure3B shows a view from the top. These figureswere turned back and forth through an angle of42° at a rate of one cycle per 1.5 sec. and theirdeforming shadows were shown to individual Ssone at a time for as many periods of 10 sec. aswere necessary to obtain a clear report. Aftereach 10-sec. exposure, S was asked for a report.

In the case of the parallelogram(Fig. 2) all of SO Ss sooner or laterduring the exposure periods reported

FIG. 3. The wire "helix" used in Exp. 2 (A)and its appearance from the top (B)

seeing a three-dimensional figure turn-ing back and forth apparently verymuch like the wire figure behind thescreen, except that it sometimes ap-peared to S in its inverted form. Inthe case of the "helix" 48 of the same50 Ss reported a three-dimensionalform like the wire figure and 2 Ss sawa flat zigzag line which distorted beforetheir eyes, a process which correspondsto the changing pattern of stimula-tion. Evidence that the three-dimen-sional forms which were perceivedwere due to the kinetic depth effectand that none of the projections repre-sented in the deforming shadow byitself would have been seen as three-dimensional was obtained in the fol-lowing way. To a new group of 22 Ssfive such projections of each figurewere presented individually in randomorder. They were the projections ofthe two extreme positions at which thefigures stopped and started to turn theother way and of three interveningpositions chosen to be at about 10°of rotation apart. None of thesestationary projections looked three-dimensional to any one of the 22 Ss.Positions intermediate between theones presented resembled them soclosely that it seems impossible thatthey would lead to a radically differentperceived form.

Often the turning wire figures wereseen three-dimensionally immediatelyupon presentation. Of 16 Ss for whomtime records were taken 11 reportedthe "parallelogram" in the correctthree-dimensional shape after the first10-sec. exposure period. In the caseof the "helix" only 4 of 16 Ss reportedits shape correctly after the first ex-posure. The reason for this differenceis yet to be investigated.

Once it has occurred, the three-dimensional impression is so strongthat one cannot voluntarily see thetwo-dimensional figure which is given

KINETIC DEPTH EFFECT 209

on the screen. It has been mentionedthat the perceived three-dimensionalfigure may resemble the inverted formof the wire figure rather than thatfigure itself. This is to be expected,inasmuch as a three-dimensional figureand its inverted form have identicalprojections, such that a given projec-tion is always a representation of both,a figure and its inverted form. Theadded fact that with prolonged ob-servation of the distorting shadowthe perceived three-dimensional figuremay spontaneously invert in Neckercubelike fashion is also a consequence.

Experiment 3: Rotation of a trun-cated cylinder.—A systematic investi-gation of the kinetic depth effect re-sulting from rotation of a solid wasattempted in the following manner.

A cylinder which is rotated about its axis castsa shadow which does not change in any way, butany cut that is taken off the cylinder and whichis not at right angles to its axis produces a charac-teristic deformation of its shadow. A large num-ber of wooden cylinders, about as high as wide,were made and cuts were varied systematically.The solid forms which were produced in thisfashion were shown in complete rotation to Sswho had no previous experience with our studies.

The results can be summarized inthe following way: (a) Shadows whoseonly deformation consists in an expan-sion and contraction in one dimensionwill look flat; a dark figure is seenwhich periodically becomes wider andnarrower. An example is the shadowof a rectangular block which is rotatedabout an axis parallel to a set of edges.(b) Shadows which display contourlines that change their direction andtheir length will appear as turningsolid forms. The roof-shaped figuredescribed above (Exp. 1) is an ex-ample; the shadow contour producedby an edge of a gable tilts and changesits length simultaneously (compareFig. IB and 1C). (c) Curved contourswhich are deformed without display-

ing a form feature which identifies aspecific point along the curve are seenas distorting, often even if for somereason the shadow is seen as a three-dimensional form. This peculiarity isin disagreement with our descriptionof the kinetic depth effect and hasdelayed our work for years. It is nowclear that the perceived distortions ofdeforming curved contours are notrelated to the kinetic depth effect atall. They will be dealt with in alater paper.

Experiment 4: Rotation of straightrods.—When it became clearly recog-nized that shadows which display con-tour lines that change their directionand length will appear as turning solidforms, we checked whether this wouldalso apply to single lines. Will a de-tached line which changes its directionon the screen and its length at thesame time display a kinetic deptheffect, i.e., will it appear to tilt intodepth in such a way as to account forits shortening ? The following experi-ments show that this is the case.

When a rod is fastened to the end ofa vertical shaft at an angle of, say, 45°and is rotated about this shaft, theshadow which it produces tips fromside to side. From a tilt of 45° towardthe left, the shadow rights itself andgoes through the vertical into a tilt of45° toward the right and back throughthe same positions. At the same timeit shortens and lengthens periodically.Its end points move on horizontal linesacross the screen. This process is in-variably seen as a motion in threedimensions, as nearly as one can tellexactly like the real movement of therod behind the screen, a rotationdescribing a conical surface about avertical axis.

This set-up lends itself to a varia-tion which is interesting because thethree-dimensional motion which isperceived is a different one from that

210 HANS WALLACH AND D. N. O'CONNELL

which the rod behind the screen under-goes. The shaft on which the rodturns is tilted toward or away fromthe screen by 15° or 20°. This changesthe pattern of expansion and contrac-tion of the rod shadow completely; itsend points now move on elliptic pathson the screen. Only rarely does therod motion seem to describe a circularcone like the real movement of the rodbehind the screen. In most cases amovement is seen in which the move-ment component of tilting toward oraway from S is much smaller than thelateral movement component suchthat the surface described is that of anelliptic cone. Whereas the real rodgoes in one rotation from a tilt towardS into a tilt away from him, the per-ceived motion of the rod is restrictedeither to a changing forward tilt or toa changing tilt away from S. Eitherone of these two different movementscan of course be perceived because,like a three-dimensional figure and itsinverted form, they would if they wereobjectively given produce the sameprojection.

It seems that what distinguishes in these ex-periments perceived movement from the two-dimensional process which is given on the screenand therefore on the retina is the fact that theperceived rod is seen with a constant length.Tilting into depth is seen instead of shortening.Inasmuch as the rod as a whole must anyway beseen to move, this tilting motion is only a modifi-cation of a necessary process and not an addedchange, which is what a perceived stretching andshrinking would amount to. Thus, a tendencyto see one motion instead of the two simultaneousmovements of the two-dimensional process (atipping from side to side, and a stretching andshrinking) may be held responsible for the deptheffect. Another possibility would be a selectiveprinciple according to which a line of constantlength is seen rather than a changing one. Nodecision between these two possibilities can bemade on the basis of our present results.

Experiment 5: Rotation of T and Afigures.—It is important to realize thata shadow line must undergo both a

displacement and a lengthening orshortening in order to produce akinetic depth effect. Both thesechanges must be given together. Achange in length alone is not sufficientto produce a reliable kinetic deptheffect. This is shown in the followingexperiment.

A piece of 1/16-in. wire 4 in. long was fastenedat right angles to a vertical shaft of the samediameter so that the two formed a figure ofT shape. When this form was turned back andforth about the vertical shaft through an angleof 42°, the shadow of the horizontal wire formeda line of 105-mm. length which periodically con-tracted to a length of 75 mm. and expandedagain. We presented it with a rate of one periodper l.S sec. for 10 sec. to 24 Ss.

Eighteen of 24 Ss saw a line in theplane of the screen expanding andcontracting and only 6 Ss perceivedthe line turning in the third dimension.Had the horizontal wire been in anoblique position with respect to theaxis of rotation so that its shadow hadshown a displacement in addition tothe change in length, the kinetic deptheffect would have been obtained withthe majority of the Ss, as the experi-ment with the oblique rod wouldpredict.

Because of its importance we hadthe experiment with the T figurerepeated by another E and obtainedthe same result: Of 40 Ss, 30 saw thehorizontal line expand and contract inthe plane of the screen and 10 saw itturn.

These results must be comparedwith those of a different wire figurewhich does produce a kinetic deptheffect under identical conditions.Comparable data come from a shadowpresentation of an equilateral triangle.Its sides consisted of wires 5 in. inlength, and one of them was tilted by15° against the horizontal. When thisfigure was turned back and forth, theshadow of one of its sides changed

KINETIC DEPTH EFFECT 211

from a slope of 45° to one of 57° andthus presented conditions favorable tothe kinetic depth effect. Of 20 Sswho observed the triangle for 10 sec.17 reported a turning in depth andonly 3 expansion and contraction.(With such a plane figure the kineticdepth effect consists, of course, in theperception of a plane figure that turnsinto depth.) This score is to be com-pared with that for the T figure whereonly one-third of the Ss saw a turning.The difference is reliable at the .001level of confidence.

Still, the 6 and 10 Ss who saw theT figure turning in depth need beaccounted for, if our claim is correctthat they are not the outcome of agenuine kinetic depth effect. Herethe following result is significant.When the T figure was presentedfollowing the presentation of the tri-angle, IS out of the 17 Ss who saw thetriangle turn saw the T figure turnalso. (Three Ss who saw the triangleexpand and contract reported thesame for the T figure.) In otherwords, when a figure that Ss saw turn-ing preceded the presentation of theT figure, a large majority of Ss saw itturning also. This shows a stronginfluence of a previous perception onthe manner in which the T figure isseen, for only one-third of the Ss sawthe T figure turning when it was givenas a first presentation. This differ-ence is significant at the .OS level ofconfidence. We suggest that in thecase of these latter Ss some such influ-ence of a previous experience, thougha more remote one, has been at workalso.

We are inclined to conclude that aline which changes in length but is notdisplaced at the same time does notgive rise to the kinetic depth effect.This agrees well with the alreadyreported finding that a solid shadowwhich expands and contracts only in

one dimension will not showkinetic depth effect either.

the

THE ACCURACY OF KINETIC DEPTHPERCEPTION

When we described the kineticdepth effect in complex figures, westated that the change in the retinalimage is accounted for in perceptionby a rotation of a three-dimensionalform. This implies, of course, that areal form which is like the perceivedone would in rotation produce asequence of retinal images very similarto that actually given, or, in otherwords, that the perceived form re-sembles closely the shadow-castingobject. That this is the case has beenconfirmed by many Ss to whom theshadow-casting object was directlyshown immediately following thekinetic presentation.

For more stringent confirmation severalmethods were used: In the case of the "helix"(Fig. 3), Ss were asked to bend a piece of wireinto the shape of the figure which they saw turn-ing on the screen. Only Ss who reported seeinga three-dimensional form turning back and forthwere given this test. Of 29 Ss, 13 made goodreproductions, 12 fair ones, and only 4 Ss madepoor reproductions. Eleven of the 12 Ss whosereproductions were fair were later asked to makeanother reproduction while they looked directlyat the turning wire figure. Of these only 7 wereable to make good reproductions and 4 made onlyfair ones under these conditions. Altogetherthere were 8 Ss who could make only fair repro-ductions when they viewed the figure directly.

In the case of the parallelogram (Fig. 2), theaccuracy of perception by virtue of the kineticdepth effect was checked by showing S foursimilar wire figures and asking him to pick outthe one that matched best the form he saw turn-ing on the screen. As mentioned earlier, thebend in the shadow-casting figure amounted toan angle of 110° between the planes of the twotriangles which made up this figure. Thi6angle is, of course, characteristic of its three-dimensional form. If this angle were 180°, thewire figure would be plane. In our four modelsthe bend amounted to angles of 95°, 110°, 125°,and 140°, respectively. The one with the 110°angle was an exact copy of the shadow-casting

212 HANS WALLACH AND D. N. O'CONNELL

figure; the other three models had the sameheight as the standard and were made to produceprojections on the frontal plane which were iden-tical with the projection of the standard. Thefour models were inserted in a wooden block andhanded to S. The choices of 30 Ss who had pre-viously reported seeing the three-dimensionalfigure were 8, 17, 4, and 1 for the 95°, 110°, 125°,and 140° figure, respectively. Only one S foundit impossible to make a choice. It is unfor-tunate that we did not include one more modelwith a still sharper angle, but even so the datagive a rough idea of the accuracy of the percep-tion of three-dimensional form which is based onthe kinetic depth effect.3

Experiment 6: Rotation of luminousrod.—Another attempt to obtain ameasure of the accuracy with whichdepth perception functions by virtueof the kinetic depth effect was madeemploying a straight line which rotatedin an oblique plane. When a line isturned in a frontal-parallel plane aboutits midpoint, the end points of itsretinal projection move on a circle.However, when it rotates in an obliqueplane, its retinal image changes inlength as it turns, and its endpointsmove on an elliptic path. Therefore,when in the dark a luminous line isrotated in a frontal-parallel planeabout its midpoint and is exposedfrom behind an elliptic aperture, itsretinal projection will be the same asthat of a line which turns in an obliqueplane, for the aperture causes the lineto be visible with the same changes inlength. If the motion of the line thatrotates in an oblique plane can becorrectly perceived with the help ofthe kinetic depth effect alone, then theline rotating behind an elliptic aper-ture should also appear to rotate in anoblique plane, because the two linesproduce identical stimulation so far asthe kinetic depth effect is concerned.Other cues for depth perception as,

3 It should be noted that a turning by 42°produces only a moderate distortion of theshadow. Its width which is most stronglyaffected suffers a reduction of only 27%.

for instance, retinal disparity, wouldgive rise to experienced rotation in anoblique plane only in the first case.Thus when the rotating line behindthe aperture is presented to a naive Sand he perceives it turning in a prop-erly oblique plane, one can be surethat this is due to the kinetic deptheffect. By this procedure, as by theuse of the shadow screen, the effectcan be studied in isolation; other cuesfor depth perception would tend onlyto prevent the line from turning in anoblique plane.

A J-in. lucite rod, approximately 23 in. long,served as light source for the luminous line. Itsends were flat and finely ground to admit amaximum of light. They were inserted in metalcaps which contained hidden flashlight bulbs andalso served as mountings. The light from thesebulbs made the lucite rod appear to glow evenlyover its whole length. The rod was inserted in aU-shaped sheet-metal trough of proper lengthand attached by the mountings. A bushing wasfastened to the back of the trough at its midpointand attached to the horizontal slow shaft of areduction gear motor, so that the lucite rod couldbe turned in a vertical plane. The trough androd were covered by a long strip of cardboard intowhich was cut an aperture 22 in. long and \ in.wide. Through this aperture part of the rod'ssurface was visible. In front of this apparatuswas a frame to which cardboards with differentelliptic apertures could be attached parallel tothe plane of rotation of the rod. Three differentelliptic apertures were used. They were 40 cm.long and 35 cm. wide, 39.S cm. long and 28.9 cm.wide, and 40 cm. long and 20.6 cm. wide, respec-tively. They produced projections of the turn-ing luminous rod identical with the projectionsproduced by a luminous line that turns in a planeforming an angle of 29°, 46°, and 59°, respec-tively, with the plane of the aperture. Theywere attached with the large axis of the ellipticopening in vertical position.

The S was seated in front of this apparatus ata distance of 9 ft. He had before him a smalltable covered with a light gray cardboard. Ametal rod was joined at right angles to a shaftwhich was fastened vertically to the table, sothat the rod could be swung around in a planeparallel to the table top about an inch above it.A degree scale was marked out on the cardboardby which the position of the rod could be read.With the help of the rod, S could indicate theposition of the plane in which the luminous line

KINETIC DEPTH EFFECT 213

seemed to turn. A darkroom amber bulb illu-minated this arrangement in such a way that Scould see the rod but not the scale markings andthat the remainder of the room was completelydark. After each setting of the rod E asked S toclose his eyes and then read the scale with aflashlight.

During testing E asked S to look at theluminous line before him and close one eye, andthat eye was covered. The luminous line which,when presented in the appropriate elliptic aper-ture, produced the projection of a 46° tilt wasset into clockwise rotation at a rate of onerevolution in 10 sec. When S reported that itturned in an oblique plane, he was asked to turnthe measuring rod before him into a positionparallel with that of the luminous line in rota-tion. This was repeated with the 59° and the 29°apertures, and thereafter the three apertureswere used twice more in random order for thepurpose of practice. Neither in this practiceperiod nor later during the experimental trialswas S told whether his settings were correct ornot correct. No time limit was set on the pres-entation of the revolving line and S made hissetting when he felt ready. After a rest periodof 3 or 4 min. the experimental series began. Itconsisted of nine presentations, that is, each oneof the three apertures was presented three timesin random order.

The means and SD's of the IS meansof the three measurements for each ofthe three degrees of tilt were 14.9(SD = 6.6), 44.0 (SD = 3.4), and59.8 (SD = 4.4) for the 29°, 46°, and59° tilt, respectively. There was nooverlap between the means of the set-tings by individual Ss from one tilt toanother, and there was no overlapbetween the individual settings whicha given S made for the three tilts.

Where projections of tilts of 46° andof 59° were presented, the averages forall Ss came close to the expected val-ues. However, in the case of the 29°tilt, the average of 14.9 deviates sig-nificantly from this value; only oneindividual setting out of 45 is as highas, or exceeds 29°.

Why this is so is not clear. However, itshould be pointed out that the change in lengthwhich a line turning with a 29° tilt undergoesamounts only to 12.5% and one of 14.9° tilt (thevalue of the average) only to 3.4%. In other

words, a tilt of 14.9° produces a change in lengththat is very likely below the limen. Yet, thatdoes not necessarily mean that those Ss whogave settings of 15° or lower did not receiveeffective stimulation for a tilt. Whereas thesmall angles of tilt (due to the negligible changeof the cosine function in this range of values)probably do not lead to a change in lengthsufficient to produce a kinetic depth effect, set-tings of such low values do not indicate that notilt was perceived when these settings were made.In experience, a tilt of 15° is of distinct signifi-cance, and objectively conditions of stimulationof 29° were given.

It would have been important to find outwhether these results can be improved by makingthe luminous line wider. To make it widerwould have the advantage that the contractionof the line would be given by a change in itsproportions, that is, in figural terms, rather thanby a change in its absolute length. Improvedresults would indicate that change in proportionsis effective in producing the kinetic depth effect.Unfortunately, this variation could not be donewith the present set-up, because a wider linewould have shown up the intersections with theelliptic aperture by their changing obliqueness.A more expensive manner of presentation wouldbe needed.

OTHER FACTORS IN KINETICDEPTH PERCEPTION

Experiment 7: The effect of angleconstancy.—Such a variation of theexperiment might have contributed tothe solution of the following problem.It has been reported that shadows ofsolid blocks will produce the kineticdepth effect only if they have contourswhich are displaced and change theirlength simultaneously. Should weassume then that the presence of suchcontours solely accounts for the kineticdepth effect in complex forms, im-parting their depth to the whole figure,or do complex forms produce such aneffect in their own right? Just as wehave considered the possibility that aline is seen to move into the thirddimension to account for the givenchange of its retinal image while it isperceived with constant length, wemight assume a tendency to see in

214 HANS WALLACH AND D. N. O'CONNELL

FIG. 4. The figure used in Exp. 7

general rigid, unchanging forms in-stead of the given distorting shapes.For the present this question mustremain unanswered.

However, a question which can beconsidered a part of the question justraised was actually put to a test.Most shadows of turning figures donot only display contours which aredisplaced and change their length;their angles also change. Is there aseparate tendency for angles to remainconstant which produces kinetic deptheffects ?

To answer this question we used afigure which consisted of three rods allmeeting in one point under angles of110° and forming a wire-edged repre-sentation of an obtuse corner (Fig. 4).When this figure was turned back andforth through an angle of 42° and itsshadow was shown to 56 Ss who beforehad seen its stationary shadow as two-dimensional, S3 Ss reported seeing arigid obtuse corner. In this presenta-tion two of the three dark lines form-ing the shadow were not only displacedbut also underwent considerablechanges in length.

Entirely different results were ob-tained when the length of the shadowlines was made indefinite. To achievethis, the shadow screen was coveredwith a cardboard with a circular aper-ture where the shadow of the cornerfigure fell on the screen. The size ofthe aperture was so chosen that theends of the shadow lines were alwayshidden from S. Thus, only movementof the corner point, angular displace-

ments of each of the three lines, andchanges of the angles which theyformed with each other were visible.As the corner point shifted sideways,one of the lines seemed to move fartherunder the aperture edge and anotherone seemed to pull out from under it,and the length of all three of themseemed indefinite.

All 22 Ss employed in this experi-ment reported seeing a flat figure whichdistorted. Had the kinetic deptheffect occurred, the Ss would haveseen instead a rigid three-dimensionalform with constant angles. However,no such effect was observed wherechanges in the length of the lineswhich constituted the figure were notgiven, because that length was indefi-nite. We may conclude that a dis-placement of lines which is linked onlywith a change of angles does not giverise to the kinetic depth effect; dis-placement of lines and change in theirlength is needed. The question re-mains unanswered whether lengthmust be understood only in absoluteterms, or whether change in propor-tion has an effect of its own.

Experiment 8: Variation of distancesbetween objects.—Not only are the ret-inal images of solid objects deformedwhen one moves about, the same istrue to various degrees of the projec-tion of the whole environment. Thatthe objects which make up the envi-ronment are seen arranged in three-dimensional space and with unchang-ing distances between each other mayalso result from a kinetic depth effect.Just as some of the contours of solidobjects produce appropriately chang-ing retinal projections when the objectsare seen from different angles, the pro-jections of many of the intervalsbetween objects change their lengthand their direction when one movesabout. That this has the effect ofproducing visual depth can be demon-

KINETIC DEPTH EFFECT 215

strated with the shadows of an arrange-ment of several objects on a rotatingplatform.

We used spheres supported by thin verticalrods because the shadow of a sphere in rotationdoes not change its shape and will therefore notproduce a kinetic depth effect of its own. Fourspheres of 1 3/16-in. diameter were arranged atthe corners of a square concentric with the plat-form. The four rods were all of different heightso that all the intervals between the shadows ofthe spheres were periodically oblique when theplatform turned, and changed length and direc-tion simultaneously. The lower part of thescreen was covered so that the shadow of theturntable itself was hidden. The arrangementwas turned at a rate of one revolution in 5 sec.and was exposed to individual Ss for 20 sec.

Under these circumstances all 30 Sswho took part reported the spheres tomove in three dimensions. - Twenty-four Ss saw the spheres in a rigidspatial arrangement which turnedabout its center just like the actualarrangement behind the screen. Theothers saw them move in open singlefile in snakelike fashion into depth.In this latter motion only the shorterintervals between spheres are rigidlymaintained, and each sphere changesdirection of rotation with each excur-sion; but there can be no doubt thatthis is an incomplete form of a kineticdepth effect. It should be mentionedthat IS of the 30 Ss had no otherexperience with these shadow experi-ments except for another experimentwith the spheres which will be reportedbelow. It is apparent that the kineticdepth effect will readily yield a per-ception of a rigid spatial arrangementof unconnected objects.

Experiment 9: Variation of distancesbetween objects.—The arrangement ofExp. 8 offers still another opportunityto check on our finding that a linemust change both in length and indirection in order to produce a ki-netic depth effect. From our experi-ments with solid blocks and with the

T figure we concluded that a shadowwhich merely expands and contractsin one dimension will not give rise tothe effect. Here we set out to showthat the same is true for intervalsbetween objects; we modified theexperiment with the spheres to corre-spond to these experiments.

All the rods were given the same height sothat the spheres were aligned on a horizontalline and the intervals between the shadowschanged in length only. This arrangement wasshown to the same 30 Ss and under exactly thesame conditions that prevailed in Exp. 8, butwas presented prior to it. The fact that theT figure proved so susceptible to the influence ofprevious perceptions made this sequence advis-able. The experiment with the luminous rodwhich has been reported at length was done withthe same Ss in between the two experiments withspheres.

As in the case of the T figure, onlya minority of the Ss now saw move-ment in three dimensions, namely 10out of 30. The difference betweenthis result and that of Exp. 8 is reliableat the .03 level of confidence. Of theIS naive Ss, 12 saw the shadows moveback and forth in the plane of thescreen, 1 S reported movement inthree dimensions, and 2 saw in thebeginning of the observation periodthe plane and later the three-dimen-sional version. For the other groupof IS Ss who had observed the shadowsof some wire figures before, the num-bers were: 8 flat, 2 three-dimensional,and 5 first flat and later three-dimen-sional. When these results are com-pared with those of the previousexperiment where imaginary linesconnecting sphere shadows changedboth in length and in direction, itbecomes again apparent that these areessential conditions for the kineticdepth effect and that a mere expandingand contracting of retinal distances isinsufficient.

This is the reason for our view thatMetzger's work (2) is not directly con-

216 HANS WALLACH AND D. N. O'CONNELL

cerned with the kinetic depth effect.He exposed shadows of arrangementsof vertical rods whose changing pat-terns presented Ss with rectangularintervals which changed in width only.No other deformations were visible,because no marks were distinguishablealong the shadow lines, and the latterended only at the edges of the aperturein which they were given. As withthe aligned spheres, no reliable deptheffects are produced spontaneously innaive Ss with such an arrangement.Whether Metzger's work contributesto an understanding of the kineticdepth effect remains to be seen whenmore of the nature of the effect isknown.

Experiment 10: Effect of set.—In ourexperiments, the kinetic depth effectresults in two perceptual character-istics: (a) a turning in the depthdimension and (b) three-dimensional-ity of form. However, when the effectis observed under realistic conditions,namely when by moving about oneobtains a changing retinal projectionfor a stationary solid object, no turn-ing is perceived. The reason for thisis that the object remains in unalteredrelation to its environment withrespect to which S perceives himselfmoving. Thus, only three-dimension-ality and rigidity of form, seen insteadof the deforming two-dimensional pat-tern which is given on the retina, arehere the overt manifestations of thekinetic depth effect.

The fact that under realistic condi-tions the object remains in unalteredrelation to its environment needs someconsideration, because this is not so inour experiments. There the deform-ing shadow of the object denotes aturning while the environment, that is,the screen on which the shadow isshown, remains stationary. Under

realistic conditions, on the other hand,both the object and its environmentare given retinally with deformationswhich denote a turning in relation toS. The kinetic depth effect trans-forms the deforming retinal projectionof the environment into a three-dimensional structure, and once thishas happened, the perception of theobject as a three-dimensional form isprobably facilitated. That such afacilitation is likely to take place isindicated by experimental resultswhich show a strong influence of pre-ceding exposures on the readiness withwhich the kinetic depth effect occurs.

The following results may serve asan example. When the "helix" (Fig. 3)was shown following the presentationof one or two figures which readilyshow the kinetic depth effect, all of 18Ss saw it as three-dimensional duringthe first 10-sec. exposure. This is tobe compared with results in Exp. 2according to which only 4 out of 16naive Ss gave a clear report of three-dimensional form for this figure afterthe first 10-sec. exposure.

The question of how this influence is exertedmust remain open. It is conceivable that itconsists merely in a set to see a turning in thedepth dimension. However that may be, theinfluence is a strong one.

If such an influence is effective between suc-ceeding exposures of different figures as shown,it should be expected to work also within a givenvisual field. Under realistic conditions, once theenvironment of a given object is perceived as arigid spatial structure which changes its orien-tation with respect to the moving S, such aninfluence should facilitate a kinetic depth effectfor the object. There are several reasons whythe environment should easily be seen in thisfashion. To mention only one: the environmentwill usually contain familiar features whichwould cause the facilitating influence of previousexperience with similar situations to operate.Thus we have good reason to believe that thekinetic depth effect takes place more readilyunder realistic conditions than it does in ourshadow-screen experiments.

KINETIC DEPTH EFFECT 217

SUMMARY

When a three-dimensional form,solid or wire-edged, is turned behind atranslucent screen and its shadow onthe screen is observed, the shadowwill appear as a rule as a three-dimen-sional rigid object which turns, quitesimilar to the physical object behindthe screen. This happens notwith-standing the fact that S actuallylooks at a plane figure which is beingdeformed.

One condition seems to be essentialfor the occurrence of this effect: theshadow must display contours or lineswhich change their length and theirdirection simultaneously. If this con-dition is not fulfilled, a plane distort-ing figure like the one on the screen isperceived unless an influence of pre-vious perception operates.

This effect is believed to operatewidely under ordinary circumstances.When one moves about, objects nearone's path are successively seen from

different angles, and this change inorientation of the object to S is thesame as occurs when the object isturned by an equivalent angle. Thus,the object's retinal projection under-goes the same deformations as doshadows in our experiments, and thesame perceptual processes shouldresult.

(Received August 11, 1952)

REFERENCES

1. FISICHELLI, V. R. Effect of rotational axisand dimensional variations on the rever-sals of apparent movement in Lissajousfigures. Amer. J. Psycho!., 1946, 59,669-675.

2. METZGER, W. Tiefenerscheinungen in op-tischen Bewegungsfeldern. Psychol.ForscL, 1934, 20, 19S-260.

3. MILES, W. R. Movement interpretation ofthe silhouette of a revolving fan. Amer.J. Psychol, 1931, 43, 392-405.

4. PHILIP, B. R., & FISICHELLI, V. R. Effect ofspeed of rotation and complexity of pat-tern on the reversals of apparent move-ment in Lissajou figures. Amer. J,Psycho!., 1945, 58, 530-539.