examination of gibson's psychophysical

Psychological Bulletin1964, Vol. 62, No. 3, 180-196

EXAMINATION OF GIBSON'S PSYCHOPHYSICALHYPOTHESISl

WILLIAM EPSTEIN AND JOHN PARK

University of Kansas

The experimental evidence regarding Gibson's psychophysical hypothesisis examined. The presentation is divided into 2 sections dealing withstatic and transforming stimulation, respectively. Under the formerheading the stimulation for surface, slant, and depth is considered.Under the latter heading the investigations of motion perspective, con-tinuous perspective transformations, and size-transformations are ex-amined. 2 general conclusions emerged from this examination: thepsychophysical hypothesis has not been unequivocally confirmed andGibson's theory requires revision to make explicit several recurrentimplicit premises.

One of the major contemporary the-oretical accounts of perception is Gib-son's (1950b, 1959, 1963) psychophys-ical theory. Unlike other theories, forexample, Gestalt and transactionalism,Gibson has attempted to develop a S-Raccount of perception; one which doesnot introduce intervening variables suchas sensory organization or neo-Helm-holtzian assumptive worlds. The cen-tral proposition of Gibson's (1959)theory is the generalized psychophysicalhypothesis:

for every aspect or property of the phe-nomenal world of an individual in contactwith his environment, however subtle, thereis a variable of the energy flux at hisreceptors, however complex, with which thephenomenal property would correspond if apsychophysical experiment could be per-formed [p. 465].

The objective of this paper is to eval-uate the evidence for this hypothesis.

The similarity between Gibson's hy-pothesis and the older discredited con-stancy hypothesis is evident. Gibson'shypothesis, however, is less vulnerable.

1 This article was written with the supportof Research Grant MH 04153-04 to the firstauthor by the National Institute of MentalHealth of the United States Public HealthService.

180

Unlike the earlier hypothesis, Gibson'sposition does not presume a picturetheory of the proximal-perceptual rela-tion. Gibson requires retinal correlates,not retinal replicas. A more importantsource of strength is Gibson's concep-tualization of the stimulus. In theearlier view the stimulus was a static,nonchanging, local correspondent of thedistal source. As long as this view pre-vailed it was a simple matter to con-tradict the constancy hypothesis bydemonstrating the equivocality of thedistal-proximal and proximal-perceptualrelationships (Koffka, 1935, pp. 75-105). This type of critical analysis isnot so readily applicable when Gibson's(1959, 1960) view of the stimulus istaken into account. In Gibson's (1959)view the effective stimulation for per-ception must be sought "in a texturedoptical array, supplemented by thetransformations relating a simultaneouspair of them, and by the transforma-tions relating a sequence of momentaryarrays [p. 474]." The stimulus is or-dinal—a pattern or gradient of stimula-tion. The order may be sequential aswell as spatial. Sequential ordinal stim-ulation refers to the lawful transforma-tions of stimulation which occur wheneither the subject or the object is in

GIBSON'S PSYCHOPHYSICAL HYPOTHESIS 181

motion. It is important to note that inGibson's view (see especially 1957 andGibson & Gibson, 19S7) the change instimulation is a stimulus to which thesubject can respond. On other occasions,the subject may respond to the aspectof stimulation which remains invariantin the flux of stimulus transformations.The invariants uniquely specify thesource of stimulation, and the percep-tual apparatus is geared to extract theseinvariants, thereby achieving veridicalperception. Thus, in Gibson's view,stimulation undergoing change is moreinformative than static stimulation sincean instance of static nontransformationcan rarely specify its source. Gibson'sconceptualization of stimulation pro-vides him with the grounds for rejectingthe frequent assertion that the distal-proximal and proximal-perceptual rela-tionships are fundamentally ambiguous.Once this assertion can be denied theway is opened for a retinal account ofperception.

In one sense the greater portion of allexperimentation on perception could beconsidered to have bearing on Gibson'shypothesis. However, our treatment willbe restricted mainly to those studieshaving the following two characteris-tics: (a) The main objective of theexperiment was to examine psycho-physical correspondence, (b) The ex-periment has sought to manipulate thetype of visual input, that is, optic array,which Gibson has stressed. For thisreason we have excluded discussion ofother studies which might be consideredrelevant, for example, the work re-viewed by Epstein, Park, and Casey(1961) and Epstein and Park (1963).The discussion will be divided into twoparts, dealing with static and trans-forming stimulation, respectively.

PSYCHOPHYSICAL CORRESPONDENCEUNDER CONDITIONS OF STATIC,

NONTEANSFORMINGSTIMULATION

This section will review the experi-mental studies of the perception of sur-face, slant, and distance.

Stimulation for the Perception ofSurface

"According to what will here becalled the texture-hypothesis, the stim-ulus for a visual surface is a fully dif-ferentiated, sharp, or textured retinalimage [Gibson & Dibble, 19S2, p.414]." Evidence for this hypothesis isadduced by Gibson from a series of ex-periments with the Ganzfeld. In an ex-periment similar to Metzger's (1930)prototypal research, Gibson and Dibble(1952) seated the subject before a graywall of coarse-textured plasterboardwhich filled nearly the entire visualfield. With full illumination, the wallappeared surfacelike and visibly tex-tured. As the illumination of the wallwas gradually reduced, the texture van-ished, and the impression of hardnesswas replaced by that of a fog. In asimilar manner the impression of sur-face vanished when Gibson and Waddell(1952) produced homogeneous visualstimulation by means of translucenteyecaps. These results are in accordwith the findings of other investigators(Cohen, 1957; Hochberg, Triebel, &Seaman, 1951; Metzger, 1930) and ap-pear to support the hypothesis that theperceived hardness of a surface is re-lated to the steepness of the gradientsof luminous intensity in the retinalimage.

While it appears reasonably certainthat texture is sufficient for the percep-tion of a surface, there is evidence thatit is not necessary. Gibson and Dibble(1952) found that a homogeneous tex-

182 WILLIAM EPSTEIN AND JOHN PARK

tureless surface viewed through a smallaperture appeared to be a hard surfacein the plane of the reduction screenrather than a film in the aperture. Theauthors suggest that the effective stim-ulus may have been the steep intensitygradient at the contour. Cohen (19S7)found that a steep gradient of intensitybetween a homogeneous disc and a ho-mogeneous field produced the impres-sion of a figure having a hard surfaceand lying on a foggy ground.

Stimulation for the Perception of Slant

Gibson (19SOa) proposed that "slantat any point may be given by the rateof increase of density of the texture atthat point [p. 371]." This hypothesishas had to be revised in the face ofevidence that rate of increase of texturedensity is not a sufficient stimulus forthe veridical perception of slant. Sincea gradient of texture density merelyspecifies a family of tridimensional ar-rangements, it is understandable thatthe corresponding percept may be var-iable. In addition, slant is generallyunderestimated when texture gradientis the chief or only cue.

Underestimation has been found byGibson (19SOa), Gruber and Clark(1956), and Clark, Smith, and Rabe(19S6). The stimuli were textured sur-faces presented at several degrees ofslant, or projections of lantern slidesmade by photographing textures at sev-eral slants. The textures employed werevarious: bricklike, mottled, or composedof irregular light dots on dark grounds.Outline perspective, binocular cues, andmotion parallax were eliminated. Per-ceived slant increased as the steepnessof texture gradient increased. Hence itwas concluded that a retinal gradient oftexture density can, in isolation fromother factors, determine perceived slant.Nevertheless, slant was underestimated(see Gruber & Clark, 1956). Althoughthe amount of underestimation was con-siderably less, some underestimation oc-

curred even for regular textures con-sisting of repeated evenly-distributedelements with linear perspective andfamiliar shape. These results may havebeen caused in part by the tendency ofperception to conform to the slant ofthe reduction screen.

These experiments failed to observethe distinction between optical slantand geographical slant. Optical slant isdependent only on the geometrical re-lation of a surface to the eye, whereasgeographical slant is dependent on therelation of the surface to other parts ofthe world or to gravity. By creatingan incongruency between the reference-axes of the eye itself and the reference-axes of their experimental room, Gibsonand Cornsweet (1952) produced a sit-uation in which the two kinds of slantcould be perceived separately. The sub-ject's head was rotated 45 degrees tothe left around its vertical axis and setat a 4 5-degree angle to the walls of theroom. The subjects were able to deter-mine accurately the point at which arotating textured surface reached eachof two normal positions: perpendicularto the line of sight (a judgment ofoptical slant) or parallel to the walls ofthe room (a judgment of geographicalslant). The results indicate that the twokinds of slant can be perceived inde-pendently, and that optical slant corre-sponds to the gradient of density oftexture at the fovea, while geographicalslant does not.

Gibson, Purdy, and Lawrence (1955)investigated the role of texture densityby means of an optical tunnel, a devicecomposed of a set of plastic sheets,alternately black and white, with cir-cular apertures, set one behind the otherso as to project onto the retina a set ofconcentric rings of alternating high andlow intensity. When subjects with mo-tionless heads and monocular visionviewed a tunnel having a zero gradientof density, they reported seeing some-thing ambiguous, something which flue-


tuated between flat and deep. Whensubjects were given another presenta-tion of this same pseudotunnel usingboth eyes and a third presentation usingboth eyes without a biting board, theyreported a surface with extended depthwhich approached the actual depth ofthe pseudotunnel. When the peripheral-to-central gradient of disparity was re-versed by a pseudoscope, the subjectssaw a striped, convex, truncated coneprotruding from a background. It ap-pears that an unambiguous appearanceof slant results from a zero gradient ofdensity only when it is supplementedby some other stimulus such as a gra-dient of disparity or deformation. Gib-son, Purdy, and Lawrence (1955) con-cluded that a gradient of texture densitycannot by itself compel a perceptionof corresponding slant because the gra-dient merely specifies a family of tri-dimensional arrangements rather thana particular distal stimulus situation.For example, a gradient of increasingtexture density may be produced eitherby a slanted surface having equal-sizedelements at constant distances from oneanother or by a frontal-parallel surfacehaving elements with progressively di-minishing sizes and separations. Whata given gradient of density determines,according to Gibson, is "a relationshipbetween apparent slant and apparentspacing of texture elements [Gibsonet al., 1955, p. 12]."

What little evidence there is regard-ing this hypothesis comes from an ex-periment by Beck (1960). He presenteda set of optical tunnels which had con-stant-sized apertures and elements un-evenly spaced so as to duplicate theincreasing (or decreasing) density gra-dients which would be present in thecross sections of rays projected byequally-striped, tapered tunnels (orcones) converging to various angles.With fixed monocular vision, these tex-ture gradients produced impressions ofnoncylindrical tapered objects. How-

ever, these impressions were quite var-iable. Hence it appears that a texturegradient in isolation is able to producea complex impression of slant and re-cession, but it is not able to uniquelydetermine slant and recession. A partic-ular impression of slant and recessionpresupposed "a presumption, attitude,or expectation," for example, that thestripes along the surface of the pseudo-tunnel were spaced equally. A linkagebetween apparent slant and apparenttexture-spacing is indicated by the factthat adding binocular parallax resultedin a change of subjects' judgments froman equally striped, tapered tunnel to anunequally striped, parallel tunnel. How-ever, some exceptions were found tothe proposed linkage between apparentslant and apparent texture-spacing.Beck also found that the introductionof binocular disparity did not alwayseliminate the ambiguity of fixed monoc-ular vision.

That texture gradient is not adequateas a cue to slant is also confirmed bySmith and Smith (1957), who requiredsubjects to make judgments of thedegree of curvature of a perfect semi-cylinder with a textured surface andhidden ends. Under monocular condi-tions the mean judgments were nearlyflat. This result was explained by theauthors as due to the tendency to seethe display in the plane of the aperture.It may also be noted that form andsize constancy were placed in opposi-tion to the texture gradient because thetexture was composed of dots of differ-ent sizes and shapes (circular and ellip-tical). Greater curvature was seen withbinocular vision for all textures.

The curvature of a semicylinder wasalso judged in a further study by Smithand Smith (1961), who presented singlyand in combination a large number ofcues to slant: linear perspective, lightand shade, texture gradient, form trans-formations, monocular movement paral-lax, binocular disparity, and interposi-


tion. When the edges of the cylinderwere obscured, all these cues in com-bination were not sufficient for veridicaljudgments. "These results indicate thatthe gradient theory . . . may be ...psychologically insufficient for account-ing for veridical perceptions of slant inall situations [Smith & Smith, 1961, p.147]." It is clear that the availability ofa set of variables, for example, a com-bination of binocular disparity, texturegradient, and motion parallax, whichuniquely specifies the source, does notinsure veridical perception. The factthat perceptions were veridical whenthe edges of the cylinder were shownmay indicate that recognition of a fa-miliar object (a cylinder) was impor-tant.

According to Gibson (1951) outlinefigures produce ambiguous percepts.Because a given retinal shape may beproduced by an indefinite number offorms at appropriate orientations, itseems logical that simple retinal form-stimulation should elicit unstable per-cepts in the absence of other cues.Gibson maintains that texture gradientis necessary for the reliable perceptionof slant, even though it is not sufficient.Contrary to Gibson's view, experimentsby A. H. Smith and his associates indi-cate that an adequate stimulus for per-ceived slant is the retinal gradient ofoutline convergence. Clark, Smith, andRabe (1955) limited the subject tomonocular vision, with motionlesshead, and required him to judgethe slants of outline forms whichwere presented in succession and at rel-atively great distance in order to elim-inate any cue arising from accommoda-tion. It was found that a trapezoidappeared unslanted and rectangularwhen slanted so as to project a rectan-gular retinal image. A trapezoid pre-sented in the frontal-parallel plane (orat 20 degrees) appeared to have thesame slant as a rectangle slanted at 20degrees (or at 40 degrees) so as to

project the same retinal image. As phys-ical slant increased, mean perceivedslant generally increased, although themean perceived slants were underesti-mations (probably due to the absenceof other cues for depth). In spite ofGibson's (1951) finding that outlineforms are ambiguous, no observer in theexperiment under consideration reportedthat the stimulus forms changed in theirapparent shape or slant. The discrep-ancy in results may be due to the factthat Gibson's figures were drawn ongrounds presented in the frontal-parallelplane; Clark, Smith, and Rabe (1955,1956) set off their outline figures fromtheir backgrounds. With Gibson's figuresthere would be a conflict between theslant percept produced by an outlinefigure and the unslanted percept re-quired by the orientation of the ground.There is considerable evidence that theslant of a figure tends to be assimilatedto the slant of its ground (Beck & Gib-son, 1955; Epstein, Bontrager, & Park,1962; Metzger, cited in Koffka, 1935,p. 124).

In a further study, Clark, Smith, andRabe (1956) found that when outlineperspective was the only cue, the accu-racy of slant perception was greaterthan when texture gradient was the onlycue. Accuracy of perceiving slant didnot improve when the gradient of out-line deformation was supplemented byadding texture to the stimulus form orto the background or to both. When theground was textured, perception wasless accurate.

Stimulation for the Perception oj Depth

Gibson maintains that depth percep-tion does not occur without the percep-tion of a surface (and hence without agradient of texture, which is requiredfor the perception of a surface). To testthis hypothesis, Weinstein (1957) inkedout all texture from a set of Gibson's(e.g., 1950b, pp. 184-185) photographsof a large open field with stakes driven


into the ground at various distancesfrom the camera. Judgments of the sizesof the stakes made by the subjects usingthe impoverished pictures were not sig-nificantly poorer than judgments madeby the subjects using the normal photo-graphs with a texture gradient present.Using the same type of impoverishedpictures, Smith (1958) obtained rela-tively good size constancy. According toSmith, it would not have been possiblefor the subject to make size judgmentsof the distant stake in the impoverishedphotographs if he had not assumed alevel ground-plane common to himselfand the test objects. Without such anassumption, the image of an object atthe same position in the light patterncould give rise to a percept of a smallnear object on a hillside or of a larger,more distant object on a level plane.The subjects in Smith's experimentwere told to assume that a plowed fieldextended from their position for a longdistance. They were also told that theirview would be that of the camera. Withthese assumptions, and an awareness ofthe angle of elevation of the eye, theyhad sufficient information to make sizeand distance judgments.

Natsoulas (1963) has pointed outthat the visual depth experienced in theGanzfeld situation contradicts Gibson'srequirement that the visual perceptionof depth be produced by certain attri-butes of the textured optical array, es-pecially variations in density, disparity,and motility. Gibson rejects this kindof finding on the ground that, like allexperiences taking place in response toimpoverished, ambiguous, or equivocalpatterns, it is unreliable, varying fromobserver to observer and from time totime in the same observer. The theoryneed not explain these experiences be-cause they are a function of somethingother than stimulation and are notveridical. Natsoulas points out that theexperience of depth in the presence ofthe Ganzfeld is not unreliable; it is an

unvarying accompaniment of the Ganz-feld situation. Gibson, Purdy, and Law-rence (1955) found variability in theirsubjects' reports because the stimulusfield was not entirely homogeneous.Among other things, there was the grossinhomogeneity between the surface ofthe first sheet of plastic and the opticaltunnel seen through the aperture in thissheet. As Cohen (1957) has demon-strated, an inhomogeneity anywhere inthe field can reduce the tendency to seea surfaceless fog in other parts of thefield. When all inhomogeneities havebeen eliminated from the field, almostall subjects have reported a surfacelessfog extending away in depth (Cohen,1957; Hochberg, Triebel, & Seaman,1951). Not only do experimental resultsof this kind make it appear that Gibsonis wrong with regard to the necessarystimulus conditions for the perceptionof distance; such findings also contra-dict the fundamental assumption of thistheory that perception, when it is reli-able and stimulus determined, is alsoveridical.

PSYCHOPHYSICAL CORRESPONDENCEUNDER CONDITIONS OF TRANS-

FORMING STIMULATION

As was the case for static stimulationthere are two related questions whichneed consideration: (a) Do transforma-tion sequences yield consistent, rela-tively unvarying percepts, and (b) arethese percepts in good correspondencewith the objective properties of thesource of stimulation? In this sectionwe will consider these questions withregard to motion perspective, perspec-tive transformations, and size trans-formations.

Motion Perspective

Motion parallax has long been rec-ognized as a depth cue. However, be-ginning with Helmholtz' (1925, pp.295-296) well-known description, theemphasis has been on the relative an-


gular velocities of isolated objects atvarious distances from the subject. Thisemphasis is reflected in the experimen-tal investigations (e.g., Graham et al.,1948) which typically have used onlytwo objects and two velocities in anotherwise uniform field of view. Thisapproach is also consistent with thetraditional "air theory" (Gibson, IQSOb,p. 6) of space, as contrasted with the"ground theory" which emphasizes thevariations in stimulation which are cor-related with a continuous backgroundsurface. When the ground or terrain istaken into account there is a continuousflow or gradient of retinal velocities.This gradient involves a continuoustransformation of the angular separa-tions between points in the field or,more simply, a transformation of pat-tern. Gibson uses the term "motionperspective" to distinguish these condi-tions from those which prevail in thetwo-velocity case. Motion perspectiveis presumed to be a stimulus correlateof perceived relative distance in thesame way that gradients of optical tex-ture are presumed to be correlates ofperceived recession of a surface (Gib-son, Olum, & Rosenblatt, 19SS). Thusmotion perspective is assigned thestatus of a stimulus for depth. Thiscontrasts with its frequent designationas a "clue" which is effective only whenother information makes the assumptionof spatial extension reasonable (e.g.,Ittelson's, 1960, neo-Helmholtzian anal-ysis).

In order to examine Gibson's inter-pretation, experiments are needed whichisolate motion perspective. Will motionperspective in isolation consistentlyyield an impression of depth which iscompatible with the variability of ret-inal velocity? An early experiment byGibson and Carel (1952) produced neg-ative results. The source of stimulationwas a battery of scattered lights havinga uniform overall density. The batterywas in the subject's frontal plane and

appeared so when motionless. The lightscould be moved across the field with avelocity which decreased from the bot-tom of the battery to the top. The dis-play was exhibited in the dark, and ob-servation was monocular. The gradientof retinal velocity thus produced shouldbe sufficient to yield the perception ofa surface which recedes from the sub-ject from bottom to top. This expecta-tion was not confirmed. A consistentimpression of recession, slant, or rela-tive distance was not induced.

Negative results were also obtainedby Smith and Smith (19S7, 1961)under different conditions. They inves-tigated the conditions necessary for theveridical perception of the convexity ofa cylindrical textured surface. Rotationof the cylinder on its horizontal (long)axis was not sufficient to cause the cyl-inder to appear curved if it appearedflat when motionless.

Subsequent experiments by Gibson,Gibson, and Smith (1959) have alsofailed to produce unequivocal results.A series of three experiments was con-ducted with the shadow projector de-scribed by Gibson (1957) and Gibsonand Gibson (1957). Experiment I wasa two-velocity experiment in which sub-jects were asked to describe what theysaw in response to the differential trans-latory velocity of two circular spots ortwo superimposed textures composed ofelements of indefinite size and contour.Theoretically, the perceived distances ofthe two spots or textures should be in-versely proportional to the optical ve-locities. The results of the experimentdid not confirm this expectation. Themagnitude of apparent separation var-ied greatly between subjects. However,even more damaging was the fact thatthe direction of the difference in depthwas not consistent between subjects,that is, almost 25% of the subjects re-ported that the spot or surface carryingthe lesser velocity appeared nearer. Theauthors speculate that "perhaps it was


(the) lack of solid continuity or rigidconnectedness between the nearer andfarther surface which prevented theideal possibility . . . from being re-alized [Gibson et al., 1959, p. 46]."

For this reason Experiment II wasconducted with a continuous flow ofvelocity produced by a single randomlytextured surface slanted 45 degreesaway from the translucent window ofthe shadow projector which was movedback and forth parallel to the screen.This situation is similar to the one pro-duced by Gibson and Carel (1952).The main result of Experiment II wasthat most subjects reported a rigid mov-ing plane surface slanting away fromthem at the top of the field. However,estimates of the slant varied from 12.5degrees to 60 degrees. Again the mag-nitude of the apparent separation washighly variable.

Smith and Smith (1963) tested theprediction that the inconsistencies ob-served by Gibson et al. (1959) wouldbe eliminated by using a combinationof two-velocity parallax and a contin-uous gradient of velocity flow. The re-sults did not support the prediction.The direction of apparent depth agreedwith the requirements of the velocityratio; however, the magnitude of sepa-ration in depth of the surfaces wasindeterminate. Also, contrary to the re-sults of Gibson et al. (1959, ExperimentII) the continuous flow of velocities didnot yield the perception of a slantedsurface.

The results of the experiments re-viewed above do not confirm Gibson'sassertion of a strict psychophysical re-lation between a continuous gradient ofoptical motion and perceived depth.The experiments failed to provide evi-dence that motion perspective in isola-tion is adequate to specify depth, slant,or the relative order of surfaces indepth. It will be recalled that thestudies of texture gradients in isolation(Beck, 1960; Gibson, Purdy, & Law-

rence, 1955) also yielded inconsistentpercepts. Apparently perception is notcorrelated with individual gradients ofstimulation in a 1:1 manner. In lightof this observation it seems more prom-ising to study various gradients in com-bination, for example, motion perspec-tive and textural density, instead ofsingle gradients in isolation. Smith andSmith's (1961) study of the perceptionof cylindricality illustrates the possibil-ities of this approach.

Several general remarks are in orderconcerning the expectation that psycho-physical correspondence would be ob-served when only a single gradient isavailable.

1. This expectation implicates certainassumptions concerning the propertiesof the environment. For example, withregard to the expected correlation be-tween apparent recession and opticaldensity, there is the assumption thatthe elements which constitute the tex-ture of the environment are the samephysical size and shape throughout.This is probably a safe assumption in-sofar as we deal with man-made sur-faces. However, when natural terrain isconsidered there is no compelling reasonto believe that this is consistently thecase. Many surfaces are admixtures ofuniform physical texture and texturecomposed of elements of variable sizeand shape. The "ecological validity"(Brunswik, 1956) of the various opticalgradients-is not known. In fact Gibsonand Flock (1962), in a discussion ofthe illusory closeness of mountains,have offered as an explanation the factthat "in the neighborhood of a moun-tain, the distant earth-shapes may bemuch larger than the nearer ones andthe usual optical gradient will then bealtered [p. 502]." This is presumed toproduce the apparent nearness of themountain despite the contradictory in-formation provided by the concurrentgradients of disparity and motion per-spective.


Gibson (1959) feels that the occur-rence of illusions and errors in percep-tion will not be explained in the sameway as veridical perception. Supplemen-tary theoretical principles are required.As yet the details of this theory havenot been advanced. However, a hint ofwhat Gibson's theory would be like withthese corollaries added is given by hiscomments on the apparent distance ofmountains (Gibson & Flock, 1962):

There are many possible types of stimulus-information for distance in a natural opticarray, some of them based on constant lawsof geometry and optics, others based onprobable but variable conditions of geologicalfeatures, atmosphere, and illumination. Illu-sory perception will depend on the combina-tion of circumstances which holds for theparticular situation, and also probably on thedegree to which the attention of the observerhas been trained to register the reliable in-formation in the array [p. 503].

This statement sounds very like thosemade by Brunswik (19S6) regardingthe learning by the observer of theecological validity of cues. In fact, itis hard to see how Gibson's system, inits final and complete form, will be ableto retain its individual identity.

2. Assumptions of a different sort areimplied when other gradients are con-sidered. Two examples will illustrate:(a) When the objects under observationare not in the same line of sight, theprediction that differential retinal veloc-ity produced by actual movement in thefield will yield veridical apparent rela-tive distance seems to require, in thecase of a moving subject, the correctregistration by that subject of the rela-tive rates of his movements when view-ing the objects whose distances are tobe compared. A correct perception ofthe magnitude of the separation be-tween the objects would involve a cor-rect perception of the absolute rate ofmovement. This is necessary if the per-ceptual system is to partial out thevarious sources of differential retinaldisplacement. Such correct registration

would be a considerable achievement ifthe subject is undergoing passive loco-motion, (b) Another example concernsthe gradient of relative size. It is evi-dent that this gradient in isolation isambiguous for the same reason that thevisual angle subtended by a single ob-ject is ambiguous. The continuous dim-inution of the angles subtended by aseries of objects does not uniquely spec-ify recession since it is equally com-patible with a frontal-parallel series ofobjects which are actually regularlycompressed in physical size. The am-biguity is eliminated if the subject as-sumes that the objects are the samesize. Gibson (19SOb) seems to recognizethis when he writes of the "retinal gra-dient of size-of-similar objects." Recentexperiments by Epstein and Baratz(1964) have shown that the apparentrelative distance produced by relativevisual angle may indeed be governed bysuch assumptions.

Continuous Perspective Transforma-tions

The projection of a form or patternon a non-frontal-parallel surface consti-tutes a perspective transformation ofthe form or pattern. In this sense theretinal projection of any form, pattern,or surface which is not in the subject'sfrontal-parallel plane will constitute aperspective transformation. When eitherobserver or object is in continuousmotion the result is a continuous se-quence of perspective transformations.

Most studies of the effect of trans-formation have presented the static endproducts of transformation, concealingfrom the subject the antecedent trans-formation sequence. This set of condi-tions must represent an atypical case.Behavior in the natural environment ismarked by continual shifts of the headand body leading to continuous trans-formations of the retinal pattern. A pre-dilection for static stimulation also isevident in those few instances where


changing stimulation has been studied.As an illustration, Wallach and O'Con-nell (1953) in interpreting the kineticdepth effect (KDE) treat the contin-uous sequence of shadow transforma-tions as a series of independent staticprojections tied together by memorytraces. It will be clear from the earlierdiscussion that Gibson takes exceptionto the traditional emphasis on staticstimulation. According to Gibson theemphasis should be reversed.

Only a small portion of the evidenceon this question has direct Gibsonianorigins. Moreover, the implications forGibson's theory have often not beenmade explicit by the original investi-gators. Therefore, their agreement withour conclusions cannot always be as-sumed. The studies reported by Gibsondealt with slant depth of surfaces. Theexperiments which derive their impetusfrom Wallach and O'Connell's (19S3)work on the KDE have involved theinternal depth and coherence of com-plex forms, for example, a bent parallel-ogram. Finally, Langdon's (1951, 1953,1955) investigations of shape constancyalso have implications for Gibson'sview.

Slant Depth. Several experiments re-viewed in this section used a devicecalled a shadow transformer inventedby Gibson and Gibson (1957). A con-tinuous sequence of shadow transfor-mations is produced on a translucentscreen by a rotating object placed be-tween the screen and a point source oflight which is positioned so as to pro-duce polar projection.

Gibson and Gibson (1957) presentedthe shadow sequences produced byturning two regular (closed-square,open-square pattern) and two irregular(closed amoeboid, broken amoeboid)forms through 4 degrees of semirota-tion. There were two main questions:(a) Would the sequence of transforma-tions yield the perception of a rigid sur-face of changing slant? ( b ) Would

judgments of the amount of slant cor-relate positively with the variations inthe length of the transformation se-quence, that is, the degree of semirota-tion? The results for all four forms wereaffirmative on both counts. A separatecontrol group was shown only the mo-tionless end point of a 60-degree trans-formation. For this group the irregularforms yielded judgments of "no slant,"whereas the regular forms were per-ceived as slanted. However, the amountof slant was greatly underestimated andwas considerably less than the slantproduced by the 60-degree transforma-tion sequence. Gibson and Gibson con-cluded that a perspective transforma-tion sequence is sufficient to produce anaccurate perception of slant and rigidityregardless of the familiarity or tex-turedness of the form which carries themotion.

This conclusion cannot be acceptedwithout reservation. The appropriateness of the control condition is ques-tionable. There is little reason to expectthat exhibiting the end points should beequivalent to displaying the form in thenumerous aspects of its transformationarc. The logical requirement is that nosingle static aspect or combination ofdiscrete static aspects yield a perceptionof slant. Therefore, what is required isthat a random sample of discrete statictransformations be presented. If thesubject fails to report changing slant,then we may conclude that a continuousand lawful sequence is essential. Thesecond objection concerns an importantdifference between the control and ex-perimental conditions which may ac-count for the results. Under the ex-perimental conditions, the subject maysafely infer that one and the sameobject is being presented in variousaspects. On the other hand, when iso-lated static aspects are presented thesubject cannot be certain of the con-tinuing identity of the shadow-castingobject. The apprehension of physical


identity is crucial since without it theshadow transformations could just aswell be perceived as continuous defor-mations in the plane of the screen.

That these arguments need to betaken seriously is indicated by the re-sults of Sidorsky( 1958),White (1962),and Epstein and Mountford (1963).Sidorsky (1958) found that subjectscould accurately judge their own ap-parent rotation in the medial planewhen presented with static perspectivetransformation of a grid-patterned sur-face as viewed at different pitch an-gles. Epstein and Mountford (1963)presented the static end products ofvarious amounts of transformation ofrectangular representational and non-representational forms. Judged slantwas found to vary systematically withthe degree of transformation. A generalrule may be that any deformation ofcontour or surface texture which rep-resents a deviation from modal regular-ity will produce a depth displacement.

White's (1962) experiment is espe-cially interesting. White puts the ques-tion this way:

If the moving presentation is effective merelybecause it provides more looks at the patternwhich are not completely redundant, thenthe order in which these looks are presentedshould not make any difference in the ac-curacy of judgment. If, however, the transi-tions between looks are important, then dis-rupting the order in which the looks arepresented should impair the accuracy of thejudgment [p. 75, italics added].

In order to examine this question Whiteshowed subjects a motion picture whichdisplayed either an orderly sequence oftransformations of an unfamiliar 3Drigid form tumbling about a fixedcenter, or a scrambled series in whichthe same frames were randomly ordered.At the conclusion of the movie the sub-ject was asked to select a still pictureof the standard form in a new orienta-tion from a set of four similar forms.There was no difference between the

judgments based on the ordered andscrambled series. It seems that insofaras accuracy of identification is con-cerned the regularity of the sequence isnot critical.

The results of these experiments havebearing on two salient aspects of Gib-son's view. First they raise questionsconcerning the evidential basis for Gib-son's reiterated insistence that the se-quence itself is a stimulus, for example,"the form of the change of form of thestimulus is what determines the percep-tion [Gibson & Gibson, 1957, p. 137]."Second, doubts arise concerning the cri-terial validity of the regular perspectivetransformation sequence. The fact thata source may be mathematically spec-ified by a given sequence in an un-equivocal manner cannot be taken toimply that the subject uses this rela-tionship.

Internal Depth. The experimental in-vestigations of the perception of inter-nal depth through motion have beenreviewed by Metzger (1953, Ch. 13)and Braunstein (1962).2 The followingdiscussion will focus on the KDE.Under certain conditions, a sequence oftransforming shadows will appear as arigid form, having internal depth andturning in depth. This has been labeledKDE by Wallach and O'Connell(1953). The above definition is incom-plete since it does not specify two im-portant conditions for demonstratingKDE. (a) The familiar cues for relativedistance must be absent. In contrastwith Gibson and Gibson's (1957) situa-tion, this requirement implies the useof parallel rather than polar projection.(b) None of the static aspects of thetransformation sequence should yield a

2 Of historical interest is Miles' (1931)discussion of the movement interpretationsof the silhouette of a revolving two-bladeelectric fan. Miles traces the irregular historyof this problem back to a description byNicholson (1802) of a theater exhibition inLondon.


perception of depth. None of the better-known studies of KDE have providedsatisfactory evidence that the secondrequirement was fulfilled. There is goodreason to doubt whether this criterioncan be met with figures which havemany interior angles and lines. Infact, Fried (1960) tested Wallach andO'Connell's (1953) figures, and con-cluded that only the single bent rodappeared flat in its various static trans-formations.

The basic fact of KDE is plainlyconsistent with Gibson's views. A con-tinuous sequence of transformations isshown to be sufficient to determine theperception of a rigid turning form.However, Gibson's theory demandsmore than this. First, it requires thatvariability of perception be small. Sec-ond, that the perceived form be in goodcorrespondence with the actual shadow-casting form. Finally, perceived turningshould also be in good agreement withthe actual turning. Data on these ques-tions can be found in the work ofWallach and O'Connell (1953, pp. 211-212), White and Mueser (1960), Green(1961), and Epstein (in press).

Wallach and O'Connell (1953) asked20 subjects to make judgments of theform of the shadow-casting object im-mediately following the kinetic presen-tation. For the wire helix, subjects wereinstructed to fashion a piece of wireinto the shape of the shadow-castingfigure. The reproductions were betterthan those made by the same subjectswhile they looked directly at the turn-ing figure. For the 110-degree parallel-ogram, subjects were asked to select amatch from a set of four alternativeswhich included a copy of the standardand three variants. Seventeen of 30 sub-jects chose the exact copy as theirmatch. It would appear, therefore, thatthe perception of internal depth basedsolely on kinetic stimulation is accurate.

This conclusion was confirmed and

extended in an experiment by Epstein(in press). Judgments of internal depthand amount of turning were found tobe in good agreement with the actualoscillation and objective depth of a120-degree bent parallelogram. Accu-racy did not vary significantly as thelength of the transformation sequencevaried from 15 to 85 degrees. Appar-ently, a sequence produced by oscilla-tion through an arc of 15 degrees issufficiently informative, and lengtheningthe transformation sequence contributesnothing to accuracy. It remains to bedetermined whether this is true inde-pendently of the locus of transforma-tion, for example, 40-55 degrees insteadof 0-15 degrees. There is the possibilityof an interaction of length and locus.Also of interest would be to determinewhether identical optical transforma-tions have equivalent perceptual effectsregardless of their source, for example,passive movement of the subject com-pared with movement of the object.

The experiments of Wallach, O'Con-nell, and Epstein have utilized as theirshadow-casting objects figures com-posed of connected lines varying inlength and orientation. However, KDEmay also be obtained by rotating a dis-play which consists of an arrangementof unconnected straight lines. For ex-ample, four vertical pegs arranged atthe corners of a square will appear as arigid spatial arrangement turning aboutits center. White and Mueser (1960)studied the subject's ability to recon-struct the arrangement of pegs undervariations of the shape and number ofpegs constituting the display, the speedof rotation, and the exposure duration.Under all conditions, excepting thestatic presentations, subjects reportedimmediate perceptions of a stable rigidarrangement rotating in depth. How-ever, most subjects were unable to re-produce the arrangement with greaterthan chance accuracy. Additional evi-


dence that accuracy is low for uncon-nected arrangements may be inferredfrom the results of Green's (1961) Ex-periment VI.

It appears that accuracy is enhancedby two properties of the display: com-plexity, for example, interior angles, andconnectedness. Should an explanation ofthis observation be forthcoming it willprobably be intimately related to theanswer to a more basic question. Whydoes the sequence of shadows appear asit does, instead of appearing as a con-tinually deforming two-dimensional pat-tern? It is not sufficient for Gibson toreiterate that sequences are stimuli fordepth and solidity. This may (or maynot) be an empirical fact; however, itcannot be adduced as the explanationof the specificity of perception. Nor isit sufficient to demonstrate that the sub-ject can discriminate between two sim-ilar transformation sequences, one pro-duced by turning a rigid surface andthe other by an elastic surface whichhas been made to contract (Fieandt &Gibson, 1959).

The answer appears to rest in Gib-son's implicit adherence to a variant ofthe Gestalt principle of Pragnanz. Ac-cording to this principle the 3D rigidappearance is a reflection of the sub-ject's preference for the simpler percept.Or in the alternative terminology of in-formation theory: "Other things equal,that perceptual response to a stimuluswill be obtained which requires theleast amount of information to specify[Hochberg, 1957, p. 83]." Gibson iscited by Hochberg (1957, p. 83) as oneof those who subscribed to this prin-ciple. If we are correct in ascribing theminimum principle to Gibson, then thisis certainly an instance where the psy-chophysical hypothesis has been dis-carded. Perception no longer is strictlya function of stimulation. Rather it ismediated by a selective principle builtinto the perceptual system. The inclu-

sion of a selective principle robs Gib-son's thesis of its attractive simplicity.It also carries the implication that asequence of transformations which re-quires less information to specify as acontinually deforming two-dimensionalpattern will be perceived as such, in-stead of as a turning rigid form. It isobvious that this outcome would be in-compatible with the unamended Gib-sonian interpretation. Some evidencethat two-dimensional deformations areperceived under these circumstanceshas, in fact, been reported by Metzger(1959).

The Perceptual Constancy of Turn-ing Shapes. The question of shape con-stancy has been discussed in great detailelsewhere (Epstein & Park, 1963). Herewe will mention only Langdon's studiesas they bear on the relationship betweentransforming stimulation and percep-tion. In normal observation the contourof an object is not given as an instanceof static nonchange, or as a series ofdiscrete transformations. Instead thecontour is usually represented by a con-tinuous family of perspective transfor-mations. While this is true for the nu-merous states of the same contour, itneed not be true for the differences be-tween the contour shapes of differentobjects, or the differences between thecontours of objects which are actuallyundergoing physical change. One impli-cation of this analysis is that the tra-ditional formulation of the constancyproblem is misleading since it focuseson the relation between discrete statictransformations and perceptual stabil-ity. A second implication is that con-tinuous transformation should enhanceshape constancy. Although Langdon hasnot followed the route we have justtaken, he has conducted a series ofexperiments which examine the secondimplication.

For the present analysis the mainfinding of Langdon's (1951, 1953,


19SS) experiments is that the rotationof shapes, under conditions such that astationary presentation yields no con-stancy, will be sufficient to restore con-stancy. The degree of perceptual con-stancy was positively correlated withspeed of rotation or rate of change ofshape. These results were obtained bothwith simple outline figures, for example,a wire circle, and complex "solids," forexample, a wire cube. Langdon criticizesthe kind of explanation which Gibsonmight advance and offers an alternative.In any event, Langdon's results provideevidence for Gibson's view that thestimulation most useful for achievinga stable visual world is not constantnonchanging stimulation, but is in-stead stimulation undergoing continu-ous change.

Size Transformations

Continuous displacement of a frontal-parallel surface in a radial line from thesubject yields a size transformation ofthe retinal image. Diminution of dis-tance produces a symmetrical expansionof the image, and increasing distanceresults in a symmetrical contraction. Ifthe surface moves back and forth, thenone transformation sequence is a se-quential inversion of the other.

While size transformations have longbeen recognized as cues for relative dis-tance there has been little experimentalwork on this topic. Some of the earlywork (e.g., Bourdon, 1902) has beenreviewed by Woodworth (1938, Ch. 26)and Boring (1942, Ch. 8). We haveuncovered only three recent studies ad-dressed to this question (Ittelson, 1951;Schiff, Caviness, & Gibson, 1962;Smith, 1951). There is some disagree-ment about whether the perceived radialmotion produced by size transformationis regulated by the subject's assump-tions about the target. Ittelson (1951)provides evidence that assumptionsabout, and prior experiences with, the

transforming target are important de-terminants. Smith's (1951) experiment,on the other hand, failed to support thisview. However, both of these investi-gators do provide clear-cut evidencethat under appropriate conditions sizetransformations will yield perceivedradial motion. In addition, the studiesconcerning prediction of time of colli-sion (Carel, 1961) have shown that thiseffect is lawfully related to the amountof transformation.

The recent experiment by Schiff,Caviness, and Gibson (1962) illustratesthe experimental investigation of thiscue. Twenty-three monkeys were ob-served responding to four stimuli: ex-pansion of a circle projected on ascreen, contraction of the circle, darken-ing and lightening of the screen. Twovery different modes of behavior wereobserved as responses to the size trans-formation. The expanding circle led toalarmed withdrawal, as if to avoid colli-sion. The contracting circle led to ex-ploratory responses. The results for thebrightness variations showed that thisvariable cannot account for the effectsof size transformation. Schiff et al.(1962) conclude that size transforma-tions are sufficient stimuli for radialmotion. They do not consider the possi-bility that size transformations merelyproduced changes in perceived sizewithout affecting perceived distance,and that sudden, rapid changes in per-ceived size produce withdrawal or ap-proach responses.

CONCLUSION

In concluding we wish to considerbriefly several general questions.

1. The possibility that the constancyhypothesis is sufficient. There were twosteps required for the successful resur-rection of the constancy hypothesis asan account of veridical perception. Firstit must be proved that some variable of


stimulation unequivocally specifies thedistal source. Secondly it must be shownthat the total variance in perception canbe attributed to variance in the prox-imal stimulation.

While Gibson has offered persuasivearguments concerning the specificity ofstimulation he has only rarely (e.g.,Gibson, Olum, & Rosenblatt, 1955)attempted the mathematical analyseswhich are demanded. Several unpub-lished theses by Gibson's students(Hay, 1961; Purdy, 19S8) have madeadmirable efforts to achieve this objec-tive, and they deserve careful study.However, certain physical properties ofthe environment (such as rigidity) havebeen accepted as primitive and hencehave escaped analysis. What makes thisprocedure unsatisfactory is not the im-plausibility of the assumptions. The as-sumptions are not extravagant, nor is itby itself improper to postulate certainpremises in writing geometrical relation-ships. Our discomfort arises from thefact that some of the properties whichare assumed are the very ones whichGibson's theory is intended to explain.

Concerning the psychophysical hy-pothesis it can be said that Gibson hasnot proved his case. The experimentaldata simply do not support the hypoth-esis of perfect psychophysical corre-spondence. Nor does the evidence sup-port the contention that perception is"in contact with the environment," thatis, veridical, in cases of psychophysicalcorrespondence.

The question of veridicality has along history in philosophical analysis,and we would wish to avoid the ques-tion. However, an evaluation of Gib-son's thinking would be incompletewithout a discussion of this matter. Weare uncertain about the value of intro-ducing the conventionally defined rela-tion of veridicality into a theory ofperception. It is clear in Gibson's casethat the account of perception is con-

tained in the psychophysical hypothesiswhich relates percepts to proximal stim-ulation, and need not involve any as-sumptions concerning the distal-prox-imal or distal-perceptual relationships.The introduction of veridicality consid-erations leads Gibson to distinguishbetween perceptual events on basesother than the subject's response, or ananalysis of stimulation. For example,suppose Subject X looks into an opticaltunnel and reports that he sees a solidtunnel. Subject Y is shown a real tunnelwhich provides identical stimulation,and he too reports that he sees a tunnel.Applying the label "veridical" to Y'sreport and "nonveridical" to X's reporthardly seems a useful exercise.

2. Is a correlational theory sufficient?In reviewing Gibson's The Perception ofthe Visual World Boring (1951) ad-vanced the following criticism:

What Gibson calls a "theory" is thus only adescription of a correlation, a theory whichtells how but skimps on why . . . eventuallyscience must go deeper into the means ofcorrelation, must show in physiology why agradient of texture produces a perceiveddepth, not merely that it does [p. 362].

Prentice (1951) in his review has madethe same criticism of Gibson.

Putting aside the question of whetherGibson needs more physiology or morepsychology we would agree that heneeds more theory. In our view Gibsonhas tried to capture too much empiricalterrain with too little theory. The con-sequence has been the unintended de-velopment of implicit theoretical prop-ositions which are applied when theexplicit theory is confronted by anemergency. These hidden theoreticalprinciples can be employed only at theperil of internal inconsistency. Gibson'stheory needs deliberate revision.

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(Received October 25, 1963)

examination of gibson's psychophysical

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