Perception &Psychophysics1979, Vol. 26 (3), 230-234

The perception of size and distanceunder monocular observation

ATSUKI HIGASHIYAMAUniversityofOsakaPrefecture, Osaka 591, Japan

A relative-perceived-size hypothesis is proposed to account for the perception of size anddistance under monocular observation in reduced-cue settings. This hypothesis is based ontwo assumptions. In primary processing, perceived size is determined by both proximalstimulation on the retina and distance information from primary cues such as oculomotorcues. In secondary processing, the relation of two primary perceived sizes determines anotherrelation of secondary perceived distances, so that an object of smaller primary perceivedsize is judged to be further away. An experiment was designed to test this hypothesis,especially the assumption of secondary processing, by making ratio judgments of perceivedsize and perceived distance for two successively presented targets. The standard square waspresented at a constant distance and varied in visual angle; the variable square was presentedwith a constant visual angle in distance. The results showed that an inverse relation betweensize and distance estimates held regardless of whether the visual angles of the targets werethe same or different.

When two objects of similar shape but differentretinal image size are presented successively or simul­taneously under reduced-cue conditions, the objectof smaller image size is judged to be further awaythan the object of larger image size. This phenomenonhas been observed in a number of studies (Epstein& Landauer, 1969; Gogel, 1969; Gogel & Sturm,1971), and the variable determining perceived relativedistance has been assumed to be relative retinal size.According to this conventional hypothesis, if thevisual angles of the objects are equal to one another,the observer will perceive them either at the same dis­tance (mainly Gogel, 1969) or at uncertain distances(Rock & McDermott, 1964), and if they are different,the observer will perceive the further distance tocorrespond with the smaller visual angle.

The alternative to the relative-retinal-size hypothesisis the relative-perceived-size hypothesis (Higashiyama,1977), which rests on the following assumptions. Thefirst assumption is that primary distance cues operateeven under completely reduced-cue conditions andprovide registered distance, an assumption supportedby a number of studies (Leibowitz & Moore, 1966;Leibowitz & Owens, 1975; Leibowitz, Shiina, &Hennessey, 1972; Owens & Leibowitz, 1976). Theperceptual system then transforms retinal image sizeinto perceived size by taking into account the registereddistance resulting from primary distance cues. Weshall refer to this as the primary process. In primaryprocessing, size perception presupposes distance per-

Requests for reprints should be addressed to Atsuki Higashiyama,Departrnent of Psychology, University of Osaka Prefecture,Mozu-umernachi, Sakai City, Osaka 591, Japan.

ception. The second assumption is that a ratio of twoprimary perceived sizesdetermines a ratio of secondaryperceived distances, which differ from primaryregistered distances produced by primary distancecues. The object of smaller primary perceived sizeis judged to be furt her away than that of larger pri­mary perceived size. Weshall refer to this as thesecondary process. In secondary processing, sizeperception precedes distance perception.

Generally speaking, primary processing uses anyof the classical distance cues to provide as accurate aspossible an estimate of distance for use in constructingperceived size. Primary distance cues can be dividedinto two subgroups-proprioceptive or oculomotorcues (e.g., accommodation and convergence), andvisual cues (e.g., binocular retinal disparity andmotion parallax). The relative-perceived-size hypoth­esis is perhaps best applied to the reduced-cue situ­ation where acommodation and accommodativevergence are avai!able, because, in this situation, theperceptual system easily ignores the primary registereddistance and accepts the secondary perceived distance(cf, Biersdorf, 1966; Heinemann, Tulving, &Nachmias, 1959; Ono, Muter, & Mitson, 1974). Onthe other hand, if primary processing uses binocularretinal disparity or motion parallax as primarydistance cues, then the perceptual systern mayfai! to produce the secondary perceived distance as anovert response, because these visual cues provide theprimary perceived distance in a more stable andcompelling way than do oculomotor cues.

Contrary to the relative-retinal-size hypothesis, thepresent hypothesis implies that the relative sizecue to distance is defined in terms of relative perceivedsize. Therefore, even if the visual angles of two

Copyright 1979 Psychonomic Soeiety, Ine. 230 0031-5117/79/090230-05$00.75/0

SIZE AND DISTANCE 231

METHOD

Figure 1. Schematic top-vlew diagram of the apparatus.

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SUBJEC

ObserversThe seven observers were university undergraduates majoring

in psychology, They all had normal visual acuity in both eyes.

ProcedureThe observer was seated on the chair in an observation booth,

and his head was positioned in a chinrest so as to align the righteye with the viewing aperture. After a lO-min dark-adaptationperiod, he viewed the two successively presented targets throughthe aperture with only the right eye while the left eye remainedopen. He was then required to assign a value of 10 to the per­ceived size of the first-presented target and a value of 100 to theperceived distance of the same target. For a given trial, after theshutter had been raised, the first stimulus was illuminated. Tenseconds later, the first stimulus was automatically extinguishedand, followingal-sec interval, the second stimulus was illuminatedfor 10 sec. The observer was required to give the appropriate ratiojudgments during the presentation of the second stimulus. Whenthe judgments had been made, the shutter was lowered and the

Apparatus and Stimulus MaterialsA sketch of the mirror arrangement used is shown in Figure I.

A half-silvered mirror (HM) was fixed at a slant of 45° in theobserver's sagittal plane, so that all images of stimulus targetswere aligned on the same line of sight for the right eye. The tar­gets wereviewedthrough an aperture .5 cm in diameter immediatelyin front of the eye,

The stimulus targets were square apertures cut in cardboard.Targets T.. T" and T3 were the comparison stimuli subtendinga visual angle of 1°44' on a side. They were presented at distancesof 33, 54.5, and 133 cm from the observer's eye position. TargetsTs were the standard stimuli presented at a distance of 151.5 cmfrom the eye, visual angles of which were 2°5', 1° 53', 1°44' ,and 1°31' on a side.

The standard and the comparison were presented successivelyby illuminating them alternately from behind with 20-W bulbs.A frosted glass (FG) was placed in front of each bulb at adistance of 155.5 cm so as to diffuse the light ofthe bulb.

objects are equal, as long as they do not appear tobe equal in perceived size, the observer will notexperience them as equidistant or at uncertain dis­tances.

The relative-perceived-size hypothesis suggests theoccurrence of the size-distance paradox-the findingthat, contrary to the size-distance invariance hypoth­esis, perceived size and perceived distance areinversely rather than directly related for a constantvisual angle in reduced-cue situations. Heinemannet al. (1959) presented in quick succession two stimulusobjects that subtended a constant visual angle, butwith the standard closer than the variable. However,most observers, viewing monocularly, judged thestandard to be further away than the variable.Biersdorf (1966) confirmed these results under asimilar viewing condition. Both Grant (1942) andHermans (1954) reported paradoxical distancejudgments for some observers even under binocularobservations.

The purpose of this study was (1) to determinewhether the relative-retinal-size hypothesis or therelative-perceived-size hypothesis provides a betteraccount of distance perception under a reduced-cuecondition where primary distance cues are limited toaccommodation and accommodative vergence, and(2) to obtain the necessary data in a systematic wayin order to establish quantitatively the paradoxicalsize-distance relationship.

Ratio judgments of both perceived sizeand perceiveddistance were obtained for two squares presentedsuccessively at different distances. The comparisontarget was presented at any one of three differentdistances so as to subtend the same visual angle. Thestandard target subtended any one of four visualangles at a constant distance.

Consider judgments of a given standard comparedwith the three comparison stimuli, with fixed visualangle, but at different locations. According to therelative-retinal-size hypothesis, the changing distanceof the comparison should make no difference to eitherperceived size or perceived distance, since retinalimage size does not change: Subjects should judgeboth relative size and distance to be the same for allcomparisons. According to the relative-perceived-sizehypothesis, the changing distance of the comparison,registered in primary processing, will combine withfixed retinal image size to make the furthest compari­son look largest, the nearest look smallest. Thensecondary processing will result in the largest com­parison looking nearest, the smallest looking furthest.In short, as distance of comparison increases, theformer hypothesis predicts no change in perceivedsize or distance, whereas the latter predicts thatperceived size will increase and perceived distancewill decrease.

232 HIGASHIYAMA

loeations of the stimulus targets were exchanged for the next trial.The experimenter emphasized in the instruetions that the observershould not make the judgments until he had attained clear imagesof the targets in a given trial. Ir the observer failed to be in foeus,he was to signal to the experimenter at onee. In this ease, thetrial was repeated.

The observers reeeived "apparent" instruetions. The essentialparts of the instruetions are: "I am going to present you with aseries of squares in total darkness. Two squares will be presentedin quiek temporal sueeession. Your task is to tell me how theyappear in size and distanee by assigning numbers to them. Thefirst square we will eall '10' in size and '100' in distanee, respee­tively. Your task will be to estimate the apparent size and theapparent distanee of the seeond square. Please try to assignnumbers proportional to your subjeetive impression. I want you tobase your judgments on the way that the squares appear. Pleasedisregard any information you may have about the physical orreal size and distanee of the squares."

Although afterimages might have been produeed by gazing atthe first target, they did not seem to interfere with the judgmentsof the seeond target. The afterimages were weak and no observereonfused the targets with the afterimages.

There were 12 possible pairs of stimulus targets, sinee each offour standard stimuli eould oeeur with eaeh of three eomparisonstimuli. For eaeh pair, four estimation trials were run, in two ofwhieh the standard preeeded the cornparison, and in the remainingtwo of which, it followed the eomparison. The order of pairpresentation was randomly determined for eaeh observer with therestrietion that all trials involving any particular standard beperformed before the trials involving another standard oeeurred.

RESULTS AND DISCUSSION

Each observer's estimates for trials where thestandard followed the comparison were transformed

so that the perceived size and the perceived distanceof the standard square were equal to 10 and 100,respectively.' Hence, for all trials, values for thecomparison that were greater than 10 and 100 meantthat it was judged larger and further away, respec­tively, than the standard. This transformation waspossible only if the observers were assumed to makeratio judgments.

Figure 2 shows the results. Each point representsthe mean of 28 (4 x 7) trials. The parameter is thevisual angle of the standard. The left panel of Figure 2shows the results for size estimates ofthe comparisonplotted against the physicaldistance of the comparisonsquares. Note that smaller distances are shown to theright of the abscissa. The reciprocal of the physicaldistance, which is appropriate to express the relativechanges of accommodation in diopter necessary toachieve a clear image, is also indicated on the abscissa.A two-way analysis of variance with repeated mea­sures was performed on the size estimates. In perform­ing this analysis, the means of the four size estimatesfor each of the 12 pairs of stimulus targets were usedas the scores for each observer. The results of thisanalysis show that the effect of distance of compari­son is significant [F(2,12) = 4.28, p < .05] and theeffect of visual angle of standard is significant [F(3,18)= 36.86, p < .01], but the interaction of distancewith visual angle is not (F < 1).

In a similar way, the right panel of Figure 2shows the results for the distance estimates of the

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SIZE AND DISTANCE 233

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Figure 3. Relation of size estimates and distance estlmates,

(2)S' C' D' c = k,

or, more generally,

where S' sand D' s are perceived size and perceiveddistance of the standard, and S ' c and D' c are thoseof the comparison. Since, according to Equations 1and 2, the value of k is equal to the product ofS' sand D' s- that value should be 1,000 in this exper­iment. This predicted curve is drawn in Figure 3. Assimple and convenient measures for direction anddegree of discrepancy, the mean and root mean squarewere computed with respect to the difference be­tween the observed and predicted distance estimates:The mean was .49 and the root mean square was3.87.

In order to evaluate the prediction that k = 1,000,Equation 2 was rewritten as D' c = k (1IS' c), and aleast squares line was fitted to the distance estimatesas a function of the reciprocal of the size estimates.In making this calculation, the assumption was madethat the line should pass through the origin.' The slopeis the estimated value of k, which was 1,001.02, andthe correlation between the values of D'c and 1IS ' cwas .978. The mean and root mean square were alsoobtained to represent the direction and degree of dis­crepancy: The mean was .39 and the root mean squarewas 3.86. These results and Figure 3 indicate that theestimated value of k is broadly comparable with thepredicted one.

Another way of evaluating the validity of Equation 2is to compare the results obtained with similar experi­mental settings and procedures. Epstein and Landauer(1969, Conditions 2 and 3) reported magnitude esti­mations of the size and distance of a variable rela­tive to a standard when the two stimulus targets haddifferent visual angles. Figure 4 shows the estimatedsize plotted against the estimated distance. The curverepresents the prediction S' c . D' c = 100, since theperceived size and distance of the standard wereassigned a value of 10. A systematic discrepancy isseen when the estimated size and distance of the vari­able were less than those of the standard, but overallthe theoretical curve is not a bad fit to the data points.

Gogel and his colleagues seem to distinguish themechanism underlying the relative size cue to relativeperceived distance from the mechanism triggering thesize-distance paradox. Gogel (1969) and Gogel andSturm (1971) defined the relative size cue as a relativeretinal size cue. On the other hand, Gogel (1973, 1974)assumed that the size-distance paradox tends to occurwhen an observer perceives an object to be smaller orlarger than expected relative to familiar size (in thepresent experiment, perceived size of the first presentedtarget is assumed to be familiar size). In this sense,the relative perceived distance induced by the relativesize cue represents a perceptual event, while the size­distance paradox contains a cognitive factor. The

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comparison. The distance estimates were analyzed bya two-way analysis of variance with repeated measures.The results of this analysis show that the effect of dis­tance of comparison is significant [F(2,12) = 10.35,p< .01], as is the effect of visual angle of standard[F(3,18) = 9.27, p< 01], while the interaction ofdistance with visual angle is not [F(6,36) = 1.26,n> .05].

Thus, the statistical analyses confirm the impres­sions given by Figure 2: Size estimates of the compar­ison increase as the visual angle of the standarddecreases, and as the physical distance of the com­parison increases; distance estimates of the comparisondecrease as the visual angle of the standard decreases,and as the physical distance of the comparisonincreases.

These results do not support the relative-retinal-sizehypothesis, which predicts no change in size or distancewhen a given standard is judged relative to the threecomparisons of the same visual angle. They do supportthe relative-perceived-size hypothesis, which predictsincreasing size and decreasing distance judgments asthe comparison increases in distance.

For the purpose of clarifying the relation betweenthem, size estimates were plotted against distanceestimates in Figure 3. The relation may be reasonablyweIl represented by the equation

234 HIGASHlYAMA

Figure 4. Relation of size estimates and distance estimates fromEpstein and Landauer (1969). The solid curve shows the functionS' c . D' c = 100.

present results may be interpreted by Gogel's hypoth­esis. However, it seems unparsimonious to assurnethat the observer's response criteria interchangerapidly, depending on whether the targets are equalto one another in visual size. In contrast, the relative­perceived-size hypothesis may be characterized asan integrative explanation of two seemingly differentphenomena.

The relative-perceived-size hypothesis is in a sensefar from a new theory. Carlson (1962) and Carlsonand Tassone (1962) pointed out that normal adultsbelieve that an object looks smaller at a greaterdistance. This belief is called the perspective attitude.What is here called the secondary process seems tobe in substance equivalent to the perspective attitude.Perhaps, the secondary process, as Carlson has pointedout, is a kind of conceptual coupling between smallersize and further distance or between larger sizeand closer distance. Rock and Kaufman (1962), indeveloping a theory of the moon illusion, proposeda mechanism similar to the secondary process toexplain the apparent near distance of the apparentlylarger horizon moon when they supposed that theparadoxical distance judgments depended on therelative size of the horizon and zenith moons.

(3)~ D'c· 1 S'c'k = I I

nlS'Ci

NOTES

where i represents any data point shown in Figure 3. This is shownas follows-from the equation: D' Ci = k (lIS' d + Ei, we obtain

I. For the trials on which the standard preceded the comparison,no transformation was necessary. For the trials on which thestandard followed the comparison, the values of 102 and 1002

were divided by size estimates and distance estimates, respectively.2. The estimates value of k was calculated from the formula:

CARLSON, V. R., & TASSONE, E. P. A verbal measure of per­spective attitude. American Journal oj Psychology, 1962, 75,644-647.

EpSTEIN, W., & LANDAUER, A. A. Size and distance judgmentsunder reduced conditions of viewing. Perception & Psycho­physics, 1969,6,269-272.

GOGEL, W. C. The sensing of retinal size. Vision Research, 1969,9, 1079-1094.

GOGEL, W. C. The organization of perceived space. 11. Conse­quences of perceptual interactions. Psychologische Forschung,1973,36,223-247.

GOGEL, W. C. Cognitive factors in spatial responses. Psychologia,1974,17,213-225.

GOGEL, W. C., & STURM, R. D. Directional separation and thesize cue to distance. Psychologische Forschung, 1971,35,57-80.

GRANT, V. W. Accommodation and convergence in visual spaceperception. Journal oj Experimental Psychology, 1942, 31,89-104.

HEINEMANN, E. G., TULVING, E., & NACHMIAS, J. The effectof oculomotor adjustrnents on apparent size. American JournalojPsychology, 1959, 72, 32-45.

HERMANS, T. G. The relationship of convergence and elcvationchanges to judgments of size. Journal oj Experimental Psy­chology, 1954,48,204-208.

HIGASHIYAMA, A. Perceived size and distance as a perceptualconflict between two processing modes. Perception & Psycho­physics, 1977,22,206-211.

LEIBOWITZ, H., & MOORE, D. Role of accommodation and con­vergence in the perception of size. Journal of the OpticalSociety ojAmerica, 1966,56,1120-1123.

LEIBOWITZ, H. W., & OWENS, D. A. Anomolous myopias and thedark focus of accommodation. Science, 1975, 189,646-648.

LEIBOWITZ, H. W., SHIINA, K., & HENNESSY, R. T. Oculomotoradjustments and size constancy. Perception & Psychophysics,1972,12,497-500.

ONO, H., MUTER, P., & MITSOM, L. Size-distance paradox withaccommodative micropsia. Perception & Psychophysics, 1974,15, 301-307.

OWENS, D. A., & LEIBOWITZ, H. W. Oculomotor adjustmentsin darkness and the specific distance tendency. Perception &Psychophysics, 1976,20,2-9.

ROCK, 1., & KAUFMAN, L. The moon illusion, 11. Science, 1962,136,1023-1031.

ROCK, 1., & McDERMOTT, W. The perception of visual angle.Acta Psychologica, 1964,22,119-134.

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REFERENCES

BIERSDORF, W. R. Convergence and apparent distance as corre­lat es of size judgrnents at near distances. Journal of GeneralPsychology, 1966, 75, 249-264.

CAHLSON, V. R. Size consrancy and perceptual compromise.Journal of Experimental Psychology; 1962,63, 68-73.

where Ei is an error that represents the discrepancy between anobserved distance estimate and an estimated distance estimate.Taking the derivative of Equation 4 with respect to k and assumingd~Ei2/dk = 0, we obtain Equation 3.

(Received for publication June 6, 1978revision accepted July 20,1979.)