The corridor illusion *

upright condition (as shown in Fig. I), the cylinders were called "baskets"; in the inverted position, the cylinders were identified as "lamps." An illusion was measured for both "lamps" and "baskets" WHITMAN RICHARDS and J. F. MILLER, JR. in order to determine whether the Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 orientation of the perspective grid Contrary to general belief, the classical corridor illusion is not due solely to the influenced the illusion. All size measurements were made using a perspective and contextual cues provided by the corridor. Additional factors that are equally important are the inherent spatial anisotropies of the visual system and fixation method of constant stimuli. The slides were presented in a haphazard order; then tendencies. the S judged whether the test cy Iinder was Figure I illustrates one form of the "pattern" condition. These slides were "taller" or "shorter," or "wider" or corridor illusion, the subject of this study. then rear projected individually in a "narrower" than the standard cylinder. The illusion is that the cylinder at the front haphazard order onto a screen of Thus, the illusion was measured both of the corridor generally looks smaller than sandblasted Plexiglas for viewing by the S. ve r t ically (cylinder height) and a cylinder of the same size placed farther The resting luminance of the screen before horizontally (cylinder width). The full back. (The front cylinder is actually 10% the test flash appeared was 6 fl. The flash range of 20 slides was used for all Ss, regardless of the illusion. At least four sets larger.) The basis for this illusion has often had an equivalent luminance of 300 fl. For most of the tests, the slides were of measurements were made for each S for been postulated as due primarily to context or to the effects of apparent depth flashed for 50 msec while the S fixated a each condition. From these data, the point induced by the perspective cues (Gibson, pinpoint fixation light, seen in the plane of where 50% of the judgments were 1966; Gregory, 1966). This explanation the projection screen. The fixation point "smaller" (or "narrower") was used as an cannot be entirely correct, however. For was always located in the same position estima te of the illusion. Such positions of example, if Fig. I is turned upside down, relative to the two cylinders, regardless of subjective equality were determined for then the perspective cues will remain whether the perspective grid was present. each set of measurements and then identical, but the magnitude of the illusion The two positions were Land B, chosen to averaged. will change. Clearly, factors other than lie on contours of the grid, as shown in RESULTS perspective or context are contributing to Fig. I. When Fixation Position L was used, this particular illusion. The following study the picture was rotated 180 deg and Steady Fixation Typical data showing the percent of shows that spatial anisotropies of the visual reversed, in order that the same retinal system and fixation behavior are the positions would be used for all tests. In the judgments of "shorter" are plotted in Figs. important factors that influence the magnitude of the corridor illusion. METHOD Twenty-one cylinders were prepared as cutouts which could be placed on top of a perspective line drawing of a corridor, shown in Fig. I. Each cylinder represented I 0 f 20 3% increment steps (or decrements) in size of the standard cylinder. Thus, the range of cylinder sizes varied from 84% to 140';0 of the standard cylinder, which measured 1.5 deg high x .65 deg Wide, seen at an observation distance of 210 em. Two sets of slides were then made from the cylinder cutouts: One set consisted of the standard cylinder paired with the test cylinder, with a homogeneous background (i.e., no perspective grid); the second set paired the standard and test cylinders in exactly the same positions but, in addition, included the perspective grid of the corridor (as in Fig. 1). The first set. without the grid, is identified as the "no-pattern" condition. The second set. which included the corridor. is the "Su p po r t c d under AFOSR Contract F 44620-69.('-01 OS. Supplementary funding was received by grants from NIMH and NASA. awarded to Professor H.-L. Teuber. Chairman. Department of Psychology, MI.T.. Cambridge. Massachusetts.

Perception & Psychophysics, 1971, Vol. 9 (5)

Fig. I. The corridor illusion used for this study. Band L identify the two different fixation positions.

Copyright 1971, Psychonomic Journals, Inc., Austin, Texas

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were made with the grid oriented in two ways: for baskets and for lamps. For each "' of these two conditions, measurements ......C 100 • K-"-~\ •.•?;~:~y were made with the grid present and :I ., I " I without the grid, in order to determine the \ , \ "1 z 80 " \I ~ basic foveal-peripheral anisotropy for each "' l<-K •• "'., '1 S. These inherent foveal-peripheral '1 ...:> anisotropies are shown in the two columns 1 60 :I ;. headed "no pattern," with the means given ., +.+ in the next-to-last column on the right. A ...C positive value indicates that a smaller 40 "' > o peripheral stimulus matches a larger foveal ", ... ~ '. stimulus. ...o X.·.)(-l< I 20 The two columns headed "pattern" list I I z the percent decrease in size necessary for \ o "' the peripheral cylinder to match the foveal \ a: ..."' cylinder when the grid is present. The -10 -30 -20 o 20 -50 -40 10 30 40 50 plr ctnt negative values given in the section under "lamps" is in the expected direction of the O/HERENCE IN CYLINDU SIZE (FOVEAL LUS PUIPHEIIAL) perspective illusion, because the grid has Fig. 2. Judgments of the relative cylinder sizes made by SM. The filled circles and been rotated 180 deg. Thus, inspection of crosses show size judgments made when the corridor was absent and indicate biases Columns 2 and 5 in the upper portion of attributable to the relative positions of the cylinders alone. The open circles show size the table shows that, for the height judgments made when the cylinders are seen as baskets in a corridor. The pluses show size illusion, RH has the greatest illusion for baskets, whereas JM has the greatest judgments made when the cylinders are seen as lamps. illusion when the cylinders are seen as 2 and 3. These results are obtained using Figure 3 shows similar results for S RH. lamps. The intermediate Ss arc rank steady fixation upon either Position B or In this case, when the cylinders are seen ordered between these two extremes. Position L. The abscissa is the percent alone (closed circles and crosses), the These individual differences in the difference in real size between the standard peripheral stimulus must be about 15% magnitude of the illusion, depending upon and test cylinders, with the foveal cylinder smaller in order to appear the same height the orientation of the corridor, show that, taken as unity. Thus, as the standard as the foveal cylinder. Presumably, because in general, the perspective cues and context cylinder appears nearer the fovea in the there is no perspective grid present, this provided by the corridor are not the "basket" condition, the customary size illusion is due solely to spatial significant factors responsible for the corridor illusion for "baskets" should anisotropies in the visual system. illusion. If they were, the illusion should appear to the right of the zero position, On Superimposed upon these inherent size have remained equally large when the the other hand, because the "lamp" anisotropies is the effect of the grid, which orientation of the corridor was inverted. condition required a rotation of the grid, causes a further 12% change in the relative By inspection of Fig. I, it can be seen that the expected perspective illusion for sizes of the cylinders (open circles and inversion of the figure changes the grid "lamps" should be to the left of the zero pluses). from an array that expands in the foveal position. Table I summarizes the results for seven region (fixation at B) to one that contracts The reason for presenting the data in Ss. For each S, apparent size measurements in the foveal region and expands in the this way becomes more obvious upon IL LU SION FOR BAS KE TS ILLUSION FOR LAMPS closer inspection of the figures. When no a: grid (or corridor) is present but only the ....... 100 cylinders are seen alone, then a rotation of C the retinal positions of the test and :I ., standard cylinders should not affect the z 80 point of subjective equality. The near "' "' coincidence of the dashed (crosses) and ::; ::> dotted lines (closed circles) shows this to 60 :I ;: be the case. For SSM (Fig. 2), these two "'... curves cross the 5lY!o horizontal near zero c 40 on the abscissa, indicating that the > "' peripheral stimulus (in either the lamp or ...0 ...0 basket condition) must be only 1070 larger 20 than the foveal cylinder for them both to ...z appear equal in height. Considering that U "' II: there is no perspective grid to cause an ..."' 50 per eent 40 10 20 30 -10 o - 50 -40 -30 - 20 illusion, this result is not surprising. When the grid is now added (open circles and DIFFERENCE IN CYLINDER SIZE (FOVEAL LESS PERIPHERAL) pluses), the test cylinders have to be decreased by about 20%, shown by a Fig. 3. Judgments of the relative cylinder sizes made by RH. Symbols same as in Fig. 2. displacement to the right in the case where the cylinders appear as baskets and to the Note that, even with no corridor present (closed circles and crosses), the peripheral cylinder appears larger by almost 15%. left where they appear as lamps. II:

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ILL USION FOR LAIIPS

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Perception & Psychophysics, 1971, Vol. 9 (5)

magnitude of the corridor illusion toward physical equality.

Table I

Mean Values of lUusion (Percent) for Steady Fixation Baskets

lamps

Means

DISCUSSION Three variables have been shown to be Grid Grid No Grid No major factors that affect the corridor Pattern Pattern Effect Subject Effect Effect Pattern Pattern illusion. The most important is whether the Height S is allowed to scan the display, as opposed 13.8 4.5 14.9 IIR RH 15.5 14.3 9.9 29.3 to steady fixation of a flashed display. 8.7 10.8 5.1 12.6 81 11.1 WR 195 7.5 With steady fixation, the magnitude of the -15.0 WD -1.8 14.8 4.7 19.7 1.5 17.3 13.0 illusion can be over twice as large, - 17.4 26.1 1.5 19.6 -5.7 13.2 HK 7.5 8.7 providing an appropriate fixation position -3.8 11.4 -3.9 -96 MK 16.8 6.0 -36 12.9 -308 SM -12.8 19.2 21.8 -10.9 20.4 -9.0 6.4 is chosen. An improper choice of fixation --13.7 JM -390 269 -16.2 25.8 -11.1 27.8 9.6 position can markedly reduce the illusion, Mean: 169 Mean: 16.3 Mean: 176 however, due to inherent foveal-peripheral Width anisotropics in judged size. These 4.0 11.4 5.9 8.0 .5 11.7 RH 15.4 8.5 anisotropies represent the second major -1.5 3.0 11.0 4.2 9.0 WR 12.9 9.9 7.5 factor that contributes to the magnitude of -0.2 -8.0 11.9 14.8 WD 8.8 9.0 32 6.8 the corridor illusion. In this respect, 12.0 2.0 9.9 -3.0 110 HK 4.8 -5.1 9.0 therefore, part of the basis for the corridor -8.1 0.0 MK -7.5 7.5 116 15.6 0.0 7.5 -IS .4 4.1 SM -6.4 -3.4 12.0 ·4.8 8.1 -2.3 illusion is similar to that underlying the -237 JM 12.9 -5.1 8.7 -8.0 108 3.6 -10,8 horizontal-vertical illusion (pearce & Matin, Mean: 5.5 Mean: 91 Mean: 12.6 1969). Superimposed upon these inherent spatial anisotropies is the effect of the grid Table 2 that creates the perspective effect. This Illusion for Roving vs Steady Fixation (Percent) factor is approximately independent of the (Height) orientation of the grid on the retina, Pattern Grid Effect because similar illusions are generated by the basket and lamp conditions where the Steady Roving=-- Difference Steady Fixation Subject . -'-'-_ _ Roving .__Difference grid was rotated 180 deg. Note that such a 13.7 6.8 (B) RH 29.3 -0.5 29.8 6.9 rotation of the grid also changes the (l) 17.4 25.9 7.5 18.4 HK 7.5 9.9 relationship between the size of the grid (l) 28.4 -0.6 JM 39.0 21.6 17.4 27.8 and its position on the retina. For the 4.8 (B) 19.5 3.0 10.8 6.0 WR 16.5 basket condition, the fovea views the fine Mean Difference: 18.3% Mean Difference: i.s» .. part of the grid creating the corridor, periphery (fixation at L). Apparently the under steady fixation but are presented whereas for the lamp condition, the coarser illusion is very sensitive to the interaction continuously, so that the S may scan the gridwork is seen by the fovea. Yet, in spite between retinal position and the spatial display, then the illusion is drastically of these altered relationships between the metric imposed by the grid of the corridor. reduced. This conclusion follows from grain of the grid and retinal position, the In order to determine the effect of the Table 2, which shows measurements size effects induced by the grid remain the grid alone, the size illusions measured with obtained from the four Ss who were able same. Such independence between grid size and withou I the grid present may be to complete the series of experiments. For and retinal location would suggest that the compared (pattern vs no pattern). For each each of these Ss, the corridor was oriented size illusion created by the grid occurs later orientation and for each individual. these in the position giving the greatest illusion in the visual pathway than do the differences appear in Columns 4 and 7 of (Column 2). Two eye-movement constraints leading to the spatial Table I. The mean result is given in the conditions were then compared: steady anisotropies. rightmost column. The average effect of fixation (SO-msec flashes) and roving the grid alone is to induce about a 17r'lc, fixation, with the display on continuously. change in the apparent height of the When the perspective grid is present and REFERENCES cylinder and only a 9% change in width for when the S is allowed to scan the display. GIBSON. 1. J_ The senses considered as perceptual systems, Boston: Houghton-Mifflm, the SO-msec displays seen with steady the illusion is reduced by 18?!' to a value 1966 Pp. 312-315. fixation. The grid was more effective in approximately one-third of the GREGORY, R. L Eye and brain: The inducing a change in apparent width when steady-fixation condition (Column 5). If psychology of seeing. New York: McGraw·Hill. 1966. the cylinders were seen as lamps; In Ioveal-pertpheral anisotropies arc factored contrast. the larger illusion for height out so only the effect of the grid alone IS PEARCE, D.. & MATlN. L. Variation of the magnitude of the horizontal-vertical illusion appeared to be unaffected hy the measured, then again the illusion is much w i t h retinal eccentricity. Perception & orientation of the grid. weaker if the S is allowed to scan the Psychophysics, 1969.6,241-243. display (last column). Scanning eye Roving Fixation If the patterns arc not seen flashed movements, therefore. reduce the (Accepted for publication November 1.1970.) FovealPeripheral Bias

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