The Tilt-Constancy Theory of Visual Illusions...visual illusions provide unique insights into...

Journal of Experimental Psychology:Human Perception and Performance2001, Vol. 27, No. 1, 206-217

Copyright 2001 by the American Psychological Association, Inc.0096-1523/01/S5.00 DOI: 10.1037//O096-1523.27.1.206

The Tilt-Constancy Theory of Visual Illusions

William PrinzmetalUniversity of California, Berkeley

Diane M. BeckUniversity College London

The authors argue that changes in the perception of vertical and horizontal caused by local visual cuescan account for many classical visual illusions. Because the perception of orientation is influenced moreby visual cues than gravity-based cues when the observer is tilted (e.g., S. E. Asch & H. A. Witkin, 1948),the authors predicted that the strength of many visual illusions would increase when observers were tilted30°. The magnitude of Zollner, Poggendorff, and Ponzo illusions and the tilt-induction effect substan-tially increased when observers were tilted. In contrast, the MiiUer-Lyer illusion and a size constancyillusion, which are not related to orientation perception, were not affected by body orientation. Othertheoretical approaches do not predict the obtained pattern of results.

For over a hundred years, visual scientists have believed thatvisual illusions provide unique insights into normally adaptivevisual processes. For example, Helmholtz (1881/1962) com-mented,

The study of what are called illusions of the senses is a very prominentpart of the senses; for just those cases which are not in accordancewith reality are particularly instructive for the discovering the laws ofthose means and processes by which normal perception originates, (p.251)

With rare exception (e.g., Ward & Coren, 1976), most theorieshave attributed visual illusions to "information processing mech-anisms that are normally adaptive" (Gregory, 1968, p. 66). Thecontroversy arises as to what mechanisms are being reflected byparticular illusions. For example, the Zollner illusion has beenattributed to a variety of mechanisms, including spatial frequencycoding in early vision (Ginsburg, 1984), inhibition among orien-tation tuned cells (Blakemore, Carpenter, & Georgeson, 1970), andthe mechanisms responsible for linear perspective (e.g., Gillam,1980; Green & Holye, 1963; Gregory, 1963).

We offer a new explanation that also involves a normallyadaptive process. We propose that the perception of line orienta-tion (e.g., Zollner illusion), collinearity (e.g., Poggendorff illu-sion), line length (e.g., Ponzo illusion), and line curvature (e.g.,Wiindt-Hering illusion) are caused by the same mechanisms thatare responsible for the perception of vertical and horizontal. Be-cause these mechanisms are related to people's ability to perceivea constant orientation despite changes in retinal orientation or even

William Prinzmetal, Department of Psychology, University of Califor-nia, Berkeley; Diane M. Beck, Department of Psychology, UniversityCollege London, London, England.

This research was supported in part by National Institutes of HealthGrant MH51400. We thank Marty Banks, Art Shimamura, Steve Palmer,Edward Hubbard, and Nancy Kim for their help on this project.

Correspondence concerning this article should be addressed to Wil-liam Prinzmetal, Department of Psychology, University of California,Berkeley, California 94720-1650. Electronic mail may be sent [email protected].

shifts in gravity in relation to body position (Howard, 1998;Howard & Childerson, 1994), we call our new account of visualillusions the tilt-constancy theory.

We first illustrate how local visual cues to orientation canaccount for many illusions. Second, we review the literature rel-evant to our claim. Finally, we present evidence in support of thetilt-constancy theory that cannot be explained by other theories.

The effect of visual context on orientation perception was dra-matically illustrated in classic studies by Asch and Witkin (1948).Observers viewed a room that was tilted 22° in the picture planeand were asked to adjust a rod so that it was oriented horizontallyor vertically with respect to gravity. The average setting wasdistorted 15° in the direction of the tilt of the room. Althoughvestibular and somatosensory information could have been used toadjust the rod, visual context dominated orientation perception.This phenomenon is called the tilted-room illusion, and it dramat-ically illustrates the powerful contribution of visual information toorientation perception. The tilted-room illusion has been exploitedin several roadside attractions and amusement parks (Banta, 1995;Shimamura & Prinzmetal, 2000). In these settings, people's mis-perception of vertical and horizontal is such that balls appear toroll uphill and people appear to stand at gravity-defying angles.Such compelling illusions have resulted in these settings beingcalled "antigravity houses" (also see www.illusionworks.com).

The rod-and-frame effect illustrates that a very sparse visualstimulus can also create orientation distortions (Witkin & Asch,1948b). In the rod-and-frame task, observers adjust a rod to ver-tical or horizontal. The rod is surrounded by a tilted frame. Ob-servers tend to adjust the rod in the direction of the tilted frame.Note that the rod-and-frame effect is local in that it is greater whenthe rod is close to the frame and is reduced in magnitude as the gapbetween the rod and frame increases (e.g., Zoccolotti, Antonucci,& Spinelli, 1993).

The rod-and-frame effect and tilted-room illusion are similar tothe tilt-induction effect (Gibson, 1937). Gibson presented stimulisimilar to Figure 1A. Observers noted that a truly vertical lineappeared to tilt in the direction opposite to the surrounding contextlines (the apparent tilt is indicated, in exaggerated form, by thedashed line). Hence, when observers adjusted the central line to

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TILT CONSTANCY AND ILLUSIONS 207

Figure 1. In all of the panels, the actual stimulus is shown in black, andthe illusion, in exaggerated form, is shown with a dashed line. (A) Thetilt-induction effect: Vertical lines are perceived to be tilted in the directionopposite the context lines. (B) The Zdllner illusion: The long obliquecontext lines in the tilt-induction figure have been replaced by many shortcontext lines. (C) The standard Zollner illusion. (D) In the tilt-inductioneffect, Gibson (1937) observed that vertical context lines increased theapparent slope of an oblique line. (E) The tilt-induction effect from PanelD in a context more similar to the Poggendorff illusion. (F) The Poggen-dorff illusion can be considered a consequence of the tilt-induction effectin Panel D.

vertical, they erred in the direction of the context lines, just as inthe tilted-room illusion (also see Bouma & Andriessen, 1970;Kramer, 1978). When the context is presented before the stimulus,the effect is known as the tilt aftereffect (e.g., Campbell & Maffei,1971; Gibson & Radner, 1937). The salient difference between thetilt-induction and rod-and-frame stimuli is the size of context: Inthe rod-and-frame effect, the stimuli typically subtend many tensof degrees of visual angle, whereas the tilt-induction experimenttypically involves smaller stimuli. However, Coren and Hoy(1986) and Wenderoth and Johnstone (1988, Experiment 4) haveobtained rod-and-frame effects with stimuli in the size range of thetilt-induction effect. We argue that the tilted-room illusion, therod-and-frame effect, and the tilt-induction effect are caused by thesame mechanisms (cf. Howard, 1982, pp. 155-156; Singer, Pur-cell, & Austin, 1970).

Several investigators have speculated that the Zollner illusion isan instance of the tilt-induction effect (Day, 1972; Howard, 1982,

pp. 156-157). The similarity of the illusions can be seen in Figures1A and IB, in which the flanking context lines in Figure 1A havebeen replaced by many shorter context lines in Figure IB. TheZollner illusion, as typically presented (Figure 1C), illustrates theeffect of local context, in which the oblique lines on the left governthe slope of the left long line and the oblique lines on the rightaffect the slope of the right long line. Moreover, the tilt-inductioneffect and the Zollner illusion behave similarly with the manipu-lation of a host of independent variables (see Prinzmetal, Shi-mamura, & Mikolinski, in press). Many visual illusions, such asthe Wundt-Hering illusion and Fraser spiral, can be understood asinstances of the Zollner illusion (Fisher, 1968). It may be that theCafe Wall illusion is also an instance of the Zollner illusion(Prinzmetal et al., in press).

Historically and functionally, the Poggendorff illusion is alsorelated to the Zollner illusion (Boring, 1942). In I860, ZSUnersubmitted his illusion for publication. The journal editor, Poggen-dorff, noticed that the oblique lines did not appear to be collinear.The functional relationship of the Poggendorff illusion to thetilt-induction effect is illustrated in Figures ID, IE, and IF. Gibson(1937) noted that, in the stimulus illustrated in Figure ID, thecentral oblique line appeared to be inclined at a larger angle thanit actually was, illustrated again by the dashed line. (We haveverified this in our laboratory.) If we simply displace the centralline and its resulting illusory percept, as we did in Figure IE, wecan see the similarities to the Poggendorff illusion in Figure IF. Asa consequence of the misperception of the orientation of the centralline (i.e., the tilt-induction effect), the oblique lines do not appearcollinear. Note that it is not just that acute angles appear larger thanthey are, because the Poggendorff illusion can be created withoutany angles at all (e.g., see Day & Jolly, 1987; Pressey & Sweeney,1972; Wilson & Pressey, 1976). We argue that the Poggendorffand Zollner illusions are caused by a misperception of orientation,not a misperception of angles.

By our account, all of the geometric illusions described thus farcan be related to orientation. Our approach can also account forother distortions, such as the line length observed in the Ponzoillusion. Figure 2 demonstrates how the Ponzo illusion can beconsidered a case of the Zollner illusion. In Figure 2A the verticallines appear further apart at the top of the figure than at the bottomof the figure (Zollner illusion). Similarly, the horizontal line at thetop of Figure 2B seems longer than the bottom horizontal line(Ponzo illusion). That is, the ends of the top horizontal lines appear

Figure 2. The relation of the Ponzo and Zollner illusions. (A) The Z6Unerillusion with the Ponzo illusion suggested with bold lines. (B) The Ponzoillusion with the Zollner illusion in the background.

208 PRINZMETAL AND BECK

further apart than the bottom horizontal lines. Figure 2A is drawnto suggest that the Ponzo illusion is part of the Zollner illusion, andin Figure 2B, the Ponzo is hidden in the Zollner illusion.

We have conducted experiments on the tilt-induction effect withstimuli similar to those shown in Figures 3 A and 3B that comparedthe magnitude of the Ponzo illusion with the tilt-induction effect(Prinzmetal et al., in press). With stimuli such as those in Figure3 A, observers adjusted the free end of the bottom horizontal line sothat it appeared to be vertically aligned, according to gravity, withthe end of the top horizontal line. The oblique line on the rightcaused a tilt-induction effect so that observers erred by making theline too long. The Ponzo illusion was measured with stimuli suchas those in Figure 3B. Observers adjusted the length of the bottomhorizontal line so that it matched the length of the top line. Becausethe Ponzo illusion involves a tilt-induction effect at either end, onewould predict that the Ponzo illusion would be twice as great at thetilt-induction task, and this is what was found. Additionally, acrossobservers, the correlation between the two illusions was .70. Prinz-metal et al. also compared predictions of several theories of thePonzo illusion with the tilt-constancy theory. The results wereconsistent with the tilt-constancy theory.

In summary, the tilt-constancy theory proposes that the tilt-induction effect and the Zollner, Poggendorff, and Ponzo illusionsare due to a misperception of orientation caused by local visualcontext. Further, we propose that the mechanism responsible forthe local misperception of location is the same as the mechanismthat causes the tilted-room illusion and the rod-and-frame effect.

The possibility that the Zollner illusion and the tilt-inductioneffects are caused by the same mechanism as the tilted-roomillusion and the rod-and-frame effects has been the subject ofcontroversy. On the one hand, Day (1972) suggested that theZollner illusion is caused by the same mechanism as the tilted-room illusion.1 On the other hand, Howard (1982, pp. 155-156)asserted that the "frame effects" (i.e., tilted room illusion, rod-and-frame effect) are caused by a different mechanism than the "tilt-normalization" effects (i.e., Zollner illusion, tilt-induction effect).Heretofore, the evidence for either position is weak.

Howard (1982) gave three reasons for believing that the frameand tilt-normalization effects are caused by different mechanisms.First, he asserted that the frame effects are many times larger thanthe normalization effects and therefore must be caused by different

mechanisms. Strangely, he cited a misperception of orientation of20°. We know of only one study that found errors of that magni-tude. In very special circumstances, Asch and Witkin (1948)reported a tilted-room illusion of 20°. However, in their experi-ment, observers were seated in a chair that was tilted 24°. Further-more, there was an elaborate procedure, lasting 7 min, to attemptto get observers to perceive the tilted room as upright. The mag-nitude of the tilted-room illusion is usually much less, and therod-and-frame effect is typically even smaller (e.g., Wenderoth,1974; Witkin & Asch, 1948b). In fact, Shimamura and Prinzmetal(2000) found that the tilted-room illusion can be of a similarmagnitude as the tilt-induction effect. In general, the larger andmore elaborate the context, the greater the illusion. This observa-tion seems hardly surprising.

Second, Howard (1982) claimed that tilted-frame effects aremuch more in evidence when the frames are in the periphery, butthe tilt-induction effect is not greater in the periphery (Muir &Over, 1970). There are two pieces of evidence for this claim. First,a series of studies by Ebenholtz and his colleagues have shown thata larger frame leads to a larger illusion in the rod-and-frame task(e.g., Ebenholtz, 1977,1985; Ebenholtz & Callan, 1980). It is clearthat as the frame becomes larger, it becomes more peripheral.However, these studies confound frame eccentricity and framesize. As we have commented, it does not seem surprising that alarger context would lead to a larger illusion.2 The second piece ofevidence for the claim that the periphery is special is a study byDiLorenzo and Rock (1982). They conducted a rod-and-frame taskwith two frames, an inner frame and an outer (peripheral) frame.They found an effect of the outer frame but not the inner frame.However, the outer frame was always presented first, alone, for aperiod of 4 min, before the inner frame was presented. Hence, theprocedure may have biased observers to use the outer frame.

Finally, Howard (1982) claimed that the tilted-room illusion isaffected by cognitive variables, whereas the tilt-induction effect(and other small-scale illusions) is not. By cognitive variables,Howard meant knowledge of the canonical orientation of objectssuch as flower vases and tables. However, there is no evidence thatthe tilt-induction effect is not influenced by cognitive variables.Furthermore, this argument is logically inconsistent in that Howardclaimed that the tilted-room and rod-and-frame effects are causedby the same mechanism because they both involve large peripheralstimulation, whereas the tilt-induction effect does not. However,the rod-and-frame effect does not involve familiar objects (as inthe tilted-room effect). Hence, by Howard's arguments, it is un-clear whether these illusions should be classified on the basis oftheir scale, on whether they involve peripheral stimulation, or onwhether they are influenced by cognitive variables.

Figure 3. The Ponzo illusion considered as a consequence of the tilt-induction effect. In Panel A, the ends of the horizontal lines do not seemto be horizontally aligned. This effect makes the top horizontal line inPanel B appear longer than the bottom horizontal line.

1 We know of no one who has suggested that the Poggendorff and Ponzoillusions were caused by the misperception of orientation. Note that themisperception of orientation is not the same as a misperception of angles,a theory that is discussed in the General Discussion section.

2 Zoccolotti et al. (1993) replicated the finding that a larger frame leadsto a larger rod-and-frame effect. As mentioned earlier, they found that witha given frame size, the size of the rod affected performance. As the rodincreased in size (so that the gap between the rod and frame got smaller),the magnitude of the illusion increased.


Day's (1972) position, that the tilted-room illusion is caused bythe same mechanism as the Zollner illusion and the tilt-inductioneffect, is consistent with the tilt-constancy theory. The position isparsimonious in that a single mechanism is proposed for bothphenomena. Furthermore, it provides a functional account of thetilt-induction illusion because the tilted-room illusion is related tothe mechanism of tilt constancy. Nevertheless, there is no com-pelling evidence to support this view. If the tilted-room illusionand the tilt-induction effect are caused by the same mechanisms,then one would predict that an independent variable that criticallyaffects the tilted-room illusion should also affect the tilt-inductioneffect. In the following experiments, we manipulated such avariable.

In summary, the tilt-constancy theory claims that the samemechanism that causes the incorrect perception of orientation inthe tilted-room illusion (e.g., Asch & Witkin, 1948) is responsiblefor a variety of illusions, including the Zollner, the Poggendorff,and Ponzo illusions as well as the tilt-induction effect. A variablethat has been known to affect the tilted-room illusion is thephysical orientation of the observer relative to gravity. Asch andWitkin (1948) found that seating observers in a chair that wastilted 24° significantly increased the magnitude of the tilted-roomillusion (Asch & Witkin, 1948). Tilting the observer also increasesthe rod-and-frame effect (DiLorenzo & Rock, 1982; Witkin &Asch, 1948b). That is, observers tend to disregard gravity-relatedcues to orientation in favor of visual cues when tilted. The findingthat observer orientation affects performance in the tilted roomleads to a straightforward prediction: If the tilt-induction effect andthe Zollner, Poggendorff, and Ponzo illusions are caused by thesame mechanism as the tilted-room illusion, they should alsoincrease when observers are seated in a tilted position. In thepresent experiments, we compared the magnitude of these illusionswhen observers were seated upright and when they were seated ina chair, tilted 30° about the observer's line of sight.

A few previous investigators have measured various illusionswith observers in postures other than upright with inconsistent andconflicting results (Campbell & Maffei, 1971; Day & Wade, 1969;Wallace & Moulden, 1973; Wolfe & Held, 1982). We believe thatthere were two critical factors when testing an effect of bodyorientation that were not controlled in previous research but werecontrolled in the present experiments. First, the visual environmentmust be adequately manipulated. In measuring the tilt-inductioneffect, if the frame on the computer monitor, or the surroundingroom, is visible, then most of the visual environment is alignedwith gravity even if the inducing lines are not. In our experiments,the observers were tested in the dark, and the stimuli consisted ofluminous lines on a black background. To ensure that observersdid not see the frame of the monitor, we required them to weargoggles with dark neutral density lenses. Second, because theperception of orientation persists over time (i.e., the tilt after-effect), observers sat in the dark for 30 s before beginning eachexperiment.

We do not believe that the tilt-constancy theory can explain allillusions, only those that are due to the misperception of orienta-tion induced by visual context. Hence, we do not expect that tiltingthe observer will increase nonorientation illusions. The Miiller-Lyer illusion is a robust illusion, but we believe that it has little todo with the perception of orientation for three reasons. First,observers who evinced strong Zollner and Poggendorff illusions

were not those who showed a strong Miiller-Lyer effect (Coren,Girgus, & Erlichman, 1976). Second, as we mentioned earlier, thestrength of many of these illusions varies with its orientation, andin our lab we have failed to find such an effect with the Muller-Lyer illusion. Finally, with the Zollner, Poggendorff, and Ponzoillusion, the orientation of the context lines critically determinesthe magnitude of the illusion. In contrast, with the Miiller-Lyerillusion, it is the distance the "wings" extend beyond the horizontalline that determines the illusion magnitude (Coren, 1986). Hence,we predicted that the Muller-Lyer illusion would not vary whenobservers were tilted. To ensure that a null finding was not theresult of a floor or ceiling effect, we manipulated the strength ofthe Miiller-Lyer illusion, as described below.

In Experiment 1, we tested the magnitude of the Zollner,Poggendorff, Ponzo, and Miiller-Lyer illusions, as well as thetilt-induction effect, with observers seated upright and tilted 30°.Asch and Witkin (1948) tilted observers 24° and Witkin and Asch(1948b) used 28°. We wanted to make sure that our manipulationwas at least as strong as theirs, so we tilted our observers 30°.Experiment 2 was a control condition to test for the effect of tiltingobservers without visual context. Experiment 3 tested observers onthe Zollner, Ponzo, and Poggendorff illusions when seated uprightand tilted, while controlling for retinal orientation. Finally, inExperiment 4, we tested the effect of tilting observers on a secondnonorientation illusion, specifically, an illusion of size induced bylinear perspective.

Experiment 1

Method

Procedure. Each observer was tested in a single session that lastedabout 1 hr. Half of the observers performed the tasks first seated upright,and then seated in a chair lilted 30° counterclockwise (from the observers'perspective), whereas the remaining observers were first tested seated inthe tilted position. The order of the tasks within the first or second half ofthe experiment was counterbalanced across observers. The results fromhalf of the observers on the Zollner task were lost because of a computer-operator error. Nevertheless, the order of conditions for the observerswhose data were included was completely counterbalanced, as describedabove.

Observers were tested for 24 trials in each task. In measuring thetilt-induction effect, observers moved the top dot back and forth so that itwas vertically aligned, according to gravity, with the bottom dot (seeFigure 4). Specifically, observers were told that if the two dots were tennisballs, the top dot should be placed so that if dropped, it would land squarelyon the bottom dot in the real world. Observers used a joystick to move thetop dot horizontally back and forth until they were satisfied with theirsetting, and then pressed a button on the joy stick to begin the next trial.Observers were told to take as much time as they wanted in making theirsettings.

In the Zollner task (Figure 5A), observers moved the dot up and down,using the joystick, until it appeared to be collinear with the long line. ThePoggendorff illusion (Figure 5B) was assessed by having observers movethe bottom oblique line back and forth, horizontally, until it appearedcollinear with the top oblique line. To measure the Ponzo illusion (Figure5C), observers adjusted the length of the vertical line on the left until itappeared to be the same length as the line on the right.

We used the Brentano version of the MUller—Lyer illusion. The ob-servers' task was to adjust the location of the central arrowhead so that itstip would bisect the horizontal "shaft." There were two versions of theMiiller-Lyer illusion, as shown in Figure 5D. On 12 trials, the "wings"


1 degree

Figure 4. The stimuli used to measure the tilt-induction effect. Observersmoved the top dot, in the direction indicated by the arrow, to be verticallyaligned with the bottom dot. The stimulus is drawn to scale, but in theactual experiment, the stimuli consisted of luminous lines on a blackbackground.

were long, and on 12 trials the wings were short. These were presented ina random order. It has been found that the length of the wings affects thestrength of the illusion: The longer the wings, the greater the illusion (seeCoren & Girgus, 1978, p. 31). We included this manipulation to ensure that

a null result of tilting the observer was not due to the MUller-Lyer illusionbeing at floor or ceiling.

Each task began with the observer sitting in the dark for 30 s, whethertilted or upright. The starting position of the adjustable component of thestimulus (e.g., vertical location of dot in the Zollner illusion) was randomlyset before each trial. In addition, in the tilt-induction task, not only was thehorizontal location of the top dot randomly set at the beginning of eachtrial, but the vertical position of the pair of dots was also randomly setwithin approximately ± 0.5° of visual angle. The reason for this randomdisplacement was so observers would not use the relationship between thedot and a particular line in the grating to determine their setting.

Stimuli. Observers were tested in a dark room while wearing goggleswith dark neutral density filters. Hence, the stimuli appeared as luminouslines in an otherwise dark field. The stimuli were presented on a Macintoshcomputer, and the observers were seated at a viewing distance of 107 cm.The stimuli are illustrated in Figures 4 and 5. These figures are drawn toscale. The context lines in the tilt-induction effect stimulus (Figure 4) forman angle of 18° from vertical. Similarly, the oblique lines in the Zollner,Poggendorff, and Ponzo illusions were 18° from horizontal. In the MUller-Lyer figure, the arrowheads formed an angle of 45°. In the tilt-inductioneffect (Figure 4), the distance between the centers of the dots sub-tended 2.84° of visual angle (160 screen pixels). The horizontal lines in theZollner and Poggendorff illusions (Figures 5A and 5B) subtended 5.68° ofvisual angle (300 pixels). The oblique lines for the Zollner and Poggendorffillusions subtended 2.84° and 1.89° of visual angle, respectively (150 and100 pixels). The length of the standard line in the Ponzo illusion sub-tended 2.84° of visual angle (150 pixels). Finally, the length of thehorizontal line in the Milller-Lyer figure subtended 4.73° of visual angle(250 pixels), whereas the arrowheads subtended either 0.379° or 0.758° ofvisual angle (20 or 40 pixels).

Apparatus. Observers were seated in a chair that could be set at uprightor tilted 30° counterclockwise. The chair was created from a standardoffice furniture chair with armrests. The armrests of the chair were padded.The chair was fitted with a footrest and a shelf on which observers restedthe joystick. Both the footrest and shelf tilted with the chair. Observers'heads were restrained by a chin rest and lateral support bars so that then-heads were at the same angle as the chair.

Figure 5. The stimuli used to measure the (A) Zollner illusion, (B) Poggendorff illusion, (C) Ponzo illusion,and (D) Muller-Lyer illusion. The arrows indicate the adjustments that observers could make. The stimuli aredrawn to scale, but in the actual experiment, the stimuli consisted of luminous lines on a black background.


Observers. Twenty observers participated in the experiment, half ofthem were male and half female. However, because of the above-mentioned computer error, the results from only 10 observers were in-cluded in the Zollner task. The average age of the observers who partici-pated in the experiment was 22 years. All reported that they had normal orcorrected-to-normal vision with no known visual deficits. Observers wererecruited from among the undergraduate population of the University ofCalifornia, Berkeley.

Results

The tilt-induction effect and the Zollner, Poggendorff, andPonzo illusions were all dramatically and significantly increasedwhen the observers were tilted 30° compared with when they werein the upright condition (see Table 1). The dependent variable forthe tilt-induction effect was the deviation from vertical of a virtualline connecting the top and bottom dots, in degrees, with positivedeviations in the direction of the grating (see Figure 4). For theZollner and Poggendorff illusions (see Figure 5), the dependentvariable was the difference, in screen pixels, from the averageadjusted height of the dot to the correct (collinear) location. (Notethat 52.8 pixels are 1° of visual angle.) The magnitude of thePonzo illusion was measured as a percentage: the length of adjust-able line divided by the length of the standard line. As shown inTable 1, tilting the observer significantly increased each of theseillusions. Table 1 also indicates the average standard deviation foreach illusion, that is, the standard deviation over the 24 trials foreach condition, averaged over observers.

An additional analysis was conducted with the Poggendorffillusion. Several investigators (e.g., Weintraub & Krantz, 1971;Weintraub, Krantz, & Olson, 1980) have suggested that the versionof the Poggendorff illusion that we used should be measured indegrees. That is, the differences, in degrees, between the angle ofthe oblique line (i.e., 18° in this experiment) and the angle formedby a virtual line connecting the dot and the intersection of theoblique line and horizontal line. This dependent variable has theadvantage that it is invariant to viewing distance. Therefore, weperformed an additional analysis on the Poggendorff illusion inwhich we first transformed each response into degrees error. Theillusion was significantly greater for the tilted than upright condi-tions, 8.45° versus 6.01°, F(l, 19) = 9.66, p < .05.

In contrast, the Miiller-Lyer illusion was not affected by theobserver orientation (see Table 1). The dependent variable for theMuller-Lyer illusion was the average distance, in screen pixels,

Table 1Results From Experiment 1

Effect Upright condition Tilted condition df F

Tilt-inductioneffect 2.4° (3.0) 9.4° (4.9) 1,19 71.72**

Zollner illusion 7.3 pixels (4.5) 26.4 pixels (7.3) 1,9 96.63**Poggendorff

illusion 28.7 pixels (9.0) 38.8 pixels (11.3) 1,19 20.86**Ponzo illusion 5.9% (3.9) 8.2% (4.4) 1, 19 7.28*

Muller-Lyerillusion 18.2 pixels (3.4) 19.0 pixels (3.7) 1,19 0.95

Note. Average standard deviations are in parentheses.*p < .05. **p < .01.

from the true bisection point. (Note that the "shaft" was 250 pixelsin length.) There was no significant effect of observer orientation,but the magnitude of the illusion was significantly greater withlong fins than short fins, 22.16 versus 14.98 pixels, F(l, 19) =103.84, p < .01. The interaction of fin length and observer orien-tation was not significant, F(l, 19) = .05. For the upright condi-tion, the average illusion for long and short fins was 21.72and 14.64 pixels, respectively. For the tilted condition, the averageillusion for long and short fins was 22.63 and 15.31 pixels,respectively.

In summary, each illusion for which the tilt-constancy theoryhas an account (tilt induction, Zollner, Poggendorff, and Ponzo)behaved like Asch and Witkin's (1948) tilted-room illusion: Theillusion increased when observers were tilted. However, tiltingobservers does not increase every illusion: It had no effect on theMiiller-Lyer illusion. We conducted a partial replication of thisexperiment with slightly different stimuli (e.g., the Zollner figurehad two horizontal lines) and 10 additional observers with identi-cal results: a significant effect of observer tilt with the Zollner,Ponzo, and Poggendorff illusions but no influence on the Miiller-Lyer illusion. Finally, we ran an analysis of the Miiller-Lyerillusion that combined the main experiment and the replication, sothat there were 30 observers, and the effect of body tilt was still notreliable. Experiments 2 and 3 address two alternative accounts ofthis effect.

Experiment 2

The dramatic effect of tilting the observer on the tilt-inductioneffect could be the result of tilting the observer per se and not theresult of visual context on perception. It is known that tilting anobserver 45° or more in the dark causes a line to appear tilted in theopposite direction. This effect is called the Aubert effect or A effect(Howard, 1982, p. 427; Witkin & Asch, 1948a), and it couldaccount for our findings with the tilt-induction effect. However,tilting the observer less than about 30° causes a line to appear tiltedin the same direction as the observer (E effect) and would runcounter to our results.

To test the effect of tilting the observer on orientation withoutcontext, we repeated the tilt-induction task of Experiment 1 butwithout the tilted grating (see Figure 1). The stimulus consisted ofjust two dots, and 20 observers were run in the tilted conditiononly.

The average setting was 0.87° in the direction opposite theobserver's body tilt. This value was not significantly differentfrom 0, f(19) = 0.98, ns, and is in the opposite direction of thatfound in Experiment 1, which included a visual context (i.e.,grating). The average standard deviation was 2.14°. Thus, theincrease of the tilt-induction effect with tilting observers in Ex-periment 1 was not the result of the A effect but rather was due toan increased effect of visual context.

Experiment 3

It has been known since the early days in the study of visualillusions that the Zollner and Poggendorff illusions are affected bythe orientation of the stimulus (e.g., Judd & Courten, 1905; Ve-linsky, 1925). For example, Judd and Courten found that themagnitude of the Zollner illusion was less in the orientation


illustrated in Figure 5 than when rotated 45°. Hence, the effect oftilting the observer in Experiment 1 might simply be an effect ofrotating the stimulus on the retina rather than rotating the observerper se. To test for this possibility, we replicated Experiment 1 withthe Zollner, Ponzo, Poggendorff, and Muller-Lyer tasks with thestimulus at the same retinal orientation when the observer wasseated upright and when the observer was seated tilted 30°. We didnot run the tilt-induction effect because we were not sure what toexpect if the orientation of the grating was changed with respect toretinal orientation because the observer's task was to indicategravitational vertical.

Table 2Results From Experiment 3

Effect Upright condition Tilted condition F(\, 23)

Zollner illusion 12.2 pixels (6.9) 20.2 pixels (8.6) 24.73**Poggendorff illusion 35.6 pixels (11.2) 40.1 pixels (10.6) 4.51*Ponzo illusion 6.9% (4.3) 8.5% (4.4) 5.77*

Muller-Lyer illusion 18.5 pixels (4.0) 16.9 pixels (4.0) 5.19*

Note. Average standard deviations are in parentheses.*p<.05. **p<.01.

Method

Procedure. Half of the observers began with the upright condition, andthe other half began with the tilted condition. Observers were tested for 30trials in each condition. For the upright condition, the stimulus was iden-tical to Figure 5 except that the Poggendorff illusion was rotated 45° in acounterclockwise direction from that shown in Figure 4B. We used a 45°orientation, because depending on the observers' eye rotation (see below),further rotating the stimulus in the tilted condition made the short lineshorizontal with respect to gravity for some observers but not for others. Wewanted to keep the stimulus similar for all observers regardless of their eyerotation. Also, for the Miiller-Lyer illusion, we used only the short wingversion (see Figure 5).

When the observer was tilted 30°, the stimulus was further rotated so thatit would form the same retinal image as when the observer was upright.When observers are tilted, their eyes rotate in their orbits in the directionopposite to their body rotation (Howard, 1982, p. 383), and the amount of eyerotation varies from observer to observer. Thus, we measured each observer'seye rotation (when seated tilted 30°) and adjusted the stimulus so that it had thesame retinal orientation when the observer was upright and tilted.

Rotational eye movements were measured in the following manner. Atthe beginning of the session, observers were seated in a normal chair in astandard upright posture. They looked at a photographic strobe light thatwas masked with a vertical slit. When the strobe flashed, it left anafterimage of a line that was retinally vertical. The observers then quicklymoved to the tilted chair. Next, observers adjusted the orientation of a lineon the computer monitor until it lined up perfectly with his or her after-image. If there was no eye rotation, then observers would set the line at 30°,the angle of body tilt. If observers' eyes rotated back to vertical, then theywould set the line to vertical (0°). Thus, eye rotation was simply thedifference between the angle that observers adjusted the line and their bodytilt. Rotational eye movements ranged from 0° to 13°, across observers, andaveraged 4.5°.

No observer reported difficulty in the eye rotation task. We checked thereliability of this method with 2 observers on several different occasionsand measurements agreed within 1°.

The viewing distance was 81 cm instead of the 107 cm used in Exper-iments 1 and 2? Hence, the horizontal lines in the Zollner and Poggendorffillusions subtended 7.4° of visual angle instead of the 5.68° in Experi-ment 1. Thus, all dimensions of the stimuli subtended approximately 75%of those in Experiment 1.

Observers. Twenty-four observers, recruited from among the under-graduate population of the University of California, Berkeley, participatedin the experiment. The average age was 19 years; 19 were female and 5were male.

Results and Discussion

The magnitude of the Zollner, Poggendorff, and Ponzo illusionswere significantly greater in the tilted condition than in the uprightcondition (see Table 2). Thus, even when we controlled for retinal

orientation, tilting the observer still increased the magnitude ofthese illusions. We had previously run a pilot experiment with justthe Zollner illusion with 10 observers, correcting for retinal ori-entation, and obtained the same results: The illusion was greaterwhen observers were tilted even when retinal orientation wascontrolled. In this pilot experiment, the viewing distance was thesame as in Experiments 1 and 2, and the Zollner stimulus wasrotated 45° (like the Poggendorff stimulus in the presentexperiment).

Note that the magnitude of the effect of tilting the observer wasless than in Experiment 1 (compare Tables 1 and 2). Hence, it maybe that there is some effect of retinal orientation. Alternatively, thedifference between the magnitude of the effects in Experiments 1and 3 may be due to the perceived orientation of the figures, notthe retinal orientation. In an ingenious study, Spivey-Knowltonand Bridgeman (1993) varied the orientation of a Poggendorffstimulus and found that the magnitude of the illusion varied withorientation, producing a function similar to previous studies (e.g.,Green & Hoyle, 1964; Greene & Pavlow, 1989; Leibowitz &Toffey, 1966). However, when they surrounded the stimulus witha luminous frame of different orientations, it was the orientation ofthe frame that was critical, not the retinal orientation.

The results for the Miiller-Lyer illusion surprised us. The illu-sion was significantly less when observers were tilted than whenthey were upright (see Table 2). The magnitude of the effect wassmall (18.5 vs. 16.9 pixels) but reliable. As discussed above, wepreviously did not obtain any effect of tilting the observer on theMiiller-Lyer illusion. Hence, it is possible that this result is a TypeI error. Nevertheless, note that tilting the observer had the oppositeeffect on the Muller-Lyer illusion as the other illusions. This resultis consistent with claim that the Miiller-Lyer illusion is caused bya different mechanism than the other illusions that we tested.

Experiment 4

In Experiment 1, the illusions that we claim are related toorientation increased when the observer was tilted (Zollner, Ponzo,Poggendorff, and tilt-induction illusions). We used the Miiller-Lyer illusion as an example of a nonorientation illusion, and itsmagnitude was unchanged by tilting the observer. Because thecauses of the Miiller-Lyer illusion are uncertain, however, we

3 Experiment 3 was conducted about 2 years after the other experimentsreported in the article. The chair apparatus and the arrangement of thelaboratory furniture had changed during that period, resulting in a changein viewing distance.


Figure 6. The stimulus used in Experiment 4. The stimulus is drawn to scale, but in the actual experiment, thestimuli consisted of luminous lines on a black background.

wanted to test a control condition that was clearly not caused bythe misperception of orientation.

The size-constancy illusion shown in Figure 6 provides aninteresting contrast to what we claim are orientation-based illu-sions.4 Most observers perceive the cylinder in the middle of thefigure to be taller than the cylinder at the bottom of the figure. Thiseffect arises because linear perspective and other cues cause thecylinder in the middle of the figure to appear further away than thecylinder at the bottom. If two objects subtend the same visualangle, the object that appears further away will be perceived aslarger. We do not think that this effect is related to orientation, sotilting the observer should not affect this illusion.

However, several theories account for the Ponzo, Zollner, andPoggendorff illusions in terms of linear perspective or perceiveddepth (e.g., Gillam, 1980; Green & Holye, 1963; Gregory, 1963).Linear perspective does not change with the retinal orientation ofthe stimulus (Gregory, 1964), but we do not know how tilting theobserver would affect linear perspective. Tilting the observer in-creases the Ponzo, Zollner, and Poggendorff illusions. If these arecaused by the mechanisms responsible for linear perspective andsize constancy, then tilting the observer might also increase theillusion illustrated in Figure 6.

Method

Procedure. Observers were presented with stimuli such as those illus-trated in Figure 6. The task was to adjust the height of the cylinder at thebottom to match the height of the cylinder in the middle. Observersadjusted the height with a joystick and were under no time pressure. Theadjustments that observers made only affected the height of the bottomcylinder and left its width unaffected (see Stimulus section). Each observermade 24 adjustments in the tilted condition and 24 adjustments in theupright condition. Half of the observers were tested upright first, and halfwere tilted first. Twenty observers, selected as before, participated in asingle session that lasted about 10 min.

Stimulus. The stimulus is shown in Figure 6. The figure is drawnaccording to the rules of linear perspective (see Gillam, 1981). It appearedas luminous and gray areas (the guitars) on a black background. Becausea line drawing using linear perspective can be ambiguous, the guitars wereadded to disambiguate the depth relations. For example, without the guitarsand sign, Figure 6 could represent a pyramid viewed from above. The sign(Home, Sweet Home) was added for artistic balance.

As in the previous experiments, the stimuli were presented on a Macin-tosh computer, and the observers were seated at a viewing distance of 107cm. At this distance, the area covered by the stimulus subtended 15.2°X 9.5° of visual angle (802 X 500 screen pixels). The standard cylinder (inthe center) subtended 8.3° in height (44 pixels) and 6.1° in width (32pixels). The initial height of the adjustable cylinder (on the bottom) wasrandomly set from 20 to 60 pixels, but the width did not change. Thechange in height was accomplished by stretching or contracting the rect-angle on which the cylinder was drawn in a vertical direction only. (Notethat the width of the cylinder might be affected by a Ponzo-like illusioncaused by the oblique lines. For this reason, the manipulation was only inthe vertical direction.) In all other respects, this experiment was similar toExperiment 1.

Results and Discussion

Every observer but 1 adjusted the cylinder too tall (n = 20). Theerror can be expressed as a percentage of the height of the standard(as with the Ponzo illusion). Observers adjusted the cylin-der 14.0% too high in the upright condition and 12.3% too high inthe tilted condition. Note that this difference, though not reliable,F(l, 19) = 1.21, is in the opposite direction as the effect of tiltingthe observer on the orientation illusions in Experiment 1. Thestandard deviations, averaged over the 20 observers, were 5.1%and 6.3% for upright and tilted conditions, respectively.

grateful to Jeremy Wolfe for suggesting this experiment.4 We are


These results would seem to be fairly damaging for accounts ofthe Ponzo, Poggendorff, Zollner, and tilt-induction illusions thatmake reference to linear perspective. Tilting the observer increasesthe tilted-room illusion (Asch & Witkin, 1948), the rod-and-frameeffect (DiLorenzo & Rock, 1982; Witkin & Asch, 1948b), as wellas the illusions tested in Experiment 1. However, tilting had noeffect on linear perspective and size constancy.

Of course it is difficult to prove the null hypothesis. One mightworry, for example, that the effect of perspective was too small,leading to a floor effect. Note that the effect of perspective on thecylinder height was similar in magnitude as the Ponzo illusion inExperiments 1 and 2 (see Tables 1 and 2). Both are illusions oflinear extent, in a vertical direction. Importantly, there is no apriori reason to believe that tilting the observer, or the stimulus,would affect linear perspective. Gregory (1964), for example,asserted that "when a perspective figure is rotated, the perspectivedoes not change" (p. 303). Nevertheless, it was important todemonstrate this dissociation between the effect of tilting theobserver in the orientation illusions and an illusion based on linearperspective.

There is one account that may allow linear perspective (andother theories) to play a role in some of these illusions, however.It may be that some of these illusions have multiple causes, assuggested by Coren and Girgus (1978). For example, it could bethat the Poggendorff illusion is caused by both tilt constancy andlinear perspective. The present experiments only manipulated thetilt-constancy component, but linear perspective (or other mecha-nisms) may still play a role.

The present experiments were designed to test the tilt-constancyexplanation and to provide an empirical link between the large-scale illusions (tilted-room and rod-and-frame effects) and theorientation illusions. To rule out other theories, one needs a situ-ation in which competing theories make different predictions. Wehave tested various theories in this manner with the Ponzo illusion(Prinzmetal et al., in press). With the Ponzo illusion, Prinzmetal etal. demonstrated that the tilt-constancy theory accounted for 100%of the Ponzo illusion, leaving little role for other mechanisms.Furthermore, Prinzmetal et al. demonstrated that the followingtheories were neither necessary nor sufficient to account for thePonzo illusion: (a) the low-pass filter theory (Ginsburg, 1984), (b)the assimilation theory (Pressey & Epp, 1992), (c) a size-comparison theory (Kunnapas, 1955), (d) the pool-and-store the-ory (Girgus & Coren, 1982), and (e) the linear perspective andsize-constancy theory (e.g., Gillam, 1980; Gregory, 1963). Moreresearch will be necessary to completely rule out the possibilitythat these theories play a role for some of the other illusions.

General Discussion

We hypothesized that the Zollner, Poggendorff, and Ponzoillusions and the tilt-induction effect were caused by the samemechanism that causes the tilted-room illusion. Tilting an observerincreases the tilted-room and the rod-and-frame effects (Asch &Witkin, 1948; DiLorenzo & Rock, 1982; Witkin & Asch, 1948b).If the same mechanisms are responsible for these illusions, thentilting the observer should also increase these illusions, and it did.The discussion that follows is organized around three issues: First,we discuss our findings in relation to our theory versus previoustheories of these illusions. Second, we suggest an algorithm for tilt

constancy and discuss its neural implementation. Finally, webriefly consider a few empirical issues left unresolved by thepresent research.

Our present results are inexplicable by previous theories of theseillusions, which include those based on linear perspective (e.g.,Gillam, 1980; Green & Holye, 1963; Gregory, 1963), the low-passfilter theory (Ginsburg, 1984), and inhibition among orientation-tuned cells (Blakemore et al., 1970). Unlike the tilt-constancytheory, none of these theories predict an increase in the magnitudeof these illusions when an observer is tilted. The present researchsuggests that the relevant mechanisms revealed by these illusionsare those that determine orientation, and in particular, local visualcues to orientation. Of course, as we pointed out previously, wecannot rule out the possibility that other mechanisms may playsome role in these illusions, but any theory of these illusions mustcontain a reference to the perception of orientation.

Our account of these results, the tilt-constancy theory, has somesimilarities with theories that appeal to size constancy and linearperspective (e.g., Day, 1972; Gillam, 1980; Gregory, 1963). Thereare several distinct variants of this theory (see Green & Hoyle,1964), but all appeal to mechanisms related to size constancy. Sizeconstancy is, of course, the ability to perceive objects in their truesize regardless of distance. Tilt constancy is the ability to perceiveobjects in their true orientation regardless of the orientation of theobserver. Hence, both theories appeal to normally adaptive pro-cesses. Furthermore, although there are a number of determinantsof perceived distance, the theories that account for the visualillusions treated in this article only appeal to linear perspective.Similarly, there are several determinants of perceived orientationin addition to visual information, such as vestibular and somato-sensory information, but we only appeal to the misperception oforientation due to visual information.

Note that both the size-constancy family of theories and thetilt-constancy theory account for a wide range of illusory phenom-ena but not precisely the same phenomena. For example, we haveno account of the Miiller-Lyer illusion, whereas the Miiller-Lyerillusion is often used as the foremost example for the size-constancy theories. Indeed, it is not a virtue for the same theory toaccount for both the Miiller-Lyer illusion and the other illusionsbecause, as we pointed out, both previous research and our presentfindings suggest that they are not caused by the same mechanisms.To this previous evidence, we add that the Zollner, Poggendorff,and Ponzo illusions and tilt-induction effect behaved differentlythan the Miiller-Lyer illusion when observers were tilted. Hence,although size constancy may provide a good explanation of theMiiller-Lyer illusion (see e.g., Gregory & Harris, 1975), it doesnot account for our results, and Experiment 4 clearly demonstratesthat size constancy behaves differently than the orientation-basedillusions.

Our theory should not be confused with another theory thatacute angles are overestimated (Hering, 1861). This theory hasbeen applied to the Zollner and Poggendorff illusions and thetilt-induction effect. It has not been applied to the Ponzo illusion.In modern physiological terms, the overestimation of angles isclaimed to be a consequence of the inhibition of neurons in VI(e.g., Blakemore et al., 1970). According to this explanation, whentwo lines forming an acute angle are presented to an observer, eachline activates a population of cells. The cells activated are thosetuned to the orientation of each line. However, cells tuned to


orientations similar to the lines are also activated. Cells activatedby both lines (i.e., those with orientations between the lines)mutually inhibit each other. Thus, the total activation is shifted sothat the angle is perceived as larger than it is.

There is now ample evidence that the acute-angle theory isinadequate to account for the Zollner and Poggendorff illusionsbecause these illusions can be obtained without any "angles" in thestimulus (e.g., Pressey & Sweeney, 1972; Wilson & Pressey,1976). Indeed, our version of the tilt-induction effect in Experi-ments 1 and 2 (see Figure 4) does not contain lines that wouldmutually inhibit each other. Indeed, Tyler and Nakayama (1984)provided an example of a Zollner illusion with only lines of oneorientation, and Day and his colleagues (Day & Jolly, 1987; Day,Jolly, & Duffy, 1987; Day, Watson, & Jolly, 1986) described aversion of the Poggendorff illusion, using a bisection task and onlytwo parallel lines (or even three dots). Furthermore, a theory basedon simple inhibition between line segments cannot explain theresults of tilting the observer. We are not suggesting that a theorybased on neural architecture is inappropriate; later, we outline thebeginning of a neural theory of perceived orientation. However, atheory based on the misperception of angles (as opposed to orien-tation) does not account for existing data. A misperception oforientation may cause a misperception of angles, but the cause ofthe illusions, according to the tilt-constancy theory, has its roots inthe perception of orientation.

A final family of theories, referred to as assimilation theories,has been used to account for many of these same illusions. Thesetheories are diverse and include the low-pass filter theory ofGinsburg (1984), the assimilation theory of Pressey and his col-leagues (Pressey, 1971; Pressey, Butchard, & Scrivner, 1971;Pressey & Epp, 1992), and the pool-and-store model of Girgus andCoren (1982). These theories also have no account of our presentfindings. Indeed, no theory that only appeals to visual mecha-nisms—as opposed to a mechanism of spatial representation—canaccount for the effects of tilting the observer.

A complete theory of these illusions should specify the neuralmechanisms underlying tilt constancy. Our results suggest that themechanisms are likely to involve neurons that are tuned to orien-tation relative to the visual environment, rather than the observer'sretinal orientation. In animal studies, Sauvan and Peterhaus (1995)searched in the cortex of awake macaque monkeys for cells whosetuning functions were related to the environment as opposed to theanimal's orientation. They found virtually no cells in the striatecortex that showed this property. All of the cells in the striatecortex were tuned in relation to retinal coordinates. However, 40%of cells in extrastriate areas (Areas V2, V3, and V3a) were tunedin relation to environmental, not retinal coordinates. Likely can-didates for the neural substrate of these illusions will be areas withan abundance of cells that are tuned to environmental coordinates.

There are probably many ways of implementing tilt constancywith simple neural hardware. Environmentally tuned cells could becreated from retinally tuned cells with a simple two-layer system.Suppose there is a population of retinally tuned vertical detectorsin the first level. These cells will fire to vertical lines, but also tolines near vertical. If the stimulus contains lines that are nearvertical, a second level of the system would be erroneously sig-naled that a vertical was present. The same process would happenwith stimulus lines near horizontal. Thus, contours in the visualenvironment near retinal vertical would define orientation. Note

that this mechanism is distinct from lateral inhibition and low-passfiltering. However, like these theories, it invokes simple neuralprocesses. A simple mechanism such as this might underlay whatGibson (1937) meant by a process of normalization.

Of course, such a simple scheme is incomplete because it doesnot include gravity-based cues to orientation (i.e., vestibular andsomatosensory cues). Our findings, along with previous findingsby Asch and Witkin (1948) and others (e.g., DiLorenzo & Rock,1982; Goodenough, Oltman, & Sigman, 1981; Templeton, 1973),suggest that when an observer is not in an upright position, visualcues play a greater role. There are many possibilities as to howvisual and extravisual information are integrated. For example, itmight be that the perceived orientation of a stimulus is a weightedlinear average of retinal and gravity-based cues (Matin & Fox,1989). Alternatively, the integration of information may be non-linear (e.g., Carlson-Radvansky & Logan, 1997). Furthermore,there are many possible sites in the brain for the integration ofvisual and other information.

In addition to the general theoretical issue discussed above,tilt-constancy theory raises a plethora of research issues, of whichwe mention only three. First, we do not have a precise descriptionof why tilting an observer increases the tilted-room illusion andrelated illusions. In the most general sense, tilting the observerincreases one's reliance on visual as opposed to gravity-basedinformation. However, this description raises a number of empir-ical issues. For example, tilting the observer may increase theorientation illusions because it creates a conflict among retinal,visual, and gravity-based cues to orientation. If this hypothesis iscorrect, only body positions that create a conflict will increasethese illusions. However, perhaps any body position that is notaligned with visual vertical will influence performance. In thiscase, a supine posture would also increase the tilt-induction effectand the Zollner, Ponzo, and Poggendorff illusions. Because therod-and-frame effect is greater when observers are in a supineposture (Goodenough et al., 1981; Templeton, 1973), we wouldpredict that supine observation would similarly affect the otherillusions. We are currently testing this hypothesis.

A second issue relates to the perception of pitch. There is awell-known pitch-box illusion that is analogous to the tilted-roomillusion. Observers' perceived eye level is affected by the pitch ofthe visual environment. If observers are looking down a hall thatis pitched down, for example, they will indicate that eye level islower than it actually is (Kleinhans, 1970; Matin & Fox, 1989;Matin & Li, 1992,1996; Stoper, 1998; Stoper & Cohen, 1986). Anissue that concerns us is whether the mechanisms of pitch percep-tion (e.g., perception of eye level) are the same as the mechanismsfor the perception of vertical and horizontal.

Finally, the concept of reference frames plays a large role inother aspects of cognitive psychology, including recognition (Mer-melstein, Banks, & Prinzmetal, 1979; Rock, 1974; Yin, 1969),object description, and attention (e.g., Behrmann & Tipper, 1999;Robertson, 1995). An important issue is whether the local framesof reference that cause distortions such as the Ponzo and Zollnerillusions are the same as these other reference frames. To theextent that they are the same, manipulations that affect the illusions(e.g., tilting the observer) should have similar effects in these otherdomains.

We proposed that the Ponzo, Zollner, and Poggendorff illusionsand the tilt-induction effect are due to the visual mechanisms that


create illusions of orientation in the tilted-room illusion (tilt-constancy theory). In the tilted-room illusion, tilting the observerincreases the effect of visual context in relation to gravitationalinformation. In a similar manner, tilting the observer also increasesthe magnitude of these illusions. The tilt-constancy theory broad-ens the functional significance of these illusions. These illusionsare not only relevant to visual processes but also informative aboutthe nature of human spatial representations.

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Received April 20, 1999Revision received May 8, 2000

Accepted May 12, 2000

The Tilt-Constancy Theory of Visual Illusions...visual illusions provide unique insights into...

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