Copyright 2001 by the American Psychological Association, Inc.
0096-1523/01/S5.00 DOI: 10.1037//O096-1523.27.1.206
Journal of Experimental Psychology:
Human Perception and Performance
2001, Vol. 27, No. 1, 206-217
The Tilt-Constancy Theory of Visual Illusions
William Prinzmetal
Diane M. Beck
University of California, Berkeley
University College London
The authors argue that changes in the perception of vertical and horizontal caused by local visual cues
can account for many classical visual illusions. Because the perception of orientation is influenced more
by 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 tilted
30°. The magnitude of Zollner, Poggendorff, and Ponzo illusions and the tilt-induction effect substantially increased when observers were tilted. In contrast, the MiiUer-Lyer illusion and a size constancy
illusion, which are not related to orientation perception, were not affected by body orientation. Other
theoretical approaches do not predict the obtained pattern of results.
shifts in gravity in relation to body position (Howard, 1998;
Howard & Childerson, 1994), we call our new account of visual
illusions the tilt-constancy theory.
We first illustrate how local visual cues to orientation can
account for many illusions. Second, we review the literature relevant to our claim. Finally, we present evidence in support of the
tilt-constancy theory that cannot be explained by other theories.
The effect of visual context on orientation perception was dramatically illustrated in classic studies by Asch and Witkin (1948).
Observers viewed a room that was tilted 22° in the picture plane
and were asked to adjust a rod so that it was oriented horizontally
or vertically with respect to gravity. The average setting was
distorted 15° in the direction of the tilt of the room. Although
vestibular and somatosensory information could have been used to
adjust the rod, visual context dominated orientation perception.
This phenomenon is called the tilted-room illusion, and it dramatically illustrates the powerful contribution of visual information to
orientation perception. The tilted-room illusion has been exploited
in several roadside attractions and amusement parks (Banta, 1995;
Shimamura & Prinzmetal, 2000). In these settings, people's misperception of vertical and horizontal is such that balls appear to
roll uphill and people appear to stand at gravity-defying angles.
Such compelling illusions have resulted in these settings being
called "antigravity houses" (also see www.illusionworks.com).
For over a hundred years, visual scientists have believed that
visual illusions provide unique insights into normally adaptive
visual processes. For example, Helmholtz (1881/1962) commented,
The study of what are called illusions of the senses is a very prominent
part of the senses; for just those cases which are not in accordance
with reality are particularly instructive for the discovering the laws of
those means and processes by which normal perception originates, (p.
251)
With rare exception (e.g., Ward & Coren, 1976), most theories
have attributed visual illusions to "information processing mechanisms that are normally adaptive" (Gregory, 1968, p. 66). The
controversy arises as to what mechanisms are being reflected by
particular illusions. For example, the Zollner illusion has been
attributed to a variety of mechanisms, including spatial frequency
coding in early vision (Ginsburg, 1984), inhibition among orientation tuned cells (Blakemore, Carpenter, & Georgeson, 1970), and
the mechanisms responsible for linear perspective (e.g., Gillam,
1980; Green & Holye, 1963; Gregory, 1963).
We offer a new explanation that also involves a normally
adaptive process. We propose that the perception of line orientation (e.g., Zollner illusion), collinearity (e.g., Poggendorff illusion), line length (e.g., Ponzo illusion), and line curvature (e.g.,
Wiindt-Hering illusion) are caused by the same mechanisms that
are responsible for the perception of vertical and horizontal. Because these mechanisms are related to people's ability to perceive
a constant orientation despite changes in retinal orientation or even
The rod-and-frame effect illustrates that a very sparse visual
stimulus can also create orientation distortions (Witkin & Asch,
1948b). In the rod-and-frame task, observers adjust a rod to vertical or horizontal. The rod is surrounded by a tilted frame. Observers 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 when
the rod is close to the frame and is reduced in magnitude as the gap
between the rod and frame increases (e.g., Zoccolotti, Antonucci,
& Spinelli, 1993).
The rod-and-frame effect and tilted-room illusion are similar to
the tilt-induction effect (Gibson, 1937). Gibson presented stimuli
similar to Figure 1A. Observers noted that a truly vertical line
appeared to tilt in the direction opposite to the surrounding context
lines (the apparent tilt is indicated, in exaggerated form, by the
dashed line). Hence, when observers adjusted the central line to
William Prinzmetal, Department of Psychology, University of California, Berkeley; Diane M. Beck, Department of Psychology, University
College London, London, England.
This research was supported in part by National Institutes of Health
Grant 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 William Prinzmetal, Department of Psychology, University of California,
Berkeley, California 94720-1650. Electronic mail may be sent to
wprinz@socrates.berkeley.edu.
206
TILT CONSTANCY AND ILLUSIONS
Figure 1. In all of the panels, the actual stimulus is shown in black, and
the illusion, in exaggerated form, is shown with a dashed line. (A) The
tilt-induction effect: Vertical lines are perceived to be tilted in the direction
opposite the context lines. (B) The Zdllner illusion: The long oblique
context lines in the tilt-induction figure have been replaced by many short
context lines. (C) The standard Zollner illusion. (D) In the tilt-induction
effect, Gibson (1937) observed that vertical context lines increased the
apparent slope of an oblique line. (E) The tilt-induction effect from Panel
D in a context more similar to the Poggendorff illusion. (F) The Poggendorff illusion can be considered a consequence of the tilt-induction effect
in Panel D.
vertical, they erred in the direction of the context lines, just as in
the 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 the
tilt-induction and rod-and-frame stimuli is the size of context: In
the rod-and-frame effect, the stimuli typically subtend many tens
of degrees of visual angle, whereas the tilt-induction experiment
typically involves smaller stimuli. However, Coren and Hoy
(1986) and Wenderoth and Johnstone (1988, Experiment 4) have
obtained rod-and-frame effects with stimuli in the size range of the
tilt-induction effect. We argue that the tilted-room illusion, the
rod-and-frame effect, and the tilt-induction effect are caused by the
same mechanisms (cf. Howard, 1982, pp. 155-156; Singer, Purcell, & Austin, 1970).
Several investigators have speculated that the Zollner illusion is
an instance of the tilt-induction effect (Day, 1972; Howard, 1982,
207
pp. 156-157). The similarity of the illusions can be seen in Figures
1A and IB, in which the flanking context lines in Figure 1A have
been replaced by many shorter context lines in Figure IB. The
Zollner illusion, as typically presented (Figure 1C), illustrates the
effect of local context, in which the oblique lines on the left govern
the slope of the left long line and the oblique lines on the right
affect the slope of the right long line. Moreover, the tilt-induction
effect and the Zollner illusion behave similarly with the manipulation of a host of independent variables (see Prinzmetal, Shimamura, & Mikolinski, in press). Many visual illusions, such as
the Wundt-Hering illusion and Fraser spiral, can be understood as
instances of the Zollner illusion (Fisher, 1968). It may be that the
Cafe Wall illusion is also an instance of the Zollner illusion
(Prinzmetal et al., in press).
Historically and functionally, the Poggendorff illusion is also
related to the Zollner illusion (Boring, 1942). In I860, ZSUner
submitted his illusion for publication. The journal editor, Poggendorff, noticed that the oblique lines did not appear to be collinear.
The functional relationship of the Poggendorff illusion to the
tilt-induction effect is illustrated in Figures ID, IE, and IF. Gibson
(1937) noted that, in the stimulus illustrated in Figure ID, the
central oblique line appeared to be inclined at a larger angle than
it actually was, illustrated again by the dashed line. (We have
verified this in our laboratory.) If we simply displace the central
line and its resulting illusory percept, as we did in Figure IE, we
can see the similarities to the Poggendorff illusion in Figure IF. As
a consequence of the misperception of the orientation of the central
line (i.e., the tilt-induction effect), the oblique lines do not appear
collinear. Note that it is not just that acute angles appear larger than
they are, because the Poggendorff illusion can be created without
any angles at all (e.g., see Day & Jolly, 1987; Pressey & Sweeney,
1972; Wilson & Pressey, 1976). We argue that the Poggendorff
and Zollner illusions are caused by a misperception of orientation,
not a misperception of angles.
By our account, all of the geometric illusions described thus far
can be related to orientation. Our approach can also account for
other distortions, such as the line length observed in the Ponzo
illusion. Figure 2 demonstrates how the Ponzo illusion can be
considered a case of the Zollner illusion. In Figure 2A the vertical
lines appear further apart at the top of the figure than at the bottom
of the figure (Zollner illusion). Similarly, the horizontal line at the
top 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 Z6Uner
illusion with the Ponzo illusion suggested with bold lines. (B) The Ponzo
illusion with the Zollner illusion in the background.
208
PRINZMETAL AND BECK
further apart than the bottom horizontal lines. Figure 2A is drawn
to suggest that the Ponzo illusion is part of the Zollner illusion, and
in Figure 2B, the Ponzo is hidden in the Zollner illusion.
We have conducted experiments on the tilt-induction effect with
stimuli similar to those shown in Figures 3 A and 3B that compared
the magnitude of the Ponzo illusion with the tilt-induction effect
(Prinzmetal et al., in press). With stimuli such as those in Figure
3 A, observers adjusted the free end of the bottom horizontal line so
that it appeared to be vertically aligned, according to gravity, with
the end of the top horizontal line. The oblique line on the right
caused a tilt-induction effect so that observers erred by making the
line too long. The Ponzo illusion was measured with stimuli such
as those in Figure 3B. Observers adjusted the length of the bottom
horizontal line so that it matched the length of the top line. Because
the Ponzo illusion involves a tilt-induction effect at either end, one
would predict that the Ponzo illusion would be twice as great at the
tilt-induction task, and this is what was found. Additionally, across
observers, the correlation between the two illusions was .70. Prinzmetal et al. also compared predictions of several theories of the
Ponzo illusion with the tilt-constancy theory. The results were
consistent with the tilt-constancy theory.
In summary, the tilt-constancy theory proposes that the tiltinduction effect and the Zollner, Poggendorff, and Ponzo illusions
are due to a misperception of orientation caused by local visual
context. Further, we propose that the mechanism responsible for
the local misperception of location is the same as the mechanism
that causes the tilted-room illusion and the rod-and-frame effect.
The possibility that the Zollner illusion and the tilt-induction
effects are caused by the same mechanism as the tilted-room
illusion and the rod-and-frame effects has been the subject of
controversy. On the one hand, Day (1972) suggested that the
Zollner illusion is caused by the same mechanism as the tiltedroom illusion.1 On the other hand, Howard (1982, pp. 155-156)
asserted that the "frame effects" (i.e., tilted room illusion, rod-andframe effect) are caused by a different mechanism than the "tiltnormalization" 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 frame
and tilt-normalization effects are caused by different mechanisms.
First, he asserted that the frame effects are many times larger than
the normalization effects and therefore must be caused by different
Figure 3. The Ponzo illusion considered as a consequence of the tiltinduction effect. In Panel A, the ends of the horizontal lines do not seem
to be horizontally aligned. This effect makes the top horizontal line in
Panel B appear longer than the bottom horizontal line.
mechanisms. Strangely, he cited a misperception of orientation of
20°. We know of only one study that found errors of that magnitude. In very special circumstances, Asch and Witkin (1948)
reported a tilted-room illusion of 20°. However, in their experiment, observers were seated in a chair that was tilted 24°. Furthermore, there was an elaborate procedure, lasting 7 min, to attempt
to get observers to perceive the tilted room as upright. The magnitude of the tilted-room illusion is usually much less, and the
rod-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 similar
magnitude as the tilt-induction effect. In general, the larger and
more elaborate the context, the greater the illusion. This observation seems hardly surprising.
Second, Howard (1982) claimed that tilted-frame effects are
much more in evidence when the frames are in the periphery, but
the 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 that
a larger frame leads to a larger illusion in the rod-and-frame task
(e.g., Ebenholtz, 1977,1985; Ebenholtz & Callan, 1980). It is clear
that as the frame becomes larger, it becomes more peripheral.
However, these studies confound frame eccentricity and frame
size. As we have commented, it does not seem surprising that a
larger context would lead to a larger illusion.2 The second piece of
evidence for the claim that the periphery is special is a study by
DiLorenzo and Rock (1982). They conducted a rod-and-frame task
with 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 a
period of 4 min, before the inner frame was presented. Hence, the
procedure may have biased observers to use the outer frame.
Finally, Howard (1982) claimed that the tilted-room illusion is
affected 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 objects
such as flower vases and tables. However, there is no evidence that
the tilt-induction effect is not influenced by cognitive variables.
Furthermore, this argument is logically inconsistent in that Howard
claimed that the tilted-room and rod-and-frame effects are caused
by the same mechanism because they both involve large peripheral
stimulation, whereas the tilt-induction effect does not. However,
the rod-and-frame effect does not involve familiar objects (as in
the tilted-room effect). Hence, by Howard's arguments, it is unclear whether these illusions should be classified on the basis of
their scale, on whether they involve peripheral stimulation, or on
whether they are influenced by cognitive variables.
1
We know of no one who has suggested that the Poggendorff and Ponzo
illusions were caused by the misperception of orientation. Note that the
misperception 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 leads
to a larger rod-and-frame effect. As mentioned earlier, they found that with
a given frame size, the size of the rod affected performance. As the rod
increased in size (so that the gap between the rod and frame got smaller),
the magnitude of the illusion increased.
TILT CONSTANCY AND ILLUSIONS
Day's (1972) position, that the tilted-room illusion is caused by
the same mechanism as the Zollner illusion and the tilt-induction
effect, is consistent with the tilt-constancy theory. The position is
parsimonious in that a single mechanism is proposed for both
phenomena. Furthermore, it provides a functional account of the
tilt-induction illusion because the tilted-room illusion is related to
the mechanism of tilt constancy. Nevertheless, there is no compelling evidence to support this view. If the tilted-room illusion
and the tilt-induction effect are caused by the same mechanisms,
then one would predict that an independent variable that critically
affects the tilted-room illusion should also affect the tilt-induction
effect. In the following experiments, we manipulated such a
variable.
In summary, the tilt-constancy theory claims that the same
mechanism that causes the incorrect perception of orientation in
the tilted-room illusion (e.g., Asch & Witkin, 1948) is responsible
for a variety of illusions, including the Zollner, the Poggendorff,
and Ponzo illusions as well as the tilt-induction effect. A variable
that has been known to affect the tilted-room illusion is the
physical orientation of the observer relative to gravity. Asch and
Witkin (1948) found that seating observers in a chair that was
tilted 24° significantly increased the magnitude of the tilted-room
illusion (Asch & Witkin, 1948). Tilting the observer also increases
the rod-and-frame effect (DiLorenzo & Rock, 1982; Witkin &
Asch, 1948b). That is, observers tend to disregard gravity-related
cues to orientation in favor of visual cues when tilted. The finding
that observer orientation affects performance in the tilted room
leads to a straightforward prediction: If the tilt-induction effect and
the Zollner, Poggendorff, and Ponzo illusions are caused by the
same mechanism as the tilted-room illusion, they should also
increase when observers are seated in a tilted position. In the
present experiments, we compared the magnitude of these illusions
when observers were seated upright and when they were seated in
a chair, tilted 30° about the observer's line of sight.
A few previous investigators have measured various illusions
with observers in postures other than upright with inconsistent and
conflicting results (Campbell & Maffei, 1971; Day & Wade, 1969;
Wallace & Moulden, 1973; Wolfe & Held, 1982). We believe that
there were two critical factors when testing an effect of body
orientation that were not controlled in previous research but were
controlled in the present experiments. First, the visual environment
must be adequately manipulated. In measuring the tilt-induction
effect, if the frame on the computer monitor, or the surrounding
room, is visible, then most of the visual environment is aligned
with gravity even if the inducing lines are not. In our experiments,
the observers were tested in the dark, and the stimuli consisted of
luminous lines on a black background. To ensure that observers
did not see the frame of the monitor, we required them to wear
goggles with dark neutral density lenses. Second, because the
perception of orientation persists over time (i.e., the tilt aftereffect), observers sat in the dark for 30 s before beginning each
experiment.
We do not believe that the tilt-constancy theory can explain all
illusions, only those that are due to the misperception of orientation induced by visual context. Hence, we do not expect that tilting
the observer will increase nonorientation illusions. The MiillerLyer illusion is a robust illusion, but we believe that it has little to
do with the perception of orientation for three reasons. First,
observers who evinced strong Zollner and Poggendorff illusions
209
were not those who showed a strong Miiller-Lyer effect (Coren,
Girgus, & Erlichman, 1976). Second, as we mentioned earlier, the
strength of many of these illusions varies with its orientation, and
in our lab we have failed to find such an effect with the MullerLyer illusion. Finally, with the Zollner, Poggendorff, and Ponzo
illusion, the orientation of the context lines critically determines
the magnitude of the illusion. In contrast, with the Miiller-Lyer
illusion, it is the distance the "wings" extend beyond the horizontal
line that determines the illusion magnitude (Coren, 1986). Hence,
we predicted that the Muller-Lyer illusion would not vary when
observers were tilted. To ensure that a null finding was not the
result of a floor or ceiling effect, we manipulated the strength of
the 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 the
tilt-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 manipulation
was at least as strong as theirs, so we tilted our observers 30°.
Experiment 2 was a control condition to test for the effect of tilting
observers without visual context. Experiment 3 tested observers on
the Zollner, Ponzo, and Poggendorff illusions when seated upright
and tilted, while controlling for retinal orientation. Finally, in
Experiment 4, we tested the effect of tilting observers on a second
nonorientation illusion, specifically, an illusion of size induced by
linear perspective.
Experiment 1
Method
Procedure. Each observer was tested in a single session that lasted
about 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 in
the tilted position. The order of the tasks within the first or second half of
the experiment was counterbalanced across observers. The results from
half of the observers on the Zollner task were lost because of a computeroperator error. Nevertheless, the order of conditions for the observers
whose data were included was completely counterbalanced, as described
above.
Observers were tested for 24 trials in each task. In measuring the
tilt-induction effect, observers moved the top dot back and forth so that it
was vertically aligned, according to gravity, with the bottom dot (see
Figure 4). Specifically, observers were told that if the two dots were tennis
balls, the top dot should be placed so that if dropped, it would land squarely
on the bottom dot in the real world. Observers used a joystick to move the
top dot horizontally back and forth until they were satisfied with their
setting, 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 their
settings.
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. The
Poggendorff illusion (Figure 5B) was assessed by having observers move
the bottom oblique line back and forth, horizontally, until it appeared
collinear with the top oblique line. To measure the Ponzo illusion (Figure
5C), observers adjusted the length of the vertical line on the left until it
appeared to be the same length as the line on the right.
We used the Brentano version of the MUller—Lyer illusion. The observers' task was to adjust the location of the central arrowhead so that its
tip would bisect the horizontal "shaft." There were two versions of the
Miiller-Lyer illusion, as shown in Figure 5D. On 12 trials, the "wings"
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PRINZMETAL AND BECK
1 degree
Figure 4. The stimuli used to measure thetilt-inductioneffect. Observers
moved the top dot, in the direction indicated by the arrow, to be vertically
aligned with the bottom dot. The stimulus is drawn to scale, but in the
actual experiment, the stimuli consisted of luminous lines on a black
background.
were long, and on 12 trials the wings were short. These were presented in
a random order. It has been found that the length of the wings affects the
strength of the illusion: The longer the wings, the greater the illusion (see
Coren & 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 illusion
being at floor or ceiling.
Each task began with the observer sitting in the dark for 30 s, whether
tilted or upright. The starting position of the adjustable component of the
stimulus (e.g., vertical location of dot in the Zollner illusion) was randomly
set before each trial. In addition, in the tilt-induction task, not only was the
horizontal location of the top dot randomly set at the beginning of each
trial, but the vertical position of the pair of dots was also randomly set
within approximately ± 0.5° of visual angle. The reason for this random
displacement was so observers would not use the relationship between the
dot and a particular line in the grating to determine their setting.
Stimuli. Observers were tested in a dark room while wearing goggles
with dark neutral density filters. Hence, the stimuli appeared as luminous
lines in an otherwise dark field. The stimuli were presented on a Macintosh
computer, 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 to
scale. The context lines in the tilt-induction effect stimulus (Figure 4) form
an angle of 18° from vertical. Similarly, the oblique lines in the Zollner,
Poggendorff, and Ponzo illusions were 18° from horizontal. In the MUllerLyer figure, the arrowheads formed an angle of 45°. In the tilt-induction
effect (Figure 4), the distance between the centers of the dots subtended 2.84° of visual angle (160 screen pixels). The horizontal lines in the
Zollner and Poggendorff illusions (Figures 5A and 5B) subtended 5.68° of
visual angle (300 pixels). The oblique lines for the Zollner and Poggendorff
illusions subtended 2.84° and 1.89° of visual angle, respectively (150 and
100 pixels). The length of the standard line in the Ponzo illusion subtended 2.84° of visual angle (150 pixels). Finally, the length of the
horizontal line in the Milller-Lyer figure subtended 4.73° of visual angle
(250 pixels), whereas the arrowheads subtended either 0.379° or 0.758° of
visual angle (20 or 40 pixels).
Apparatus. Observers were seated in a chair that could be set at upright
or tilted 30° counterclockwise. The chair was created from a standard
office furniture chair with armrests. The armrests of the chair were padded.
The chair was fitted with a footrest and a shelf on which observers rested
the joystick. Both the footrest and shelf tilted with the chair. Observers'
heads wererestrainedby a chin rest and lateral support bars so that thenheads 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 are
drawn to scale, but in the actual experiment, the stimuli consisted of luminous lines on a black background.
TILT CONSTANCY AND ILLUSIONS
Observers. Twenty observers participated in the experiment, half of
them were male and half female. However, because of the abovementioned computer error, the results from only 10 observers were included in the Zollner task. The average age of the observers who participated in the experiment was 22 years. All reported that they had normal or
corrected-to-normal vision with no known visual deficits. Observers were
recruited from among the undergraduate population of the University of
California, Berkeley.
Results
The tilt-induction effect and the Zollner, Poggendorff, and
Ponzo illusions were all dramatically and significantly increased
when the observers were tilted 30° compared with when they were
in the upright condition (see Table 1). The dependent variable for
the tilt-induction effect was the deviation from vertical of a virtual
line connecting the top and bottom dots, in degrees, with positive
deviations in the direction of the grating (see Figure 4). For the
Zollner and Poggendorff illusions (see Figure 5), the dependent
variable was the difference, in screen pixels, from the average
adjusted height of the dot to the correct (collinear) location. (Note
that 52.8 pixels are 1° of visual angle.) The magnitude of the
Ponzo illusion was measured as a percentage: the length of adjustable line divided by the length of the standard line. As shown in
Table 1, tilting the observer significantly increased each of these
illusions. Table 1 also indicates the average standard deviation for
each illusion, that is, the standard deviation over the 24 trials for
each condition, averaged over observers.
An additional analysis was conducted with the Poggendorff
illusion. Several investigators (e.g., Weintraub & Krantz, 1971;
Weintraub, Krantz, & Olson, 1980) have suggested that the version
of the Poggendorff illusion that we used should be measured in
degrees. That is, the differences, in degrees, between the angle of
the oblique line (i.e., 18° in this experiment) and the angle formed
by a virtual line connecting the dot and the intersection of the
oblique line and horizontal line. This dependent variable has the
advantage that it is invariant to viewing distance. Therefore, we
performed an additional analysis on the Poggendorff illusion in
which we first transformed each response into degrees error. The
illusion was significantly greater for the tilted than upright conditions, 8.45° versus 6.01°, F(l, 19) = 9.66, p < .05.
In contrast, the Miiller-Lyer illusion was not affected by the
observer orientation (see Table 1). The dependent variable for the
Muller-Lyer illusion was the average distance, in screen pixels,
Table 1
Results From Experiment 1
Effect
Upright condition
Tilted condition
df
F
71.72**
96.63**
Tilt-induction
effect
Zollner illusion
Poggendorff
illusion
Ponzo illusion
2.4° (3.0)
7.3 pixels (4.5)
9.4° (4.9)
26.4 pixels (7.3)
1,19
1,9
28.7 pixels (9.0)
5.9% (3.9)
38.8 pixels (11.3)
8.2% (4.4)
1,19 20.86**
1, 19 7.28*
Muller-Lyer
illusion
18.2 pixels (3.4)
19.0 pixels (3.7)
1,19
Note. Average standard deviations are in parentheses.
*p < .05. **p < .01.
0.95
211
from the true bisection point. (Note that the "shaft" was 250 pixels
in length.) There was no significant effect of observer orientation,
but the magnitude of the illusion was significantly greater with
long fins than short fins, 22.16 versus 14.98 pixels, F(l, 19) =
103.84, p < .01. The interaction of fin length and observer orientation was not significant, F(l, 19) = .05. For the upright condition, the average illusion for long and short fins was 21.72
and 14.64 pixels, respectively. For the tilted condition, the average
illusion for long and short fins was 22.63 and 15.31 pixels,
respectively.
In summary, each illusion for which the tilt-constancy theory
has an account (tilt induction, Zollner, Poggendorff, and Ponzo)
behaved like Asch and Witkin's (1948) tilted-room illusion: The
illusion increased when observers were tilted. However, tilting
observers does not increase every illusion: It had no effect on the
Miiller-Lyer illusion. We conducted a partial replication of this
experiment with slightly different stimuli (e.g., the Zollner figure
had two horizontal lines) and 10 additional observers with identical results: a significant effect of observer tilt with the Zollner,
Ponzo, and Poggendorff illusions but no influence on the MiillerLyer illusion. Finally, we ran an analysis of the Miiller-Lyer
illusion that combined the main experiment and the replication, so
that there were 30 observers, and the effect of body tilt was still not
reliable. Experiments 2 and 3 address two alternative accounts of
this effect.
Experiment 2
The dramatic effect of tilting the observer on the tilt-induction
effect could be the result of tilting the observer per se and not the
result of visual context on perception. It is known that tilting an
observer 45° or more in the dark causes a line to appear tilted in the
opposite direction. This effect is called the Aubert effect or A effect
(Howard, 1982, p. 427; Witkin & Asch, 1948a), and it could
account for our findings with the tilt-induction effect. However,
tilting the observer less than about 30° causes a line to appear tilted
in the same direction as the observer (E effect) and would run
counter to our results.
To test the effect of tilting the observer on orientation without
context, we repeated the tilt-induction task of Experiment 1 but
without the tilted grating (see Figure 1). The stimulus consisted of
just two dots, and 20 observers were run in the tilted condition
only.
The average setting was 0.87° in the direction opposite the
observer's body tilt. This value was not significantly different
from 0, f(19) = 0.98, ns, and is in the opposite direction of that
found in Experiment 1, which included a visual context (i.e.,
grating). The average standard deviation was 2.14°. Thus, the
increase of the tilt-induction effect with tilting observers in Experiment 1 was not the result of the A effect but rather was due to
an increased effect of visual context.
Experiment 3
It has been known since the early days in the study of visual
illusions that the Zollner and Poggendorff illusions are affected by
the orientation of the stimulus (e.g., Judd & Courten, 1905; Velinsky, 1925). For example, Judd and Courten found that the
magnitude of the Zollner illusion was less in the orientation
212
PRINZMETAL AND BECK
illustrated in Figure 5 than when rotated 45°. Hence, the effect of
tilting the observer in Experiment 1 might simply be an effect of
rotating the stimulus on the retina rather than rotating the observer
per se. To test for this possibility, we replicated Experiment 1 with
the Zollner, Ponzo, Poggendorff, and Muller-Lyer tasks with the
stimulus at the same retinal orientation when the observer was
seated upright and when the observer was seated tilted 30°. We did
not run the tilt-induction effect because we were not sure what to
expect if the orientation of the grating was changed withrespectto
retinal orientation because the observer's task was to indicate
gravitational vertical.
Table 2
Results From Experiment 3
Method
orientation, tilting the observer still increased the magnitude of
these illusions. We had previously run a pilot experiment with just
the Zollner illusion with 10 observers, correcting forretinalorientation, and obtained the same results: The illusion was greater
when observers were tilted even when retinal orientation was
controlled. In this pilot experiment, the viewing distance was the
same as in Experiments 1 and 2, and the Zollner stimulus was
rotated 45° (like the Poggendorff stimulus in the present
experiment).
Note that the magnitude of the effect of tilting the observer was
less than in Experiment 1 (compare Tables 1 and 2). Hence, it may
be that there is some effect of retinal orientation. Alternatively, the
difference between the magnitude of the effects in Experiments 1
and 3 may be due to the perceived orientation of the figures, not
the retinal orientation. In an ingenious study, Spivey-Knowlton
and Bridgeman (1993) varied the orientation of a Poggendorff
stimulus and found that the magnitude of the illusion varied with
orientation, producing a function similar to previous studies (e.g.,
Green & Hoyle, 1964; Greene & Pavlow, 1989; Leibowitz &
Toffey, 1966). However, when they surrounded the stimulus with
a luminous frame of different orientations, it was the orientation of
the frame that was critical, not the retinal orientation.
The results for the Miiller-Lyer illusion surprised us. The illusion was significantly less when observers were tilted than when
they were upright (see Table 2). The magnitude of the effect was
small (18.5 vs. 16.9 pixels) but reliable. As discussed above, we
previously did not obtain any effect of tilting the observer on the
Miiller-Lyer illusion. Hence, it is possible that this result is a Type
I error. Nevertheless, note that tilting the observer had the opposite
effect on the Muller-Lyer illusion as the other illusions. This result
is consistent with claim that the Miiller-Lyer illusion is caused by
a different mechanism than the other illusions that we tested.
Procedure. Half of the observers began with the upright condition, and
the other half began with the tilted condition. Observers were tested for 30
trials in each condition. For the upright condition, the stimulus was identical to Figure 5 except that the Poggendorff illusion was rotated 45° in a
counterclockwise 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 lines
horizontal with respect to gravity for some observers but not for others. We
wanted to keep the stimulus similar for all observers regardless of their eye
rotation. Also, for the Miiller-Lyer illusion, we used only the short wing
version (see Figure 5).
When the observer was tilted 30°, the stimulus was further rotated so that
it would form the same retinal image as when the observer was upright.
When observers are tilted, their eyes rotate in their orbits in the direction
opposite to their body rotation (Howard, 1982, p. 383), and the amount of eye
rotation varies from observer to observer. Thus, we measured each observer's
eye rotation (when seated tilted 30°) and adjusted the stimulus so that it had the
same retinal orientation when the observer was upright and tilted.
Rotational eye movements were measured in the following manner. At
the beginning of the session, observers were seated in a normal chair in a
standard upright posture. They looked at a photographic strobe light that
was masked with a vertical slit. When the strobe flashed, it left an
afterimage of a line that was retinally vertical. The observers then quickly
moved to the tilted chair. Next, observers adjusted the orientation of a line
on the computer monitor until it lined up perfectly with his or her afterimage. 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 they
would set the line to vertical (0°). Thus, eye rotation was simply the
difference between the angle that observers adjusted the line and their body
tilt. Rotational eye movements ranged from 0° to 13°, across observers, and
averaged 4.5°.
No observer reported difficulty in the eye rotation task. We checked the
reliability of this method with 2 observers on several different occasions
and measurements agreed within 1°.
The viewing distance was 81 cm instead of the 107 cm used in Experiments 1 and 2? Hence, the horizontal lines in the Zollner and Poggendorff
illusions subtended 7.4° of visual angle instead of the 5.68° in Experiment 1. Thus, all dimensions of the stimuli subtended approximately 75%
of those in Experiment 1.
Observers. Twenty-four observers, recruited from among the undergraduate population of the University of California, Berkeley, participated
in the experiment. The average age was 19 years; 19 were female and 5
were male.
Effect
Upright condition
Tilted condition
F(\, 23)
Zollner illusion
Poggendorff illusion
Ponzo illusion
12.2 pixels (6.9)
35.6 pixels (11.2)
6.9% (4.3)
20.2 pixels (8.6)
40.1 pixels (10.6)
8.5% (4.4)
24.73**
4.51*
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.
Experiment 4
In Experiment 1, the illusions that we claim are related to
orientation increased when the observer was tilted (Zollner, Ponzo,
Poggendorff, and tilt-induction illusions). We used the MiillerLyer illusion as an example of a nonorientation illusion, and its
magnitude was unchanged by tilting the observer. Because the
causes of the Miiller-Lyer illusion are uncertain, however, we
Results and Discussion
The magnitude of the Zollner, Poggendorff, and Ponzo illusions
were significantly greater in the tilted condition than in the upright
condition (see Table 2). Thus, even when we controlled for retinal
3
Experiment 3 was conducted about 2 years after the other experiments
reported in the article. The chair apparatus and the arrangement of the
laboratory furniture had changed during that period, resulting in a change
in viewing distance.
TILT CONSTANCY AND ILLUSIONS
213
Figure 6. The stimulus used in Experiment 4. The stimulus is drawn to scale, but in the actual experiment, the
stimuli consisted of luminous lines on a black background.
wanted to test a control condition that was clearly not caused by
the misperception of orientation.
The size-constancy illusion shown in Figure 6 provides an
interesting contrast to what we claim are orientation-based illusions.4 Most observers perceive the cylinder in the middle of the
figure to be taller than the cylinder at the bottom of the figure. This
effect arises because linear perspective and other cues cause the
cylinder in the middle of the figure to appear further away than the
cylinder at the bottom. If two objects subtend the same visual
angle, the object that appears further away will be perceived as
larger. We do not think that this effect is related to orientation, so
tilting the observer should not affect this illusion.
However, several theories account for the Ponzo, Zollner, and
Poggendorff illusions in terms of linear perspective or perceived
depth (e.g., Gillam, 1980; Green & Holye, 1963; Gregory, 1963).
Linear perspective does not change with the retinal orientation of
the stimulus (Gregory, 1964), but we do not know how tilting the
observer would affect linear perspective. Tilting the observer increases the Ponzo, Zollner, and Poggendorff illusions. If these are
caused by the mechanisms responsible for linear perspective and
size constancy, then tilting the observer might also increase the
illusion illustrated in Figure 6.
Method
Procedure. Observers were presented with stimuli such as those illustrated in Figure 6. The task was to adjust the height of the cylinder at the
bottom to match the height of the cylinder in the middle. Observers
adjusted the height with a joystick and were under no time pressure. The
adjustments that observers made only affected the height of the bottom
cylinder and left its width unaffected (see Stimulus section). Each observer
made 24 adjustments in the tilted condition and 24 adjustments in the
upright condition. Half of the observers were tested upright first, and half
were tilted first. Twenty observers, selected as before, participated in a
single session that lasted about 10 min.
Stimulus. The stimulus is shown in Figure 6. The figure is drawn
according to the rules of linear perspective (see Gillam, 1981). It appeared
as luminous and gray areas (the guitars) on a black background. Because
a line drawing using linear perspective can be ambiguous, the guitars were
added to disambiguate the depth relations. For example, without the guitars
and 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 Macintosh computer, and the observers were seated at a viewing distance of 107
cm. 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 (in
the center) subtended 8.3° in height (44 pixels) and 6.1° in width (32
pixels). The initial height of the adjustable cylinder (on the bottom) was
randomly set from 20 to 60 pixels, but the width did not change. The
change in height was accomplished by stretching or contracting the rectangle on which the cylinder was drawn in a vertical direction only. (Note
that the width of the cylinder might be affected by a Ponzo-like illusion
caused by the oblique lines. For this reason, the manipulation was only in
the vertical direction.) In all other respects, this experiment was similar to
Experiment 1.
Results and Discussion
Every observer but 1 adjusted the cylinder too tall (n = 20). The
error can be expressed as a percentage of the height of the standard
(as with the Ponzo illusion). Observers adjusted the cylinder 14.0% too high in the upright condition and 12.3% too high in
the tilted condition. Note that this difference, though not reliable,
F(l, 19) = 1.21, is in the opposite direction as the effect of tilting
the observer on the orientation illusions in Experiment 1. The
standard deviations, averaged over the 20 observers, were 5.1%
and 6.3% for upright and tilted conditions, respectively.
4
We are grateful to Jeremy Wolfe for suggesting this experiment.
PRINZMETAL AND BECK
214
These results would seem to be fairly damaging for accounts of
the Ponzo, Poggendorff, Zollner, and tilt-induction illusions that
make reference to linear perspective. Tilting the observer increases
the tilted-room illusion (Asch & Witkin, 1948), the rod-and-frame
effect (DiLorenzo & Rock, 1982; Witkin & Asch, 1948b), as well
as the illusions tested in Experiment 1. However, tilting had no
effect on linear perspective and size constancy.
Of course it is difficult to prove the null hypothesis. One might
worry, for example, that the effect of perspective was too small,
leading to a floor effect. Note that the effect of perspective on the
cylinder height was similar in magnitude as the Ponzo illusion in
Experiments 1 and 2 (see Tables 1 and 2). Both are illusions of
linear extent, in a vertical direction. Importantly, there is no a
priori 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 perspective
does not change" (p. 303). Nevertheless, it was important to
demonstrate this dissociation between the effect of tilting the
observer in the orientation illusions and an illusion based on linear
perspective.
There is one account that may allow linear perspective (and
other theories) to play a role in some of these illusions, however.
It may be that some of these illusions have multiple causes, as
suggested by Coren and Girgus (1978). For example, it could be
that the Poggendorff illusion is caused by both tilt constancy and
linear perspective. The present experiments only manipulated the
tilt-constancy component, but linear perspective (or other mechanisms) may still play a role.
The present experiments were designed to test the tilt-constancy
explanation and to provide an empirical link between the largescale illusions (tilted-room and rod-and-frame effects) and the
orientation illusions. To rule out other theories, one needs a situation in which competing theories make different predictions. We
have tested various theories in this manner with the Ponzo illusion
(Prinzmetal et al., in press). With the Ponzo illusion, Prinzmetal et
al. 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 following
theories were neither necessary nor sufficient to account for the
Ponzo illusion: (a) the low-pass filter theory (Ginsburg, 1984), (b)
the assimilation theory (Pressey & Epp, 1992), (c) a sizecomparison theory (Kunnapas, 1955), (d) the pool-and-store theory (Girgus & Coren, 1982), and (e) the linear perspective and
size-constancy theory (e.g., Gillam, 1980; Gregory, 1963). More
research will be necessary to completely rule out the possibility
that these theories play a role for some of the other illusions.
General Discussion
We hypothesized that the Zollner, Poggendorff, and Ponzo
illusions and the tilt-induction effect were caused by the same
mechanism that causes the tilted-room illusion. Tilting an observer
increases 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, then
tilting 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 previous
theories of these illusions. Second, we suggest an algorithm for tilt
constancy and discuss its neural implementation. Finally, we
briefly consider a few empirical issues left unresolved by the
present research.
Our present results are inexplicable by previous theories of these
illusions, which include those based on linear perspective (e.g.,
Gillam, 1980; Green & Holye, 1963; Gregory, 1963), the low-pass
filter theory (Ginsburg, 1984), and inhibition among orientationtuned cells (Blakemore et al., 1970). Unlike the tilt-constancy
theory, none of these theories predict an increase in the magnitude
of these illusions when an observer is tilted. The present research
suggests that the relevant mechanisms revealed by these illusions
are those that determine orientation, and in particular, local visual
cues to orientation. Of course, as we pointed out previously, we
cannot rule out the possibility that other mechanisms may play
some role in these illusions, but any theory of these illusions must
contain a reference to the perception of orientation.
Our account of these results, the tilt-constancy theory, has some
similarities with theories that appeal to size constancy and linear
perspective (e.g., Day, 1972; Gillam, 1980; Gregory, 1963). There
are several distinct variants of this theory (see Green & Hoyle,
1964), but all appeal to mechanisms related to size constancy. Size
constancy is, of course, the ability to perceive objects in their true
size regardless of distance. Tilt constancy is the ability to perceive
objects in their true orientation regardless of the orientation of the
observer. Hence, both theories appeal to normally adaptive processes. Furthermore, although there are a number of determinants
of perceived distance, the theories that account for the visual
illusions treated in this article only appeal to linear perspective.
Similarly, there are several determinants of perceived orientation
in addition to visual information, such as vestibular and somatosensory information, but we only appeal to the misperception of
orientation due to visual information.
Note that both the size-constancy family of theories and the
tilt-constancy theory account for a wide range of illusory phenomena but not precisely the same phenomena. For example, we have
no account of the Miiller-Lyer illusion, whereas the Miiller-Lyer
illusion is often used as the foremost example for the sizeconstancy theories. Indeed, it is not a virtue for the same theory to
account for both the Miiller-Lyer illusion and the other illusions
because, as we pointed out, both previous research and our present
findings 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 differently
than the Miiller-Lyer illusion when observers were tilted. Hence,
although size constancy may provide a good explanation of the
Miiller-Lyer illusion (see e.g., Gregory & Harris, 1975), it does
not account for our results, and Experiment 4 clearly demonstrates
that size constancy behaves differently than the orientation-based
illusions.
Our theory should not be confused with another theory that
acute angles are overestimated (Hering, 1861). This theory has
been applied to the Zollner and Poggendorff illusions and the
tilt-induction effect. It has not been applied to the Ponzo illusion.
In modern physiological terms, the overestimation of angles is
claimed to be a consequence of the inhibition of neurons in VI
(e.g., Blakemore et al., 1970). According to this explanation, when
two lines forming an acute angle are presented to an observer, each
line activates a population of cells. The cells activated are those
tuned to the orientation of each line. However, cells tuned to
TILT CONSTANCY AND ILLUSIONS
orientations similar to the lines are also activated. Cells activated
by both lines (i.e., those with orientations between the lines)
mutually inhibit each other. Thus, the total activation is shifted so
that the angle is perceived as larger than it is.
There is now ample evidence that the acute-angle theory is
inadequate to account for the Zollner and Poggendorff illusions
because these illusions can be obtained without any "angles" in the
stimulus (e.g., Pressey & Sweeney, 1972; Wilson & Pressey,
1976). Indeed, our version of the tilt-induction effect in Experiments 1 and 2 (see Figure 4) does not contain lines that would
mutually inhibit each other. Indeed, Tyler and Nakayama (1984)
provided an example of a Zollner illusion with only lines of one
orientation, and Day and his colleagues (Day & Jolly, 1987; Day,
Jolly, & Duffy, 1987; Day, Watson, & Jolly, 1986) described a
version of the Poggendorff illusion, using a bisection task and only
two parallel lines (or even three dots). Furthermore, a theory based
on simple inhibition between line segments cannot explain the
results of tilting the observer. We are not suggesting that a theory
based on neural architecture is inappropriate; later, we outline the
beginning of a neural theory of perceived orientation. However, a
theory based on the misperception of angles (as opposed to orientation) does not account for existing data. A misperception of
orientation may cause a misperception of angles, but the cause of
the illusions, according to the tilt-constancy theory, has its roots in
the perception of orientation.
A final family of theories, referred to as assimilation theories,
has been used to account for many of these same illusions. These
theories are diverse and include the low-pass filter theory of
Ginsburg (1984), the assimilation theory of Pressey and his colleagues (Pressey, 1971; Pressey, Butchard, & Scrivner, 1971;
Pressey & Epp, 1992), and the pool-and-store model of Girgus and
Coren (1982). These theories also have no account of our present
findings. Indeed, no theory that only appeals to visual mechanisms—as opposed to a mechanism of spatial representation—can
account for the effects of tilting the observer.
A complete theory of these illusions should specify the neural
mechanisms underlying tilt constancy. Our results suggest that the
mechanisms are likely to involve neurons that are tuned to orientation relative to the visual environment, rather than the observer's
retinal orientation. In animal studies, Sauvan and Peterhaus (1995)
searched in the cortex of awake macaque monkeys for cells whose
tuning functions were related to the environment as opposed to the
animal's orientation. They found virtually no cells in the striate
cortex that showed this property. All of the cells in the striate
cortex were tuned in relation to retinal coordinates. However, 40%
of cells in extrastriate areas (Areas V2, V3, and V3a) were tuned
in relation to environmental, not retinal coordinates. Likely candidates for the neural substrate of these illusions will be areas with
an abundance of cells that are tuned to environmental coordinates.
There are probably many ways of implementing tilt constancy
with simple neural hardware. Environmentally tuned cells could be
created from retinally tuned cells with a simple two-layer system.
Suppose there is a population of retinally tuned vertical detectors
in the first level. These cells will fire to vertical lines, but also to
lines near vertical. If the stimulus contains lines that are near
vertical, a second level of the system would be erroneously signaled that a vertical was present. The same process would happen
with stimulus lines near horizontal. Thus, contours in the visual
environment near retinal vertical would define orientation. Note
215
that this mechanism is distinct from lateral inhibition and low-pass
filtering. However, like these theories, it invokes simple neural
processes. A simple mechanism such as this might underlay what
Gibson (1937) meant by a process of normalization.
Of course, such a simple scheme is incomplete because it does
not include gravity-based cues to orientation (i.e., vestibular and
somatosensory cues). Our findings, along with previous findings
by 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, visual
cues play a greater role. There are many possibilities as to how
visual and extravisual information are integrated. For example, it
might be that the perceived orientation of a stimulus is a weighted
linear average of retinal and gravity-based cues (Matin & Fox,
1989). Alternatively, the integration of information may be nonlinear (e.g., Carlson-Radvansky & Logan, 1997). Furthermore,
there are many possible sites in the brain for the integration of
visual and other information.
In addition to the general theoretical issue discussed above,
tilt-constancy theory raises a plethora of research issues, of which
we mention only three. First, we do not have a precise description
of why tilting an observer increases the tilted-room illusion and
related illusions. In the most general sense, tilting the observer
increases one's reliance on visual as opposed to gravity-based
information. However, this description raises a number of empirical issues. For example, tilting the observer may increase the
orientation illusions because it creates a conflict among retinal,
visual, and gravity-based cues to orientation. If this hypothesis is
correct, only body positions that create a conflict will increase
these illusions. However, perhaps any body position that is not
aligned with visual vertical will influence performance. In this
case, a supine posture would also increase the tilt-induction effect
and the Zollner, Ponzo, and Poggendorff illusions. Because the
rod-and-frame effect is greater when observers are in a supine
posture (Goodenough et al., 1981; Templeton, 1973), we would
predict that supine observation would similarly affect the other
illusions. We are currently testing this hypothesis.
A second issue relates to the perception of pitch. There is a
well-known pitch-box illusion that is analogous to the tilted-room
illusion. Observers' perceived eye level is affected by the pitch of
the visual environment. If observers are looking down a hall that
is pitched down, for example, they will indicate that eye level is
lower than it actually is (Kleinhans, 1970; Matin & Fox, 1989;
Matin & Li, 1992,1996; Stoper, 1998; Stoper & Cohen, 1986). An
issue that concerns us is whether the mechanisms of pitch perception (e.g., perception of eye level) are the same as the mechanisms
for the perception of vertical and horizontal.
Finally, the concept of reference frames plays a large role in
other aspects of cognitive psychology, including recognition (Mermelstein, 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 frames
of reference that cause distortions such as the Ponzo and Zollner
illusions are the same as these other reference frames. To the
extent that they are the same, manipulations that affect the illusions
(e.g., tilting the observer) should have similar effects in these other
domains.
We proposed that the Ponzo, Zollner, and Poggendorff illusions
and the tilt-induction effect are due to the visual mechanisms that
PRINZMETAL AND BECK
216
create illusions of orientation in the tilted-room illusion (tiltconstancy theory). In the tilted-room illusion, tilting the observer
increases the effect of visual context in relation to gravitational
information. In a similar manner, tilting the observer also increases
the magnitude of these illusions. The tilt-constancy theory broadens the functional significance of these illusions. These illusions
are not only relevant to visual processes but also informative about
the nature of human spatial representations.
References
Asch, S. E., & Witkin, H. A. (1948). Studies in space orientation: 0.
Perception of the upright with displaced visual fields and with body
tilted. Journal of Experimental Psychology, 38, 455-477.
Banta, C. (1995). Seeing is believing: Haunted shacks, mystery spots, and
other delightful phenomena. Agoura Hills, CA: Funhouse Press.
Behrmann, M., & Tipper, S. P. (1999). Attention accesses multiple reference frames: Evidence from visual neglect. Journal of Experimental
Psychology: Human Perception and Performance, 25, 83-101.
Blakemore, C , Carpenter, R. H., & Georgeson, M. A. (1970). Lateral
inhibition between orientation detectors in the human visual system.
Nature, 228, 37-39.
Boring, E. G. (1942). Sensation and perception in the history of experimental psychology. New York: Appleton-Century-Croft.
Bouma, A., & Andriessen, J. J. (1970). Inducted changes in the perceived
orientation of line segments. Vision Research, 10, 333-349.
Campbell, F. W., & Maffei, L. (1971). The tilt after-effect: A fresh look.
Vision Research, 11, 833-840.
Carlson-Radvansky, L. A., & Logan, G. D. (1997). The influence of
reference frame selection on spatial template construction. Journal of
Memory and Language, 37, 411-437.
Coren, S. (1986). An efferent component in the visual perception of
direction and extent. Psychological Review, 93, 391-410.
Coren, S., & Girgus, J. S. (1978). Seeing is deceiving: The psychology of
visual illusions. Hillsdale, NJ: Erlbaum.
Coren, S., Girgus, J., & Erlichman, H. (1976). An empirical taxonomy of
visual illusions. Perception <£ Psychophysics, 20, 129-137.
Coren, S., & Hoy, V. S. (1986). An orientation illusion analog to the rod
and frame: Relational effect in the magnitude of the distortion. Perception & Psychophysics, 39, 159-163.
Day, R. H. (1972). Visual spatial illusions: A general explanation. Science,
175, 1335-1340.
Day, R. H., & Jolly, W. J. (1987). A note on apparent displacement of lines
and dots on oblique parallels. Perception & Psychophysics, 41, 187-189.
Day, R. H., Jolly, W. J., & Duffy, F. M. (1987). No evidence for apparent
extent between parallels as the basis of the Poggendorff effect. Perception & Psychophysics, 42, 561-568.
Day, R. H., & Wade, N. J. (1969). Thereferencefor visual normalization.
American Journal of Psychology, 82, 191-197.
Day, R. H., Watson, W. L., & Jolly, W. J. (1986). The Poggendorff
displacement effect with only three dots. Perception & Psychophysics, 39, 351-354.
DiLorenzo, J., & Rock, I. (1982). The rod and frame effect as a function of
the righting of the frame. Journal of Experimental Psychology: Human
Perception and Performance, 8, 536—546.
Ebenholtz, S. M. (1977). Determinants of the rod and frame effect: The
role of retinal size. Perception & Psychophysics, 22, 531-538.
Ebenholtz, S. M. (1985). Absence of relational determination in the rodand-frame effect. Perception & Psychophysics, 37, 303-306.
Ebenholtz, S. M, & Callan, J. W. (1980). Modulation of the rod and frame
effect: Retinal size vs. apparent size. Psychological Research, 42, 327334.
Fisher, G. H. (1968). An experimental comparison of rectilinear and
curvilinear illusions. British Journal of Psychology, 59, 23-28.
Gibson, J. J. (1937). Adaptation, after-effect, and contrast in the perception
of tilted lines: II. Simultaneous contrast and the areal restriction of the
after-effect. Journal of Experimental Psychology, 20, 553-569.
Gibson, J. J., & Radner, M. (1937). Adaptation, after-effect and contrast in
the perception of tilted lines: I. Quantitative studies. Journal of Experimental Psychology, 20, 453-467.
Gillam, B. (1980). Geometrical illusions. Scientific American, 242, 102111.
Gillam, B. (1981). False perspective. Perception, 10, 313-318.
Ginsburg, A. P. (1984). Visual form perception based on biological filtering. In L. Spillmann & B. R. Wotten (Eds.), Sensory experience, adaptation, and perception: Festschiriftfor Ivo Kohler (pp. 53-72). Hillsdale,
NJ: Erlbaum.
Girgus, J. S., & Coren, S. (1982). Assimilation and contrast illusions:
Differences in plasticity. Perception & Psychophysics, 32, 555-561.
Goodenough, D. G., Oltman, P. K., & Sigman, E. (1981). The rod-andframe illusion in erect and supine observers. Perception & Psychophysics, 29, 365-370.
Green, R. T., & Holye, E. M. (1963). The Poggendorff illusion as a
constancy phenomenon. Nature, 200, 611-612.
Green, R. T, & Hoyle, E. M. (1964). The influence of spatial orientation
on the Poggendorff illusion. Acta Psychologica, 22, 348-366.
Greene, E., & Pavlow, G. (1989). Angular induction as a function of
contact and target orientation. Perception, 18, 143-154.
Gregory, R. L. (1963). Distortion of visual space as inappropriate constancy scaling. Nature, 199, 678-680.
Gregory, R. L. (1964). Response to Brown and Houssiaadas. Nature, 204,
302-303.
Gregory, R. L. (1968). Visual illusions. Scientific American, 219, 66-76.
Gregory, R. L., & Harris, J. P. (1975). Illusion-destruction by appropriate
scaling. Perception, 4, 203-220.
Helmholtz, H. von. (1925). Handbuch der Physiologischen Optik [Treatise
on physiological optics]. Lancaster, PA: Optical Society of America.
Helmholtz, H. V. (1962). Popular lectures on scientific subjects (M. Kline,
Ed., & E. Atkinson, Trans.). New York: Dover. (Original work published 1881)
Hering, E. (1861). Beitrage zur Psychologie [Contributions to psychology].
Leipzig, Germany: Engleman.
Howard, I. P. (1982). Human visual orientation. New York: Wiley.
Howard, I. (1998, December). Knowing which way is up. Paper presented
at the Vision Science Symposium, University of California, Berkeley.
Howard, I. P., & Childerson, L. (1994). The contribution of motion, the
visual frame, and visual polarity to sensations of body tilt. Perception, 23, 753-762.
Judd, C. H., & Courten, H. C. (1905). The Zollner illusion. Psychological
Review Monograph Supplements, 7 (Whole No. 27), 112-141.
Kleinhans, J. L. (1970). Perception of spatial orientation in sloped,
slanted, and tilted visual field. Unpublished doctoral dissertation, Rutgers University of New Jersey.
Kramer, K. S. (1978). Inhibitory interactions as an explanation of visual
orientation illusions. Unpublished doctoral dissertation, University of
California, Los Angeles.
Kunnapas, T. M. (1955). Influence of frame size on apparent length of a
line. Journal of Experimental Psychology, 50, 168-170.
Leibowitz, H., & Toffey, S. (1966). The effect of rotation and tilt on the
magnitude of the Poggendorff illusion. Vision Research, 6, 101-103.
Matin, L., & Fox, C. R. (1989). Visually perceived eye level and perceived
elevation of objects: Linearly additive influences from visual field pitch
and from gravity. Vision Research, 29, 315-324.
Matin, L., & Li, W. (1992). Visually perceived eye level: Changes induced
by a pitched-from-vertical 2-lin visual field. Journal of Experimental
Psychology: Human Perception and Performance, 18, 257-289.
Matin, L., & Li, W. (1996). Visually perceived eye level is influenced
TILT CONSTANCY AND ILLUSIONS
identically by lines from erect and pitched planes. Perception, 25,
831-852.
Mermelstein, R., Banks, W., & Prinzmetal, W. (1979). Figural goodness
effects in perception and memory. Perception & Psychophysics, 26,
472-480.
Muir, D., & Over, R. (1970). Tilt aftereffect in central and peripheral
vision. Journal of Experimental Psychology, 85, 165-170.
Pressey, A. (1971). An extension of assimilation theory to illusions of size,
area, and direction. Perception & Psychophysics, 9, 172-176.
Pressey, A. W., Butchard, N., & Scrivner, L. (1971). Assimilation theory
and the Ponzo illusion: Quantitative predictions. Canadian Journal of
Psychology, 25, 486-497.
Pressey, A. W., & Epp, D. (1992). Spatial attention in Ponzo-like patterns.
Perception & Psychophysics, 52, 211-221.
Pressey, A. W., & Sweeney, O. (1972). Acute angles and the Poggendorff
illusion. Quarterly Journal of Experimental Psychology, 24, 169-174.
Prinzmetal, W., Shimamura, A. P., & Mikolinski, M. (in press). The Ponzo
illusion and the tilt-constancy theory. Perception & Psychophysics.
Robertson, L. C. (1995). Covert orienting biases in scene-based reference
frames: Orientation priming and visual field differences. Journal of
Experimental Psychology: Human Perception and Performance, 21,
707-718.
Rock, I. (1974). The perception of disoriented figures. Scientific American,
230, 78-86.
Sauvan, X. M., & Peterhaus, E. (1995). Neural integration of visual
information and direction of gravity in prestriate cortex of the alert
monkey. In T. Mergner & F. Hlavacka (Eds.), Multisensory control of
posture (pp. 43-49). New York: Plenum Press.
Shimamura, A. P., & Prinzmetal, W. (2000). The mystery spot illusion and
its relation to other visual illusions. Psychological Science, 10, 501-507.
Singer, G., Purcell, A. T., & Austin, M. (1970). The effect of structure and
degree of tilt on the tilted room illusion. Perception & Psychophysics, 7,
250-252.
Spivey-Knowlton, M., & Bridgeman, B. (1993). Spatial context affects the
Poggendorff illusion. Perception & Psychophysics, 53, Mil-414.
Stoper, A. E. (1998). Height and extent: Two kinds of size perception. In
E. Winograd, R. Fivush, & W. Hirst (Eds.), Ecological approaches to
cognition (pp. 97-121). Hillsdale, NJ: Erlbaum.
Stoper, A. E., & Cohen, M. M. (1986). Judgments of eye level in light and
in darkness. Perception & Psychophysics, 40, 311-316.
Templeton, W. B. (1973). The role of gravitational cues in the judgment of
visual orientation. Perception & Psychophysics, 14, 451-457.
217
Tyler, C. W., & Nakayama, K. (1984). Size interactions in the perception
of orientation. In L. Spillman & B. R. Wooten (Eds.), Sensory experience, adaptation, and perception: Festschrift for Ivo Kohler (pp. 529546). Hillsdale, NJ: Erlbaum.
Velinsky, S. (1925). Explication physiologique de l'illusion der Poggendorff [Physiological explanation of the Poggendorff illusion]. Annie
Psychologique, 107-116.
Wallace, G. K., & Moulden, B. (1973). The effect of body tilt on the
Zollner illusion. Quarterly Journal of Experimental Psychology, 25,
10-21.
Ward, L. M., & Coren, S. (1976). The effect of optically induced blur on
the magnitude of the Mueller-Lyer illusion. Bulletin of the Psychonomic
Society, 7, 483-484.
Weintraub, D. J., & Krantz, D. H. (1971). Poggendorff illusion: Amputations, rotations, and other perturbations. Perception & Psychophysics, 10, 257-263.
Weintraub, D., Krantz, D., & Olson, T. (1980). The Poggendorff illusion:
Consider all angles. Journal of Experimental Psychology, 6, 718-725.
Wenderoth, P. M. (1974). The distinction between the rod-and-frame
illusion and the rod-and-frame test. Perception, 3, 205-212.
Wenderoth, P., & Johnstone, S. (1988). The mechanism of the direct and
indirect tilt illusions. Vision Research, 28, 301-312.
Wilson, A. E., & Pressey, A. W. (1976). The role of apparent distance in
the Poggendorff illusion. Perception & Psychophysics, 20, 309-316.
Witkin, H. A., & Asch, S. E. (1948a). Studies in space orientation: III.
Perception of upright in absence of a visual field. Journal of Experimental Psychology, 38, 603-614.
Witkin, H. A., & Asch, S. E. (1948b). Studies in space orientation: IV.
Further experiments of the upright with displaced visual fields. Journal
of Experimental Psychology, 38, 762-782.
Wolfe, J., & Held, R. (1982). Gravity and the tilt aftereffect. Vision
Research, 22, 1075-1078.
Yin, R. (1969). Looking at upside-down faces. Journal of Experimental
Psychology, 81, 141-145.
Zoccolotti, P., Antonucci, G., & Spinelli, D. (1993). The gap between rod
and frame influences the rod-and-frame effect with small and large
inducing displays. Perception & Psychophysics, 54, 14-19.
Received April 20, 1999
Revision received May 8, 2000
Accepted May 12, 2000