Tilt-Constancy & Illusions
This article will appear in the Journal of Experimental Psychology:
Human Perception and Performance. The final version of this
manuscript will differ in minor ways from this version. This version
is provided for personal use only.
The Tilt-Constancy Theory of Visual Illusions
William Prinzmetal
University of California, Berkeley
Diane M. Beck
University College London
We 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., see Asch & Witkin, 1948), we predicted that
the strength of many visual illusions would increase when observers were tilted
30 degrees. The magnitude of Zöllner, Poggendorff, and Ponzo illusions and the
tilt-induction effect substantially increased when observers were tilted. In
contrast, the Müller-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.
For over a hundred years
visual scientists have believed that
visual illusions provide unique
insights into normally adaptive
visual processes.
For example,
Helmholtz 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" (1925). With
rare exception (e.g., Ward & Coren,
1976), most theories have attributed
visual illusions to "information
processing mechanisms that are
normally adaptive" (Gregory, 1968).
The controversy arises as to what
mechanisms are being reflected by
particular illusions. For example, the
Zöllner 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. Gregory, 1963;
Gillam, 1980; Green & Holye, 1963).
We offer a new explanation
that also involves a normally
adaptive process. We propose that
the perception of line orientation
(e.g., Zöllner illusion), collinearity
(e.g., Poggendorff illusion), line
length (e.g., Ponzo illusion,) and line
curvature
(e.g.,
Wündt-Hering
illusion) are caused by the same
mechanisms that are responsible for
the perception of vertical and
horizontal.
Because
these
mechanism are related to our ability
to perceive a constant orientation
despite changes in retinal orientation
or even shifts in gravity relative to
body
position
(Howard
&
Childerson, 1994; Howard, 1998) we
Tilt-Constancy & Illusions
will call our new account of visual
illusions, the Tilt-Constancy Theory.
We will first illustrate how
local visual cues to orientation can
account for many illusions. Second,
we will review the literature relevant
to our claim. Finally, we will present
evidence in support of the Tilt
Constancy Theory that can not 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 degrees 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
degrees 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 tiltedroom illusion has been exploited in
several roadside attractions and
amusement parks (Banta, 1995;
Shimamura & Prinzmetal, 2000). In
these settings our 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 “anti-gravity houses” (also see
www.illusionworks.com).
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
gray line). Hence, when observers
adjusted the central line to vertical,
they erred in the direction of the
context lines, just as in the tiltedroom 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 tiltinduction 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, p.
155-156; Singer & Purcell, 1970).
Several investigators have
speculated that the Zöllner illusion is
an instance of the tilt-induction effect
Tilt-Constancy & Illusions
(Howard, 1982, p.156-157; Day,
1972). The similarity of the illusions
can be seen in Figures 1a and b,
where the flanking context lines in
Figure 1a have been replaced by
many shorter context lines in Figure
1b. The Zöllner illusion, as typically
presented (Figure 1c), illustrates that
the effect of local context such that
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 Zöllner illusion behave
similarly with the manipulation of a
host of independent variables (see
Prinzmetal,
Shimamura,
&
Mikolinski, in press). Many visual
illusions, such as the Wündt-Hering
illusion and Fraser spiral can be
understood as instances of the
Zöllner illusion (Fisher, 1968). It may
be that the Cafe Wall illusion is also
an instance of the Zöllner illusion
(Prinzmetal, et al, in press).
Historically and functionally,
the Poggendorff illusion is also
related to the Zöllner illusion
(Boring, 1942).
In 1860 Zöllner
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 tiltinduction effect is illustrated in
Figure 1d, e, and f. Gibson (1937)
noted that, in the stimulus illustrated
in Figure 1d, the central oblique line
appeared to be inclined at a larger
angle than it actually was, illustrated
again by the gray 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 1e, we can see the
similarities to the Poggendorff
illusion in Figure 1f.
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 Zöllner 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 Zöllner illusion. In Figure
2a the vertical lines appear further
apart at the top of the figure than at
the bottom of the figure (Zöllner
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 further apart than the
bottom horizontal lines. Figure 2a is
drawn to suggest that the Ponzo
illusion is part of the Zöllner illusion,
and in Figure 2b, the Ponzo is hidden
in the Zöllner illusion.
We
have
conducted
experiments on the tilt-induction
effect with stimuli similar to those
shown in Figures 3a and b that
compared the magnitude of the
Ponzo illusion with the tilt-induction
effect (Prinzmetal, Shimamura, and
Mikolinski, in press). With stimuli
like those in Figure 3a, observers
adjusted the free end of the bottom
horizontal line so it appeared to be
vertically aligned, according to
gravity, with the end of the top
Tilt-Constancy & Illusions
horizontal line. The oblique line on
right caused a tilt-induction effect so
that observers erred by making the
line too long. The Ponzo illusion was
measured with stimuli like 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 tiltinduction task, and this is what was
found.
Additionally,
across
observers, the correlation between
the two illusions was r = 0.70.
Prinzmetal,
Shimamura,
and
Mikolinski
also
compared
predictions of several theories of the
Ponzo illusion with the TiltConstancy Theory.
The results
were consistent with the TiltConstancy Theory.
In
summary,
the
TiltConstancy Theory proposes that the
tilt-induction effect and the Zöllner,
Poggendorff, and Ponzo illusions are
due to a misperception of orientation
due to 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
Zöllner 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 Zöllner illusion is
caused by the same mechanism as
the tilted room illusion.1 On the
other hand, Howard (1982, p. 155156) asserts 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. Zöllner
illusion,
tilt-induction
effect).
Heretofore, the evidence for either
position is weak.
Howard gives three reasons
for believing that the frame and tiltnormalization effects are caused by
different mechanisms.
First, he
asserts that the frame effects are
many times larger than the
normalization effects and therefore
must be caused by different
mechanisms. Strangely, he cites a
misperception of orientation of 20
degrees. 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 degrees. However, in this
experiment, observers were seated
in a chair that was tilted 24 degrees.
Furthermore, there was an elaborate
procedure, lasting 7 minutes, 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., Witkin & Asch, 1948b;
Wenderoth, 1974).
In fact,
Shimamura and Prinzmetal (2000)
found the tilted room illusion can be
of a similar magnitude as the tiltinduction effect. In general, the
larger and more elaborate the
context, the greater the illusion. This
observation seems hardly surprising.
Second, Howard claims 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, series of studies by Ebenholtz
and his colleagues showing that a
larger frame leads to a larger illusion
in the rod and frame task (e.g.
Ebenholtz, 1985; Ebenholtz, 1977;
Tilt-Constancy & Illusions
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 minutes, before the inner
frame was presented. Hence the
procedure
may
have
biased
observers to use the outer frame.
Finally, Howard claims that
the tilted-room illusion is affected by
cognitive variables, whereas the tiltinduction effect (and other smallscale illusions) are not. By cognitive
variables,
Howard
means
knowledge
of
the
canonical
orientation of objects such of flower
vases and tables. However, there is
no evidence that the tilt-induction
effects is not influenced by cognitive
variables.
Furthermore,
this
argument is logically inconsistent in
that Howard claims that the tiltedroom and rod and frame effects are
caused buy the same mechanism
because the 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).
Hence, by
Howard's arguements, it is unclear
whether these illusions should be
classified on the basis on their scale,
on whether they involve peripheral
stimulatiion, or on whether they are
influence by cognitive variables.
Day’s position, that the tiltedroom illusion is caused by the same
mechanism as the Zöllner 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 since the tiltedroom 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 tiltinduction 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 tiltinduction effect. In the following
experiments we manipulated such a
variable.
In
summary,
the
TiltConstancy 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
Zöllner, 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 degrees, 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
Tilt-Constancy & Illusions
performance in the tilted-room leads
to a straightforward prediction: If
the tilt-induction effect and the
Zöllner, 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 degrees
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;
Wolfe & Held, 1982; Wallace &
Moulden, 1973). 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, they wore 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 seconds 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 Müller-Lyer
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
Zöllner
and
Poggendorff illusions were not those
who showed a strong Müller-Lyer
effect (Coren, Girgus, & Erlichman,
1976). Second, as we mentioned
above, 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 Müller-Lyer
illusion. Finally, with the Zöllner,
Poggendorff, and Ponzo illusion, the
orientation of the context lines
critically determines the magnitude
of the illusion. In contrast, with the
Müller-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 MüllerLyer illusion would not vary when
observers were tilted. To ensure
that a null finding was not the results
of a floor or ceiling effect, we
manipulated the strength of the
Müller-Lyer illusion, as described
below.
In Experiment 1, we tested the
magnitude
of
the
Zöllner,
Poggendorff, Ponzo, and MüllerLyer illusions, and the tilt-induction
effect, with observers seated upright
and tilted 30 degrees. Asch and
Witkin (1948) tilted observers 24
degrees and Witkin and Asch (1948b)
used 28 degrees. We wanted to
make sure that our manipulation
was at least as strong as they used,
so we tilted our observers 30
degrees. Experiment 2 was a control
condition to test for the effect of
tilting observers without visual
Tilt-Constancy & Illusions
context.
Experiment 3 tested
observers on the Zöllner, 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 hour. Half of the observers
performed the tasks first seated
upright, and then seated in a chair
tilted 30 degrees counterclockwise
(from the observers perspective),
while 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 Zöllner
task were lost do to a computer
operator error. Nevertheless, the
order of conditions for the observers
whose data were included was
completely
counterbalanced,
as
describe 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 Zöllner 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 Müller-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 Müller-Lyer illusion,
as shown in Figure 5d. On 12 trials,
the "wings" 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 Müller-Lyer illusion being
at floor or ceiling.
Each task began with the
observer sitting in the dark for 30
seconds, whether tilted or upright.
The starting position of the
adjustable
component
of
the
stimulus (e.g., vertical location of dot
in the Zöllner 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
Tilt-Constancy & Illusions
the pair of dots was randomly set
within +/- approximately 0.5
degrees 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 tiltinduction effect stimulus (Figure 4)
form an angle of 18° from vertical.
Similarly, the oblique lines in the
Zöllner, Poggendorff, and Ponzo
illusions were 18° from horizontal.
In the Müller-Lyer 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 degrees of
visual angle (160 screen pixels). The
horizontal lines in the Zöllner and
Poggendorff illusions (Figure 5A and
B) subtended 5.68 degrees of visual
angle (300 pixels). The oblique lines
for the Zöllner and Poggendorff
illusions subtended 2.84 and 1.89
degrees of visual angle, respectively
(150 and 100 pixels). The length of
the standard line in the Ponzo
illusion subtended 2.84 degrees of
visual angle (150 pixels). Finally, the
length of the horizontal line in the
Müller-Lyer figure subtended 4.73
degrees of visual angle (250 pixels)
while the arrowheads subtended
either .379 or .758 degrees of visual
angle (20 or 40 pixels).
Apparatus. Observers were
seated in a chair that could be set at
upright or tilted 30 degrees
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 were restrained by
a chin rest and lateral support bars
so that their heads were at the same
angle as the chair.
Observers. Twenty observers
participated in the experiment, half
of them were male and half female.
However, because of the above
mentioned computer error, the
results from only 10 observers in
included in the Zöllner task. The
average of the observers who
participated in the experiment was
22. 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, the
Zöllner, the Poggendorff, and the
Ponzo illusions were all dramatically
and significantly increased when the
observers were tilted 30 degrees
compared to 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
Zöllner 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
Tilt-Constancy & Illusions
pixels are 1 degree of visual angle.)
The magnitude of the Ponzo illusion
was measured as a percent: 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, i.e., 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, & Olson, 1980;
Weintraub, & Krantz, 1971) 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° vs.
6.01°, F(1,19) = 9.66, p < .05
In contrast, the Müller-Lyer
illusion was not affected by the
observer orientation (Table 1). The
dependent variable for the MüllerLyer illusion was the average
distance, in screen pixels, 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 vs. 14.98 pixels,
F(1,19) = 103.84, p < .01.
The
interaction of fin length and
observer
orientation
was
not
significant, F(1,19) = .05. For the
upright condition, the average
illusion for long and short fins as
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, Zöllner,
Poggendorff, and Ponzo) behaved
like Asch and Witkin's tilted-room
illusion: the illusion increased when
observers were tilted.
However,
tilting observers does not increase
every illusion: it had no effect on the
Müller-Lyer illusion. We conducted
a partial replication of this
experiment with slightly different
stimuli (e.g., the Zöllner figure had
two horizontal lines) and 10
additional observers with identical
results: a significant affect of
observer tilt with the Zöllner, Ponzo,
Poggendorff illusions, but
no
influence on the Müller-Lyer illusion.
Finally, we ran an analysis of the
Müller-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
degrees or more in the dark causes a
line to appear tilted in the opposite
direction. This effect is called the
Aubert or A effect (Howard, 1982, p.
427; Witkin & Asch, 1948a) and it
Tilt-Constancy & Illusions
could account for our findings with
the tilt-induction effect. On the other
hand, tilting the observer less than
about 30 degrees 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 tiltinduction task of Experiment 1 but
without the tilted grating (see Figure
1). The stimulus consisted of just 2
dots and 20 observers were run in
the tilted condition only.
The average setting was 0.87
degrees in the direction opposite
observer's body tilt. This value was
not significantly different from 0
(t(19) = .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 degrees. Thus the
increase of the tilt-induction effect
with tilting observers in Experiment
1 was not the result of the A effect,
but rather it 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 Zöllner 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 Zöllner illusion was less in the
orientation illustrated in Figure 5
than when rotated 45 degrees.
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 Zöllner,
Ponzo, Poggendorff, and Müller-
Lyer tasks with the stimulus at the
same retinal orientation when the
observer was seated upright and
when the observer was seated tilted
30 degrees. We did not run the tiltinduction effect because we were not
sure what to expect if the orientation
of the grating was changes with
respect to retinal orienation since the
observer's task is to indicate
gravitational vertical
Method
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 for the Poggendorff illusion
was rotated 45-degrees in a
counterclockwise direction from that
shown in Figure 4B. We used a 45degree
orientation,
because
depending on the observers eye
rotation (see below), further rotating
the stimulus in the tilted conditon
made the short lines horizontal with
respect to gravity for
some
observers, but not others.
We
wanted to keep the stimulus similar
for all observers regardless of their
eye rotation. Also, for the MüllerLyer illusion we used only the short
wing version (see Figure 5).
When the observer was tilted
30 degrees, 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 observers
eye
rotation (when seated tilted 30
degrees) and adjusted the stimulus
so that it had the same retinal
Tilt-Constancy & Illusions
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 were no eye
rotation, then observers would set
the line at 30 degrees, the angle of
body tilt. If observers’ eyes rotated
back to vertical, then they would set
the line to vertical (0 degrees). 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
degrees, across observers, and
averaged 4.5 degrees.
No
observer
reported
difficulty in the eye rotation task.
We checked the reliability of this
method with two observers on
several different occasions and
measurements agreed within 1
degree.
The viewing distance was 81
cm instead of the 107 cm used in
Experiments 1 and 2.3 Hence the
horizontal lines in the Zöllner and
Poggendorff illusions subtended 7.4
degrees of visual angle instead of the
5.68 degrees 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.
Results and Discussion
The magnitude of the Zöllner,
Poggendorff, and Ponzo illusions
were significantly greater in the
tilted condition than in the upright
condition (see Table 2). Thus even
when we controled for retinal
orientation, tilting the observer still
increased the magnitude of these
illusions. We had previously run a
pilot experiment with just the
Zöllner illusion with 10 observers
correcting for retinal orientation 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 Zöllner
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. On the other hand, 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
Tilt-Constancy & Illusions
orientations, it was the orientation of
the frame that was critical, not the
retinal orientation.
The results for the MüllerLyer 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 Müller-Lyer illusion.
Hence it is possible that this result is
a Type 1 error. Nevertheless, note
that tilting the observer had the
opposite effect on the Müller-Lyer
illusion as the other illusions. This
result is consistent with claim that
the Müller-Lyer illusion is caused by
a different mechanism than the other
illusions that we tested.
Experiment 4
In Experiment 1, the illusions
that we claim are related to
orientation, increased when the
observer was tilted (Zöllner, Ponzo,
Poggendorff, tilt-induction).
We
used the Müller-Lyer illusion as an
example of a non-orientation illusion
and its magnitude was unchanged
by tilting the observer. Because the
causes of the Müller-Lyer illusion are
uncertain, however, we 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.
On the other hand, several
theories account for the Ponzo,
Zöllner, and Poggendorff illusions in
terms of linear perspective and/or
perceived depth (e.g., Gregory, 1963;
Gillam, 1980; Green & Holye, 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, Zöllner, and Poggendorff
illusions. If these are caused by the
mechanisms responsible for linear
perspective and/or size-constancy,
then tilting the observer might also
increase the illusion illustrated in
Figure 6.
Method
Procedure. Observers were
presented with stimuli like 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). Each observer made 24
adjustments
tilted
and
24
adjustments upright in the chair
described above.
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 minutes.
Stimulus.
The stimulus is
shown in Figure 6. The figure is
drawn according to the rules of
Tilt-Constancy & Illusions
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 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
degrees of visual angle (802 x 500
screen pixels). The standard cylinder
(in the center) subtended 8.3 degrees
in height (44 pixels) and 6.1 degrees
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 like Experiment 1.
Results and Discussion
Every observer but one
adjusted the cylinder too tall (n=20).
The error can be expressed as a
percent 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(1,19) = 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.
These results would seem to
be fairly damaging for accounts of
the Ponzo, Poggendorff, Zöllner,
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, 1942; 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,
for example, asserted that "when a
perspective figure is rotated, the
perspective does not change" (1964,
p. 303).
Nevertheless, it was
important to demonstrate that 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
Tilt-Constancy & Illusions
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 and 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. In order to rule
out other theories, one needs a
situation where competing theories
make different predictions.
We
have tested various theories in this
manner with the Ponzo illusion
(Prinzmetal,
Shimamura,
&
Mikolinski, 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: (1) the lowpass filter theory (Ginsburg, 1984),
(2) the assimilation theory (Pressey
& Epp, 1992), (3) a size-comparison
theory (Kunnapas, 1955), (4) the
pool-and-store theory (Girgus &
Coren, 1982) and (5) the linear
perspective and size constancy
theory (e.g., Gregory, 1963; Gillam,
1980).
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
Zöllner, 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
illusion. 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 current research.
These results are inexplicable
by previous theories of these
illusions, which include those based
on linear perspective (e.g., Gregory,
1963; Gillam, 1980; Green & Holye,
1963), the low-pass filter theory
(Ginsburg, 1984), and inhibition
among orientation tuned cells
(Blakemore,
Carpenter,
&
Georgeson, 1970). Unlike the TiltConstancy 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 can
not rule out the possibility that other
mechanisms may play some role in
these illusions, but any theory of
these illusion 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;
Gregory, 1963; Gillam, 1980). There
Tilt-Constancy & Illusions
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 paper
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 Müller-Lyer
illusion, whereas the Müller-Lyer
illusion is often used as the foremost
example for the size constancy
theories. Indeed, it is not a virtue for
the same theory to account for both
the Müller-Lyer illusion and the
other illusions because, as we
pointed out, both previous research
and our current findings suggests
that they are not caused by the same
mechanisms.
To this previous
evidence, we add that the Zöllner,
Poggendorff, Ponzo illusions and tiltinduction effect behaved differently
than the Müller-Lyer illusion when
observers were tilted.
Hence,
although size
constancy
may
provide a good explanation of the
Müller-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 orientationbased illusions.
Our theory should not be
confused with another theory that
acute angles are over estimated
(Hering ,1861). This theory has been
applied to the Zöllner, 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 V1 (e.g.,
Blakemore,
Carpenter,
&
Georgeson, 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 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 Zöllner
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)
have an example of a Zöllner illusion
with only lines of one orientation
and Day and his colleagues (Day,
Tilt-Constancy & Illusions
Watson, & Jolly, 1986; Day, Jolly, &
Duffy, 1987; Day & Jolly, 1987) have
described
a
version
of
the
Poggendorff illusion, using a
bisection task and only two parallel
lines (or even 3 dots). Furthermore,
a theory based on simple inhibition
between line segments can not
explain the results of tilting the
observer. Note that we are not
suggesting a theory based on neural
architecture is inappropriate and
later we will 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 animal's retinal
orientation. Recently, 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 extra-striate areas
(areas V2, V3, V3a) were tuned in
relation to environmental, not retinal
coordinates. Likely candidates for
the neural substrate of these illusions
will be areas with an of abundance
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 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
Tilt-Constancy & Illusions
orientation (i.e., vestibular and
somatosensory cues). Our findings,
along with previous finding 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
questions 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 will mention only three. First,
we do not have a very 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 between retinal,
visual, and gravity-based cues to
orientation. If this hypothesis is
correct, only body positions that
create a conflict will increase these
illusions.
On the other hand,
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
Zöllner, Ponzo, and Poggendorff
illusions. Because the rod and frame
effect is greater when observers are
in a supine posture (Goodenough,
Oltman, & Sigman, 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 wellknown 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; Matin & Li,
1996; Stoper & Cohen, 1986; Stoper,
1998). An issue that concerns us is
whether the mechanisms of pitch
perception (e.g., perception of eye
level) is 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.,
Roberston, 1995; Behrmann &
Tipper, 1999). An important issue is
whether the local frames of
reference that cause distortions such
as the Ponzo and Zöllner 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,
Zöllner, Poggendorff illusions and
the tilt-induction effect are due to the
Tilt-Constancy & Illusions
visual mechanisms that create
illusions of orientation in the tiltedroom
illusion
(Tilt-Constancy
Theory). In the tilted-room illusion,
tilting the observer increases the
effect of visual context relative 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 just relevant to visual processes,
but also informative about the
nature
of
human
spatial
representations.
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Author Notes
We would like to thank Marty
Banks, Art Shimamura, Steve
Palmer, Edward Hubbard, and
Nancy Kim for their help on this
project. This research was supported
in part by NIH grant MH51400.
Footnotes
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 will is discussed
in the General Discussion.
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.
3. Experiment 3 was conducted
about 2 years after the other
experiments reported in the paper.
The chair apparatus and the
arrangement of the laboratory
furniture had changed during that
period resulting a change in viewing
distance.
4. We are grateful to Jeremy Wolfe
for suggesting this experiment.
Tilt-Constancy & Illusions
Tilt-Constancy & Illusions
Effect
Tilt-induction
effect
Zöllner illusion
Table 1
Results from Experiment 1
Upright
Tilted
Condition
Condition
2.4 degrees
9.4 degrees
(3.0)
(4.9)
7.3 pixels (4.5)
26.4 pixels (7.3)
Poggendorff
illusion
Ponzo illusion
28.7 pixels (9.0)
5.9 % (3.9)
38.8 pixels
(11.3)
8.2 % (4.4)
Müller-Lyer
illusion
18.2 pixels (3.4)
19.0 pixels (3.7)
F(1,19) =
71.72**
F(1,9)
=96.63**
F(1,19) =
20.86**
F(1,19) =
7.28*
F(1,19) = 0.95
ns
** p < .01, * p < .05, Illusion magnitude from Experiment 1, average
standard deviation in parentheses.
Tilt-Constancy & Illusions
Effect
Zöllner illusion
Table 2
Results from Experiment 3
Upright
Tilted Condition
Condition
12.2 pixels (6.9)
20.2 pixels (8.6)
Poggendorff
illusion
Ponzo illusion
35.6 pixels (11.2)
40.1 pixels (10.6)
F(1,23)
=24.73**
F(1,23) = 4.51*
6.9 % (4.3)
8.5 % (4.4)
F(1,23) = 5.77*
Müller-Lyer
illusion
18.5 pixels (4.0)
16.9 pixels (4.0)
F(1,23) = 5.19
*
** p < .01, * p < .05, Illusion magnitude from Experiment 3, average
standard deviation in parentheses.
Tilt-Constancy & Illusions
Figure Captions
Figure 1. In all of the panels, the actually stimulus is shown in black,
and the illusion, in exaggerated form, is shown with a dashed gray
line. (a) The tilt-induction effect: Vertical lines are perceived to be
tilted in the direction opposite the context lines. (b) The Zöllner
illusion: The long oblique context lines in the tilt-induction figure
have been replaced by many short context lines. (c) The standard
Zöllner illusion. (d) In the tilt-induction effect, Gibson 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.
Figure 2. The relation of the Ponzo and Zöllner illusions. (a) the
Zöllner illusion with the Ponzo illusion suggested with bold lines. (b)
the Ponzo illusion with the Zöllner illusion in the background
Figure 3. The Ponzo illusion considered as a consequence of the tiltinduction effect. In (a) the ends of the horizontal lines do not seem
to be horizontally aligned. This effect makes the top horizontal line
in (b) appear longer than the bottom horizontal line.
Figure 4. The stimuli used to measure the tilt-induction effect.
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.
Figure 5. The stimuli used to measure the (a) Zöllner illusion, (b)
Poggendorff illusion, (c) Ponzo illusion, and (d) Müller-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.
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.
Tilt-Constancy & Illusions
Figure 1
A
B
C
D
E
F
Tilt-Constancy & Illusions
B
A
Figure 2
A
Figure 3
B
Tilt-Constancy & Illusions
1 degree
Figure 4
Tilt-Constancy & Illusions
B
A
1 degree
C
Figure 5
Figure 6
D