Psychology
2012. Vol.3, No.3, 257-264
Published Online March 2012 in SciRes (http://www.SciRP.org/journal/psych) http://dx.doi.org/10.4236/psych.2012.33036
Inconstancy and Inconsistency of Visual Illusory Phenomena?
The Case of the Poggendorff Figure
Alberto Gal l ace1, Marialuisa Martelli2, Roberta Daini1
1Department of Psychology, Università degli Studi di Milano-Bicocca, Milan, Italy
2Department of Psychology, Università di Roma “La Sapienza”, Rome, Italy
Received November 22nd, 2011; re v is e d D e cember 19th, 2011; accepted January 14th, 2012
Since its conception, the Poggendorff Figure has always been studied by considering the absolute role of
the variables involved in determining the illusion (e.g. the angle or the distance between the inducer and
the test stimuli). By contrast, we suggest that the role of such variables is relative to the specific condi-
tions in which the illusory configuration is presented; in particular, we propose that multiple variables en-
ter the computation leading to the Poggendorff Illusion, but that their relative weight varies as a function
of the specific experimental conditions adopted. Here, we measured the point of subjective collinearity
between the oblique lines of the Poggendorff Figure as a function of the orientation of the inducer (a
square), the orientation of the test stimuli (changing the linear distance between them) and the size of the
whole configuration. We found that when the inducer square was upright the illusory effect varied ac-
cording to the distance between the test segments, while when the square was tilted the effect was deter-
mined only by its orientation. Critically, the latter condition led to a reversal of the “classic” illusory ef-
fect. Leveling the playing field in terms of the information available to the observer, the results indicate
that the illusory effect is determined by different types of processing in different conditions of stimulus
presentation.
Keywords: Visual Illusion; Perception; Psychophysics; Behavioral
Introduction
Visual illusions, with the insights they provide into visual
processing by breaking it into separate mechanisms (e.g. Gre-
gory, 1968), have attracted the attention of psychologists and
cognitive scientists since the last century (e.g., Gillam, 1980,
1998). It has also been suggested that the study of the mecha-
nisms underlying visual illusions may play an important role in
understanding the nature of human spatial representations
(Printzmetal & Beck, 2001). However, despite the large body of
research dedicated to exploring this domain of perception, the
computations underlying many visual illusions are still unclear
(e.g. Coren & Girgus, 1978; Eagleman, 2001; Purves & Lotto,
2002).
One of the oldest and most widely studied perceptual illu-
sions is the figure of Poggendorff (Poggendorff, 1860; see also
Burmester, 1896; Day & Dickenson, 1976; Fineman, 1996):
when two oblique collinear lines are separated by an area de-
fined by two vertical (or horizontal) bars, a visual illusion of
two unaligned lines will result (see Figure 1(a)). Different in-
terpretations have been proposed to account for this illusory
effect; most of which fall into two main categories: 1) “length
distortion” hypotheses; and 2) “angle distortion” hypotheses.
Interpretations in the first category su stain that the perceived
displacement of the two oblique lines is determined by the per-
ceptual shrinkage of the space between the two parallel lines
(e.g., Zanuttini, 1976). In fact, if the distance separating the two
segments along the horizontal meridian is perceived as being
smaller than it really is, then the test lines must be moved closer
along the vertical meridian in order to appear collinear. The
shrinkage theory is based on two observations: 1) that the space
upon which a figure is amodally completed is perceived as
being shorter than it really is (e.g., Kanizsa, 1972, 1974); and 2)
that a particular linear distance extending across an empty
space is underestimated (Tong & Weintraub, 1974). Within this
category of interpretation, the Poggendorff Illusion can be con-
sidered to be similar to the Muller-Lyer Illusion (e.g., Judd,
1902; Porac, 1994; Predebon, 2001), in which the positioning
of four lines forming two arrowheads (inward pointing or out-
ward pointing) at the extremities of a line modifies the percep-
tion of its length (see Figure 1(b)). An interpretation common
to both the Poggendorff and the Muller-Lyer Illusions holds
that the distortion is a consequence of a compulsory computa-
tion of the “veridical” distance between the parallel lines in
addition to the computation of the distance between the oblique
segments (e.g., Judd, 1902; Porac , 1994; Predebon, 2001; Greist -
Bousquet & Schiffman, 1981, 1985; Pressey, 1988). This is
called the assimilation theory (Pressey, 1974; 1988). All of
these models share the observation that the perceived distance
between the parallel lines strongly affects the bias in the Pog-
gendorff figure (e.g., Bazzeo, Vicario, & Zambianchi, 1993;
Masini, Costa, Ferraro, & De Marco, 1994; Zanuttini, 1973,
1976; but see Vezzani, 1999). This has been taken as evidence
of the validity of the length distortion interpretation of this illu-
sion (e.g., Buxton, 2001; Masini, Costa, Ferraro, & De Marco,
1997; Masini, Sciaky, & Pascarella, 1992; Wilson, 1983; but
see Finlay & Caelli, 1976).
Interpretations in the second category sustain that the illusory
effect is the consequence of an overestimation of the acute an-
gle between the oblique and the parallel lines composing the
figure (Hering, 1861). If the acute angle is perceived as greater

A. GALLACE ET AL.
than it really is, then the lines need to be moved closer along
the vertical meridian in order to appear collinear. The fact that
the illusory effect increases as the angle between the oblique
and parallel lines decreases has been taken as evidence for this
interpretation (e.g., Hotopf & Ollerearnshaw, 1973; Weintraub,
Krantz, & Olson, 1981). The mutual inhibition of the neurons
responding to different orientations in brain Area V1 has been
suggested as a possible physiological basis for the overestima-
tion of the acute angle in this and other illusions (e.g., Black-
more, Carpenter, & Georgeson, 1970). In other words, each line
activates a population of neurons responding to a specific ori-
entation. Orientation tuning in Area V1 is approximately 30
degrees in width (e.g., De Valois, De Valois, 1990; De Valois,
De Valois, & Yund, 1979) thus, when the angle in the illusion
is less than 30 degrees the two lines activate almost the same
population of neurons. These cells inhibit each other due to
proximity, thus the maximum response is related to the activity
of cells tuned to adjacent orientations, away from the tilt of the
lines. However, this effect does not fully explain the illusion as
the illusory effect is reduced, but not absent, when the angle is
larger than 30 degrees.
Recently, Prinzmetal and Beck (2001) made a thorough in-
vestigation that attempted to explain several illusions within the
same framework. On the basis of the results obtained from their
examination of the Rod-and-frame Illusion (Witkin & Asch,
1948), they suggested that the tilt of the body affects the mag-
nitude of certain illusory phenomena such as the Poggendorff,
Zollner, Ponzo and Wundt-Hering Illusions, but not others
(Muller-Lyer and size constancy effect). Tilting the body re-
duces the gravitational input while keeping the visual input
constant. The magnitude of the Poggendorff Illusion increases
as gravitational input weakens. The vestibular system plays a
fundamental role in the computation of orientation and the fact
that the gravitational cue modulates the Poggendorff Illusion
would seem to indicate that this is an “orientation illusion” just
like the Tilt illusion and the Rod and Frame Illusion. In these
configurations a vertical test stimulus is perceived as tilted
when surrounded by a tilted inducer (see Figure 1(c)). A global
model of orientation analysis has been proposed to account for
the orientational effects obtained with these illusions, according
to which the axis of symmetry of the inducing figure closer to
the vertical meridian exerts attraction or repulsion over the test
figure, generating misperception of the orientation (Wenderoth
& Beth, 1977; Zoccolotti et al., 1993; Wenderoth & van der
Zwan, 1991).
The literature about the Poggendorff Figure, including the
study by Prinzmetal and Beck (2001), has considered the abso-
lute role of one or more variables involved in determining the
illusion. So, for example, mechanisms of length processing
affect some illusions and those of orientation processing affect
other illusions.
By contrast, we suggest that the perceptual processing that
leads to the specific illusory phenomena depends on the spe-
cific conditions of stimulus presentation. That is, exactly the
same configuration activates different mechanisms as a func-
tion of the available and relevant information. According to this
view the computations regarding the length and the orientation
of the inducer are not relevant per se, but can be differently
weighted under different c o nditions of stimulus presentation.
In order to demonstrate this hypothesis we chose to manipu-
late two main features of the global configuration of the Pog-
gendorff Figure: the length and the orientation of the inducer (a
a) b)c)
(a) (b)(c)
Figure 1.
Standard versions of: (a) Poggendorff illusion; (b) Müller-Lyer illusion;
(c) Rod and frame illusion.
square). This choice is justified by the fact that length has been
the most studied variable in this domain, while global orienta-
tion is directly related to the interpretation of the Poggendorff
Illusory effect in terms of orientation illusion (Prizmetal &
Beck, 2001). As far as the length distortion hypothesis is con-
cerned, we manipulated the orientation of the test segments
with respect to the inducer, which affects the distance connect-
ing the two segments, but not the distance between the parallel
lines (side length).
In order to test for the role of global orientation distortion we
varied the orientation of the whole figure. A square figure was
used instead of the classical parallel lines or rectangle so as to
maintain all other variables constant while varying global ori-
entation. In order to avoid lateral inhibition effects, the angles
between the test lines and the inducer were always greater than
30 degrees (Carpenter & Blackmore, 1973).
We hypothesized that the role of length or orientation on the
computation leading to the illusory effect might vary despite
the fact that the relative physical dimensions of these variables
were kept constant. In the first experiment the main axis of the
inducer figure was laid on the horizontal and vertical spatial
axes, while in the second experiment the square was tilted and
the two segments were either vertical or horizontal. Note that in
both conditions the physical parameters of the stimulus re-
mained unchanged.
Experiment 1
Methods
Participants. 14 right-handed participants (5 males and 9
females) took part in this experiment as volunteers (mean age
of 27 years, range of 21 - 33 years; mean education of 16.4
years, range 15 - 17 years). All of the participants had normal
or corrected to normal vision.
Apparatus and materials. Stimuli were drawn and pre-
sented with the Matlab program on a PC platform. A modifica-
tion of the Poggendorff Figure was used as a stimulus, consist-
ing of a black line drawing on a white background of an upright
square and two abutting oblique line segments (see Figure 2).
Two different sizes of square were used covering a visual angle
of 9 degrees and 15 degrees. The length of the line segments
was 1/6 of the length of the side of the square. The two oblique
lines could either be placed to the left and right (vertical ar-
rangement condition) or to the top and bottom (horizontal ar-
rangement condition) of the square. Two orientations of the
oblique segments with respect to the connecting side of the
square were used, producing angles of 60 degrees and 75 de-
grees. Different positions of the test lines relative to their
veridical collinearity were used: the position of the right obli-
que line (in the vertical arrangement condition) and of the top
oblique line (in the horizontal arrangement condition; hereafter
258

A. GALLACE ET AL.
Figure 2.
Figures used in Experiment 1 for each orientation of the test lines (60
and 75 degrees) and for each position of the inducing figure (horizontal
and vertical). The dotted lines represent the axes of symmetry of the
inducing figure.
“match lines”) were maintained constant during the experiment.
The position of the left (or the bottom; hereafter “test lines”)
was varied between trials achieving 11 different possible posi-
tions. In the 9 degree square size condition, the test line was
moved in steps of 0.3 degrees from –0.3 to 2.7 degrees from
true collinearity with respect to the match line. In the 15 degree
square figure condition the range of distances varied from –0.5
to 4.5 degrees in steps of 0.5 degrees. The steps were chosen in
a preliminary experiment so as to be able to capture the size of
the illusion (the preliminary data are not included in the re-
sults).
Each position for the 3 conditions (square size, arrangement,
and angle of the oblique lines) was repeated 8 times for a total
of 704 trials. The vertical and horizontal arrangement condi-
tions were always presented in separate blocks of 352 trials
each, in a counterbalanced order across observers. All the other
conditions were completely randomized within each block of
trials.
Procedure. The experiment was conducted in a totally dark
room. The participants were seated comfortably on a chair at a
distance of 57 cm from a 17’’ PC monitor; they viewed the
stimuli through a circular window (23.5 degrees in diameter) in
a 45 degree diameter cardboard mask placed over the screen
frame to cover the monitor. The stimuli were presented for 700
msec and then replaced by a random dot mask (the color of the
dots in the mask varied from light grey to black) that filled the
screen until a response was given. A two alternatives forced
choice method was used to measure the perceived collinearity
between the test and the match line. Participants were asked
whether the test line should be moved up or down (or left or
right) to appear collinear with the match line; they gave their
answer by pressing one of two keys on a PC keyboard (arrow
pointing up or down in the vertical arrangement condition, and
left or right arrow in the horizontal arrangement condition). At
the beginning of the experiment the participants received writ-
ten instructions on how to proceed and at the beginning of each
block of trials they were told about the arrangement of the two
lines (vertical and horizontal) and of the two keys to be used for
their responses. The participants chose when to start each block
of trials by pressing a key on the keyboard. They were asked to
be as accurate as possible in their judgments and no time limit
was given. The experiment took approximately 25 minutes to
complete.
Data Analysis
Figure 3(b) shows hypothetical functions representing how
collinearity judgments change as a function of line displace-
ment relative to true collinearity. The dashed line represents the
absence of the illusory effect. The displacement (solid line)
along the horizontal axis indicates the magnitude of the illusion.
For each participant, the probability of judging the test line to
be above or below (or to the left or right of) the point of per-
ceived collinearity with the match line was measured as a func-
tion of distance from true alignment. Distance from alignment
was measured as a percentage displacement relative to the size
of the square.
A logistic model was applied to the data to calculate the
(a)
(b)
Figure 3.
Methods adopted to calculate the illusory effect in Ex-
periment 1 and 2. The variant of the Poggendorff Illu-
sion used in the present experiment is illustrated on the
left (a). The upper and lower segments appear mis-
aligned. To achieve perceived collinearity the upper line
is usually moved toward the right. On the right, two
hypothetical psychometric functions relate proportion of
“right” responses as a function of the distance of the
line from true alignment (b). The dashed line indicates
the absence of an illusory effect, the solid line repre-
sents the illusory effect that can be obtained using the
display on the left. The magnitude of the illusion is the
horizontal shift of the function, i.e. how far the line
needs to be moved away from true alignment in order to
be perceived as collinear. This is calculated at p = .5.

A. GALLACE ET AL.
260
point of subjective equivalence (PSE) for each observer in each
condition. The PSE is the percentage displacement at which the
function representing the participants’ responses crosses the 0.5
value (i.e. the point at which the participants judged equally
often that the test line had to be moved u p or down (right or left)
in order to be aligned with the match line). These values were
then submitted to a repeated measures ANOVA.
Results and Discussion
Figure 4 shows the psychometric functions for each indi-
vidual observer (dashed lines) and their average (solid line) for
the vertical alignment condition. A greater illusory effect was
observed when the angle between the lines and the side of the
square measured 60 degrees for both the 9 degree and the 15
degree square sizes (Figure 4 top row), but diminished when
the angle increased for both sizes (Figure 4 bottom row).
A repeated measures ANOVA was applied to the PSEs cal-
culated on the data of each individual observer in each condi-
tion: arrangement (horizontal and vertical), size of the test fig-
ure (9 and 15 deg of visual angle) and angle (60 degrees and 75
degrees) as factors. This analysis revealed a significant main
effect of angle [F(1,10) = 82.05; p < .0001], but not of size
[F(1,10) < 1; n.s.], nor of arrangement [F(1,10) < 1; n.s.]. None
of the interactions were significant [All F(1,10) <1; n.s.]. The
illusory effect was greater for the 60 degrees angle than for the
75 degrees angle between the test stimulus and the inducing
figure (see Figure 5).
Given that the PSEs were calculated as a percentage dis-
placement of relative to the square size, the absence of the main
effect of size indicates that the computation was invariant along
the size dimension.
Experiment 1 showed a significant difference between the
two angles adopted, suggesting a role for the linear distance
between the parallels and the distance between the two seg-
ments. In fact, changing the orientation changes the veridical
linear distance between the test line. As a consequence, the
effect of angle indicates that this measure enters the length
computation responsible for the illusory effect (e.g. assimilation
theory), at least under these conditions of stimulus presentation.
Experiment 2
As previously stated, tilting the participants’ position by 30
degrees while they observe the Poggendorff, Zollner and Ponzo
Illusions, increases the strength of the illusory effects (e.g., Prin-
(a) (b)
(c) (d)
Figure 4.
Psychometric functions for each observer (dashed line) and their mean (solid line) for four condi-
tions. Individual observers’ data are fitted using a logistic function. The upper row shows the data
obtained with an angle of 60 degrees between the test lines and the side of the square for both a 9
degree (a) and a 15 degree wide square (b). The lower row shows the psychometric functions ob-
tained with an angle of 75 degrees for squares with a width of 9 degrees (c) and 15 degrees (d).
Distance from alignment is expressed as a percentage difference from the point of collinearity
which scales with size. Psychometric functions for the 9 and the 15 degree wide squares are closely
matched, while the 75 degree angle cur ves look shallower tha n tho se for 60 degree angles.

A. GALLACE ET AL.
Figure 5.
Mean percentage of collinearity error in judging the alignment of the
test lines of the Poggendorff Figure in Experiment 1, as a function of
the angle between the test line and the inducing figure (60 and 75 de-
grees) , the size of the inducing figure (9 and 15 cm) and the orientation
of the figure (H = Horizontal and V = Vertical). Error bars represent
standard errors of the mean.
zmetal & Beck, 2001; Prinzmetal et al., 2001) which may be
attributed to a conflict between retinal, visual and gravity-
based cues to orientation. On the basis of these considerations,
it could be deduced that reducing the conflict between these
coordinate systems may diminish the illusory effect. This could
be achieved by aligning the oblique lines of the visual illusion
with the gravitational axis of the participant.
According to our hypothesis, a change in global orientation
should affect not only the computation regarding the integration
of orientation cues, but also the computation of length informa-
tion. That is, this manipulation might affect the relative weights
given to the different variables available, rather than affecting
the activation of constant mechanisms (leading to a main effect
of length, just as it has been found in Experiment 1, or its in-
teraction with orientation).
Methods
Participants. 10 of the right-handed participants (3 males
and 7 females) who took part in Experiment 1 volunteered for
Experiment 2 (mean age of 28.1 years, range of 21 - 33 years;
mean education of 16.7 years, range 15 - 17 years). The experi-
ment took approximately 25 minutes to complete.
Apparatus, materials, design, and procedure. The experi-
mental set-up, procedure and conditions were the same as those
used in Experiment 1 with the following exceptions: the whole
figure was tilted in order to keep the test and match lines verti-
cal (or horizontal) with respect to gravity; the position range
varied from –1.2 to 1.8 degrees in steps of 0.3 degrees in the 9
degree size condition, and from –2 to 3 in steps of 0.5 degrees
in the 15 degree condition (see Figure 6). The steps were iden-
tified in a preliminary study to capture the size of the illusion.
The preliminary data are not included in the results of the ex-
Figure 6.
Figures used in Experiment 2 for each orientation of the inducing figure
(60 and 75 degrees) and for each position of the test lines (horizontal
and vertical). The dotted lines represent the axes of symmetry of the
inducing figure.
periment.
Data Analysis
The PSEs were determined for each condition with the same
procedure used in Experiment 1.
Results and Discussion
The illusory effect was greatly diminished in all conditions
by tilting the figure to align the test and match lines to the ver-
tical and horizontal spatial axes (see Figure 7, for the aggre-
gated data for all observers and for each condition).
The points of subjective equivalence (PSE) calculated for
each participant were submitted to a repeated measures
ANOVA with global orientation (horizontal and vertical), size
of the test figure (9 and 15 cm) and angle (60 and 75 degrees)
as factors. This analysis revealed a significant main effect of
global orientation [F(1,6) = 9.03; p < .05], but not of size [F(1,6)
< 1; n.s.], nor of angle [F(1,6) = 5.2; n.s.]. None of the interac-
tions were significant. The illusory effect was large when the
test lines were aligned with the horizontal axis (mean = 2.15
mm). The direction of the effect reversed when the test lines
were aligned with the vertical axis (mean = –1.68 mm); see
Figure 8.
The results of Experiment 2 show that the illusory effect ob-
tained by rotating the main axis of the Poggendorff Figure was:
1) strongly reduced; and 2) determined solely by the computa-
tion of global orientation (i.e. vertical vs. horizontal). In par-
ticular, when the oblique lines were aligned to the vertical spa-
tial axes the point of subjective equivalence was reversed as
compared to the direction of the standard Poggendorff effect. It
is worth noting that the overall decrease of the illusory effect
has been reported in previous studies in which the standard
Poggendorff Configuration was tilted with reference to the
main axis of the figure (Green & Hoyle, 1964; Leibowitz &

A. GALLACE ET AL.
Figure 7.
Mean psychometric functions for the main significant conditions. The
upright square condition is indicated by a solid line, while the tilted
square condition is represented by a dashed line. Circles refer to a 60
degree angle between the line and the side of the square, and diamonds
to a 75 degree angle. The functions for the upright square reveal a large
effect when the angle is smaller (60 degrees) as opposed to a wider
angle (75 degrees). Surprisingly the illusory effect disappears when the
square is tilted.
Figure 8.
Mean percentage of collinearity error in judging the alignment of the
test lines of the Poggendorff Figure in Experiment 2, as a function of
the orientation of the test line with respect to the main axis of the par-
ticipant (Horizontal and Vertical), the size of the inducing figure (9 and
15 cm) and the angle between the test line and the inducing figure (60
and 75 degrees). Error bars represent standard errors of the m ea n.
Toffey, 1964). This result might be related to the coincidence of
visual and gravity-based cues to orientation (see Prinzmetal &
Beck, 2001). Alternatively, we suggest that the novel and some-
how surprising inversion of the effect found in Experiment 2
might be due to the same computation underlying the Rod and
Frame-like effect (Wenderoth, 1977). Critically, we found no
evidence of an influence of length on the illusory effect. This is
particularly relevant given that in Experiment 2 the distances
between inducer and test segments were the same as in Expe-
riment 1 (where the effect of length was found).
General Discussion
The results of Experiment 1 show that when the Poggendorff
Figure was oriented in its canonical way (upright) the illusory
effect was mainly influenced by the computation of length.
None of the other factors considered (i.e. orientation arrange-
ment) significantly contributed to the computation underlying
the illusory effect. On the contrary, when the Poggendorff Fig-
ure was rotated in Experiment 2, a significant effect of orienta-
tion was obtained, but not of the other factors (i.e. size and
angle). That is, it appears that the factors entering the computa-
tions that led to the illusory effect varied as a function of the
conditions of stimulus presentation.
Prinzmetal and Beck (2001) suggested that the Poggendorff
Illusion might be determined by the same mechanism that un-
derlies the rod-and-frame and tilted-room illusions (see Asch &
Witkin, 1948, 1949), and specifically that all these illusory
effects might be determined by a misperception of orientation
caused by a peripheral visual frame. The observation that all
these effects can be influenced by tilting the head of the obser-
ver relative to gravity has provided support for this theory (e.g.,
Asch & Witkin, 1948; DiLorenzo & Rock, 1982; Prinzmetal &
Beck, 2001; but see also Wenderoth & Burke, 2006). The re-
sults of Experiment 2, which show that the illusory effect de-
creased when the visual and gravity-related cues were coinci-
dent, appear to confirm this hypothesis.
It must be said, however, that Prinzmetal and Beck (2001)
found that the Muller-Lyer Illusion was not affected by body
orientation, which would suggest that the Poggendorff and the
Muller-Lyer Illusions are based on different mechanisms. This
conjecture is not supported by our results (Experiment 1). In the
Muller-Lyer Figure the illusory effect is modulated by the dis-
tance separating the wings endings, which can be manipulated
either by elongating the wings or by increasing the angle that
they subtend, and the length of the shaft (i.e. Day & Dickinson,
1976; Pressey & Di Lollo, 1978). Experiment 1 showed that the
Poggendorff Illusion was modulated by the distance between
the parallels of the inducing figure and that between the oblique
test lines. Both visual illusions are thus influenced by the two
distances, suggesting that they likely share a common mecha-
nism that computes length.
Moreover, according to Prinzmetal and Beck (2001) the
Poggendorff Illusion should “always” be due to a misperception
of orientation, while we found a significant effect of global
orientation in Experiment 2, but not in Experiment 1.
In line with our hypothesis, the perceptual computations un-
derlying visual illusions are weighted as a function of the spe-
cific conditions of demand and stimulus presentation. Many di-
fferent features can enter the computation of collineariry, and
these may interact at many different levels of information pro-
cessing (cf. Prinzmetal & Back, 2001). Experiment 2 showed
that rotating the Poggendorff Figure induced an effect that was
both quantitatively and qualitatively different from that ob-
tained with a canonically-oriented figure. This effect might be
due to the fact that when the Poggendorff Figure is canonically
262

A. GALLACE ET AL.
oriented the square can be used to define the spatial “frame of
reference” for the judgment of collinearity. This does not occur
when the figure is rotated (note that in this case the main axes
of the square are no more aligned with the main visual and
gravitational axes), requiring the participant to use another source
of information for the collinearity judgment (or to change the
relative weights given to any source of information available).
That is, the information that is available to the participant at any
given time modifies the type of processing that leads to the
collinearity judgment.
Studies of the Rod and Frame Illusion have shown that the
perceived orientation of a rod is an angular function of the ori-
entation of the frame that surrounds it (e.g. Gibson & Radner,
1937). This effect has been explained in terms of both the re-
pulsion and attraction of the rod towards the axis of symmetry
of the frame (e.g. Gibson, 1937; Gibson & Radner, 1937; Wen-
deroth, 1977; Wenderoth & van der Zwan, 1991). Specifically,
for frame orientations of between 60 and 90 degrees the rod is
subjectively perceived as tilted in the direction opposite to that
of the frame, with the greatest effect at around 75 degrees (see
Wenderoth, 1977). In the vertical condition of Experiment 2 the
closest symmetry axis to the vertical is the diagonal of the
square, which is taken as the reference for judging the orienta-
tion of the test lines. Therefore, in this condition the orientation
of the test line is misperceived in the direction opposite to that
of the diagonal, resulting in the inversion of the illusory effect.
In other words, when the square is considered as the equivalent
of a frame and the oblique lines as the equivalents of a rod, the
rod-and-frame angular function can accurately predict the di-
rection of the Poggendorff Illusory Effect.
In our opinion, the Poggendorff Illusion (and probably other
illusions) is not the consequence of one or a few specific me-
chanisms, but the result of ordinary processing by the general
purpose structure/functions of the visual system. Thus it can be
assumed that in the Poggendorff Illusion, collinearity judg-
ments require both length and orientation computations, but
that the presence of gravitational cues: 1) can modify which of
the various inputs (visual, gravitational, or proprioceptive) are
included in the computation; and 2) can determine the relevance
of each input for the computation itself (cf. Ernst & Banks,
2002).
On the basis of these observations, we suggest that approa-
ches based on single mechanisms or unified theories (Parks,
2009) might not be effective in accounting for visual illusions.
We propose instead that the Gestalt approach of explaining
visual perception by general perceptual grouping laws can be
more useful for this purpose. For example, the concept of
“frame of reference”, which refers to the influence of one ob-
ject on the perception of the characteristics of another (see
Gregory, 1972; Hochberg, 1987; Rock, 1990) is coherent with
our results. That is, in the case of our experiments, the inducer,
represented by a square, might be considered the main frame of
reference on the basis of which the judgments of test lines col-
linearity are performed.
This frame of reference affects the weight of those variables
(length and orientation) which enter the computation at the
basis of the Poggendorff Effect.
This explanation is not necessarily limited to the Poggen-
dorff Configuration. Indeed, our experiments showed that when
the square of the Poggendorff Figure was oriented in the up-
right position the illusory effect was determined by the compu-
tation of length, just as in the Müller-Lyer Illusion (e.g., Coren,
1986). On the other hand, when the square was tilted so that the
obliq ue lines were aligned wi th the vert ical and hor izontal a xis,
the figure behaved like the Rod-and-Frame Illusion (e.g., Wit-
kin & Asch, 1948; Wenderoth, 1977), revealing that orientation
computation plays a main role. This result is congruent with the
idea that the Muller-Lyer, Poggendorff and Rod and Frame
Figures are likely computed on the basis of the same principles
of perceptual organization.
Acknowledgements
R. D. and A. G. were supported by grants from the MIUR to
Giuseppe Vallar; M. M. was supported by grants fr om the MIUR
to Pierluigi Zoccolotti. Correspondence regarding this article
should be addressed to: Roberta Daini, University of Milano-
Bicocca, Department of Psychology, Piazza dell’Ateneo Nuovo
1, 20126 Milano, Italy.
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