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The Oppel-Kundt Illusion is Effective in Modulating Horizontal Space Representation in Humans

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  • IOB - Institute of Molecular and Clinical Ophthalmology Basel

Abstract and Figures

A modified version of the Oppel-Kundt illusion (i.e., a filled space is perceived as more expanded than an empty space of the same length) has been previously employed to distort space representation both in patients with neglect (i.e., failure to report/react to stimuli located in the space contralateral to the brain lesion) and in healthy participants. In those experiments, participants had to bisect or extend horizontal segments on backgrounds of exponentially spaced vertical lines. The exclusive use of visuo-motor tasks, however, did not allow excluding that the results were accounted for by a bias occurring at a response level of stimulus processing rather than by a visual illusion. To address this issue, in addition to a traditional line bisection task, a line length estimation task was employed, which allowed separating response and illusion-related factors. The results demonstrated that performance depended on the visual illusion rather than on a response bias. It was concluded that this version of the Oppel-Kundt illusion can be successfully employed to modulate space representation in humans.
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Perceptual & Motor Skills: Perception
2012, 115, 3, 729-742. © Perceptual & Motor Skills 2012
DOI 10.2466/24.22.27.PMS.115.6.729-742 ISSN 0031-5125
The Oppel-KundT illusiOn is effecTive in mOdulaTing
hOrizOnTal space represenTaTiOn in humans
1, 2
lOrenzO pia and marcO neppi-mòdOna
Psychology Department and Neuroscience Institute of Turin
University of Turin, Italy
federica Bianca rOsselli
International School for
Advanced Studies (SISSA)
Neurobiology and Cognitive
Neuroscience Sectors, Trieste, Italy
virginia muscaTellO and rOsalBa rOsaTO
Psychology Department
University of Turin, Italy
raffaella ricci
Psychology Department and Neuroscience Institute of Turin
University of Turin, Italy
Summary.—A modied version of the Oppel-Kundt illusion (i.e., a lled space
is perceived as more expanded than an empty space of the same length) has been
previously employed to distort space representation both in patients with neglect
(i.e., failure to report/react to stimuli located in the space contralateral to the brain
lesion) and in healthy participants. In those experiments, participants had to bisect
or extend horizontal segments on backgrounds of exponentially spaced vertical
lines. The exclusive use of visuo-motor tasks, however, did not allow excluding
that the results were accounted for by a bias occurring at a response level of stimu-
lus processing rather than by a visual illusion. To address this issue, in addition to
a traditional line bisection task, a line length estimation task was employed, which
allowed separating response and illusion-related factors. The results demonstrated
that performance depended on the visual illusion rather than on a response bias.
It was concluded that this version of the Oppel-Kundt illusion can be successfully
employed to modulate space representation in humans.
The term geometrical illusion derives from the German “geometrisch-
optische täuschung” and describes any misperception of stimulus length,
size, shape, or direction due to a non-correspondence between the percept
and the actual stimulus. Oppel (1854/1855) originally demonstrated that
the visual space enclosed within a series of dots is perceived longer than
an empty space of the same dimension (see Fig. 1, upper part). The princi-
ple underlying such an illusion, later (Kundt, 1863) called the Oppel-Kundt
1
Address correspondence to Lorenzo Pia, Psychology Department & Neuroscience Institute of
Turin, University of Turin, Via Po 14, 10123 Turin, Italy or e-mail (lorenzo.pia@unito.it).
2
This work was supported by a PRIN (2009) grant to Lorenzo Pia, Marco Neppi-Mòdona, and
Raaella Ricci, and by a Marie Curie Grant (n°39537) to Marco Neppi-Mòdona (2006-2008).
The manuscript is original, not previously published, and not under concurrent consider-
ation elsewhere. We state no conict of interests and respect of requirements for authorship.
L. Pia, et al.
730
illusion, is also eective when the space is enclosed within vertical lines
(Kundt, 1863; Lewis, 1912; Ni, 1934; Coren, Girgus, Ehrlichman, & Hakistan,
1976; see Fig. 1, middle part), for horizontal lines subdivided by vertical
lines (Oppel, 1860/1861; Ricci, Calhoun, & Chatterjee, 2000; Ricci, Pia, &
Gindri, 2004; see Fig. 1, lower part), and in 3D visual space (Deregowski &
McGeorge, 2006). The magnitude of the illusory eect is a function of mul-
tiple properties of the stimuli, such as texture and illusory gradient (Giora
& Gori, 2010; Wackermann & Kastner, 2010). Interestingly, the principles un-
derlying the illusion are also eective within sensory modalities other than
vision, such as haptic (e.g., haptic line bisection; Suzuki & Arashida, 1992)
audition (e.g., estimation of time intervals; Russo & Dellantonio, 1989). Ad-
ditionally, the illusion is eective also across modalities. Gallace and co-
workers (Gallace, Auvray, & Spence, 2007), for instance, showed that haptic
line bisection in healthy participants is aected cross-modally by varying
the visual background that participants viewed.
Fig. 1. The Oppel-Kundt illusion. Some examples.
OPPEL-KUNDT ILLUSION
731
Ricci and coworkers (Ricci, et al., 2004) developed a modied version
of the Oppel-Kundt illusion to modulate space representation in patients
with unilateral neglect (i.e., a disorder of contralesional space awareness;
see Halligan, Fink, Marshall & Vallar, 2003, for a review) and in healthy
participants. The aim of that study was to induce in healthy participants
the anisometrical (i.e., non-linear) spatial distortion hypothesized to un-
derlie neglect (Bisiach, Ricci, & Neppi-Mòdona, 1998; Bisiach, Neppi-Mò-
dona, & Ricci, 2002), and to counteract this distortion in patients. Indeed,
according to Bisiach’s account, in neglect patients, “the left–right dimen-
sion of space representation is settled, as it were, on a logarithmic scale,
with compression on the ipsilesional side and expansion on the contral-
esional side” (Bisiach, Pizzamiglio, Nico, & Antonucci, 1996, p. 855-856).
At a perceptual level, this results in an underestimation of contralesional
stimuli with respect to ipsilesional ones. Hence, Ricci and coworkers (Ric-
ci, et al., 2004) employed visual backgrounds composed of vertical lines
whose distance progressively decreased from one side of the page to the
other, according to an exponential function. In this way, they dened lled
and empty portions of space by means of non-linearly or anisometrically
distributed vertical lines (in the original version of the Oppel-Kundt illu-
sion, space is subdivided into equal, isometric intervals). On the above-
mentioned visual backgrounds, participants had to perform a line bisec-
tion task (i.e., mark the midpoint of a horizontal line) and a line extension
task (i.e., extend a horizontal segment leftward or rightward to double its
original length). According to the principles underlying the original ver-
sion of the Oppel-Kundt illusion, the more densely segmented portion
of the background was expected to induce perceptual expansion of the
line (overestimation of stimulus length) with respect to the less dense-
ly segmented portion (underestimation of stimulus length). The authors
predicted a displacement of the subjective midpoint and shorter line ex-
tensions towards the denser side of the background. The performance of
both neglect patients and healthy participants conrmed these predic-
tions. Interestingly, patients with neglect showed an improvement of their
rightward bisection bias when the visual illusion induced a perceptual
distortion opposite to that hypothesized to underlie neglect (i.e., illuso-
ry expansion of left space), whereas healthy participants exhibited a ne-
glect-like bisection bias when the visual illusion induced a perceptual dis-
tortion mimicking the one hypothesized to underlie neglect (i.e., illusory
contraction of the left space). Subsequent studies, employing similar ver-
sions of the Oppel-Kundt illusion, replicated and extended Ricci and co-
workers’ (Ricci, et al., 2004) ndings, namely the displacement of the sub-
jective midpoint towards the denser side of the illusory background in the
line bisection task both in neglect patients (Savazzi, Posteraro, Veronesi, &
L. Pia, et al.
732
Mancini, 2007) and healthy participants (Binetti, Aiello, Merola, Bruschini,
Lecce, Macci, et al., 2011).
The validity of the above-mentioned ndings (Ricci, et al., 2004;
Savazzi, et al., 2007; Binetti, et al., 2011) can be challenged by the argu-
ment that these tasks do not provide a direct measure of the eects of the
illusion because participants do not explicitly judge horizontal lengths.
Hence, such tasks do not allow excluding the possibility that participants’
performance is strongly driven by a response bias towards the denser side
of the background. Indeed, given that stimulus characteristics may auto-
matically draw attention to particular regions of space (see, for instance,
Mark, Kooistra, & Heilman, 1988), the side of the background with the
highest density of vertical lines might have automatically attracted partic-
ipants’ attention. This, in turn, might have biased participants’ motor re-
sponses towards this side (see Ricci, et al., 2004, p. 234, and Savazzi, et al.,
2007, p. 10, for details on this point).
The present study aims to clarify this issue. To this end, it compares
the eect of the above mentioned modied version of the Oppel-Kundt
illusion on a traditional line bisection and on the landmark task (Milner,
Brechmann, & Pagliarini, 1992; Bisiach, Ricci, Lualdi, & Colombo, 1998), a
task conceived to separate perceptual and response-related factors in the
estimation of horizontal lengths. Here, participants have to perform a line
length estimation task by choosing which of two segments (left or right)
composing a pre-bisected line is shorter, in one condition, and longer, in
the other. If participants’ behavior is driven by the visual illusion, they are
expected to choose more often the segment lying on the more sparse side
in the Shorter condition, and the opposite segment (lying on the denser
side) in the Longer condition. Conversely, if the participants’ performance
is the consequence of a response bias towards the denser side of the back-
ground, they should consistently choose the segment lying on this side in-
dependent of task demands.
Method
Participants
Thirty-ve right-handed (Oldeld, 1971), randomly chosen, healthy
participants participated in this study (16 men, 19 women). In order to
compare the results of the present work to those obtained in the aforemen-
tioned studies (Ricci, et al., 2004; Savazzi, et al., 2007; Binetti, et al., 2011),
participants were selected to be comparable for age and educational lev-
el (M age = 69.2 yr., SD = 9.3; M education = 11.1 yr., SD = 4.8). All partici-
pants gave their informed consent to participate in the study, which was
approved by the local ethical committee.
Stimuli
The visual background consisted of 25 0.5 mm thick and 88.25 mm
OPPEL-KUNDT ILLUSION
733
fig. 2. Backgrounds used in line bisection and the landmark tasks. Uniform Densi-
ty = evenly spaced vertical lines (baseline); Dense Left = exponentially spaced vertical lines
with distances progressively decreasing leftwards; Dense Right = exponentially spaced verti-
cal lines with distances progressively decreasing rightwards.
Uniform Density
Dense Left
Dense Right
long vertical lines parallel to the shorter side of an A4 sheet of paper (print-
ed in black against a white background). Vertical lines were interrupted by
a 14 mm high and 297 mm long rectangular empty gap located in the mid-
dle of the sheet. In one condition (Uniform Density), the lines were evenly
spaced at a distance of 10 mm. This condition served as baseline. In the
L. Pia, et al.
734
other two conditions (i.e., Dense Left and Dense Right), they were expo-
nentially spaced with distances progressively decreasing from one side of
the page to the other (toward the left in the former and towards the right
in the latter, according to the exponential function Y = e
x
; x [−0.50; 1.9]
in steps of 0.10 (see Fig. 2). The Dense Left condition was designed to in-
duce an illusory spatial expansion of the left spatial sector and a contrac-
tion of the right spatial sector. Conversely, the Dense Right condition was
designed to induce the opposite illusion.
Procedures
Line bisection task.—A 200 mm long and 0.5 mm thick horizontal line
segment was printed within the rectangular horizontal gap interrupt-
ing the vertical background lines. The center of the line segment was dis-
placed leftward or rightward (by 3 mm) of the midpoint of the page to
prevent participants from using the background lines as a visual cue to
estimate the objective midpoint of the line. Participants were explicitly in-
formed that such a strategy would be misleading and throughout the ex-
ecution of the task the examiner took care in preventing from participants
used this strategy. Participants were given 60 trials (10 repetitions × 3
backgrounds × 2 line positions) in a pseudo-random order (there were no
consecutive identical trials). The sheet of paper was centered on the partic-
ipant’s saggittal mid-plane and presented at reaching distance under nor-
mal room lighting conditions. The visual angle subtending the line was
about 30°. Participants were asked to mark the midpoint of the horizontal
line with a pencil.
Landmark task.—The 200 mm long and 0.5 mm thick horizontal line,
printed within the rectangular horizontal gap was pre-bisected with a 0.5
mm thick and 4 mm long vertical black line placed to the left or to the
right (by 1 or 2 mm) of the objective midpoint or centered on it. As for the
line bisection task, the center of the line segment was displaced 3 mm left-
ward (or rightward) to prevent the use of the background as a visual cue
to estimate the segment midpoint. Indeed, participants were informed of
the ineectiveness of the strategy and were controlled during the task.
The sheet of paper was centered on the participant’s saggittal mid-plane
and presented at reaching distance under normal room lighting condi-
tions. The visual angle subtending the line was about 30°. Participants
were required to make a binary forced-choice decision (right/left) accord-
ing to opposing question conditions: in one condition, they had to point
with the right hand towards the longer side of the segment (left or right),
whereas in the other, they had to point with the right hand towards the
shorter side of the segment (left or right). Longer and Shorter question
conditions were grouped in four separate blocks following an ABBA or-
der (which was counterbalanced across participants). The overall number
OPPEL-KUNDT ILLUSION
735
of trials was 120 (2 question conditions × 2 repetitions × 3 backgrounds × 2
line positions × 5 bisector positions). Left and right responses were record-
ed. The order of the two tasks (i.e., line bisection and landmark task) was
counterbalanced across participants.
Statistical Analysis
Line bisection task.—Bisection errors were measured with an approx-
imation to the nearest mm. Positive values were assigned to rightward
deviations and negative values to leftward deviations. Measures were
distributed normally (Kolmogorov-Smirnov test) and variance was ho-
mogeneous (Box’s M test). Hence, the authors performed a repeated-mea-
sures analysis of variance (ANOVA) with Background (three levels: Uni-
form Density, Dense Left and Dense Right) as within-subjects factors, and
bisection error as the dependent variable. In this task, both the illusory
and the response bias interpretations predicted statistically signicant bi-
section errors toward the denser portion of the background.
Landmark task.—For each participant, the proportion of left and right
side responses with respect to the bisector positions was estimated by
means of a stratied logistic analysis on each combination of Background
and Question condition levels. Then the parameters of the logistic func-
tion were used to estimate the point of subjective equality (hereinafter
PSE) obtained as a 0.5 threshold value of the function, namely the point
where the two halves of the segment are subjectively perceived as identi-
cal (Kingdom & Prins, 2010). Positive values were assigned to rightward
deviations, negative values to leftward deviations. Since measures were
distributed normally (Kolmogorov-Smirnov test) and variance was homo-
geneous (Box’s M test), we performed a repeated-measures ANOVA with
Background (three levels: Uniform Density, Dense Left, and Dense Right)
and Question (two levels: Longer and Shorter) as within-subjects factors,
and PSEs as dependent variables (missing values were replaced with the
group mean). A statistically signicant misplacement of the PSE toward
the denser portion of the background, and no Background × Question con-
dition interaction was expected in the presence of an illusory perceptual
bias (choosing the segment lying on the more sparse side as shorter, and
the one lying on the denser side as longer gives rise to the same PSE). On
the other hand, a signicant interaction between Background × Question
conditions (PSE towards the denser side for the Longer condition and to-
wards the sparse side for the Shorter condition) was expected to be ob-
served in the presence of a response bias.
Results
Line Bisection Task
The ANOVA was signicant (F
2,68
= 94.73, p < .0001, partial η
2
= 0.74;
L. Pia, et al.
736
observed power = 1.0). A post hoc analysis (Duncan) showed that each con-
dition was signicantly dierent from the others (p < .0005). The bisec-
tion error was displaced towards the denser side of the Background (Uni-
form Density: M = 1.321 mm, SE = 0.529 mm; Dense Left: M = −2.385 mm,
SE = 0.474 mm; Dense Right: M = 4.321 mm, SE = 0.691 mm). Each condi-
Uniform Density
Deviation from the Midpoint (mm)
0 0.5−0.5−1.5−2.5−3.5−4.5−5.5 1.5 2.5 3.5 4.5 5.51.0−1.0−2.0−3.0−4.0−5.0 2.0
*
*
*
3.0 4.0 5.0
Dense Left
Dense Right
fig. 3. Line bisection. Mean bisection error in the dierent Background conditions.
Uniform Density = evenly spaced vertical lines (baseline); Dense Left = exponentially spaced
vertical lines with distances progressively decreasing leftwards; Dense Right = exponentially
spaced vertical lines with distances progressively decreasing rightwards. Positive and nega-
tive values indicate, respectively, a rightward and a leftward deviation of the midpoint.
Bisector Position (mm)
Probability
0 1−1−2 2
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Fig. 4. Landmark task. Psychometric curves tted according to Background and Ques-
tion condition levels. Shorter Uniform Density ( ); Shorter Dense Left ( ); Shorter Dense Right
( ); Longer Uniform Density ( ); Longer Dense Left ( ); Longer Dense Right ( ).
OPPEL-KUNDT ILLUSION
737
tion was also dierent from the veridical midpoint (p < .05). Fig. 3 shows
the mean bisection errors (mm) for each Background condition.
Landmark Task
Fig. 4 depicts the psychometric function. In the ANOVA, only the main
factor Background was signicant (F
2,68
= 8.68, p < .0005, partial η
2
= 0.20;
observed power = 0.96). A post hoc analysis (Duncan) showed that each
condition was signicantly dierent from the others (p < .05). The PSE was
displaced towards the denser side of the Background (Uniform Density:
M = 0.043 mm, SE = 0.41 mm; Dense Left: M = −0.968 mm, SE = 0.381 mm;
Dense Right: M = 1.09 mm, SE = 0.263 mm). Dense Left and Dense Right
conditions were also dierent from the veridical midpoint (p < .05). Fig. 5
shows the mean PSE (mm) for each Background condition.
discussion
The present results show that the eects of a variant of the Oppel-
Kundt illusion on line length estimations tightly depend on a perceptual
illusion of length rather than on a motor response bias. Previous studies
have used a modied (i.e., non-linear) version of the Oppel-Kundt illu-
sion in healthy participants and neglect patients to modulate spatial rep-
Uniform Density
Deviation from the Midpoint (mm)
0 0.5−0.5−1.5−2.5−3.5−4.5−5.5 1.5 2.5 3.5 4.5 5.51.0−1.0−2.0−3.0−4.0−5.0 2.0
*
*
*
3.0 4.0 5.0
Dense Left
Dense Right
Fig. 5. Landmark task. PSE in the dierent Background conditions. Uniform Densi-
ty = evenly spaced vertical lines (baseline); Dense Left = exponentially spaced vertical lines
with distances progressively decreasing leftwards; Dense Right = exponentially spaced ver-
tical lines with distances progressively decreasing rightwards. Positive and negative values
indicate, respectively, a rightward and a leftward deviation of the midpoint.
L. Pia, et al.
738
resentation (Ricci, et al., 2004; Savazzi, et al., 2007; Pia, Folegatti, Guagliar-
do, Genero, & Gindri, 2009; Binetti, et al., 2011; Pia, Ricci, Gindri, & Vallar,
2012). One of the aims of these studies was to investigate the anisometric
spatial distortion thought to underpin spatial neglect (Bisiach, et al., 1996;
Bisiach, Ricci, & Neppi-Mòdona, 1998; Bisiach, et al., 2002). Those studies
reported that participants mis-bisected horizontal lines towards the dens-
er portion of the background. This result could be interpreted as due to
the illusion (inducing line length overestimation in correspondence of the
denser side of the background), or to a motor response bias towards this
side. To investigate this issue, healthy participants were asked to perform,
under the same illusory backgrounds, a traditional line bisection task and
a landmark task in which they had to evaluate the horizontal extension of
two segments composing a pre-bisected line. Consistent with the above-
mentioned ndings (Ricci, et al., 2004; Savazzi, et al., 2007; Binetti, et al.,
2011), participants mis-bisected the lines toward the denser portion of the
background, a result consistent with both an illusory and a “bias of re-
sponse” interpretation. The landmark task disambiguated these alterna-
tives in favor of the illusory interpretation. Indeed, participants judged
the segment lying on the denser side as longer and the segment lying on
the more sparse side of the background as shorter, rather than consistently
pointing towards the denser side independently of task demands. In ac-
cordance with this behavior, the PSE calculated from participants’ choices
was displaced towards the denser side of the background and it was con-
sistent under both task demands.
It is worth noticing that in the landmark task, participants respond-
ed with a pointing movement. The theory of separate vision-for-percep-
tion and vision-for-action subsystems (Milner & Goodale, 2008) predicts
that visually guided actions should be immune from illusions. It is worth
noticing, however, that whether this prediction is convincingly support-
ed by experimental results is still controversial (e.g., Carey, 2001; Smeets,
Brenner, de Grave, & Cuijpers, 2002). Indeed, some data suggest that il-
lusory eects do not solely depend on response modality (motor tasks
as opposed to procedures designed to tap into conscious perception) but,
rather, other factors modulate the eect of the illusion on motor respons-
es (Bruno, Bernardis, & Gentilucci, 2008). The current results support this
conclusion and are in line with a recent study demonstrating that some
system mediating motor activity may remain vulnerable to the Oppel-
Kundt illusion (Savazzi, Emanuele, Scalf, & Beck, 2012).
The fact that this illusion is eective in both healthy participants and
neglect patients (Ricci, et al., 2004; Savazzi, et al., 2007; Binetti, et al., 2011)
adds to previous evidence showing that space representation in the in-
tact brain and in left unilateral neglect possesses similar susceptibilities to
OPPEL-KUNDT ILLUSION
739
a variety of manipulations. Non-invasive brain stimulation such as tran-
scranial magnetic stimulation can improve neglect and induce neglect-like
symptoms in healthy participants (e.g., Fierro, Brighina, Oliveri, Piazza,
La Bua, Bua et al., 2000; Brighina, et al., 2003). Sensory manipulations, for
instance, neck-proprioceptive or vestibular stimulations (Karnath, Fetter,
& Dichgans, 1996), can improve neglect symptoms and reproduce them in
healthy participants. Prism adaptation is known to improve neglect and
induce a neglect-like bias in healthy participants (Loftus, Vijayakumar, &
Nicholls, 2009). As regards to visual illusions, in addition to the Oppel-
Kundt illusion, the Judd and the Brentano variants of the Mueller-Lyer
illusion have also been used to alter the metric of space representation
in neglect patients and healthy participants (Fleming & Behrmann, 1998;
Daini, Angelelli, Antonucci, Cappa, & Vallar, 2002). In these visual illu-
sions, the eect of spatial expansion is obtained by increasing the physi-
cal amount of the horizontal stimulus. In other words, the outwards thin
side increases the overall horizontal conguration (i.e., the length of the
horizontal stimulus toward the outwards thin side). Instead, in the Op-
pel-Kundt illusion, perceptual modulation of line length is obtained with-
out changing the horizontal physical length of the line. The possibility of
inuencing the internal spatial representation of stimuli without chang-
ing their horizontal physical dimension might provide a valuable tool to
study the mechanisms underlying space representation in both the intact
and the lesioned brain.
A nal relevant point is the possible link between our data and the na-
ture of the anisometrical spatial distortion thought to underlie neglect. As
mentioned above, Bisiach and coworkers (Bisiach, Ricci, & Neppi-Mòdo-
na, 1998; Bisiach, et al., 2002) proposed that neglect is caused by a patholog-
ical distortion of the representational medium, progressively compressed
towards the ipsilesional space and relaxed towards the contralesional one
in a logarithmic manner. Indeed, “the distortion underlying neglect and
related phenomena has been likened to a pathological (spatial) remap-
ping of an Euclidean onto a logarithmic scale, with spatial expansion on
the contralesional and compression on the ipsilesional side, giving rise
to something similar to the Oppel-Kundt illusion” (Bisiach, 1997, p. 491).
This kind of distortion is mimicked by the Dense Right condition of our
experiment on which participants behaved in a qualitatively similar way
to neglect patients (showing a small but signicant rightward bisection er-
ror). Hence, the data support the view that in the intact brain the metric of
the representational medium can be distorted similarly to the anisometri-
cal spatial distortion described in neglect (Ricci, et al., 2004; Savazzi, et al.,
2007; Binetti, et al., 2011; Savazzi, et al., 2012). However, even though there
is a similarity, illusions of length (among which there is the Oppel-Kundt
L. Pia, et al.
740
Illusion) and space anisometry (resultant from lesion-induced alterations
of the space processing neural system) are to be interpreted as indepen-
dent phenomena. Indeed, it is known that they are likely to occur at in-
termediate and late stages of visual processing (respectively), which have
been found to doubly dissociate (Driver, Baylis, & Rafal, 1992; Vecera &
Behrmann, 1997; Ricci, Vaishnavi, & Chatterjee, 1999). It has been specu-
lated that the neurophysiological signature of space anisometry might be
ascribed to the changes of the response properties of the receptive elds
of fronto-parietal neurons surviving the lesion (Bisiach, Ricci, & Modo-
na, 1998): “It might turn out that the characteristics of such neurons, and
therefore the metrics of space representation, are contingent upon the
equilibrium emerging within a widespread neuronal network from, as it
were, a system of functional counterforts. Unilateral brain damage could
result in one-sided lack of counterpoise within such a system and lead to
skewness of the medium for space representation.
We must acknowledge the main limitation of the present study. The
ndings are simple and straightforward (i.e., validating a tool to study the
mechanisms underlying space representation in humans) and purely be-
havioral. Hence, further research is necessary to obtain information about
the neural mechanisms underlying modulation of space perception through
the Oppel-Kundt illusion in the healthy and in the lesioned brain. Results,
for instance, should be replicated in patients with visuo-spatial neglect.
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Accepted November 14, 2012.
... Using this task the authors found that the modulation of the patients' performance was in line with the space anisometry hypothesis, and thus, again, ruling out the attentional explanation. More importantly, some additional pieces of evidence in favour of the space anisometry hypothesis come from a recent paper by Pia et al. (2012b) in which the authors investigated the effect of the OKI not only on a bisection task but also on a landmark task ( Milner, Brechmann, & Pagliarini, 1992;Bisiach, Ricci, Lualdi, & Colombo, 1998a), a task conceived to distinguish between perceptual and response biases. In this task the participants were presented with pre-bisected lines and asked to indicate which portion of the line was shorter in half of the trials and longer in the other half. ...
... Interestingly, similarly to what proposed by the space anisometry hypothesis ( Bisiach, 1997, page 491), the "mental number line" has been found to consist of a mental continuum logarithmically compressed along the horizontal dimension ( Dehaene, 2003), thus suggesting a possible similar way for the physical and numerical space to be represented and distorted in neglect. All in all, the picture emerging for the present data and from those already present in literature demonstrate that the same nonlinear metric (which is postulated by the space anisometry hypothesis) produces such a spatial distortion able to predict the behaviour of neglect patients in several different tasks, for example, in reading words (the present data and those reported by Savazzi et al., 2004), in numerically bisect a numerical interval (present data), in bisecting words (the present data), long lines ( Ricci et al., 2004 andSavazzi et al., 2007) and very short lines ( Savazzi et al., 2007), in visual search ( Ricci et al., 2004) and in line length estimation ( Pia et al., 2012b). Therefore, we believe that these accumulating pieces of evidence, advocating for an internal representation of the outside world logarithmically distorted along the horizontal dimension, can explain most of the typical abnormalities observed in neglect patients. ...
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The Oppel-Kundt illusion (OKI) consists of the perception of a filled space as larger than an empty space of the same size. Here, we used a modified version of that illusion composed of a gradient of vertical lines whose spacing decreased progressively from one side to the other: space is expected to be perceived as larger where the lines are more compressed. We tested the hypothesis that a horizontal stimulus presented in a space perceived as larger will produce faster RTs by asking forty-four healthy subjects to respond as quickly as possible to lateralized stimuli (horizontal bars, vertical bars and circles) presented on different backgrounds (control condition: evenly spaced vertical lines or an empty space; illusory conditions: vertical lines progressively compressed to the right or the left). Subjects' RTs were reliably faster for horizontal stimuli presented on the space perceived as larger than on the space perceived as smaller. To verify that this effect was actually due to a size illusion, the same subjects were asked to adjust the size of the stimuli presented on the same backgrounds as to make them equal to a reference stimulus. For horizontal stimuli, subjects produced adjustments in accordance with the predicted effect of the illusion. Together, these data show that the OKI produces a distortion of space that extends to stimuli placed in front of it and that RTs are influenced by the perceived and not the physical size of the stimuli. Implications for neural bases of illusions and for spatial neglect are discussed.