Cerebral Cortex July 2010;20:1586--1595

doi:10.1093/cercor/bhp217

Advance Access publication October 29, 2009

The Temporal Dynamics of the Muller-LyerIllusion

R. Weidner1, F. Boers2, K. Mathiak3,4, J. Dammers2,3 and

G. R. Fink1,5

1Cognitive Neurology Section, Institute for Neuroscience and

Medicine—INM 3, 2Brain Imaging Physics, Institute for

Neuroscience and Medicine—INM-4, 3Human Brain Mapping,

Institute for Neuroscience and Medicine—INM-1, Research

Centre Julich, 52425 Julich, Germany, 4Department of

Psychiatry and Psychotherapy, University Hospital Aachen,

RWTH Aachen University, 52074 Aachen, Germany and5Department of Neurology, University Hospital Cologne,

Cologne University, 50924 Cologne, Germany

By attaching arrows to a line’s ends, the Muller-Lyer illusion can beused to modulate perceived line length. In the present study, weinvestigated the dynamics of the brain processes underlying thisillusion using magnetoencephalography. Subjects were presentedwith a horizontal line with arrows attached to its ends. Acrosstrials, the angles formed by the arrows were repeatedly changedsuch that 2 variants of the Muller-Lyer length illusion were eitherinduced or not. The onset of both variants of the illusion revealedconsistent activations in visual areas between 85 and 130 ms afterstimulus onset, as well as strong and longer lasting activationsalong the ventral visual processing stream including inferioroccipital, inferior temporal, and fusiform gyrus within the rangeof 195--220 ms. Subsequent neural activation was observed in theright superior temporal cortex, as well as in the right inferiorparietal and the right inferior frontal cortex. The time course andthe location of the activations suggest that the mechanismsinvolved in generating the Muller-Lyer illusion are closely linked tothe ones associated with object perception, consistent withtheories considering a relevant contribution of higher visual areasto the generation of the Muller-Lyer illusion.

Keywords: MEG, perception, vision, illusion

Introduction

Perception is not a passive projection of a visual stimulus onto

an internal representation, rather it is an active interpretation

of optic signals entering the visual system. A reasonable

interpretation of a visual stimulus is feasible only if spatial

and temporal adjacent information are taken into account.

Often the human brain integrates context information auto-

matically. This becomes obvious, for example, when looking at

optical geometrical illusions. There the size of a figure or an

object is modulated depending on its surrounding. In the

famous Ebbinghaus illusion (Ebbinghaus 1905), the size of

a circle appears smaller or bigger depending on the size of

surrounding circles. In the Muller-Lyer illusion (Muller-Lyer

1889), the perceived line length is modulated depending on

whether oriented arrows are attached to the line’s ends or not.

The perceived line length is decreased by inward arrows,

whereas it is increased by outward arrows (Fig. 1). Although

the illusion has been known for almost 120 years, up to now

there is no consensus on the neural processes generating the

illusion and accordingly a large number of divergent theories

have been proposed so far (for a review see Bertulis and

Bulatov 2001). The presumed mechanisms include uncertainty

in visual processing (Fermuller and Malm 2004), as well as

filtering properties of signal processing in primary visual areas

(Bulatov et al. 1997), centroid-based models where positional

information of objects within receptive fields are combined

(Morgan et al. 1990; Morgan and Glennerster 1991), or visual

constancy scaling (Gregory 1963, 1967, 1968).

There is evidence that the neural mechanisms underlying the

Muller-Lyer illusion are located in extrastriate visual areas—more

precisely in lateral occipital cortex along the ventral visual

processing stream. This view is supported by a number of brain

lesion studies (Vallar et al. 2000; Daini et al. 2002). The loss of

experiencing the illusion was shown to be associated with

lesions in extrastriate visual cortex. In good accordance with

this, an functional magnetic resonance imaging (fMRI) study of

healthy volunteers (Weidner and Fink 2007) revealed in-

creasing blood oxygen level--dependent signal strength along

with increasing strength of the Muller-Lyer illusion in lateral

occipital cortex as well as in the superior parietal gyrus. To

date, however, little is known about the temporal dynamics of

the brain processes underlying the illusion. We accordingly set

out to investigate the temporal dynamics of the neural

processes underlying the Muller-Lyer illusion.

We performed a magnetoencephalography (MEG) study

with healthy subjects observing a horizontal line terminated

either by vertical lines (j-j) or outward or inward arrows. The

Muller-Lyer illusion was induced by outward ( >- <) or inward

arrows ( <- >) and was eliminated by changing the arrows to

vertical lines (Fig. 1).

Contributions of early visual processing to the generation of

the Muller-Lyer illusion were expected to affect early MEG

components between 55 and 90 ms after illusion onset (Di

Russo et al. 2002). In contrast, processes related to object

perception critically involved in generating the illusion were

expected to occur later within a time range starting at around

150 ms until 300 ms after illusion onset (Johnson and

Olshausen 2003). Finally, cognitive processing related to the

Muller-Lyer illusion was hypothesized to affect components

around or after 300 ms (for a review, see Fabiani et al. 2000).

Materials and Methods

SubjectsThirteen subjects participated in the MEG experiment (7 female and 6

male; age range 23--50 years, mean age 30.6 years). All subjects had either

normal or corrected-to-normal vision. All subjects gave informed consent

prior to the experiment in accordance with the Helsinki declaration.

Task and DesignWhite-line configurations were presented on a gray background with

constant luminescence (3.1 cd/m2). A horizontal line was presented

continuously that was terminated by vertical bars (j-j), outward ( >- <),

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or inward arrows ( <- >). Stimulus presentation started with a line with

vertical lines at its ends (j-j), which then started to alternate with the

illusion-inducing arrows ( <- > or >- <) (Fig. 1). After 120 transitions

from no-illusion to illusion stimuli and accordingly 120 transitions from

illusion to no-illusion stimuli, stimulus presentation ended with the line

with vertical ends. Consequently, this stimulus sequence involved

transitions from no-illusion to illusion stimuli that either increased the

perceived line length (j-j to >- <) or decreased the perceived line length

(j-j to <- >). Each of these transitions was equally likely, and their order

was randomized across the stimulus sequence. After a short break,

a second stimulus sequence with another 120 transitions from illusion

to no-illusion stimuli and vice versa was presented.

The tilt angle between the 2 fins of the arrow was either 90� ( >- <,outward) or 270� ( <- >, inward). Each fin had a length of 5� visual angle(Fig. 1).

The stimuli were generated by a stimulus generator board (ViSaGe;

Cambridge Research System Ltd, Rochester, UK) and projected using

an LCD Projector (Sony VLP-600E) onto a mirror system inside the

magnetically shielded room back on a screen in front of the subject’s

eyes. The stimuli were presented jitter-free with a refresh rate of 60 Hz.

All subjects observed the stimulation in supine position.

Two stimulus sequences each including 120 illusion-inducing stimuli

were presented. The onset time for stimuli was 1.5 s (±0.5 s).

Overall, the experiment involved 240 transitions from a no illusion--

inducing stimulus to an illusion-inducing figure and in addition 240

transitions back to a no-illusion--inducing stimulus. As 2 different

illusion-inducing figures were used ( <- > or >- <), the experiment

involved 1) 120 transitions from a no-illusion stimulus configuration to

a configuration that reduced the perceived line length (i.e., from

vertical bars j-j to inward arrows: <- >), 2) 120 transitions from

a stimulus configuration that reduced the perceived line length to

a neutral stimulus configuration (from inward arrows: <- > to neutral

bars: j-j), 3) 120 transitions from a no illusion stimulus configuration to

a configuration that increased the perceived line length (from neutral

bars j-j to outward arrows: >- <), and 4) in the opposite direction

a transition from a stimulus configuration that increased the perceived

line length to a neutral stimulus configuration (from pointing arrows:>-< to neutral bars: j-j).The effect of the Muller-Lyer illusion on the MEG data was tested by

comparing the onset of an illusion (illusion condition, i.e., transitions

from neutral stimuli to illusion-inducing stimulus configurations)

relative to the offset of an illusion (no illusion condition, i.e., transitions

from the illusion to neutral stimuli); this was done for both variants of

the illusion.

Behavioral ExperimentIn order to avoid task- and motor-related brain signals, subjects did not

perform an explicit task during the MEG session. However, in order to

demonstrate that the effect of the Muller-Lyer illusion is robust,

a behavioral experiment was performed with 12 different subjects. It

was designed such that the visual stimulation was virtually identical to

the functional experiment. In contrast to the functional experiment,

subjects were asked to judge variations of the perceived line length

induced by transitions from illusion to no-illusion stimuli. After each

transition from illusion to no-illusion stimuli (e.g., <- > to j-j or >- < to

j-j), subjects had to indicate via button press whether they perceived an

increase or a decrease of the line length during the transition from

illusion to no-illusion stimuli. On a trial-by-trial basis, the Parameter

Estimation by Sequential Testing algorithm (Taylor and Creelman 1967)

was used to adjust the perceived line length of the illusion stimuli such

that variations of the perceived line length were eliminated. Once the

perceived line length of illusion and no-illusion stimuli was adjusted,

the difference between the real line length of illusion and no-illusion

stimuli was taken as estimate for illusion strength. Whereas the inward

version ( <- >) of the illusion was expected to require a greater real line

length in order to equate the perceived line length of the no illusion

stimulus, the outward variant ( >- <) was expected to result in

a decreased line length.

MEG Measurement

MEG Recording

The MEG data were recorded using a whole-head 148 magnetometer

system (Magnes WH 2500; 4D-Neuroimaging, San Diego, CA). The

neuromagnetic activity was continuously recorded using a bandwidth

from 0.1 to 400 Hz at a sampling rate of 1017.25 Hz. Recording of eye

movements and heart beats, that is, electrooculography and electro-

cardiography allowed for off-line artifact rejection.

Prior to the MEG measurement, 5 head location coils were attached

to the subject’s head. The position of the coils and the head itself were

digitized using a 3D digitizer (Polhemus, 3 Space/Fastrack, Colchester,

VT). Before and after each recording block, the subject’s head position

was monitored by the head location coils. For coregistration of the

acquired head position with the individual brain anatomy, high-

resolution T1-weighted magnetic resonance images (MRIs) were

acquired for each subject with a voxel size of 1 3 1 3 1 mm3. The

rendered head shape was matched to the surface of the scalp by means

of customized software, providing a transformation matrix between MEG

head coordinate and MRI coordinate systems (Dammers et al. 2007).

Data Analysis

MEG Signal Processing

After acquisition, all data were band-pass filtered in the range of 1--200

Hz including notch filters at the power line frequency (50 Hz and the

harmonics). Independent component analysis and automatic artifact

rejection based on combined amplitude and phase statistics of

independent components (Dammers et al. 2008) were applied to the

data in order to remove artifacts from heart beat and eye blinks. After

artifact rejection, the data were low-pass filtered with a cutoff

frequency of 45 Hz. For each stimulus condition, epochs were

extracted in the time range of 300 ms prestimulus to 600 ms

poststimulus onset. The data were corrected for the time delay

between generating and projecting the stimuli onto the screen. Before

averaging, each trial of each condition was inspected visually to identify

Figure 1. (a) Muller-Lyer figures used in the experiment. Muller-Lyer figure withinward-pointing arrows resulting in a reduced line length perception (left), a nonillusionfigure with straight lines attached to its end (middle) and a Muller-Lyer figure withoutward-pointing arrows result in an increased perceived line length (right). Note thatthe horizontal lines of the 3 figures are of equal length. (b) Example trial sequencesindicating alterations between illusion and no-illusion stimuli.

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additional artifacts that were excluded. On average, 7.5 trials of 120

were rejected prior to analysis.

Source Reconstruction

Magnetic field tomography (MFT; Ioannides et al. 1990) was used for

the reconstruction of the distributed sources minimizing depth bias

and smoothness heterogeneity. The method provides vector-valued

volumes of the reconstructed primary current density j (r,t), where r

denotes the spatial coordinate (a voxel at location r) within the source

space (the segmented brain) at time t (Ioannides et al. 1990; Ioannides

1994). A succinct description of the logical steps of MFT can be found

in Ioannides (1995). Briefly, MFT belongs to the class of weighted

minimum norm estimates. The method, which has been reported to

effectively reconstruct superficial and deeper sources (Dammers and

Ioannides 2000; Ioannides and Fenwick 2005; Dammers et al. 2007),

uses continuous probabilistic estimates of the primary current density

to construct 3D volumes of brain activity. For solving the forward

problem, the multiple-sphere model was used to describe the

conductivity profile, and hence, the volume currents are not restricted

to be within the source space. In order to avoid the tendency of

minimum norm techniques to overemphasize superficial activity, the

sensitivity profiles of the sensors (lead fields) are stretched (weighted)

by a Gaussian function whose only parameter is the rate of the decay

(Ioannides et al. 1990). Within MFT, an iterative scheme is used to

reweight the a priori probability weight in regions where activity has

been defined. This iterative weighting is applied in order to 1) recover

both superficial and deeper sources and 2) sharpen up the solution,

which otherwise would be more blurred in deeper brain regions, due

to the nature of the lead fields (Taylor et al. 1999). Finally, one

regularization parameter is introduced and adjusted to accomplish the

conflicting requirements of high spatial resolution and insensitivity to

noise. Both parameters, the Gaussian decay factor and the regulariza-

tion parameter, are determined once by means of source simulations

and remain fixed throughout the analysis.

For reconstruction, the whole brain served as the source space using

an isometric grid spacing of 5 mm. MFT analysis was then applied to

signal averages using a time window of 300 ms before and 600 ms after

stimulus onset. Time courses of the 3D MFT solutions were extracted in

steps of 5 ms before and after illusion onset. Volumes of the modulus of

the current density jj J jj were exported into Nifti format (http://

nifti.nimh.nih.gov/nifti-1) using an interpolated isometric voxel size of 2

mm3 in order to combine the MFT solution with the Statistical

Parametric Mapping software SPM5 (Wellcome Department of Imaging

Neuroscience, London; Friston et al. 1995; http://www.fil.ion.ucl.ac.uk/

spm/software/spm5).

For each condition and for each time slice, one image was generated

on the basis of the coregistered MFT solutions. The individual

(unsegmented) T1-weighted MR image was normalized to the Montreal

Neurological Institute single-subject template (Collins et al. 1998;

Ashburner and Friston 2005) using the ‘‘unified segmentation’’ function

in SPM5. For each time slice, the normalized and smoothed MFT

solutions were then taken to the second-level analysis, where they were

subjected to a within-subject analysis of variance. Differential contrasts

were calculated testing for the difference between the onset of the

illusion relative to its offset. This was done separately for both variants of

the illusion (i.e., >- < onsetminus >- < offset; <- > onsetminus <- > offset).In order to test whether there were consistent effects of illusion

onset (relative to illusion offset) across both variants of the illusion,

a conjunction analysis testing the global null hypothesis (Friston et al.

2005) was performed [i.e., ( >- < onset minus >- < offset) \ ( <- > onset

minus <- > offset)]. A conservatively family-wise error (FWE) corrected

threshold of P < 0.01 with an additional extent-threshold of 10 voxels

was applied. The size of the cluster threshold was chosen on the basis

of the reconstructed MFT source space (which has an isometric grid

spacing of 5 mm). We decided to include clusters only if they involve

two-thirds of a voxel from the original MFT source space resolution

(5 3 5 3 5). On the basis of the resampled voxel size in the Nifti-images

(2 3 2 3 2 mm), this would involve 83 mm3 corresponding to 10.4

voxels from the resampled Nifti-images. We therefore applied a voxel

threshold of 10 consecutive voxels.

Furthermore, contrasts were calculated testing for differential effects

of illusion onset (relative to illusion offset) for the 2 illusion variants

[i.e., ( >- < onset minus >- < offset) minus ( <- > onset minus <- > offset)

and vice versa] using a conservatively corrected threshold of P < 0.01

(FWE) with an additional extent threshold of 10 voxels.

Time Course ExtractionFor those brain regions that showed above threshold clusters in the

conjunction analysis and the differential effects analysis, the time

course was extracted from –300 before illusion onset to 600 ms after

illusion onset.

Results

Behavioral Data

Both types of Muller-Lyer figures induced a reliable illusion in

all subjects (Fig. 2). The actual line length of the horizontal part

of the Muller-Lyer figure was 14.25� visual angle. A horizontal

line with inward wings ( <- >, Fig. 2) had to be increased by

2.48� visual angle (standard error of the mean [SEM]: 0.32�visual angle) in order to adjust the perceived line length to the

no-illusion stimulus with a horizontal line and vertical lines at

its ends. In contrast, a horizontal line with outward-pointing

arrows ( >- <, Fig. 2) had to be decreased by 1.94� visual angle(SEM: 0.23� visual angle) in order to equate its perceived line

length with the no-illusion stimulus. Two-tailed one-sample t-

tests were applied in order to test whether the illusions were

significantly different from 0, which revealed a significant effect

for both inward t(11) = 7.8, P < 0.001 and outward arrows

t(11) = 8.5, p < 0.001. Finally, a test was applied in order to

compare the strength of both illusions. We applied a one-

sample paired t-test to test for absolute differences in the

magnitude of both illusions. This was done by comparing the

absolute value of the decrease in the outward condition against

Figure 2. Perceived alterations in line length related to inward wings (upper half) andthe perceived alterations in line length related to outward wings (lower half)presented separately for 12 subjects.

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the absolute increase in the inward condition. This analysis

revealed no significant difference in illusion magnitude

t(11) = 1.3, P = 0.11, not significant (n.s.), indicating no

differential illusion magnitude in the 2 illusion conditions.

MEG Data

Illusion Onset Versus Offset

The neural correlates of the Muller-Lyer illusion were identified

by a voxel-wise comparison of the normalized MFT source

reconstructions associated with illusions relative to no-illusions.

The illusion onsets from the different variants of the illusion

were separately compared with their referring offsets. In order

to test for consistent effects within these contrasts, a conjunc-

tion analysis testing the global null hypothesis as described by

Friston et al. (2005) was performed. The respective contrast

can be described as [( >- < onset minus >- < offset) \ ( <- > onset

minus <- > offset)]. This comparison was done separately for

every time slice within 300 ms before and 600 ms after stimulus

onset at P < 0.01, FWE with an additional extent threshold of

10 voxels (Figs 3, 4 and 5; a movie depicting illusion-associated

activations can be found as Supplementary Material). A higher

signal for illusions compared with no-illusions was observed as

early as 85 ms after illusion onset in the right cuneus as well as

in the right lingual gyrus at 125 ms after stimulus onset and 130

ms after stimulus onset in the left middle occipital gyrus.

Following these relatively early components, one activation

cluster in the right hemisphere was observed along the ventral

visual pathway within the period of 195--220 ms after illusion

onset/offset. Moving forward in time, this cluster was traveling

in anterior direction from the anterior end of the inferior

occipital gyrus along the inferior temporal gyrus, medially

extending to the fusiform gyrus between 205 and 220 ms and

was accompanied by a right hippocampus activation at 215 ms.

Left superior temporal gyrus activation was observed at 230 ms.

Right parietal cortex was activated in the time range of 240--

260 ms. This activation was located in the postcentral gyrus

extending to the supramarginal gyrus from 240 to 250 ms and

from there moved in posterior direction in the time range of

255--260 ms. In addition, a transient activation was observed in

the right inferior frontal gyrus at 390--395 ms.

The opposite contrast [(>- < offset - >- < onset) \ ( <- > offset -

<- > onset)] did not reveal significant activations at any time

point (Table 1).

Figure 3. Event-related MEG signals as response to the onset (top) and the offset (bottom) of the illusion, separately shown for the illusion involving inward-pointing arrows (left)and outward-pointing arrows (right).

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Figure 4. Surface renderings of stronger activation related to the onset relative to the offset of the Muller-Lyer illusion. A conjunction analysis tested for the consistency of effectsof both variants of the illusion (statistical parametric mapping 5: [([-\onset vs.[-\offset) \ (\-[onset vs.\-[offset)]; FWE-corrected P\ 0.01 with an extent threshold of10 voxels) separately for different time points relative to illusion onset (left). Time courses extracted at the location of the maximal t-value depicted separately for the onset and offsetof the different variants of the illusion. Shaded areas mark intervals exceeding the threshold according to FWE-corrected P\ 0.01 and cluster extent[10 voxel (right).

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Differential Effects

Furthermore, in order to determine the differences and the

similarities between the 2 different types of illusions, we

calculated additional contrasts, comparing the differences

between the on and off conditions related to the different

illusion directions.

Higher signals related to the inward wings ( <- > on vs. off)

compared with the outward-pointing wings ( >- < on vs. off)

version were found in V1 (Amunts et al. 2000) within the

lingual gyrus (75 ms) as well as in the left inferior temporal

gyrus (80 and 85 ms) and the precuneus (155 ms) (Fig. 5a and

Table 2).

The illusion effect induced by the inward-pointing wings

( >- < on vs. off) compared with the illusion effect induced by

the outward-pointing wings ( <- > on vs. off) revealed stronger

activations in the right superior temporal cortex between 205

and 230 ms (Fig. 5b and Table 2).

Discussion

The Muller-Lyer illusion is known to reliably induce an altered

length perception of a line as was observed in the present

study. On the neural level, the illusion has been shown to be

associated with increased neural activity in lateral occipital

cortex and right parietal cortex (Weidner and Fink 2007). The

superior temporal resolution of MEG allowed us to further

explore the temporal dynamics of the processes related to the

perception of the Muller-Lyer illusion and to delineate the time

course of the activation observed within the different brain

areas.

Figure 5. Surface renderings of stronger activation related to (a) inward relative to outward wings and (b) outward relative to inward wings (FWE-corrected P\ 0.01 with anextent threshold of 10 voxels) (left) and time courses extracted at the location of the maximal t-value separately for illusion onset and offset within the time range 200 ms beforeuntil 500 ms after illusion onset. Shaded areas mark intervals exceeding the threshold according to FWE-corrected P\ 0.01 and cluster extent [10 voxel (right).

Table 1List of activation clusters that were consistently stronger active following illusion onset (relative

to illusion offset) for both illusion variants (according to FWE-corrected P\ 0.01 with an extent

threshold of 10 voxels)

Structure Side MNI Time(ms)

Conjunction ([-\ on vs. [-\ off) \ (\-[ on vs. \-[ off)Cuneus Right 28 �64 28 85Lingual gyrus Right 16 �68 2 125Middle occipital gyrus Left �26 �72 34 130Inferior temporal gyrus/inferior occipital gyrus Right 50 �60 �12 195

48 �62 �14 200Inferior temporal gyrus/fusiform gyrus Right 44 �56 �18 205

52 �54 �20 21538 �58 �10 21556 �54 �20 220

Hippocampus Right 36 �8 �22 215Superior temporal gyrus Left �50 �6 12 230Postcentral gyrus/supramarginal gyrus Right 50 �10 30 240

48 �10 30 24546 �10 30 250

Supramarginal gyrus Right 48 �24 28 25552 �30 28 260

Inferior frontal gyrus Right 26 14 24 395Right 30 8 24 395

Note: Coordinates are defined within Montreal Neurological Institute (MNI) space.

Table 2List of activation clusters related to differences between the 2 variants of the illusion (according

to FWE-corrected P\ 0.01 with an extent threshold of 10 voxels)

Structure Side MNI Time (ms)

(\-[ on vs. \-[ off) � ([-\ on vs. [-\ off)Lingual gyrus Bilateral 0 �76 �4 75Inferior temporal gyrus Left �48 �52 �6 80

�48 �56 �1 85Precuneus Left �6 �40 46 155

([-\ on vs. [-\ off) � (\-[ on vs. \-[ off)Superior temporal gyrus Right 42 �24 10 205

40 �24 8 21042 �20 0 22532 �12 �2 23042 �18 0 230

Note: Coordinates are defined within Montreal Neurological Institute (MNI) space.

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Visual Areas

The results of the differential contrasts suggest that the inward

arrow variant ( <- >) elicits stronger activation than its outward-

pointing arrow pendant ( >- <). Differential effects were found

in the early components and were located in the lingual gyrus

as well as in the left inferior temporal gyrus and the precuneus.

These effects can, however, not equivocally be related to the

illusion effect per se but may rather be attributed to differential

visual stimulation by the 2 variants of the illusion.

Although the inward arrow variant elicits stronger activation

in the early components, the conjunction analysis indicates

that both variants of the illusion consistently contribute to this

early effect. The conjunction analysis revealed illusion

effects as early as 85 after illusion onset in the right cuneus.

Di Russo et al. (2002) suggested that the generators of the C1

component in visually evoked potentials, which peaks at

around 90 ms, is located in early visual areas.

The early activation in the conjunction analysis was located

superior to V1 and V2 but is nevertheless broadly consistent

with this notion.

More visual activation consistently related to both variants of

the illusion was found in ventral visual areas. According to

Goodale and Milner (1992), the ventral visual pathway subserves

object perception in an allocentric fashion (i.e., an object is

perceived relative to its surrounding). The altered length

perception of a horizontal line due to flanking arrows obviously

requires such a relative object coding. Consequently, optical

geometric illusions have been suggested to be a function of the

ventral visual pathway (Goodale 2008). Consistent with this

notion, we found robust activations along the ventral visual

pathway in lateral occipital areas and the inferior temporal

cortex. In fact, a recent fMRI study by Weidner and Fink (2007)

revealed a robust involvement of the lateral occipital cortex

associated with the strength of the Muller-Lyer illusion. The

present study confirms but extends these previous findings by

showing the dynamics of these areas while processing the

Muller-Lyer illusion. The fusiform gyrus and the inferior

temporal gyrus contribute to the generation of the Muller-Lyer

illusion within a time range of 195--230 ms after illusion onset.

The higher activation for illusion relative to no-illusion

thereafter traveled from the fusiform gyrus in anterior di-

rection to the middle and inferior temporal cortex.

The neural implementation of processing the Muller-Lyer

illusion seems to share a number of features with object

perception. It is known that the representation of an object

category is widely distributed across ventral stream visual areas

(Haxby et al. 2001). In addition, the temporal dynamics

observed for processing the Muller-Lyer illusion seem to

parallel those related to visual object recognition (Thorpe

et al. 1996). Thorpe et al. (1996) reported event related

potentials (ERP) components related to object recognition 150

ms after stimulus onset, and Johnson and Olshausen (2003)

described ERPs components between 150 and 300 ms, which

covaried with target detection times. Furthermore, the spatial

location and the temporal dynamics of ventral stream activation

observed in our study parallels those reported by Allison et al.

(1999). Cortical surface recordings in patients revealed object-

related negativity at around 200 ms after stimulus onset, which

was located in occipitotemporal cortex (Allison et al. 1999),

suggesting an involvement of object perception in the

generation of the Muller-Lyer illusion.

The Role of Parietal Areas

Congruent with the data by Weidner and Fink (2007), right

parietal activation was observed. The location of the activation in

the present study was located inferior to the one reported by

Weidner and Fink (2007), most likely reflecting the different

task requirements in the 2 studies. Because subjects either

performed a demanding spatial judgment or luminance judg-

ment task in the experiment reported by Weidner and Fink

(2007), top-down control was required throughout the whole

experiment. This consistently activated superior parietal cortex,

which is known to be part of the dorsal top-down attention

network (Corbetta and Shulman 2002). Although no explicit

task was performed in the present experiment, attention

processes are nevertheless relevant because the alterations

between illusion and no-illusion stimuli are salient visual events,

which attract subject’s attention. Consequently, the parietal

activation observed in the present study was located within the

ventral attention network, which is associated with target

detection and bottom-up attentional control (Corbetta and

Shulman 2002). Thus, parietal activation seems to, at least in

parts, reflect the task demands associated with processing the

illusion. However, because the saliency of stimulus changes was

matched in the illusion and no-illusion condition, the parietal

activation reported in the present study still reflects processes

related to the perception of visual illusions.

Its temporal dynamics clearly indicate that right parietal

cortex is activated subsequently to activations in the ventral

stream. Taken together, the data suggest that illusion-related

representations are first formed in the ventral visual pathway and

that these representations are then subsequently processed in

parietal cortex. Weidner and Fink (2007) suggested that the

posterior parietal cortex is related to the integration of object

representations into a spatial reference frame, resolving possible

ambiguities such as object distance and its perceived size.

In addition, it has been suggested that parietal cortex is

involved in binding ventral stream features. This is supported

by patient data. Friedman-Hill et al. (1995) reported that

patient R.M. who suffered from bilateral parietal lesions,

involving both superior and inferior parietal lobes, miscom-

bined color and shape and was unable to judge relative or

absolute locations. Additional support is provided by functional

imaging data (Shafritz et al. 2002). Shafritz et al. suggested that

the spatial attention network of the posterior parietal cortex is

involved in integrating visual features when spatial information

is available to resolve ambiguities about the relationships

between objects features. Our data support this interpretation

and suggest that right parietal areas are involved in resolving

spatial ambiguities induced by processing Muller-Lyer figures in

ventral visual stream areas and that the parietal involvement

depends on active task requirements.

Contribution of Frontal Areas

In the frontal cortex, the onset of the Muller-Lyer illusion

(relative to no illusion) elicited an MEG component at 395 ms

after illusion onset. This is in good accordance with electro-

encephalography (EEG) data reported by Qiu et al. (2008).

Their data indicate an ERP component 400 ms after stimulus

onset. According to Qiu et al., this component was located in

the anterior cingulate cortex and superior frontal regions,

whereas our data indicate that the generator is located in right

posterior inferior frontal gyrus. This discrepancy can be

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attributed to the different methods used in both

studies—dipole source localization on the basis of EEG on

the one hand compared with MFT and MEG on the other hand.

The higher spatial resolution of the methods used in the

present study might argue in favor of the right posterior

inferior frontal gyrus rather than the anterior cingulate cortex

as the source of this component. Qiu et al. suggested that this

component reflects high-level cognitive control related to

judging the illusion. In our MEG study, however, subjects did

not perform a task. They were instructed to simply observe

length changes of the presented line. Thus, the process

reflected by this component may, therefore, be stimulus driven

rather than based on high-level cognitive control. This in-

terpretation is in line with data reported by Vossel et al. (2009),

who found right posterior inferior frontal gyrus activated by

(irrelevant) stimulus changes in an oddball task.

At first glance, the right inferior frontal gyrus activation

observed in our current study may seem at variance with the

findings reported by Weidner and Fink (2007). In that study, no

frontal activation was related to the strength of the Muller-Lyer

illusion. However, one should keep in mind that the major

difference between the study by Weidner and Fink (2007)

compared with the study by Qiu et al. and the present study

concerns the instructions given to the subject. In those studies,

subjects did explicitly pay attention to the illusion per se,

whereas in the study by Weidner and Fink (2007), subjects

focused on either the landmark task or a luminance control

task. The latency of the activation observed in our study indeed

seems to support the assumption of higher cognitive process-

ing. We therefore suggest that the inferior frontal gyrus

activation reflects processes related to the conscious percep-

tion of the illusion.

Mechanisms Underlying the Muller-Lyer Illusion

How can perceiving the Muller-Lyer illusion be related with

more complex processing within the visual system? One aspect

that has to be considered is that stimulus complexity may be

higher for illusion stimuli because they containmore angles than

neutral stimuli. However, because the results from the present

study are in good accordance with those from our previous fMRI

study where stimulus complexity was held constant while at the

same time the illusion strength varied (Weidner and Fink 2007),

we argue that the effects observed in the present study are

related to the strength of the illusion rather than to differences

in stimulus complexity. Accordingly, additional processing may

be generated by the processing system itself. Such additional

processing may be associated with additional effort of the

perceptual system in interpreting incoming visual information.

Visual information may be more ambiguous when less in-

formation is available for the visual system. In order to resolve

such perceptual ambiguities (Robinson 1998), more and

complex visual processing may be required. Different theories

regarding the Muller-Lyer illusion suggest different mechanisms

that may be represented by additional processing such as altered

spatial filtering (Bulatov et al. 1997; Bertulis and Bulatov 2001),

forming 3D interpretations from 2D figures (Gregory 1963,

1967, 1968), or pooling of positional signals (Morgan et al. 1990;

Morgan and Glennerster 1991).

Spatial Filtering

According to Bertulis, Bulatov and their colleagues (Bulatov

et al. 1997; Bertulis and Bulatov 2001), the illusion is induced

by spatial filtering operations generated by visual field

representations in the layer 4Cb of V1. The V1 activation,

which was observed when the different illusion variants were

contrasted, may be indicative of a stronger V1 illusion effect in

the outward ( <- >) relative to inward illusion condition ( >- <)but may as well simply reflect differences in low-level features.

More conclusive evidence could be drawn from the early

component around 85 ms, which was revealed by the

conjunction analysis. This could apparently be taken as an

argument in favor of theories suggesting a contribution of

primary and secondary visual areas in generating the illusion

(Bulatov et al. 1997; Bertulis and Bulatov 2001). However, the

source of this component was not located in V1 or V2 and can

therefore not be taken as strong evidence in favor of this

model. On the other hand, the absence of activation in V1 and

V2 can also not be taken as evidence ‘‘against’’ a possible

contribution of these areas in generating the illusion. This null

finding could be accounted, for example, by the spatial

resolution of MEG. In the primary and secondary visual areas

of new world primates, the average distances between cortical

columns sensitive for identical orientations are within the

range of 575 lm (V1) to 1 mm (V2) (McLoughlin and Schiessl

2006). Because these distances are too small to be resolved

with the applied spatial resolution of 5 3 5 3 5 mm, a possible

differential contribution of these areas is likely to be missed.

Thus, although we did not find evidence for a potential

contribution of these visual areas, we cannot exclude

a potential contribution of primary visual areas to the

generation of the Muller-Lyer illusion. However, the strong

contribution of higher visual brain areas along the ventral visual

stream (as discussed below) clearly indicates that the illusion is

not primarily based on neural processes originating in early

visual areas.

Size Constancy

An alternative explanation is concerned with the estimation of

object size. The perceived size of an object is a function of its

size coded on the retina and the estimated distance of the

object. Integration of this information involves the ventral

stream. Studies with monkeys indicate (Humphrey and

Weiskrantz 1969; Ungerleider et al. 1977) that lesions in

inferior temporal cortex cause deficits in choosing the larger of

2 objects presented at different distances, suggesting a loss of

size constancy. In line with these data are reports from patient

studies (Cohen et al. 1994). Cohen et al. reported erroneous

size perceptions in 2 patients with lesions of lateral occipital

areas and for one patient with lesions in parts of the inferior

middle and superior temporal lobe. Furthermore, Frassinetti

et al. (1999) reported selectively disrupted size perception in

the contralesional hemifield of a patient suffering from lesions

in the right occipital, prestriate area. The activations observed

in the current and previous studies (Weidner and Fink 2007)

spatially overlap with regions associated with object size

perception. This supports earlier accounts related to the origin

of the Muller-Lyer illusion as put forward by Gregory (1963,

1968). That account presupposes that an inappropriate size-

constancy scaling due to ambiguous distance estimation is the

key component for the generation of the illusion.

Centroids and Large Receptive Fields

Alternatively, the present data could be interpreted in terms of

the centroid model suggested by Morgan and colleagues

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(Morgan et al. 1990; Morgan and Glennerster 1991). According

to their model, the mechanism behind the Muller-Lyer illusion

is an integration of adjacent spatial positional signals from

receptive fields in ‘‘eclectic’’ units that code the position of an

object at its centroid. Arrows located at a line’s endpoints

would therefore result in a shift of their perceived location.

The receptive field size of these eclectic units is according to

Morgan and Glennerster (1991) large with a size of at least 1� innear-foveal vision, indicating that they are functionally located

beyond V1 (Smith et al. 2001). In the current experiment, each

fin subtended 5� of visual angle. Mislocalizing an arrow of that

size requires the integration of information across a large area

in the visual field. Receptive fields with an appropriate size are

found in inferior temporal areas that are known to vary

between 9� and 39� visual angle (Rolls et al. 2003) and

therefore resemble the features suggested for ‘‘eclectic units’’.

In line with this suggestion, Marois et al. (2000) reported data

that implicate that the perception of object locations and

object identity involve inferior temporal cortex.

Conclusions

The converging evidence from the current study using MEG

and from our previous study using fMRI strengthens the claim

that lateral occipital and inferior temporal regions together

with dorsal stream areas play an essential role in the generation

of the Muller-Lyer illusion. This is consistent with theories

considering a relevant contribution of higher visual areas to the

generation of the Muller-Lyer illusion, such as the size-

constancy theory by Gregory (1963, 1968) or the centroid

model by Morgan and colleagues (Morgan et al. 1990; Morgan

and Glennerster 1991).

The temporal dynamics of the activations observed indicate

that processing within the ventral visual pathway precedes

processing in parietal areas. A possible interpretation is that

first object representations are formed within ventral stream

involving lateral occipital and inferior temporal areas and that

this processing step is followed by a dorsal stream activation

that may reflect the integration of these object representations

into spatial reference frames. It is up to future research to

further specify the processes underlying the perception of

optical geometric illusions and in addition to test the functional

relevance of these activations. Studies using transcranial

magnetic stimulation or studies with patients suffering from

focal lesions may be appropriate to pursue this question.

Supplementary Material

Supplementary material can be found at: http://www.cercor.

oxfordjournals.org/.

Notes

We are grateful to all our volunteers and our colleagues at the Institute

for Neuroscience and Medicine, Research Center Julich. Conflict of

Interest : None declared.

Address correspondence to Ralph Weidner, Kognitive Neurologie,

Institut fur Neurowissenschaften, und Medizin (INM 3), Forschungs-

zentrum Julich, Leo-Brandt-Strasse 5, 52425 Julich, Germany. Email:

r.weidner@fz-juelich.de.

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