Abstract

By attaching arrows to a line's ends, the Müller-Lyer illusion can be used to modulate perceived line length. In the present study, we investigated the dynamics of the brain processes underlying this illusion using magnetoencephalography. Subjects were presented with a horizontal line with arrows attached to its ends. Across trials, the angles formed by the arrows were repeatedly changed such that 2 variants of the Müller-Lyer length illusion were either induced or not. The onset of both variants of the illusion revealed consistent activations in visual areas between 85 and 130 ms after stimulus onset, as well as strong and longer lasting activations along the ventral visual processing stream including inferior occipital, inferior temporal, and fusiform gyrus within the range of 195–220 ms. Subsequent neural activation was observed in the right superior temporal cortex, as well as in the right inferior parietal and the right inferior frontal cortex. The time course and the location of the activations suggest that the mechanisms involved in generating the Müller-Lyer illusion are closely linked to the ones associated with object perception, consistent with theories considering a relevant contribution of higher visual areas to the generation of the Müller-Lyer 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 automatically. 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 Müller-Lyer illusion (Müller-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 (Fermüller 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).

Figure 1.

(a) Müller-Lyer figures used in the experiment. Müller-Lyer figure with inward-pointing arrows resulting in a reduced line length perception (left), a nonillusion figure with straight lines attached to its end (middle) and a Müller-Lyer figure with outward-pointing arrows result in an increased perceived line length (right). Note that the horizontal lines of the 3 figures are of equal length. (b) Example trial sequences indicating alterations between illusion and no-illusion stimuli.

Figure 1.

(a) Müller-Lyer figures used in the experiment. Müller-Lyer figure with inward-pointing arrows resulting in a reduced line length perception (left), a nonillusion figure with straight lines attached to its end (middle) and a Müller-Lyer figure with outward-pointing arrows result in an increased perceived line length (right). Note that the horizontal lines of the 3 figures are of equal length. (b) Example trial sequences indicating alterations between illusion and no-illusion stimuli.

There is evidence that the neural mechanisms underlying the Müller-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 increasing blood oxygen level–dependent signal strength along with increasing strength of the Müller-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 Müller-Lyer illusion.

We performed a magnetoencephalography (MEG) study with healthy subjects observing a horizontal line terminated either by vertical lines (|-|) or outward or inward arrows. The Müller-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 Müller-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 Müller-Lyer illusion was hypothesized to affect components around or after 300 ms (for a review, see Fabiani et al. 2000).

Materials and Methods

Subjects

Thirteen 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 Design

White-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 (|-|), outward (>-<), or inward arrows (<->). Stimulus presentation started with a line with vertical lines at its ends (|-|), 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 (|-| to >-<) or decreased the perceived line length (|-| 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 |-| 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: |-|), 3) 120 transitions from a no illusion stimulus configuration to a configuration that increased the perceived line length (from neutral bars |-| 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: |-|).

The effect of the Müller-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 Experiment

In 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 Müller-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 |-| or >-< to |-|), 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 electrocardiography 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 × 1 × 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 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 regularization 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 ||J|| 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., >-< onset minus >-< offset; <-> onset minus <-> 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 × 5 × 5). On the basis of the resampled voxel size in the Nifti-images (2 × 2 × 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 Extraction

For 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 Müller-Lyer figures induced a reliable illusion in all subjects (Fig. 2). The actual line length of the horizontal part of the Müller-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 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.

Figure 2.

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

Figure 2.

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

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).

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).

MEG Data

Illusion Onset Versus Offset

The neural correlates of the Müller-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 conjunction 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.

Figure 4.

Surface renderings of stronger activation related to the onset relative to the offset of the Müller-Lyer illusion. A conjunction analysis tested for the consistency of effects of both variants of the illusion (statistical parametric mapping 5: [(>-< onset vs. >-< offset) (<-> onset vs. <-> offset)]; FWE-corrected P < 0.01 with an extent threshold of 10 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 offset of 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).

Figure 4.

Surface renderings of stronger activation related to the onset relative to the offset of the Müller-Lyer illusion. A conjunction analysis tested for the consistency of effects of both variants of the illusion (statistical parametric mapping 5: [(>-< onset vs. >-< offset) (<-> onset vs. <-> offset)]; FWE-corrected P < 0.01 with an extent threshold of 10 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 offset of 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).

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 an extent 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 before until 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).

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 an extent 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 before until 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).

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).

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).

Table 1

List 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 85 
    Lingual gyrus Right 16 −68 2 125 
    Middle occipital gyrus Left −26 −72 34 130 
    Inferior temporal gyrus/inferior occipital gyrus Right 50 −60 −12 195 
  48 −62 −14 200 
    Inferior temporal gyrus/fusiform gyrus Right 44 −56 −18 205 
  52 −54 −20 215 
  38 −58 −10 215 
  56 −54 −20 220 
    Hippocampus Right 36 −8 −22 215 
    Superior temporal gyrus Left −50 −6 12 230 
    Postcentral gyrus/supramarginal gyrus Right 50 −10 30 240 
  48 −10 30 245 
  46 −10 30 250 
    Supramarginal gyrus Right 48 −24 28 255 
  52 −30 28 260 
    Inferior frontal gyrus Right 26 14 24 395 
 Right 30 8 24 395 
Structure Side MNI Time (ms) 
Conjunction (>-< on vs. >-< off) ∩ (<-> on vs. <-> off)    
    Cuneus Right 28 −64 28 85 
    Lingual gyrus Right 16 −68 2 125 
    Middle occipital gyrus Left −26 −72 34 130 
    Inferior temporal gyrus/inferior occipital gyrus Right 50 −60 −12 195 
  48 −62 −14 200 
    Inferior temporal gyrus/fusiform gyrus Right 44 −56 −18 205 
  52 −54 −20 215 
  38 −58 −10 215 
  56 −54 −20 220 
    Hippocampus Right 36 −8 −22 215 
    Superior temporal gyrus Left −50 −6 12 230 
    Postcentral gyrus/supramarginal gyrus Right 50 −10 30 240 
  48 −10 30 245 
  46 −10 30 250 
    Supramarginal gyrus Right 48 −24 28 255 
  52 −30 28 260 
    Inferior frontal gyrus Right 26 14 24 395 
 Right 30 8 24 395 

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

Table 2

List 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 75 
    Inferior temporal gyrus Left −48 −52 −6 80 
  −48 −56 −1 85 
    Precuneus Left −6 −40 46 155 
(>-< on vs. >-< off) − (<-> on vs. <-> off)    
    Superior temporal gyrus Right 42 −24 10 205 
  40 −24 8 210 
  42 −20 0 225 
  32 −12 −2 230 
  42 −18 0 230 
Structure Side MNI Time (ms) 
(<-> on vs. <-> off) − (>-< on vs. >-< off)    
    Lingual gyrus Bilateral 0 −76 −4 75 
    Inferior temporal gyrus Left −48 −52 −6 80 
  −48 −56 −1 85 
    Precuneus Left −6 −40 46 155 
(>-< on vs. >-< off) − (<-> on vs. <-> off)    
    Superior temporal gyrus Right 42 −24 10 205 
  40 −24 8 210 
  42 −20 0 225 
  32 −12 −2 230 
  42 −18 0 230 

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

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 Müller-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 Müller-Lyer illusion and to delineate the time course of the activation observed within the different brain areas.

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 Müller-Lyer illusion. The present study confirms but extends these previous findings by showing the dynamics of these areas while processing the Müller-Lyer illusion. The fusiform gyrus and the inferior temporal gyrus contribute to the generation of the Müller-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 direction to the middle and inferior temporal cortex.

The neural implementation of processing the Müller-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 Müller-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 Müller-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 judgment 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, miscombined 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 Müller-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 Müller-Lyer illusion (relative to no illusion) elicited an MEG component at 395 ms after illusion onset. This is in good accordance with electroencephalography (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 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 interpretation 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 Müller-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 processing. We therefore suggest that the inferior frontal gyrus activation reflects processes related to the conscious perception of the illusion.

Mechanisms Underlying the Müller-Lyer Illusion

How can perceiving the Müller-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 contain more 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 information 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 Müller-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 4Cβ 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 μm (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 × 5 × 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 Müller-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 Müller-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 (Morgan et al. 1990; Morgan and Glennerster 1991). According to their model, the mechanism behind the Müller-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° in near-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 Müller-Lyer illusion. This is consistent with theories considering a relevant contribution of higher visual areas to the generation of the Müller-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/.

We are grateful to all our volunteers and our colleagues at the Institute for Neuroscience and Medicine, Research Center Jülich. Conflict of Interest: None declared.

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