Perceptual Similarity and the Neural Correlates of Geometrical Illusions in Human Brain Structure
Geometrical visual illusions are an intriguing phenomenon, in which subjective perception consistently misjudges the objective, physical properties of the visual stimulus. Prominent theoretical proposals have been advanced attempting to find common mechanisms across illusions. But empirically testing the similarity between illusions has been notoriously difficult because illusions have very different visual appearances. Here we overcome this difficulty by capitalizing on the variability of the illusory magnitude across participants. Fifty-nine healthy volunteers participated in the study that included measurement of individual illusion magnitude and structural MRI scanning. We tested the Muller-Lyer, Ebbinghaus, Ponzo, and vertical-horizontal geometrical illusions as well as a non-geometrical, contrast illusion. We found some degree of similarity in behavioral judgments of all tested geometrical illusions, but not between geometrical illusions and non-geometrical, contrast illusion. The highest similarity was found between Ebbinghaus and Muller-Lyer geometrical illusions. Furthermore, the magnitude of all geometrical illusions, and particularly the Ebbinghaus and Muller-Lyer illusions, correlated with local gray matter density in the parahippocampal cortex, but not in other brain areas. Our findings suggest that visuospatial integration and scene construction processes might partly mediate individual differences in geometric illusory perception. Overall, these findings contribute to a better understanding of the mechanisms behind geometrical illusions.Fifty-nine healthy volunteers with normal or corrected-to-normal vision participated in the study. Average age: 27 (MSE: 0.71) years; 30 females. All participants signed an informed consent form. The study was approved by the ethics committee of the Tel Aviv Sourasky Medical Center (Israel). All the methods were carried out in accordance with the these guidelines and regulations. Participants received either monetary payment or psychology course credit points for their participation in the experiment. All experimental procedures were performed in accordance with the guidelines provided by the ethics committee.Samsung notebook (NP350U2A), screen size 12.5, 1366 768 resolution, and refresh rate 60 Hz, Microsoft Windows 7 Home Edition, Service Pack 1 operating system was used. The experiment was programmed as a Web application, running locally using an Apache 2.2 Web server () and Google Chrome browser. During the experiment, participants sat in a comfortable office chair; their distance from the monitor was 40 cm.Four geometrical illusions (i.e., vertical-horizontal, Ebbinghaus, Ponzo, and Muller-Lyer) and one non-geometrical illusion (i.e., contrast illusion) were used. Illusory stimuli are shown in . The stimuli were grayscale and were presented in the center of the screen. Illusory stimuli could be adjusted within some boundaries (i.e., a spectrum of possible adjustments). The boundaries were measured in a preliminary pilot experiment (different participants). In other words, the boundaries reflected the reasonable spectrum of variability across participants. While adjusting the stimuli participants were not aware of the boundaries (i.e., the adjustment limits). In addition, the boundaries were not reached by any of the participants in any of the illusions. The parameters of the stimuli were as the following. In the vertical-horizontal illusion the length of the horizontal line was 12 and the vertical line was adjustable, the minimal and maximal height was 12 and 17. In the Ebbinghaus illusion, the radius of the inducers was 0.25 (left side) and 2 (right side). The radius of the left target circle was 0.9 and the right target circle was adjustable, and the minimal and maximal radius were 0.9 and 1.5, respectively. The distance between the central circle and inducers for the left side was 0.1 and for the right side it varied between 0.5 (largest central circle) and 1 (smallest central circle). In the Muller-Lyer illusion, the total length of the line was 18. The position of the central arrow was adjustable, and the maximal and minimal length of the left segment was 9 and 6.5, respectively. The arrows had a length of 2.6 and a slope of 57. In the Ponzo illusion, the length of the bottom horizontal line was 4.6, and the top horizontal line was adjustable, with the minimal and maximal size 3.45 and 5.2, respectively. The length of the surround lines was 18.7 and the slope of 21. In the contrast illusion, the horizontal and vertical length of the whole figure was 20 and 12, respectively. Left and right rectangles were of the same size and the circles were located at the centre of the rectangles; the radius of the central circle was 0.85. The luminance of the surrounding part at the left and right side was 36.55 cd/m and 5.73 cd/m; the luminance of the left central circle was 12.7 cd/m and the luminance of the right central circle was adjustable between 5.9 cd/m (most dark) and 15.9 cd/m (most light).Participants were shown an illusion figure with a short instruction text. Their task was using two buttons on the screen to adjust an element in the illusion figure until the two elements (fixed and adjusted one) appeared to them as perceptually equivalent. Adjustment was achieved by clicking buttons displayed on the screen with a computer mouse. In particular, for the vertical-horizontal illusion they had to change the length of the vertical bar so that it would appear to them as equal to the horizontal bar; for the Ebbinghaus illusion they had to resize the right circle so it would appear to them as equal in size to the left circle; for the Muller-Lyer illusion they had to move the central arrow to the center of the horizontal segment; for the Ponzo illusion they were asked to change the length of the top horizontal bar so it would appear to them as equal to the bottom horizontal bar; and for the contrast illusion they had to change the brightness (i.e., variations of gray) of the right circle so it would be the same as the left circle. Upon completing adjustment for a given illusion, participants clicked on the presented OK button that was constantly present on the screen. Then, they proceeded to the next illusion figure (see below). Participants were forbidden to approach their hands/fingers to the monitor or to use any auxiliary devices (e.g., ruler) while doing the experiment. The experimenter closely monitored the participants to ensure they performed the experiment based strictly only on their vision. Participants were also asked not to make calculations in their mind (e.g., mental rotation of the vertical-horizontal illusion), but to go with their intuitive perception (i.e., gut feeling). Each illusion was repeated several times (see below), while the starting configuration (e.g., arrow position of the Muller-Lyer illusion) varied between rounds. The starting configurations were uniformly sampled through the whole spectrum of possible configurations (i.e., the possible boundaries, explained above). By initiating the illusion adjustment from different starting positions, we minimized the influence of the starting position on the perceptual decision. Twenty-three participants completed four repetitions for each illusion and 36 participants completed five repetitions. The order of the illusions and the order of the starting configuration for each illusion were pseudo-randomized. No two examples of the same illusion appeared in direct succession. Before the main experimental session, participants performed a short training session, where each illusion appeared once. All participants confirmed they understood the instructions.Structural MRI data (SPGR sequence) were collected for each participant using a 3 T GE MRI scanner (8-channel head coil) located at the Sourasky Ichilov Medical Center in Tel Aviv, Israel. Scanning resolution was 1 1 1 mm, providing full brain coverage, with TE = 3.52 ms, TR = 9.104 ms.Data analysis was performed in MATLAB (R2009B version). The raw result values across several repetitions of the illusion were averaged. This resulted in a single raw value per participant/illusion. The magnitude of the illusory effect was calculated as a ratio between participants perceptual estimation and physically correct stimulus properties. The ratio values were subsequently transformed using the binary logarithm (base 2) to correct for potential non-linearity of the data. After transformation, values larger than 0 reflected an illusory effect. Specifically, for each illusion the illusory magnitude (i.e., the ratio) was calculated as follows. For the Ponzo illusion, the length of the bottom horizontal bar divided by the length of the top horizontal bar. For the vertical-horizontal illusion the length of horizontal bar divided by the vertical bar. For the Muller-Lyer illusion the length of the right horizontal segment (until the arrow) divided by the left horizontal segment. For the Ebbinghaus illusion, the radius of the right center circle was divided by the radius of the left central circle. For Ponzo, the vertical-horizontal, and Muller-Lyer illusions the illusory magnitude was calculated for the length of the segments. Accordingly, for consistency, we also used the length measure (i.e., radius) for the Ebbinghaus illusion. We validated that when an area of the circle was used instead of radius, very similar results were obtained in all subsequent analyses.Behavioral correlation analysis between the magnitude of the illusory effects was conducted using Spearman rank correlation. Spearman correlation is less sensitive to potential outliers than classical Pearson correlation. In addition, Spearman correlation is a more preferable method because it can accommodate any monotonic relationship, whereas a Pearson correlation assumes a linear relationship. We also validated that qualitatively similar results were obtained when the robust skipped correlation and Shepherd correlation methods were used. We calculated significance p-values and confidence intervals using the bootstrap method (10,000 bootstrap sets). To assess the significance of the correlations between illusions, Bonferroni multiple-comparison correction was applied based on the number of illusions. Confidence intervals were calculated for the percentiles by taking into account the Bonferroni multiple-comparison correction (i.e., 99.5% confidence interval for ten comparisons). Principal Component Analysis (PCA) for the magnitudes of the illusions (five illusions) was conducted using princomp MATLAB function (the input matrix: 59 participants 5 illusions). Prior to submitting the data to PCA, for each illusion separately, the log-transformed magnitudes of the illusions were z-standardized (mean = 0, standard deviation = 1). The explained variance of each component was calculated as an eigenvalue of each component divided by the sum of eigenvalues. The scores of the first principal component (i.e., the representation of the input data in the principal component space) was used as a regressor in VBM analysis (see below).The structural data processing pipeline was the same as in our previous publications. The data were analyzed using mainly SPM 8 (Wellcome Trust Centre for Neuroimaging, London, UK; ), except for the localization of significant clusters, which was performed using the Non-Stationary Cluster Extent Correction for SPM toolbox in SPM 5 (see below). Structural anatomical images were segmented to gray and white matter using a unified segmentation algorithm. Then, an inter-subject registration of the gray matter images was performed using Diffeomorphic Anatomical Registration through the Exponentiated Lie Algebra (DARTEL) SPM toolbox. The resultant gray matter images were smoothed using the Gaussian kernel (FWHM = 8 mm) and then transformed to the MNI coordinate system (using a transformation matrix of segmentation step). Multiple regression model was estimated for first principal component (covariate of interest: scores of first PCA component). In addition, for each of five illusions separate multiple regression models were estimated (covariate of interest: magnitude of the illusory effect). Covariates of no interest (i.e., influence that was regressed out) in all models were age and gender of the participants and global gray matter density. Given our predictions that the illusory processing of the tested geometrical illusions might be related to visuospatial and scene-integration processing, we focused primarily on the parahippocampal cortex and hippocampus. To define this region, a single binary mask of the bilateral parahippocampal and hippocampus was constructed based on the aal masks of these regions (). The models estimated for the main analysis () were restricted to this binary mask. To establish statistical significance, in all analyses we applied cluster-level correction using the Non-Stationary Cluster Extent Correction for SPM toolbox (). We applied non-stationary correction, since it has been suggested that the use of standard cluster-based random field theory might be inappropriate because there is local variation in smoothness in structural images. In the VBM analyses of individual illusions, localization of significant clusters was conducted using Bonferroni multiple comparison correction for the number of illusions (p When no significant clusters were found at this corrected threshold, data were inspected using a more liberal threshold (p 05, corrected is specified explicitly in the text. In accordance with recommendations, in all analyses the primary threshold was p In addition to the main focus of our study, the parahippocampal cortex/hippocampus, we conducted VBM analyses for additional regions. This permitted us to establish regional specificity of the results found in the PHC. The regions included scene-selective parahippocampal place area (PPA), retrosplenial cortex (RSC), and the transverse occipital sulcus (TOS), object-selective lateral occipital (LO) complex, and the inferior intraparietal lobule (inferior IPL). These regions were defined as a sphere with a radius of 8 mm, centered in coordinates previously reported in the literature. In particular, the coordinates (in MNI space) for the PPA and RSC were used from ref. and were as follows: left PPA: 27,46,15; right PPA: 30, 44, 14; left RSC: 16, 64, 13, and right RSC: 20, 63, 17. The coordinates for the TOS were used from ref. and were as follows: left TOS: 33, 80, 19; right TOS: 34, 77, 19. The coordinates for the LO and inferior IPL were used from ref. and were as follows: left LO: 43, 82, 8; right LO: 43, 82,8; left inferior IPL: 31, 86, 23, and right inferior IPL: 31, 86, 23. Note, that similar coordinates for these regions were reported in many other previous studies (e.g., refs , , , ). To search for neural correlates outside the a-priori regions, for each illusion we estimated a model without anatomical restrictions.For the significant clusters found using VBM analysis we extracted gray matter density using the MarsBar region of interest toolbox for SPM and custom code. The extraction of gray matter was performed for each participant, resulting in one data point per participant/per cluster. The extracted gray matter density was correlated with the behavioral illusory effect of each illusion. We took special precautions to avoid potential circular (double-dipping) analysis. Our general strategy was as follows: For the clusters that were identified using the same or partly the same behavioral data (i.e., non-independent correlation analysis), no statistical inference was conducted (i.e., no p-values or confidence intervals). These analyses were used only for qualitative (i.e., visualization and inspection) assessment of whether there was an association between the two variables. For the clusters, which were identified using different behavioral data (i.e., independent correlation analysis), we calculated correlation Rho, p-values, and confidence intervals. In general, our analysis pipeline included two types of VBM analysis: a) analysis where the first principal component of illusion magnitude was used as a regressor, and b) a set of analyses where each illusion magnitude was used as a regressor. For the clusters identified using the first principal component (), no statistical inference was conducted for the correlation analysis between local gray matter and individual illusion magnitudes (i.e., the behavioral data was partially dependent). Despite this partial dependence, inspection of the association between two variables was still informative. That is, while relatively high correlation could be found for some illusions, no correlation was found for other illusions. For the clusters identified in the VBM analysis using the Muller-Lyer illusion, no statistical inference was conducted in correlation analysis between local gray matter and Muller-Lyer illusion magnitude (). For the two clusters that were identified Muller-Lyer illusion, we conducted set of statistical correlation analyses using four remaining illusions (). There is no circularity in this type of analysis because the identified cluster reflected strong correlation between local gray matter density (i.e., variable 1) and the behavioral scores of the Muller-Lyer illusion (i.e., variable 2). Then, gray matter volume in this cluster was correlated with the behavioral scores of the lets say Ponzo illusion (i.e., variable 3). Because variables 2 and 3 are independent, the selection of a cluster based on the correlation between variables 1 and 2, does not introduce a bias for the correlation between variables 1 and 3. In the supplementary material, we provide a MATLAB simulation code that illustrates this idea. Finally, for the clusters identified using the Ebbinghaus illusion, no statistical inference was conducted in correlation analysis between the local gray matter and the Ebbinghaus illusion magnitude (). The statistical analysis was conducted for the correlations between local gray matter and four remaining illusions (; the same logic as for the Muller-Lyer illusion described previously). In all correlation analyses Bonferroni multiple comparison correction was applied to correct for the number of illusions (n = 5). Correlation analyses were conducted using the same methods as explained in the behavioral data analysis section.