Behind the Looking-Glass: A Review on Human Symmetry Perception

Perception of wide-expanse symmetric patterns

Humans are remarkably proficient at the task of distinguishing between symmetric and non-symmetric visual patterns. The neural mechanisms underlying this ability are still unclear. Here we examine symmetry perception along a dimension that can help place some constraints on the nature of these mechanisms. Specifically, we study whether and how human performance on the task of classifying patterns as bilaterally symmetric versus non-symmetric changes as a function of the spatial separation between the flanks. Working with briefly flashed stimuli that embody flank separations of 6 degrees to 54 degrees, we find that classification performance declines significantly with increasing inter-flank distance, but remains well above chance even at the largest separations. Response time registers a progressive increase as the space between the flanks expands. Baseline studies show that these performance changes cannot be attributed solely to reduced acuity in the visual periphery, or increased conduction times for relaying information from those locations. The findings argue for the need to adapt current feedforward models of symmetry perception to be more consistent with the empirical data, and also point to the possible involvement of recurrent processing, as suggested by recent computational results.

The role of task on the human brain's responses to, and representation of, visual regularity defined by reflection and rotation

Identifying and segmenting objects in an image is generally achieved effortlessly and is facilitated by the presence of symmetry: a principle of perceptual organisation used to interpret sensory inputs from the retina into meaningful representations. However, while imaging studies show evidence of symmetry selective responses across extrastriate visual areas in the human brain, whether symmetry is processed automatically is still under debate. We used functional Magnetic Resonance Imaging (fMRI) to study the response to and representation of two types of symmetry: reflection and rotation. Dot pattern stimuli were presented to 15 human participants (10 female) under stimulus-relevant (symmetry) and stimulus-irrelevant (luminance) task conditions. Our results show that symmetry-selective responses emerge from area V3 and extend throughout extrastriate visual areas. This response is largely maintained when participants engage in the stimulus irrelevant task, suggesting an automaticity to processing visual symmetry. Our multi-voxel pattern analysis (MVPA) results extend these findings by suggesting that not only spatial organisation of responses to symmetrical patterns can be distinguished from that of non-symmetrical (random) patterns, but also that representation of reflection and rotation symmetry can be differentiated in extrastriate and object-selective visual areas. Moreover, task demands did not affect the neural representation of the symmetry information. Intriguingly, our MVPA results show an interesting dissociation: representation of luminance (stimulus irrelevant feature) is maintained in visual cortex only when task relevant, while information of the spatial configuration of the stimuli is available across task conditions. This speaks in favour of the automaticity for processing perceptual organisation: extrastriate visual areas compute and represent global, spatial properties irrespective of the task at hand.

High mirror symmetry in mouse exploratory behavior

The physicality of the world in which the animal acts-its anatomical structure, physiology, perception, emotional states, and cognitive capabilities-determines the boundaries of the behavioral space within which the animal can operate. Behavior, therefore, can be considered as the subspace that remains after secluding all actions that are not available to the animal due to constraints. The very signature of being a certain creature is reflected in these limitations that shape its behavior. A major goal of ethology is to expose those constraints that carve the intricate structure of animal behavior and reveal both uniqueness and commonalities between animals within and across taxa. Exploratory behavior in an empty arena seems to be stochastic; nevertheless, it does not mean that the moving animal is a random walker. In this study, we present how, by adding constraints to the animal's locomotion, one can gradually retain the 'mousiness' that characterizes the behaving mouse. We then introduce a novel phenomenon of high mirror symmetry along the locomotion of mice, which highlights another constraint that further compresses the complex nature of exploratory behavior in these animals. We link these findings to a known neural mechanism that could explain this phenomenon. Finally, we suggest our novel finding and derived methods to be used in the search for commonalities in the motion trajectories of various organisms across taxa.

Event related potentials (ERP) reveal a robust response to visual symmetry in unattended visual regions

Visual symmetry at fixation generates a bilateral Event Related Potential (ERP) called the Sustained Posterior Negativity (SPN). Symmetry presented in the left visual hemifield generates a contralateral SPN over the right hemisphere and vice versa. The current study examined whether the contralateral SPN is modulated by the focus of spatial attention. On each trial there were two dot patterns, one to the left of fixation, and one to the right of fixation. A central arrow cue pointed to one of the patterns and participants discriminated its regularity (symmetry or random). We compared contralateral SPN amplitude generated by symmetry at attended and unattended spatial locations. While the response to attended symmetry was slightly enhanced, the response to unattended symmetry was still substantial. Although visual symmetry detection is a computational challenge, we conclude that the brain processes visual symmetry in unattended parts of the visual field.

The brain does not process horizontal reflection when attending to vertical reflection, and vice versa

Previous work has found that feature attention can modulate electrophysiological responses to visual symmetry. In the current study, participants observed spatially overlapping clouds of black and white dots. They discriminated vertical symmetry from asymmetry in the target dots (e.g., black or white) and ignored the regularity of the distractor dots (e.g., white or black). We measured an electroencephalography component called the sustained posterior negativity (SPN), which is known to be generated by visual symmetry. There were five conditions with different combinations of target and distractor regularity. As well as replicating previous results, we found that an orthogonal axes of reflection in the distractor dots had no effect on SPN amplitude. We conclude that the visual system can processes reflectional symmetry in independent axis-orientation specific channels.

The quest for psychological symmetry through figural goodness, randomness, and complexity: A selective review

Of the four interrelated concepts in the title, only symmetry has an exact mathematical definition. In mathematical development, symmetry is a graded variable-in marked contrast with the popular binary conception of symmetry in and out of the laboratory (i.e. an object is either symmetrical or nonsymmetrical). Because the notion does not have a direct graded perceptual counterpart (experimental participants are not asked about the amount of symmetry of an object), students of symmetry have taken various detours to characterize the perceptual effects of symmetry. Current approaches have been informed by information theory, mathematical group theory, randomness research, and complexity. Apart from reviewing the development of the main approaches, for the first time we calculated associations between figural goodness as measured in the Garner tradition and measures of algorithmic complexity and randomness developed in recent research. We offer novel ideas and analyses by way of integrating the various approaches.

Social groups and polarization of aesthetic values from symmetry and complexity

When deciding what images we prefer, our brain must weigh many aesthetic variables, such as symmetry and complexity. To date, aesthetic research has mainly focused on investigating one variable at a time. In this article, we use symmetry and complexity to study the problem of multi aesthetic-variable interactions. For symmetry and complexity, there are two simple interaction hypotheses. The independence hypothesis proposes that the evaluation of aesthetic variables is mutually independent. Meanwhile, Birkhoff's aesthetic-measure hypothesis predicts that people prefer images high in symmetry and low in complexity, and dislike the opposite. To test these hypotheses, we generated images that systematically varied in levels of symmetry and complexity. We then compared the subjects' preference maps to identify regions of likes and dislikes. Unlike the predictions from these hypotheses, we found that most, but not all subjects, formed two distinct natural clusters, termed "islands," in terms of likes and dislikes. We also found that people with more art exposure were less likely to belong to an island. If someone did belong to an island, their gender influenced which cluster they belonged to. We discuss alternate hypotheses, possible mechanisms for the occurrence of islands, and their possible social implications.

Characterising and dissecting human perception of scene complexity

Humans can effortlessly assess the complexity of the visual stimuli they encounter. However, our understanding of how we do this, and the relevant factors that result in our perception of scene complexity remain unclear; especially for the natural scenes in which we are constantly immersed. We introduce several new datasets to further understanding of human perception of scene complexity. Our first dataset (VISC-C) contains 800 scenes and 800 corresponding two-dimensional complexity annotations gathered from human observers, allowing exploration for how complexity perception varies across a scene. Our second dataset, (VISC-CI) consists of inverted scenes (reflection on the horizontal axis) with corresponding complexity maps, collected from human observers. Inverting images in this fashion is associated with destruction of semantic scene characteristics when viewed by humans, and hence allows analysis of the impact of semantics on perceptual complexity. We analysed perceptual complexity from both a single-score and a two-dimensional perspective, by evaluating a set of calculable and observable perceptual features based upon grounded psychological research (clutter, symmetry, entropy and openness). We considered these factors' relationship to complexity via hierarchical regressions analyses, tested the efficacy of various neural models against our datasets, and validated our perceptual features against a large and varied complexity dataset consisting of nearly 5000 images. Our results indicate that both global image properties and semantic features are important for complexity perception. We further verified this by combining identified perceptual features with the output of a neural network predictor capable of extracting semantics, and found that we could increase the amount of explained human variance in complexity beyond that of low-level measures alone. Finally, we dissect our best performing prediction network, determining that artificial neurons learn to extract both global image properties and semantic details from scenes for complexity prediction. Based on our experimental results, we propose the "dual information" framework of complexity perception, hypothesising that humans rely on both low-level image features and high-level semantic content to evaluate the complexity of images.

Contribution of higher-order structure to perception of mirror symmetry: Role of shapes and corners

Visual mirror symmetry is a global feature that is dependent on specific low-level relationships between component elements. Initially conceptualized as virtual lines between paired elements, it has been suggested that higher-order structure between pairs of symmetric elements forming virtual four cornered shapes may also be important for strengthening the percept of mirror symmetry. We utilize corner elements, formed by joining two Gabor elements along a central midline creating vertices with variable internal angles, in a temporal integration paradigm. This allows us to specifically manipulate the presence and type of higher-order versus lower-order structure in patterns with symmetrically placed elements. We show a significant contribution of higher-order structure to the salience of visual symmetries compared with patterns with only lower-order structures. We also find that although we are more sensitive to patterns with higher-order structure, there is no difference in the temporal processing of higher-order versus lower-order patterns. These findings have important implications for existing spatial filter models of symmetry perception that rely on lower-order structures alone and reinforces the need for elaborated models that can more readily capture the complexities of real-world symmetries.

Different symmetries, different mechanisms

Three common symmetries exist in the natural visual world: (i) mirror symmetry, i.e., reflections around a vertical axis, (ii) radial symmetry, i.e., rotations around a point, and (iii) translational symmetry, i.e., shifted repetitions. Are these processed by a common class of visual mechanism? Using stimuli comprising arrays of Gaussian blobs we examined this question using a visual search protocol in which observers located a single symmetric target patch among varying numbers of random-blob distractor patches. The testing protocol used a blocked present/absent task and both search times and accuracy were recorded. Search times for mirror and radial symmetry increased significantly with the number of distractors, as did translational-symmetry patterns containing few repetitions. However translational-symmetry patterns with four repeating sectors produced search slopes close to zero. Fourier analysis revealed that, as with images of natural scenes, the structural information in both mirror- and radial-symmetric patterns is carried by the phase spectrum. However, for translational patterns with four repeating sectors, the amplitude spectrum appears to capture the structure, consistent with previous analyses of texture regularity. Modeling revealed that while the mirror and radial patterns produced an approximately Gaussian-shaped energy response profile as a function of spatial frequency, the translational pattern profiles contained a distinctive spike, the magnitude of which increased with the number of repeating sectors. We propose distinct mechanisms for the detection of different symmetry types: a mechanism that encodes local positional information to detect mirror- and radial-symmetric patterns and a mechanism that computes energy in narrowband filters for the detection of translational symmetry containing many sectors.

The Complexity of Reasoning about and with Chemical Representations

External visual representations of chemical entities and processes (chemical representations) play a critical role in chemical thinking and practice. They support reasoning by serving as bridges between the macroscopic world and the chemical models that help us make sense of the properties and behaviors of substances in our surroundings. Consequently, many chemistry education research studies have been carried out to explore and foster students' representational competency in our discipline. Nevertheless, in this Perspective I argue that investigations in this area would benefit from a more in-depth analysis of how the distinctive characteristics of chemical representations affect student reasoning. I identify four dimensions of variation in these representations (iconicity, quantitativeness, granularity, dimensionality) that affect students' ability to interpret, connect, generate, and use chemical representations. I discuss how these features influence the unpacking or packing of information during different types of tasks, affecting sense-making and perceptual competency. Implications for chemistry education research and practice are considered.

How Facial Symmetry Influences the Learning Effectiveness of Computer Graphic Design in Makeup Design

This study explored the learning effectiveness of drawing makeup designs by computer graphic design and compared the learning differences between traditional hand-drawn and computer-assisted teaching in cosmetology students at universities. The statistical analysis methods of factor analysis, descriptive statistical analysis, and paired sample t-test are used to analyze the difference in students’ learning attitudes before and after the course. It also explored students’ learning effectiveness. The subjects were 55 students from a cosmetology department of a university in Taiwan. The results showed that using a computer tool to create makeup designs improved the overall student learning effectiveness and effectively promoted students’ interest in learning. Moreover, through focus group interviews, changes in the learning effectiveness that were brought about by the use of computer graphic design tools were obtained. Among them, the mirror function could best meet the needs of students for makeup symmetry and design drawing speed and improve their satisfaction with computer graphic makeup. The results of this study are improving the learning effectiveness, maintaining a positive attitude and increasing willingness to learn, and the systematization and digitization of makeup design, and the results could promote teachers to obtain more efficient teaching quality, improve students’ professional skills, and result in better learning results.

All Is Perception

This editorial addresses the universality and importance of the science of perception. In particular, recently published studies in this journal illustrate the natural variations in perception. These articles are a reminder of perception as a natural process with inherent variations and that any two individuals are not guaranteed to form the same representation of an object, regardless of whether it originates from the senses or not. Since perception is a foundation for higher cognition, it also has an immense influence on studies of humanity and interpretations of natural processes.

Color Variability Constrains Detection of Geometrically Perfect Mirror Symmetry

Symmetry in nature is a result of biological self-organization, driven by evolutionary processes. Detected by the visual systems of various species, from invertebrates to primates, symmetry determines survival relevant choice behaviors and supports adaptive function by reducing stimulus uncertainty. Symmetry also provides a major structural key to bio-inspired artificial vision and shape or movement simulations. In this psychophysical study, local variations in color covering the whole spectrum of visible wavelengths are compared to local variations in luminance contrast across an axis of geometrically perfect vertical mirror symmetry. The chromatic variations are found to delay response time to shape symmetry to a significantly larger extent than achromatic variations. This effect depends on the degree of variability, i.e., stimulus complexity. In both cases, we observe linear increase in response time as a function of local color variations across the vertical axis of symmetry. These results are directly explained by the difference in computational complexity between the two major (magnocellular vs. parvocellular) visual pathways involved in filtering the contrast (luminance vs. luminance and color) of the shapes. It is concluded that color variability across an axis of symmetry proves detrimental to the rapid detection of symmetry, and, presumably, other structural shape regularities. The results have implications for vision-inspired artificial intelligence and robotics exploiting functional principles of human vision for gesture and movement detection, or geometric shape simulation for recognition systems, where symmetry is often a critical property.

Lessons from a catalogue of 6674 brain recordings

It is now possible for scientists to publicly catalogue all the data they have ever collected on one phenomenon. For a decade, we have been measuring a brain response to visual symmetry called the sustained posterior negativity (SPN). Here we report how we have made a total of 6674 individual SPNs from 2215 participants publicly available, along with data extraction and visualization tools (https://osf.io/2sncj/). We also report how re-analysis of the SPN catalogue has shed light on aspects of the scientific process, such as statistical power and publication bias, and revealed new scientific insights.

Haemodynamic Signatures of Temporal Integration of Visual Mirror Symmetry

EEG, fMRI and TMS studies have implicated the extra-striate cortex, including the Lateral Occipital Cortex (LOC), in the processing of visual mirror symmetries. Recent research has found that the sustained posterior negativity (SPN), a symmetry specific electrophysiological response identified in the region of the LOC, is generated when temporally displaced asymmetric components are integrated into a symmetric whole. We aim to expand on this finding using dynamic dot-patterns with systematically increased intra-pair temporal delay to map the limits of temporal integration of visual mirror symmetry. To achieve this, we used functional near-infrared spectroscopy (fNIRS) which measures the changes in the haemodynamic response to stimulation using near infrared light. We show that a symmetry specific haemodynamic response can be identified following temporal integration of otherwise meaningless dot-patterns, and the magnitude of this response scales with the duration of temporal delay. These results contribute to our understanding of when and where mirror symmetry is processed in the visual system. Furthermore, we highlight fNIRS as a promising but so far underutilised method of studying the haemodynamics of mid-level visual processes in the brain.

The Contribution of Shape Features and Demographic Variables to Disembedding Abilities

Humans naturally perceive visual patterns in a global manner and are remarkably capable of extracting object shapes based on properties such as proximity, closure, symmetry, and good continuation. Notwithstanding the role of these properties in perceptual grouping, studies highlighted differences in disembedding performance across individuals, which are summarized by the field dependence dimension. Evidence suggests that age and educational attainment explain part of this variability, whereas the role of sex is still highly debated. Also, which stimulus features primarily influence inter-individual variations in perceptual grouping has still to be fully determined. Building upon these premises, we assessed the role of age, education level, and sex on performance at the Leuven Embedded Figure Test—a proxy of disembedding abilities—in 391 cisgender individuals. We also investigated to what extent shape symmetry, closure, complexity, and continuation relate to task accuracy. Overall, target asymmetry, closure, and good continuation with the embedding context increase task difficulty. Simpler shapes are more difficult to detect than those with more lines, yet context complexity impairs the recognition of complex targets (i.e., those with 6 lines or more) to a greater extent. Concerning demographic data, we confirm that age and educational attainment are significantly associated with disembedding abilities and reveal a perceptual advantage in males. In summary, our study further highlights the role of shape properties in disembedding performance and unveils sex differences not reported so far.

The Role of Art Expertise and Symmetry on Facial Aesthetic Preferences

Humans, like other species, have a preference for symmetrical visual stimuli, a preference that is influenced by factors such as age, sex, and artistic training. In particular, artistic training seems to decrease the rejection of asymmetry in abstract stimuli. However, it is not known whether the same trend would be observed in relation to concrete stimuli such as human faces. In this article, we investigated the role of expertise in visual arts, music, and dance, in the perceived beauty and attractiveness of human faces with different asymmetries. With this objective, the beauty and attractiveness of 100 photographs of faces with different degrees of asymmetry were evaluated by 116 participants with different levels of art expertise. Expertise in visual arts and dance was associated with the extent to which facial asymmetry influenced the beauty ratings assigned to the faces. The greater the art expertise in visual arts and dance, the more indifferent to facial asymmetry the participant was to evaluate beauty. The same effect was not found for music and neither for attractiveness ratings. These findings are important to help understand how face aesthetic evaluation is modified by artistic training and the difference between beauty and attractiveness evaluations.

Meaning of Gaze Behaviors in Individuals' Perception and Interpretation of Commercial Interior Environments: An Experimental Phenomenology Approach Involving Eye-Tracking

A critical question in interior design is how multisensory information is integrated into occupant perception and interpretation of the environmental contexts and meanings. Although there have been efforts to identify and theorize visual perception of interior factors or features (e.g., colors, fixtures, and signs), the hidden meanings behind visual attention and behaviors have been neglected in interior design research. This experimental phenomenological study investigates the impact of auditory stimuli on the gaze behaviors of individuals and the hidden meanings of their audio-visual perceptions of commercial interiors. Implementing eye-tracking and open-ended interviews, this study explored how the neurophysiological and phenomenological methods in complementary can serve for interior design research on the meaning of gaze behaviors. The study used a convenience sample of 26 participants, three coffee shop interior images, and two musical stimuli. Essential to this study is the interpretive analysis of corresponding eye-tracking and interview data. The results show that visual perception is affected by auditory stimuli and other interior elements and factors associated with personal experiences; however, no distinct gaze pattern is identified by the type of auditory stimuli. The fixation patterns showed mixed reflections of the participants' perceptions, e.g., a single fixation pattern reflecting participants' likes and dislikes. Findings included six essential meanings of participants' gaze behaviors. This study suggested that auditory and visual stimuli are reciprocal in individuals' perceptions. Rather than one affects the other, the interaction between sensory stimuli contributes to the complexity and intensity of multisensory stimuli people associate with their experiences and conceptualize with meanings they establish.

The temporal integration windows for visual mirror symmetry

Symmetry perception in dot patterns is tolerant to temporal delays of up to 60 ms within and between element pairs. However, it is not known how factors effecting symmetry discrimination in static patterns might affect temporal integration in dynamic patterns. One such feature is luminance polarity. Using dynamic stimuli with increasing temporal delay (SOA) between the onset of the first and second element in a symmetric pair, we investigated how four different luminance-polarity conditions affected the temporal integration of symmetric patterns. All four luminance polarity conditions showed similar upper temporal limits of approximately 60 ms. However psychophysical performance over all delay durations showed significantly higher symmetry thresholds for unmatched-polarity patterns at short delays, but also significantly less sensitivity to increasing temporal delay relative to matched-polarity patterns. These varying temporal windows are consistent with the involvement of a fast, sensitive first-order mechanism for matched-polarity patterns, and a slower, more robust second-order mechanism for unmatched-polarity patterns. Temporal integration windows for unmatched-polarity patterns were not consistent with performance expected from attentional mechanisms alone, and instead supports the involvement of second-order mechanisms that combines information from ON and OFF channels.

Electrophysiological priming effects demonstrate independence and overlap of visual regularity representations in the extrastriate cortex

An Event Related Potential (ERP) component called the Sustained Posterior Negativity (SPN) is generated by regular visual patterns (e.g. vertical reflectional symmetry, horizontal reflectional symmetry or rotational symmetry). Behavioural studies suggest symmetry becomes increasingly salient when the exemplars update rapidly. In line with this, Experiment 1 (N = 48) found that SPN amplitude increased when three different reflectional symmetry patterns were presented sequentially. We call this effect ‘SPN priming’. We then exploited SPN priming to investigate independence of different symmetry representations. SPN priming did not survive changes in retinal location (Experiment 2, N = 48) or non-orthogonal changes in axis orientation (Experiment 3, N = 48). However, SPN priming transferred between vertical and horizontal axis orientations (Experiment 4, N = 48) and between reflectional and rotational symmetry (Experiment 5, N = 48). SPN priming is interesting in itself, and a useful new method for identifying functional boundaries of the symmetry response. We conclude that visual regularities at different retinal locations are coded independently. However, there is some overlap between different regularities presented at the same retinal location.

Failures of stereoscopic shape constancy over changes of viewing distance and size for bilaterally symmetric polyhedra

Two shape matching experiments examined the effects of viewing distance and object size on observers' judgments of 3D metric shape under binocular viewing. Unlike previous studies on this topic, the stimuli were specifically designed to satisfy the minimal conditions for computing veridical shape from symmetry. Concretely, the stimuli were complex, mirror-symmetric polyhedra whose symmetry planes were oriented at an angle of 45o relative to the line of sight in a shape-matching task. Although it is mathematically possible to accurately compute the 3D shapes of these stimuli using relatively simple algorithms, the results indicated that human observers are unable to do so. Indeed, the apparent shapes of the objects were systematically expanded or compressed in depth as a function of viewing distance, in exactly the same way as has been reported for simpler stimuli that do not satisfy the minimal conditions for an accurate computational analysis. For objects presented at near distances, we also obtained statistically significant effects of object size on observers' shape judgments.

Interaction of surface pattern and contour shape in the tilt after effects evoked by symmetry

Integration of multiple properties of an object is a fundamental function of the visual cortex in object recognition. For instance, surface patterns and contour shapes are thought to be crucial characteristics that jointly contribute to recognition. However, the mechanisms of integration and corresponding cortical representations have not been fully clarified. We investigated the integration of surfaces and shapes by examining the tilt after effects (TAEs) evoked by the symmetry of patterns and contours. As symmetry in both pattern and contour evokes TAEs, we can directly measure the interaction between the two. The measured TAEs exhibited mutual transfer between the symmetry of the pattern (SP) and that of the contour shape (SS), i.e., adaptation by SP (SS) evoked TAEs when tested by SS (SP), suggesting the existence of an integrated representation. Next, we examined the interaction between SP and SS when both were simultaneously presented in adaptation. Congruent adaptors wherein their symmetry axes aligned evoked compressive interaction, whereas incongruent adaptors wherein the axes of SP and SS tilted to the opposite directions evoked subtractive interaction. These results suggest the existence of a cortical representation that integrates the properties of the surface and shape with suppressive interactions, which can provide crucial insights into the formation of object representation as well as the integration of visual information in the cortex.

Right lateralized alpha desynchronization increases with the proportion of symmetry in the stimulus

Research into the neural basis of symmetry perception has intensified in the last two decades; however, the functional role of neural oscillations remains unclear. In previous work Makin et al. (2014, Journal of Vision, 14, 1-12) and Wright et al. (2015, Psychophysiology, 52, 638-647) examined occipital alpha event-related desynchronization (alpha ERD). It was concluded that alpha ERD is right lateralized during active regularity discrimination but not during a secondary task. Furthermore, alpha ERD was unaffected by stimulus properties, such as the type of regularity. These conclusions are refuted by new time-frequency analysis on an electroencephalography (EEG) data set first introduced by Makin et al. (2020, Journal of Cognitive Neuroscience, 32, 353-366). We compared alpha ERD across five tasks. First, we found that right lateralization of alpha ERD was evident in all tasks, not just active regularity discrimination. This was caused by hemispheric differences in alpha power during prestimulus baseline (left < right), which equalized after stimulus onset (left = right). Second, we found that Alpha ERD increased with the proportion of symmetric elements in the image (PSYMM). Sensitivity to PSYMM was stronger on the right. These findings suggest that known extrastriate symmetry activations are accompanied by reduced alpha power.

Human Symmetry Uncertainty Detected by a Self-Organizing Neural Network Map

Symmetry in biological and physical systems is a product of self-organization driven by evolutionary processes, or mechanical systems under constraints. Symmetry-based feature extraction or representation by neural networks may unravel the most informative contents in large image databases. Despite significant achievements of artificial intelligence in recognition and classification of regular patterns, the problem of uncertainty remains a major challenge in ambiguous data. In this study, we present an artificial neural network that detects symmetry uncertainty states in human observers. To this end, we exploit a neural network metric in the output of a biologically inspired Self-Organizing Map Quantization Error (SOM-QE). Shape pairs with perfect geometry mirror symmetry but a non-homogenous appearance, caused by local variations in hue, saturation, or lightness within and/or across the shapes in a given pair produce, as shown here, a longer choice response time (RT) for “yes” responses relative to symmetry. These data are consistently mirrored by the variations in the SOM-QE from unsupervised neural network analysis of the same stimulus images. The neural network metric is thus capable of detecting and scaling human symmetry uncertainty in response to patterns. Such capacity is tightly linked to the metric’s proven selectivity to local contrast and color variations in large and highly complex image data.

Visual Awareness Is Essential for Grouping Based on Mirror Symmetry

We examined whether symmetry-based grouping can take place in the absence of visual awareness. To this end, we used a priming paradigm, sandwich masking as an invisibility-inducing method, and primes and targets composed of two vertical symmetric or asymmetric lines. The target could be congruent or incongruent with the prime in symmetry. In Experiment 1, participants were presented with masked primes and clearly visible targets. In each trial, the participants performed a two-alternative discrimination task on the target, and then rated the visibility of the prime on a subjective visibility four-point scale (used to assess prime awareness). Subjectively invisible primes failed to produce response priming, suggesting that symmetry processing might depend on visual awareness. However, participants barely saw the prime, and the results for the visible primes were inconclusive, even when we used a conservative criterion for awareness. To rule out the possibility that our prime stimuli could not produce priming per se, we conducted a control visibility experiment (Experiment 2), in which participants were presented with unmasked, clearly visible primes and performed a target task. The results showed that our primes could elicit significant response priming when visible. Taken together, our findings indicate that symmetry-based grouping requires visual awareness.

Influence of 3D Centro-Symmetry on a 2D Retinal Image

An object is 3D centro-symmetrical if the object can be segmented into two halves and the relationship between them can be represented by a combination of reflection about a plane and a rotation through 180° about an axis that is normal to the plane. A 2D orthographic image of the 3D centro-symmetrical object is always 2D rotation-symmetrical. Note that the human visual system is known to be sensitive to 2D rotational symmetry. This human sensitivity to 2D rotational symmetry might also be used to detect 3D centro-symmetry. If it is, can this detection of 3D centro-symmetry be helpful for the perception of 3D? In this study, the geometrical properties of 3D centro-symmetry and its 2D orthographic and perspective projections were examined to find out whether 3D centro-symmetry plays any role in the perception of 3D. I found that, from a theoretical point-of-view, it is unlikely that 3D centro-symmetry can be used by the human visual system to organize a 2D image of an object in a way that makes it possible to recover the 3D shape of an object from its 2D image.

Hmong Textiles, Symmetries, Perception and Culture

As part of this Special Issue, this paper attempts to add to a reflexive discussion and confront the simplistic understanding of why humans construct symmetries. This paper examines Hmong textiles called paj ntaub. The Hmong became a transnational people due to happenstance and the Vietnam War. Despite great trials and tribulations, the Hmong people and their art and culture survived. They express themselves and their identity through oral traditions and cultural practices, one of which is their textiles. The old textile styles, known as paj ntaub, are non-representational symmetric designs. The research for this paper was done in Laos. Grounded research, textual analysis and participant observation were the methods used. Though their textiles are a salient part of Hmong culture, little work has been done on the ontology of paj ntaub. This paper proposes a novel perspective to examining the paj ntaub by using anthropological symmetry, the gestalt theory on perception, and ethnographic analysis of the culture, meanings, and choices in design embedded in the textiles, as well as the process of making of the paj ntaub. This work proposes that the paj ntaub is not merely an expression of identity but a holistic expression in Hmong culture and reflects their relationship to their world.

In plain sight: implicit priming of patterns and faces using change symmetry

Aksentijevic–Gibson complexity is an original complexity measure based on the amount of change in a string or 2D array that has been successfully implemented on data from psychology to physics. The key ingredient to computing the measure is a change symmetry (CS)—a novel form of structure (also known as generalised palindrome) which represents a central or mirror symmetry based on the redundant arrangement not of symbols but of changes. This results in patterns that although globally symmetrical do not appear as such when inspected locally. We used this property to (a) affect the registration of a target, (b) prime the symmetry judgment of 2D arrays and (c) faces using 1D patterns possessing change symmetry. In Experiment 2, we applied the lock and key principle to complete the prime without showing its structure at once. In Experiments 3 and 4, we presented subjects with fast sequences of CSs such that the configuration of an individual pattern was masked by the subsequent pattern leaving only the structural “essence” of the prime symmetry. The results strongly support the contention that higher-level hidden structure of change symmetry successfully primes the symmetry perception of 2D arrays as well as facial attractiveness.

The Effect of Blindness on Spatial Asymmetries

The human cerebral cortex is asymmetrically organized with hemispheric lateralization pervading nearly all neural systems of the brain. Whether the lack of normal visual development affects hemispheric specialization subserving the deployment of visuospatial attention asymmetries is controversial. In principle, indeed, the lack of early visual experience may affect the lateralization of spatial functions, and the blind may rely on a different sensory input compared to the sighted. In this review article, we thus present a current state-of-the-art synthesis of empirical evidence concerning the effects of visual deprivation on the lateralization of various spatial processes (i.e., including line bisection, mirror symmetry, and localization tasks). Overall, the evidence reviewed indicates that spatial processes are supported by a right hemispheric network in the blind, hence, analogously to the sighted. Such a right-hemisphere dominance, however, seems more accentuated in the blind as compared to the sighted as indexed by the greater leftward bias shown in different spatial tasks. This is possibly the result of the more pronounced involvement of the right parietal cortex during spatial tasks in blind individuals compared to the sighted, as well as of the additional recruitment of the right occipital cortex, which would reflect the cross-modal plastic phenomena that largely characterize the blind brain.

Electrophysiological priming effects confirm that the extrastriate symmetry network is not gated by luminance polarity

It is known that the extrastriate cortex is activated by visual symmetry. This activation generates an ERP component called the Sustained Posterior Negativity (SPN). SPN amplitude increases (i.e., becomes more negative) with repeated presentations. We exploited this SPN priming effect to test whether the extrastriate symmetry response is gated by element luminance polarity. On each trial, participants observed three stimuli (patterns of dots) in rapid succession (500 ms. with 200 ms. gaps). The patterns were either symmetrical or random. The dot elements were either black or white on a grey background. The triplet sequences either showed repeated luminance (black > black > black, or white > white > white) or changing luminance (black > white > black, or white > black > white). As predicted, SPN priming was comparable in repeated and changing luminance conditions. Therefore, symmetry with black elements is not processed independently from symmetry with white elements. Source waveform analysis confirmed that this priming happened within the extrastriate symmetry network. We conclude that the network pools information across luminance polarity channels.

A Theoretical Framework for How We Learn Aesthetic Values

How do we come to like the things that we do? Each one of us starts from a relatively similar state at birth, yet we end up with vastly different sets of aesthetic preferences. These preferences go on to define us both as individuals and as members of our cultures. Therefore, it is important to understand how aesthetic preferences form over our lifetimes. This poses a challenging problem: to understand this process, one must account for the many factors at play in the formation of aesthetic values and how these factors influence each other over time. A general framework based on basic neuroscientific principles that can also account for this process is needed. Here, we present such a framework and illustrate it through a model that accounts for the trajectories of aesthetic values over time. Our framework is inspired by meta-analytic data of neuroimaging studies of aesthetic appraisal. This framework incorporates effects of sensory inputs, rewards, and motivational states. Crucially, each one of these effects is probabilistic. We model their interactions under a reinforcement-learning circuitry. Simulations of this model and mathematical analysis of the framework lead to three main findings. First, different people may develop distinct weighing of aesthetic variables because of individual variability in motivation. Second, individuals from different cultures and environments may develop different aesthetic values because of unique sensory inputs and social rewards. Third, because learning is stochastic, stemming from probabilistic sensory inputs, motivations, and rewards, aesthetic values vary in time. These three theoretical findings account for different lines of empirical research. Through our study, we hope to provide a general and unifying framework for understanding the various aspects involved in the formation of aesthetic values over time.

Time for Change: Implementation of Aksentijevic-Gibson Complexity in Psychology

Given that complexity is critical for psychological processing, it is somewhat surprising that the field was dominated for a long time by probabilistic methods that focus on the quantitative aspects of the source/output. Although the more recent approaches based on the Minimum Description Length principle have produced interesting and useful models of psychological complexity, they have not directly defined the meaning and quantitative unit of complexity measurement. Contrasted to these mathematical approaches are various ad hoc measures based on different aspects of structure, which can work well but suffer from the same problem. The present manuscript is composed of two self-sufficient, yet related sections. In Section 1, we describe a complexity measure for binary strings which satisfies both these conditions (Aksentijevic–Gibson complexity; AG). We test the measure on a number of classic studies employing both short and long strings and draw attention to an important feature—a complexity profile—that could be of interest in modelling the psychological processing of structure as well as analysis of strings of any length. In Section 2 we discuss different factors affecting the complexity of visual form and showcase a 2D generalization of AG complexity. In addition, we provide algorithms in R that compute the AG complexity for binary strings and matrices and demonstrate their effectiveness on examples involving complexity judgments, symmetry perception, perceptual grouping, entropy, and elementary cellular automata. Finally, we enclose a repository of codes, data and stimuli for our example in order to facilitate experimentation and application of the measure in sciences outside psychology.

The extrastriate symmetry response can be elicited by flowers and landscapes as well as abstract shapes

Previous research has investigated the neural response to visual symmetry. It is well established that symmetry activates a network of extrastriate visual regions, including V4 and the Lateral Occipital Complex. This symmetry response generates an event-related potential called the sustained posterior negativity (SPN). However, previous work has used abstract stimuli, typically dot patterns or shapes. We tested the generality of the SPN. We confirmed that the SPN wave was present and of similar amplitude for symmetrical shapes, flowers and landscapes, whether participants were responding either to image symmetry or to image color. We conclude that the extrastriate symmetry response can be generated by any two-dimensional image and is similar in different stimulus domains.

What Experts Appreciate in Patterns: Art Expertise Modulates Preference for Asymmetric and Face-Like Patterns

This study set out to investigate whether and how aesthetic evaluations of different types of symmetric, as well as abstract vs. representational patterns are modulated by art expertise. To this end, we utilized abstract asymmetric, symmetric, and “broken” patterns slightly deviating from symmetry, as well as more representational patterns resembling faces (also symmetric or broken). While it has already been shown that symmetry preference decreases with art expertise, it was still unclear whether an already established relationship between art expertise and preference for abstract over representational art can be similarly found as a preference for abstract over representational patterns, as these are non-art objects. Nevertheless, we found profound differences in aesthetic preferences between art experts and laypersons. While art experts rated asymmetric patterns higher than laypersons, as expected, they rated face-like patterns lower than laypersons. Also, laypersons rated all other types of patterns higher than asymmetric patterns, while art experts rated the other patterns similar or lower than asymmetric patterns. We found this both for liking and for interest ratings. As no differences between art experts and laypersons were found regarding memory recognition of new and old patterns, this effect is not likely due to differences in memory performance. In sum, this study further extends our knowledge about the influence of art expertise on aesthetic appreciation.

Anticipatory Defocusing of Attention and Contextual Response Priming but No Role of Aesthetic Appreciation in Simple Symmetry Judgments when Switching between Tasks

Visual attention can be adjusted to task requirements. We asked participants to switch between judging the symmetry of vertically presented three-letter strings and identifying the central stimulus (i.e., Eriksen task) to investigate anticipatory adjustment of attention. Our experiments provide evidence for anticipatory adjustment of visual attention, depending on the cued task (i.e., focusing and defocusing of attention after the Eriksen task cue and after the symmetry task cue, respectively). Although, symmetry judgments were, overall, considerably slower than the identification of the central letter, the effects of response congruency between tasks were comparable in the two tasks, which suggested strong response priming from concurrent symmetry judgment in Eriksen task trials. Symmetry judgment performance was best for homogeneous letter strings (e.g., HHH), worst for strings that were symmetrical and inhomogeneous (e.g., XHX), and intermediate for asymmetrical strings (e.g., HHX). The difficulty of categorizing symmetrical-inhomogeneous items markedly deviated from the aesthetic ratings of the stimuli, displaying a pronounced preference for symmetrical strings, but only little difference among the symmetrical items, and might be accounted by conflict with response priming based on inhomogeneity detection. Although our study provides little evidence for an effect of aesthetic appreciation in simple symmetry judgments, it demonstrates the strong role of contextual dependencies.

Symmetric patterns with different luminance polarity (anti-symmetry) generate an automatic response in extrastriate cortex

People can quickly detect bilateral reflection in an image. This is true when elements of the same luminance are matched on either side of the axis (symmetry) and when they have opposite luminance polarity (anti-symmetry). Using electroencephalography, we measured the well-established sustained posterior negativity (SPN) response to symmetry and anti-symmetry. In one task, participants judged the presence or absence of regularity (Regularity Discrimination Task). In another, they judged the presence or absence of rare colored oddball trials (Colored Oddball Task). Previous work has concluded that anti-symmetry is only detected indirectly, through serial visual search of element locations. This selective attention account predicts that the anti-symmetry SPN should be abolished in the Colored Oddball Task because there is no need to search for anti-symmetry. However, this prediction was not confirmed: The symmetry and anti-symmetry SPN waves were not modulated by task. We conclude that at least some forms of anti-symmetry can be extracted from the image automatically, in much the same way as symmetry. This is an important consideration for models of symmetry perception, which must be flexible enough to accommodate opposite luminance polarity, while also accounting for the fact anti-symmetry is often perceptually weaker than symmetry.

The Automatic Evaluation of Regularity and Semantic Decodability in Wallpaper Decorative Patterns

The perception and evaluation of decorative patterns can have a high impact in daily life but has received little empirical attention. This article attempts to offer some insight in terms of the regularity and semantic decodability. The implicit attitudes of subjects were measured by the Implicit Association Test. The results showed that regularity and semantic information can be automatically evaluated. The regular and realistic wallpaper decorative patterns are implicitly preferred to random and abstract ones. The Implicit Association Test effect of the former was greater than the latter. The increase in the number of motifs led to a decrease in the response latencies of regular and realistic patterns. The findings indicated that the processing fluency of wallpaper patterns is enhanced by a translational symmetry operation and a higher conceptual fluency of motifs. The resulting processing acceleration in high-density patterns may be due to the formation of a better Gestalt when the motifs are closer to one another.

Stimulus information supporting bilateral symmetry perception

A classification image (a psychophysical reverse-correlation) method was used to investigate what stimulus regions and information the visual system uses for bilateral symmetry perception. The stimuli were symmetric random-dot patterns with either low or high dot density. First, the spatial integration region supporting symmetry perception was estimated, by analyzing the trial-to-trial correlation between the spatial location of symmetric dots and the corresponding response. It was observed that the integration region was rather compact (3 deg² with dense stimulus), vertically elongated and located near to the axis of symmetry. The size of the area was dependent on the pattern density, being larger with low-density stimulus. Next, the resolution of the symmetry matching was probed by estimating how close to the perfect symmetry the dots in two stimulus parts must be to be perceived as symmetric (classification image for symmetry tolerance). Dot pairings up to 6 arc min off from the mirror symmetry correlated with symmetry response, suggesting that the process underlying symmetry matching has large tolerance and low resolution. Outside the integration region, the symmetry tolerance classification image weights were essentially zero, suggesting that the lack of symmetry integration there is not a byproduct of high tolerance.

The processing of compound radial frequency patterns

Radial frequency (RF) patterns can be combined to construct complex shapes. Previous studies have suggested that such complex shapes may be encoded by multiple, narrowly-tuned RF shape channels. To test this hypothesis, thresholds were measured for detection and discrimination of various combinations of two RF components. Results show evidence of summation: sensitivity for the compounds was better than that for the components, with little effect of the components' relative phase. If both RF components are processed separately at the point of detection, they would combine by probability summation (PS), resulting in only a small increase in sensitivity for the compound compared to the components. Summation exceeding the prediction of PS suggests a form of additive summation (AS) by a common mechanism. Data were compared to predictions of winner-take-all, where only the strongest component contributes to detection, a single channel AS model, and multi-channel PS and AS models. The multi-channel PS and AS models were modelled under both Fixed and Matched Attention Window scenarios, the former assuming a single internal noise source for both components and compounds or different internal noise sources for components and compounds respectively. The winner-take-all and single channel models could be rejected. Of the remaining models, the best performing one was an AS model with a Fixed Attention Window, consistent with detection being mediated by channels that are efficiently combined and limited by a single source of noise for both components and compounds.

The development of symmetry concept in preschool children

Young children are exposed to symmetrical figures frequently before they are taught the concept of symmetry, which is a valuable experience for the development of geometry; however, limited research has explored how this concept develops. This study investigated the developmental sequence of "general symmetry" concept and "specific symmetry" concepts (i.e., bilateral, rotational, and translational symmetry) with 106 4-6-year-old children using a symmetry deviant detection task. The test examined children's conception of general symmetry against asymmetry, specific symmetry against asymmetry, and discrimination of specific symmetries. The results suggested that the concept of symmetry develops as a differentiation process. The concept of general symmetry was acquired first, followed by specific symmetries which were acquired in sequential order.

Sustained response to symmetry in extrastriate areas after stimulus offset: An EEG study

Electrophysiological (EEG) studies of human perception have found that amplitude at posterior electrodes is more negative for symmetrical patterns compared to asymmetrical patterns. This negativity lasts for hundreds of milliseconds and it has been called sustained posterior negativity (SPN). Symmetry activates a network of visual areas, including the lateral occipital complex (LOC). The SPN is a response to presence of symmetry in the image. Given the sustained nature of this activation, in this study we tested the persistence of the SPN after stimulus offset. Two shapes were presented (for 0.5 s each) with a 1 s blank interval in between. We observed a sustained response after stimulus offset, irrespective of whether the task required processing of shape information. This supports the idea that the response to symmetry is generated by information in the image, independently of task, and that it is sustained over approximately one second post stimulus onset.

A shape-level flanker facilitation effect in contour integration and the role of shape complexity

The detection of an object in the visual field requires the visual system to integrate a variety of local features into a single object. How these local processes and their global integration is influenced by the presence of other shapes in the visual field is poorly understood. The detectability (contour integration) of a central target object in the form of a two dimensional Gaborized contour was compared in the presence or absence of nearby surrounding objects. A 2-AFC staircase procedure added orientation jitter to the constituent Gabor patches to determine the detectability of the target contour. The set of contours was generated using shape profiles of everyday objects and geometric forms. Experiment 1 examined the effect of three types of congruencies between the target and two flanking contours (contour shape, symmetry and familiarity). Experiment 2 investigated the effect of varying the number and spatial positions of the flankers. In addition, a measure of shape complexity (reciprocal of shape compactness) was used to assess the effects of contour complexity on detection. Across both experiments the detectability of the target contour increased when the target and flanker had the same shape and this was related to both the number of flankers and the complexity of the target shapes. Another factor that modulated this shape-level flanker facilitation effect was the presence of symmetry. The overall results are consistent with a contour integration process in which the visual system incorporates contextual information to extract the most likely smooth contour within a noise field.

The representation of symmetry in multi-voxel response patterns and functional connectivity throughout the ventral visual stream

Several computational models explain how symmetry might be detected and represented in the human brain. However, while there is an abundance of psychophysical studies on symmetry detection and several neural studies showing where and when symmetry is detected in the brain, important questions remain about how this detection happens and how symmetric patterns are represented. We studied the representation of (vertical) symmetry in regions of the ventral visual stream, using multi-voxel pattern analyses (MVPA) and functional connectivity analyses. Our results suggest that neural representations gradually change throughout the ventral visual stream, from very similar part-based representations for symmetrical and asymmetrical stimuli in V1 and V2, over increasingly different representations for symmetrical and asymmetrical stimuli which are nevertheless still part-based in both V3 and V4, to a more holistic representation for symmetrical compared to asymmetrical stimuli in high-level LOC. This change in representations is accompanied by increased communication between left and right retinotopic areas, evidenced by higher interhemispheric functional connectivity during symmetry perception in areas V2 and V4.