Symmetry versus repetition in cyclopean vision: A microgenetic analysis

A quasi-comprehensive exploration of the mechanisms of spatial working memory

Why are some spatial patterns remembered more easily than others? There are many possible mechanisms underlying spatial working memory function. Here, the author explores different mechanisms simultaneously in a single conceptual model. He conducts a large-scale experiment (35.4 million responses used to measure human observers' spatial working memory across 80,000 patterns) and builds a convolutional neural network as a benchmark for what is expected to be explainable. The author then creates a quasi-comprehensive exploration model of spatial working memory based on classic concepts, as well as new notions, including spatial uncertainty, Bayesian integration, out-of-range responses, averaging, grouping, categorical memory, line detection, gap detection, blurring, lateral inhibition, chunking, multiple spatial-frequency channels, redundancy, response bias and random guess. This model provides a tentative overarching framework for the mechanisms of spatial working memory.

Overlapping Neural Responses to Reflectional Symmetry and Glass Patterns Revealed by an ERP Priming Paradigm

The extrastriate visual cortex is activated by visual regularity and generates an ERP known as the sustained posterior negativity (SPN). Spatial filter models offer a biologically plausible account of regularity detection based on the spectral properties of an image. These models are specific to reflection and therefore imply that reflectional symmetry and Glass patterns are coded by different neural populations. We utilised the SPN priming effect to probe representational overlap between reflection and Glass patterns. For each trial, participants were presented with a rapid succession of three patterns. In the Repeated condition, three reflections or three Glass patterns were presented. In the Changing condition, patterns alternated between reflection and Glass patterns. An increase in SPN amplitude (priming) was observed in both the Repeated and Changing conditions. Results indicate a greater representational overlap in the brain between reflection and Glass patterns than predicted by spatial filter models.

Electrophysiological evidence of the amodal representation of symmetry in extrastriate areas

Extrastriate visual areas are strongly activated by image symmetry. Less is known about symmetry representation at object-level rather than image-level. Here we investigated electrophysiological responses to symmetry, generated by amodal completion of partially-occluded polygon shapes. We used a similar paradigm in four experiments (N = 112). A fully-visible abstract shape (either symmetric or asymmetric) was presented for 250 ms (t0). A large rectangle covered it entirely for 250 ms (t1) and then moved to one side to reveal one half of the shape hidden behind (t2, 1000 ms). Note that at t2 no symmetry could be extracted from retinal image information. In half of the trials the shape was the same as previously presented, in the other trials it was replaced by a novel shape. Participants matched shapes similarity (Exp. 1 and Exp. 2), or their colour (Exp. 3) or the orientation of a triangle superimposed to the shapes (Exp. 4). The fully-visible shapes (t0-t1) elicited automatic symmetry-specific ERP responses in all experiments. Importantly, there was an exposure-dependent symmetry-response to the occluded shapes that were recognised as previously seen (t2). Exp. 2 and Exp.4 confirmed this second ERP (t2) did not reflect a reinforcement of a residual carry-over response from t0. We conclude that the extrastriate symmetry-network can achieve amodal representation of symmetry from occluded objects that have been previously experienced as wholes.

Electrophysiological response to visual symmetry: Effects of the number of symmetry axes

The symmetry axes of a stimulus are a critical determinant of visual perception. Although much is known about the effects of a single symmetry axis on perception, the effects of multiple symmetry axes are still poorly understood. Here, we investigated the influence of the number of symmetry axes on brain activity using event-related potentials (ERPs). Our results showed that altering the number of symmetry axes affects both the amplitude and the latency of ERPs. Specifically, the amplitude of ERP components increased as the number of symmetry axes increased, starting at the N1 (165-175 ms) component and lasting until the P2 (230-250 ms) component in the bilateral posterior areas and until the N2 (340 ms) component in the frontal-central areas. Importantly, the latency of ERP components was reduced when the number of symmetry axes increased, starting at the N1 in the right posterior area and lasting until the P2 component in the bilateral posterior areas. The temporal and spatial differences in these effects imply that activity related to symmetry axes gradually changes throughout the ventral visual streams in the human brain.

Neural responses to reflection symmetry for shapes defined by binocular disparity, and for shapes perceived as regions of background

Human perception of symmetry is associated with activation in an extended network of extrastriate visual areas. This activation generates an ERP called the Sustained Posterior Negativity (SPN). In most studies so far, the stimuli have been defined by luminance. We tested whether the SPN is present when stimuli are defined by stereoscopic disparity using random dot stereograms (RDS). In Experiment 1, we compared the SPN signal for contours specified by binocular disparity and contours specified by monocular cues. The SPN was equivalent, suggesting that the type of contour does not alter the SPN signal. In Experiment 2 we exploited the unique property of RDS to provide unambiguous figure-ground arrangements. Psychophysical work has shown that symmetry is more easily detected when it is a property of a single object (i.e., within a figure), compared to a property of a gap between two objects (i.e., the ground). Therefore, the target regions in this experiment could either be foreground or background. The SPN onset was delayed when the symmetry was in a ground region. This may be because object formation interferes with the processing of shape information in the ground region.

Spinning objects and partial occlusion: Smart neural responses to symmetry

In humans, extrastriate visual areas are strongly activated by symmetry. However, perfect symmetry is rare in natural visual images. Recent findings showed that when parts of a symmetric shape are presented at different points in time the process relies on a perceptual memory buffer. Does this temporal integration need a retinotopic reference frame? For the first time we tested integration of parts both in the temporal and spatial domain, using a non-retinotopic frame of reference. In Experiment 1, an irregular polygonal shape (either symmetric or asymmetric) was partly occluded by a rectangle for 500 ms (T1). The rectangle moved to the opposite side to reveal the other half of the shape, whilst occluding the previously visible half (T2). The reference frame for the object was static: the two parts stimulated retinotopically corresponding receptive fields (revealed over time). A symmetry-specific ERP response from ~300 ms after T2 was observed. In Experiment 2 dynamic occlusion was combined with an additional step at T2: the new half-shape and occluder were rotated by 90°. Therefore, there was a moving frame of reference and the retinal correspondence between the two parts was disrupted. A weaker but significant symmetry-specific response was recorded. This result extends previous findings: global symmetry representation can be achieved in extrastriate areas non-retinotopically, through integration in both temporal and spatial domain.

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.

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.

Speed tuning properties of mirror symmetry detection mechanisms

The human visual system is often tasked with extracting image properties such as symmetry from rapidly moving objects and scenes. The extent to which motion speed and symmetry processing mechanisms interact is not known. Here we examine speed-tuning properties of symmetry detection mechanisms using dynamic dot-patterns containing varying amounts of position and local motion-direction symmetry. We measured symmetry detection thresholds for stimuli in which symmetric and noise elements either drifted with different relative speeds, were relocated at different relative temporal frequencies or were static. We also measured percentage correct responses under two stimulus conditions: a segregated condition in which symmetric and noise elements drifted at different speeds, and a non-segregated condition in which the symmetric elements drifted at two different speeds in equal proportions, as did the noise elements. We found that performance (i) improved gradually with increasing the difference in relative speed between symmetric and noise elements, but was invariant across relative temporal frequencies/lifetime duration differences between symmetric and noise elements, (ii) was higher in the segregated compared to non-segregated conditions, and in the moving compared to the static conditions. We conclude that symmetry detection mechanisms are broadly tuned to speed, with speed-selective symmetry channels combining their outputs by probability summation.

Temporal dynamics of mirror-symmetry perception

Recent studies have suggested that temporal dynamics rather than symmetrical motion-direction contribute to mirror-symmetry perception. Here we investigate temporal aspects of symmetry perception and implicitly, its temporal flexibility and limitations, by examining how symmetrical pattern elements are combined over time. Stimuli were dynamic dot-patterns consisting of either an on-going alternation of two images (sustained stimulus presentation) or just two images each presented once (transient stimulus presentation) containing different amounts of symmetry about the vertical axis. We varied the duration of the two images under five temporal-arrangement conditions: (a) whole patterns in which a symmetric pattern alternated with a noise pattern; (b) delayed halves—the halves of the symmetric and noise patterns were presented with temporal delay; (c) matched-pairs—two alternating images each containing equal amounts of symmetrical matched-pairs; (d) delayed matched-pairs—the same as arrangement (c), but with matched-pairs presented with delay; and (e) static—both images presented simultaneously as one. We found increased sensitivity in sustained compared to transient stimulus presentations and with synchronous compared to delayed matched-pairs stimuli. For the delayed conditions, sensitivity decreased gradually with longer image durations (>60 ms), prominently for the transient stimulus presentations. We conclude that spatial correlations across-the-symmetry-midline can be integrated over time (∼120 ms), and symmetry mechanisms can tolerate temporal delays between symmetric dot-pairs of up to ∼60 ms.

The neural basis of visual symmetry and its role in mid- and high-level visual processing

Symmetry is an important and prominent feature of the visual world. It has been studied as a basis for image segmentation and perceptual organization, but it also plays a role in higher level processes, such as face and object perception. Over the past decade, there has been progress in the study of the neural mechanisms of symmetry perception in humans and other animals. There is extended activity in the ventral stream, including the lateral occipital complex (LOC) and VO1; this activity starts in V3 and it occurs independently of the task (automatic response). Additionally, when the task requires processing of symmetry, the activation may emerge for objects that are symmetrical, even though they do not project a symmetrical image. There is also some evidence of hemispheric lateralization, especially for the LOC. We review the studies on the cortical basis of visual symmetry processing and its links to encoding of other aspects of the visual world, such as faces and objects.

The role of contour polarity, objectness, and regularities in haptic and visual perception

Regularities like symmetry (mirror reflection) and repetition (translation) play an important role in both visual and haptic (active touch) shape perception. Altering figure-ground factors to change what is perceived as an object influences regularity detection. For vision, symmetry is usually easier to detect within one object, whereas repetition is easier to detect across two objects. For haptics, we have not found this interaction between regularity type and objectness (Cecchetto & Lawson, Journal of Experimental Psychology: Human Perception and Performance, 43, 103-125, 2017; Lawson, Ajvani, & Cecchetto, Experimental Psychology, 63, 197-214, 2016). However, our studies used repetition stimuli with mismatched concavities, convexities, and luminance, and so had mismatched contour polarities. Such stimuli may be processed differently to stimuli with matching contour polarities. We investigated this possibility. For haptics, speeded symmetry and repetition detection for novel, planar shapes was similar. Performance deteriorated strikingly if contour polarity mismatched (keeping objectness constant), whilst there was a modest disadvantage for between-2objects:facing-sides compared to within-1object:outer-sides comparisons (keeping contour polarity constant). For the same task for vision, symmetry detection was similar to haptics (strong costs for mismatched contour polarity, weaker costs for between-2objects:facing-sides comparisons), but repetition detection was very different (weak costs for mismatched contour polarity, strong benefits for between-2objects:facing-sides comparisons). Thus, objectness was less influential than contour polarity for both haptic and visual symmetry detection, and for haptic repetition detection. However, for visual repetition detection, objectness effects reversed direction (within-1object:outer-sides comparisons were harder) and were stronger than contour polarity effects. This pattern of results suggests that regularity detection reflects information extraction as well as regularity distributions in the physical world.

The role of motion and number of element locations in mirror symmetry perception

The human visual system has specialised mechanisms for encoding mirror-symmetry and for detecting symmetric motion-directions for objects that loom or recede from the observers. The contribution of motion to mirror-symmetry perception has never been investigated. Here we examine symmetry detection thresholds for stationary (static and dynamic flicker) and symmetrically moving patterns (inwards, outwards, random directions) with and without positional symmetry. We also measured motion detection and direction-discrimination thresholds for horizontal (left, right) and symmetrically moving patterns with and without positional symmetry. We found that symmetry detection thresholds were (a) significantly higher for static patterns, but there was no difference between the dynamic flicker and symmetrical motion conditions, and (b) higher than motion detection and direction-discrimination thresholds for horizontal or symmetrical motion, with or without positional symmetry. In addition, symmetrical motion was as easy to detect or discriminate as horizontal motion. We conclude that whilst symmetrical motion per se does not contribute to symmetry perception, limiting the lifetime of pattern elements does improve performance by increasing the number of element-locations as elements move from one location to the next. This may be explained by a temporal integration process in which weak, noisy symmetry signals are combined to produce a stronger signal.

Effects of Line Separation and Exploration on the Visual and Haptic Detection of Symmetry and Repetition

Detection of regularities (e.g., symmetry, repetition) can be used to investigate object and shape perception. Symmetry and nearby lines may both signal that one object is present, so moving lines apart may disrupt symmetry detection, while repetition may signal that multiple objects are present. Participants discriminated symmetrical/irregular and repeated/irregular pairs of lines. For vision, as predicted, increased line separation disrupted symmetry detection more than repetition detection. For haptics, symmetry and repetition detection were similarly disrupted by increased line separation; also, symmetry was easier to detect than repetition for one-handed exploration and for body midline-aligned stimuli, whereas symmetry was harder to detect than repetition with two-handed exploration of stimuli oriented across the body. These effects of exploration and stimulus orientation show the influence of modality-specific processing rather than properties of the external world on regularity detection. These processes may, in turn, provide insights into the nature of objectness in vision and in touch.

Conditions for view invariance in the neural response to visual symmetry

Symmetry detection is slow when patterns are distorted by perspective, perhaps due to a time-consuming normalization process, or because discrimination relies on remaining weaker regularities in the retinal image. Participants viewed symmetrical or random dot patterns, either in a frontoparallel or slanted plane (±50°). One group performed a color discrimination task, while another performed a regularity discrimination task. We measured a symmetry-related event-related potential (ERP), beginning around 300 ms. During color discrimination, the ERP was reduced for slanted patterns, indexing only the remaining retinal structure. During regularity discrimination, the same ERP was view invariant, and identical for frontoparallel or slanted presentation. We conclude that normalization occurs rapidly during active symmetry discrimination, while symmetry-sensitive networks respond only to regularity in the retinal image when people are attending to other features.

Processing convexity and concavity along a 2-D contour: figure-ground, structural shape, and attention

Interest in convexity has a long history in vision science. For smooth contours in an image, it is possible to code regions of positive (convex) and negative (concave) curvature, and this provides useful information about solid shape. We review a large body of evidence on the role of this information in perception of shape and in attention. This includes evidence from behavioral, neurophysiological, imaging, and developmental studies. A review is necessary to analyze the evidence on how convexity affects (1) separation between figure and ground, (2) part structure, and (3) attention allocation. Despite some broad agreement on the importance of convexity in these areas, there is a lack of consensus on the interpretation of specific claims--for example, on the contribution of convexity to metric depth and on the automatic directing of attention to convexities or to concavities. The focus is on convexity and concavity along a 2-D contour, not convexity and concavity in 3-D, but the important link between the two is discussed. We conclude that there is good evidence for the role of convexity information in figure-ground organization and in parsing, but other, more specific claims are not (yet) well supported.

Using the kinetic Zollner illusion to quantify the interaction between form and motion information in depth

In the kinetic Zollner illusion a stimulus moving over a background of oriented lines appears tilted away from the line orientation. This "motion-tilt" illusion is a powerful demonstration of how form information can influence the computation of motion, particularly in signaling motion direction. In the present study, using a random dot stereogram of the kinetic Zollner illusion, we examined whether and how the degree of motion tilt is affected when form and motion components of the illusion are separated in depth. In Experiment 1 we showed that increasing the depth separation (by increasing binocular disparity) between the moving stimulus and oriented lines attenuated the motion-tilt effect. Motion tilt induction was observed for depth separations of -18 to 18 arcmin in uncrossed and crossed directions, but not at larger separations. In Experiment 2 we showed that motion tilt induction in the kinetic Zollner illusion was also observed when multiple oriented planes were presented in conjunction with a moving stimulus. However, the direction and extent of the illusory motion tilt was determined by the nearest oriented plane. Collectively, these findings show that the interaction of form and motion is dependent on depth and is optimally tuned for a small range of separations.

Grouping by closure influences subjective regularity and implicit preference

A reflection between a pair of contours is more rapidly detected than a translation, but this effect is stronger when the contours are closed to form a single object compared to when they are closed to form 2 objects with a gap between them. That is, grouping changes the relative salience of different regularities. We tested whether this manipulation would also change preference for reflection or translation. We measured preference for these patterns using the Implicit Association Test (IAT). On some trials, participants saw words that were either positive or negative and had to classify them as quickly as possible. On interleaved trials, they saw reflection or translation patterns and again had to classify them. Participants were faster when 1 button was used for reflection and positive words and another button was used for translation and negative words, compared to when the reverse response mapping was used (translation and positive vs. reflection and negative). This reaction time difference indicates an implicit preference for reflection over translation. However, the size of the implicit preference was significantly reduced in the Two-objects condition. We concluded that factors that affect perceptual sensitivity also systematically affect implicit preference formation.

Cognitive architecture of perceptual organization: from neurons to gnosons

What, if anything, is cognitive architecture and how is it implemented in neural architecture? Focusing on perceptual organization, this question is addressed by way of a pluralist approach which, supported by metatheoretical considerations, combines complementary insights from representational, connectionist, and dynamic systems approaches to cognition. This pluralist approach starts from a representationally inspired model which implements the intertwined but functionally distinguishable subprocesses of feedforward feature encoding, horizontal feature binding, and recurrent feature selection. As sustained by a review of neuroscientific evidence, these are the subprocesses that are believed to take place in the visual hierarchy in the brain. Furthermore, the model employs a special form of processing, called transparallel processing, whose neural signature is proposed to be gamma-band synchronization in transient horizontal neural assemblies. In neuroscience, such assemblies are believed to mediate binding of similar features. Their formal counterparts in the model are special input-dependent distributed representations, called hyperstrings, which allow many similar features to be processed in a transparallel fashion, that is, simultaneously as if only one feature were concerned. This form of processing does justice to both the high combinatorial capacity and the high speed of the perceptual organization process. A naturally following proposal is that those temporarily synchronized neural assemblies are "gnosons", that is, constituents of flexible self-organizing cognitive architecture in between the relatively rigid level of neurons and the still elusive level of consciousness.

Interactions between constituent single symmetries in multiple symmetry

As a rule, the discriminability of multiple symmetries from random patterns increases with the number of symmetry axes, but this number does not seem to be the only determinant. In particular, multiple symmetries with orthogonal axes seem better discriminable than multiple symmetries with nonorthogonal axes. In six experiments on imperfect two-fold symmetry, we investigated whether this is due to extra structure in the form of so-called correlation rectangles, which arise only in the case of orthogonal axes, or to the relative orientation of the axes as such. The results suggest that correlation rectangles are not perceptually relevant and that the percept of a multiple symmetry results from an orientation-dependent interaction between the constituent single symmetries. The results can be accounted for by a model involving the analysis of symmetry at all orientations, smoothing (averaging over neighboring orientations), and extraction of peaks.

Bayesian confusions surrounding simplicity and likelihood in perceptual organization

In the study of perceptual organization, the Occamian simplicity principle (which promotes efficiency) and the Helmholtzian likelihood principle (which promotes veridicality) have been claimed to be equivalent. Proposed models of these principles may well yield similar outcomes (especially in everyday situations), but as argued here, claims that the principles are equivalent confused subjective probabilities (which are used in Bayesian models of the Occamian simplicity principle) and objective probabilities (which are needed in Bayesian models of the Helmholtzian likelihood principle). Furthermore, Occamian counterparts of Bayesian priors and conditionals have led to another confusion, which seems to have been triggered by a dual role of regularity in perception. This confusion is discussed by contrasting complete and incomplete Occamian approaches to perceptual organization.

Sensitivity to Reflection and Translation is Modulated by Objectness

The salience of a transformation between a pair of contours depends on the type of transformation (eg a reflection or a translation) and also on figure – ground organisation. Reflection is most salient when both contours belong to the same surface, and translation is most salient when they do not connect a surface. These findings are based on reaction time (RT). Here I replicate and extend them by measuring both RT and sensitivity. The figure – ground relations were changed unambiguously by using stereograms. I compared reflection and translation when they were present within a surface or across surfaces (experiment 1), and within an object or a hole (experiments 2 – 4). Holes are interesting because they are not objects, but their presence does not increase the number of total objects in the scene. The within-surface advantage for reflection was present in all experiments. There was a between-surface advantage for translation in experiment 1 but there was no hole advantage for translation in experiments 2 – 4. Thus the effect of context, ie objectness, on detection of regularity is a robust and general phenomenon present in every experiment, but the type of interaction differs for reflection and translation.

Detection of (anti)symmetry and (anti)repetition: perceptual mechanisms versus cognitive strategies

Symmetry and repetition are recognized as cues in perceptual organization, but there is disagreement on whether they are detected automatically. This disagreement is resolved by noting that some studies mixed up shape regularities and shape antiregularities (i.e., symmetries and repetitions with mismatches in contour curvature polarity). The results of two experiments indicate that a task-irrelevant regularity is automatically picked up by the visual system, whereas a task-irrelevant antiregularity is not. This suggests that detection of regularities is part of the visual system's intrinsic encoding, whereas detection of antiregularities requires higher cognitive strategies involving selective attention.