Behind the Looking-Glass: A Review on Human Symmetry Perception
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paper_title: Goodness of visual regularities: A non-transformational approach

paper_content:

Until recently, the transformational approach provided the only available formal analysis of visual regularities like repetition and mirror symmetry. This theoretical study presents a new analysis, based on the recently developed concept of holographic regularity. This concept applies to the intrinsic character of regularity and specifies the unique formal status of perceptually relevant regularities. The crucial point is that the two analyses imply the same structure for repetition but a different structure for mirror symmetry. Transformationally, mirror symmetry is an all-or-nothing property, whereas holographically, it is a graded property. This difference pervades the understanding of both perfect regularities and perturbed regularities. Whereas the transformational approach explains hardly any goodness phenomenon, the holographic approach explains a wide variety of goodness phenomena in a coherent way that is ecologically plausible as well.
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paper_title: Visual signalling by asymmetry: a review of perceptual processes

paper_content:

Individual levels of asymmetry in traits that display fluctuating asymmetry could be used as visual signals of phenotypic (and perhaps genotypic) quality, as asymmetry can often be negatively related to fitness parameters. There are some data to support this hypothesis but the experimental protocols employed have commonly resulted in asymmetries far larger than those observed in nature. To date, there has been little consideration of the ability of animals to accurately discriminate small asymmetries (of the magnitude observed in the wild) from perfect symmetry. This is key to assessing the plausibility of the asymmetry-signalling hypothesis. Here, I review the perceptual processes that may lead to the discrimination of asymmetry and discuss a number of ecologically elevant factors that may influence asymmetry signalling. These include: signal orientation, distance of trait elements from the axis of symmetry, trait complexity, trait contrast and colour, and the behaviour of both signaller and receiver. I also discuss the evolution of symmetry preferences and make suggestions as to where researchers should focus attention to examine the generality of asymmetry-signalling theory. In highly developmentally stable signalling systems the magnitude of asymmetry may be too small to be detected accurately and reliably, hence asymmetry signalling is unlikely to have evolved in these situations.
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paper_title: Characteristics and models of human symmetry detection

paper_content:

Symmetry is everywhere - in natural objects, from crystals to living organisms, in manufactured articles of many kinds, and in art works from all cultures. Symmetry is a salient visual property that is detected efficiently and rapidly by the human visual system. In this paper, several decades of experimental research on human symmetry detection are reviewed. By examining the effects of several factors on symmetry detection, this research has revealed some important characteristics of how humans perceive symmetry. These characteristics constrain the general principles of putative underlying mechanisms and models of human symmetry detection. For example, the orientation of the axis of symmetry and its location in the visual field have effects that suggest that the bilateral symmetry of the visual system at cortical levels of the brain might partly determine the salience of vertical mirror symmetry. At the same time, there is a surprisingly high degree of flexibility and robustness that remains to be explained. Thus, symmetry provides a major challenge to model human flexibility and efficiency within the constraints of the biology of the visual system.
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paper_title: Human Symmetry Perception and Its Computational Analysis

paper_content:

Contents: Part I:Introduction. C.W. Tyler, Human Symmetry Perception. Part II:Empirical Evaluation of Symmetry Perception. J. Wagemans, Detection of Visual Symmetries. P. Wenderoth, The Role of Pattern Outline in Bilateral Symmetry Detection With Briefly Flashed Dot Patterns. K.E. Higgins, A. Arditi, K. Knoblauch, Detection and Identification of Mirror-Image Letter Pairs in Central and Peripheral Vision. P.T. Quinlan, Evidence for the Use of Scene-Based Frames of Reference in Two-Dimensional Shape Recognition. G. Leone, M. Lipshits, J. McIntyre, V. Gurfinkel, Independence of Bilateral Symmetry Detection From a Gravitational Reference Frame. J.P. Szlyk, I. Rock, C.B. Fisher, Level of Processing in the Perception of Symmetrical Forms Viewed From Different Angles. S. Hong, M. Pavel, Determinants of Symmetry Perception. C.W. Tyler, L. Hardage, Mirror Symmetry Detection: Predominance of Second-Order Pattern Processing Throughout the Visual Field. P.J. Passmore, A. Johnston, Human Discrimination of Surface Slant in Fractal and Related Textured Images. Part III:Theoretical Issues in Symmetry Analysis. S.C. Dakin, R.J. Watt, Detection of Bilateral Symmetry Using Spatial Filters. C. Latimer, W. Joung, C. Stevens, Modelling Symmetry Detection With Back-Propagation Networks. M.A. Kurbat, A Network Model for Generating Differential Symmetry Axes of Shapes Via Receptive Fields. I. Rentschler, E. Barth, T. Caelli, C. Zetzsche, M. Juttner, On the Generalization of Symmetry Relations in Visual Pattern Classification. F. Labonte, Y. Shapira, P. Cohen, J. Faubert, A Model for Global Symmetry Detection in Dense Images. H. Zabrodsky, D. Algom, Continuous Symmetry: A Model for Human Figural Perception. Y. Bonneh, D. Reisfeld, Y. Yeshurun, Quantification of Local Symmetry: Application to Texture Discrimination. J.S. Joseph, J.D. Victor, A Continuum of Non-Gaussian Self-Similar Image Ensembles With White Power Spectra. L.L. Kontsevich, Symmetry as a Depth Cue. T. Vetter, T. Poggio, Symmetric 3D Objects Are an Easy Case for 2D Object Recognition. L. Matin, W. Li, Mirror Symmetry and Parallelism: Two Opposite Rules for the Identity Transform in Space Perception and Their Unified Treatment by the Great Circle Model. J.R. Pani, The Generalized Cone in Human Spatial Organization.
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paper_title: Detection of visual symmetries.

paper_content:

—This paper reviews empirical evidence for the detection of visual symmetries and explanatory theories and models of symmetry detection. First, mirror symmetry is compared to other types of symmetry. The idea that symmetry detection is preattentive is then discussed and other roles that attention might play in symmetry detection are considered. The major part of the article consists of a critical examination of the extensive literature about the effects on symmetry detection of several major factors such as the orientation of the symmetry axis, the location of the stimulus in the visual field, grouping, and perturbations. Constraints on plausible models of symmetry detection are derived from this rich database and several proposals are evaluated against it. As a result of bringing this research together, open questions and remaining gaps to be filled by future research are identified.
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paper_title: Descriptive and evaluative judgment processes: Behavioral and electrophysiological indices of processing symmetry and aesthetics

paper_content:

Descriptive symmetry and evaluative aesthetic judgment processes were compared using identical stimuli in both judgment tasks. Electrophysiological activity was recorded while participants judged novel formal graphic patterns in a trial-by-trial cuing setting using binary responses (symmetric, not symmetric; beautiful, not beautiful). Judgment analyses of a Phase 1 test and main experiment performance resulted in individual models, as well as group models, of the participants’ judgment systems. Symmetry showed a strong positive correlation with beautiful judgments and was the most important cue. Descriptive judgments were performed faster than evaluative judgments. The ERPs revealed a phasic, early frontal negativity for the not-beautiful judgments. A sustained posterior negativity was observed in the symmetric condition. All conditions showed late positive potentials (LPPs). Evaluative judgment LPPs revealed a more pronounced right lateralization. It is argued that the present aesthetic judgments engage a two-stage process consisting of early, anterior frontomedian impression formation after 300 msec and right-hemisphere evaluative categorization around 600 msec after onset of the graphic patterns.
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paper_title: Visual signalling by asymmetry: a review of perceptual processes

paper_content:

Individual levels of asymmetry in traits that display fluctuating asymmetry could be used as visual signals of phenotypic (and perhaps genotypic) quality, as asymmetry can often be negatively related to fitness parameters. There are some data to support this hypothesis but the experimental protocols employed have commonly resulted in asymmetries far larger than those observed in nature. To date, there has been little consideration of the ability of animals to accurately discriminate small asymmetries (of the magnitude observed in the wild) from perfect symmetry. This is key to assessing the plausibility of the asymmetry-signalling hypothesis. Here, I review the perceptual processes that may lead to the discrimination of asymmetry and discuss a number of ecologically elevant factors that may influence asymmetry signalling. These include: signal orientation, distance of trait elements from the axis of symmetry, trait complexity, trait contrast and colour, and the behaviour of both signaller and receiver. I also discuss the evolution of symmetry preferences and make suggestions as to where researchers should focus attention to examine the generality of asymmetry-signalling theory. In highly developmentally stable signalling systems the magnitude of asymmetry may be too small to be detected accurately and reliably, hence asymmetry signalling is unlikely to have evolved in these situations.
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paper_title: Bilateral symmetry and sexual selection: a meta-analysis.

paper_content:

A considerable body of primary research has accumulated over the last 10 yr testing the relationship between developmental instability in the form of fluctuating asymmetry and performance of individuals in mating success itself or sexual attractiveness. This research comprises 146 samples from 65 studies of 42 species of four major taxa. We present the results of a meta-analysis of these studies, which demonstrates that there is indeed an overall significant, moderate negative relationship: for studies, the overall mean Pearson's r or effect size = -.42, P <.0005; for species, the overall mean r = -.34, .01 < P < .025. Based on calculated fail-safe numbers, the effect-size estimates are highly robust against any publication or reporting bias that may exist. There is considerable evidence that the magnitude of the negative correlation between fluctuating asymmetry and success related to sexual selection is greater for males than for females, when a secondary sexual trait rather than an ordinary trait is studied, with experimentation compared with observation, and for traits not involved with mobility compared with traits affecting mobility. There is also limited evidence that higher taxa may differ in effect size and that intensity of sexual selection negatively correlates with effect size.
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paper_title: Affordance and symmetry in user interfaces

paper_content:

Affordance is a widely used term in human–computer interaction (HCI) that, while familiar and attractive, does not have a clear operational definition. Using the mathematical concept of symmetry, this paper shows that it is possible to begin developing an operational definition for significant aspects of affordance by forming the theoretical concept of symmetry-affordance. The proposed definition restricts symmetry-affordance to particular contexts but in doing so makes it more useful, as it is clear how to exploit symmetry to aid design. The definition is in standard mathematics (in fact, group theory and model theory) and requires little additional structure. In examining symmetry-affordance, it becomes clear that some other HCI notions can be similarly interpreted by symmetry. The paper provides examples and design insights. ::: Symmetry, as wide or as narrow as you may define its meaning, is one idea by which man through the ages has tried to comprehend and create order, beauty, and perfection. Hermann Weyl [(1952) Symmetry, Princeton University Press, Princeton, NJ]
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paper_title: Symmetry perception in an insect

paper_content:

Symmetrical visual patterns have a salient status in human perception, as evinced by their prevalent occurrence in art, and also in animal perception, where they may be an indicator of phenotypic and genotypic quality. Symmetry perception has been demonstrated in humans, birds, dolphins and apes. Here we show that bees trained to discriminate bilaterally symmetrical from non-symmetrical patterns learn the task and transfer it appropriately to novel stimuli, thus demonstrating a capacity to detect and generalize symmetry or asymmetry. We conclude that bees, and possibly flower-visiting insects in general, can acquire a generalized preference towards symmetrical or, alternatively, asymmetrical patterns depending on experience, and that symmetry detection is preformed or can be learned as perceptual category by insects, because it can be extracted as an independent visual pattern feature. Bees show a predisposition for learning and generalized symmetry because, if trained to it, they choose it more frequently, come closer to and hover longer in front of the novel symmetrical stimuli than the bees trained for asymmetry do for the novel asymmetrical stimuli. Thus, even organisms with comparatively small nervous systems can generalize about symmetry, and favour symmetrical over asymmetrical patterns.
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paper_title: Facial attractiveness, symmetry and cues of good genes

paper_content:

Cues of phenotypic condition should be among those used by women in their choice of mates. One marker of better phenotypic condition is thought to be symmetrical bilateral body and facial features. However, it is not clear whether women use symmetry as the primary cue in assessing the phenotypic quality of potential mates or whether symmetry is correlated with other facial markers affecting physical attractiveness. Using photographs of men's faces, for which facial symmetry had been measured, we found a relationship between women's attractiveness ratings of these faces and symmetry, but the subjects could not rate facial symmetry accurately. Moreover, the relationship between facial attractiveness and symmetry was still observed, even when symmetry cues were removed by presenting only the left or right half of faces. These results suggest that attractive features other than symmetry can be used to assess phenotypic condition. We identified one such cue, facial masculinity (cheek-bone prominence and a relatively longer lower face), which was related to both symmetry and full- and half-face attractiveness.
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paper_title: Human (Homo sapiens) facial attractiveness and sexual selection: the role of symmetry and averageness.

paper_content:

We hypothesized from the parasite theory of sexual selection that men (Homo sapiens) would prefer averageness and symmetry in women's faces, that women would prefer averageness and symmetry in men's faces, and that women would prefer largeness (not averageness) of the secondary sexual traits of men's faces. We generated computer images of men's and women's faces and of composites of the faces of each sex, and then had men and women rate opposite-sex faces for 4 variables (attractive, dominant, sexy, and healthy). Symmetry, averageness, and the sizes of facial features were measured on the computerized faces. The hypotheses were supported, with the exception of the hypothesized effects of averageness of female and male faces on attractiveness ratings. This is the first study to show that facial symmetry has a positive influence on facial attractiveness ratings. Although adult facial attractiveness ratings are replicable, even cross-culturally (see reviews and discussions in Jones & Hill, 1993, and Langlois & Roggman, 1990), there has been considerable controversy around attempts to identify in research the facial features that actually cause faces to be judged attractive or unattractive. As discussed by Langlois and Roggman, studies of individual facial features (e.g., nose size) often have yielded inconsistent results between studies. Faces created by combining individual faces into composites have been shown to be more attractive than the individual faces, which is felt to be a preference for average facial features (Langlois & Roggman, 1990; Symons, 1979). Averageness effaces can be calculated metrically or constructed photogrammetrically. Gallon (1879) constructed composites of individual pictures with the photographic method of simply projecting them one over the other on a negative. According to Gallon, this method "enables us to obtain with mechanical precision a generalized picture; one that represents no man in particular, but portrays an imaginary figure possessing the average features of any given group of man" (1879, p. 341). Indeed, Treu (1914) had the impression that these composites are "singularly beautiful" (p. 441). However, as Alley and Cunningham (1991; see also Benson & Perrett, 1991) pointed out, composites are also more symmetrical and rather free of
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paper_title: Categorization of visual stimuli in the honeybee Apis mellifera

paper_content:

Categorization refers to the classification of perceptual input into defined functional groups. We present and discuss evidence suggesting that stimulus categorization can also be found in an invertebrate, the honeybee Apis mellifera, thus underlining the generality across species of this cognitive process. Honeybees show positive transfer of appropriate responding from a trained to a novel set of visual stimuli. Such a transfer was demonstrated for specific isolated features such as symmetry or orientation, but also for assemblies (layouts) of features. Although transfer from training to novel stimuli can be achieved by stimulus generalization of the training stimuli, most of these transfer tests involved clearly distinguishable stimuli for which generalization would be reduced. Though in most cases specific experimental controls such as stimulus balance and discriminability are still required, it seems appropriate to characterize the performance of honeybees as reflecting categorization. Further experiments should address the issue of which categorization theory accounts better for the visual performances of honeybees.
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paper_title: Aesthetic issues in spatial composition: effects of position and direction on framing single objects

paper_content:

Artists who work in two-dimensional visual media regularly face the problem of how to compose their subjects in aesthetically pleasing ways within a surrounding rectangular frame. We performed psychophysical investigations of viewers' aesthetic preferences for the position and facing direction of single, directed objects (e.g. people, cars, teapots and flowers) within such rectangular frames. Preferences were measured using two-alternative forced-choice preference judgments, the method of adjustment, and free choice in taking photographs. In front-facing conditions, preference was greatest for pictures whose subject was located at or near the center of the frame and decreased monotonically and symmetrically with distance from the center (the center bias). In the left- or right-facing conditions, there was an additional preference for objects to face into rather than out of the frame (the inward bias). Similar biases were evident using a method of adjustment, in which participants positioned objects along a horizontal axis, and in free choice photographs, in which participants were asked to take 'the most aesthetically pleasing picture' they could of everyday objects. The results are discussed as affirming the power of the center and facing direction in the aesthetic biases viewers bring to their appreciation of framed works of visual art (e.g. Alexander, 2002; Arnheim, 1988).
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paper_title: Physical Attractiveness and Health: Comment on Weeden and Sabini (2005)

paper_content:

Evolutionary behavioral biology suggests that certain characteristics of the human face and body areimportant for mate preferences and are therefore subject to sexual selection. J. Weeden and J. Sabini(2005) identify a number of weaknesses in the association between traits’ attractiveness and health. Incontrast, the authors argue that (a) studies on preferences for physical characteristics that rely on 1 traitpermit only limited interpretation, (b) limitations placed on J. Weeden and J. Sabini’s review excludeimportant associations, (c) there are misconceptions in their treatment of some traits, and (d) theirselected literature provides an inaccurate picture regarding effect size. The authors suggest that futureresearch in this field should seek conceptual and methodological constancy in trait selection and in theevaluation of attractiveness- and health-related traits.
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paper_title: Darwinian aesthetics: sexual selection and the biology of beauty

paper_content:

Current theoretical and empirical findings suggest that mate preferences are mainly cued on visual, vocal and chemical cues that reveal health including developmental health. Beautiful and irresistible features have evolved numerous times in plants and animals due to sexual selection, and such preferences and beauty standards provide evidence for the claim that human beauty and obsession with bodily beauty are mirrored in analogous traits and tendencies throughout the plant and animal kingdoms. Human beauty standards reflect our evolutionary distant and recent past and emphasize the role of health assessment in mate choice as reflected by analyses of the attractiveness of visual characters of the face and the body, but also of vocal and olfactory signals. Although beauty standards may vary between cultures and between times, we show in this review that the underlying selection pressures, which shaped the standards, are the same. Moreover we show that it is not the content of the standards that show evidence of convergence – it is the rules or how we construct beauty ideals that have universalities across cultures. These findings have implications for medical, social and biological sciences.
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paper_title: Visual Symmetry Recognition by Pigeons

paper_content:

Pigeons learned to discriminate a large number of bilateral symmetric and asymmetric visual patterns successively projected on the pecking-key of an operant conditioning chamber. Responses to the positive stimuli were reinforced according to a variable interval schedule. Once acquisition was complete generalization trials, involving sets of new stimuli, were instituted under extinction. The birds classified these novel test stimuli with high accuracy throughout, according to their symmetry or asymmetry. Their performance was not disturbed by sets of test stimuli whose geometrical style differed considerably from the training stimuli. Pigeons were even able to discriminate when only allowed the use of one eye. The generalization series were partly designed to test some classical symmetry recognition theories. None was found to be adequate. Subsidiary experiments suggested that most pigeons have a slight spontaneous preference for asymmetric patterns and that symmetry/asymmetry differences can aid pattern discrimination learning at an early stage. It is concluded that pigeons, much like humans, can discriminate bilaterally symmetric from non-symmetric visual forms in a concept-like, generalizing way. The ontogenetic and phylogenetic development of this competence is considered. A novel symmetry recognition hypothesis based on spatial frequency analysis and neuronal feature-detector considerations is proposed.
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paper_title: Brain correlates of aesthetic judgment of beauty

paper_content:

Functional MRI was used to investigate the neural correlates of aesthetic judgments of beauty of geometrical shapes. Participants performed evaluative aesthetic judgments (beautiful or not?) and descriptive symmetry judgments (symmetric or not?) on the same stimulus material. Symmetry was employed because aesthetic judgments are known to be often guided by criteria of symmetry. Novel, abstract graphic patterns were presented to minimize influences of attitudes or memory-related processes and to test effects of stimulus symmetry and complexity. Behavioral results confirmed the influence of stimulus symmetry and complexity on aesthetic judgments. Direct contrasts showed specific activations for aesthetic judgments in the frontomedian cortex (BA 9/10), bilateral prefrontal BA 45/47, and posterior cingulate, left temporal pole, and the temporoparietal junction. In contrast, symmetry judgments elicited specific activations in parietal and premotor areas subserving spatial processing. Interestingly, beautiful judgments enhanced BOLD signals not only in the frontomedian cortex, but also in the left intraparietal sulcus of the symmetry network. Moreover, stimulus complexity caused differential effects for each of the two judgment types. Findings indicate aesthetic judgments of beauty to rely on a network partially overlapping with that underlying evaluative judgments on social and moral cues and substantiate the significance of symmetry and complexity for our judgment of beauty.
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paper_title: Visual signalling by asymmetry: a review of perceptual processes

paper_content:

Individual levels of asymmetry in traits that display fluctuating asymmetry could be used as visual signals of phenotypic (and perhaps genotypic) quality, as asymmetry can often be negatively related to fitness parameters. There are some data to support this hypothesis but the experimental protocols employed have commonly resulted in asymmetries far larger than those observed in nature. To date, there has been little consideration of the ability of animals to accurately discriminate small asymmetries (of the magnitude observed in the wild) from perfect symmetry. This is key to assessing the plausibility of the asymmetry-signalling hypothesis. Here, I review the perceptual processes that may lead to the discrimination of asymmetry and discuss a number of ecologically elevant factors that may influence asymmetry signalling. These include: signal orientation, distance of trait elements from the axis of symmetry, trait complexity, trait contrast and colour, and the behaviour of both signaller and receiver. I also discuss the evolution of symmetry preferences and make suggestions as to where researchers should focus attention to examine the generality of asymmetry-signalling theory. In highly developmentally stable signalling systems the magnitude of asymmetry may be too small to be detected accurately and reliably, hence asymmetry signalling is unlikely to have evolved in these situations.
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paper_title: Foundations of Cyclopean Perception

paper_content:

This classic work on cyclopean perception has influenced a generation of vision researchers, cognitive scientists, and neuroscientists and has inspired artists, designers, and computer graphics pioneers. In Foundations of Cyclopean Perception (first published in 1971 and unavailable for years), Bela Julesz traced the visual information flow in the brain, analyzing how the brain combines separate images received from the two eyes to produce depth perception. Julesz developed novel tools to do this: random-dot stereograms and cinematograms, generated by early digital computers at Bell Labs. These images, when viewed with the special glasses that came with the book, revealed complex, three-dimensional surfaces; this mode of visual stimulus became a paradigm for research in vision and perception. This reprint edition includes all 48 color random-dot designs from the original, as well as the special 3-D glasses required to view them.Foundations of Cyclopean Perception has had a profound impact on the vision studies community. It was chosen as one of the one hundred most influential works in cognitive science in a poll conducted by the University of Minnesota's Center for Cognitive Sciences. Many copies are "permanently borrowed" from college libraries; used copies are sought after online. Now, with this facsimile of the 1971 edition, the book is available again to cognitive scientists, neuroscientists, vision researchers, artists, and designers.
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paper_title: Orientational effects and component processes in symmetry detection

paper_content:

In previous research on symmetry detection, factors contributing to orientational effects (axis and virtual lines connecting symmetrically positioned dots) and component processes (axis selection and pointwise evaluation) have always been confounded. The reason is the restriction to bilateral symmetry (BS), with pointwise correspondences being orthogonal to the axis of symmetry. In our experiments, subjects had to discriminate random dot patterns from symmetries defined by combining 12 axis orientations (every 15°) with seven reflection angles (0°, yielding BS, and three clockwise and counterclockwise 15° steps, yielding skewed symmetry, SS). In Experiment 1, with completely randomized trial order, a significant interaction between axis and skewing angle was obtained, indicating that classically observed orientational effects are restricted to BS and that the orientation of the pointwise correspondences is important. These basic findings were replicated in three subsequent experiments, which differed in t...
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paper_title: Goodness of visual regularities: A non-transformational approach

paper_content:

Until recently, the transformational approach provided the only available formal analysis of visual regularities like repetition and mirror symmetry. This theoretical study presents a new analysis, based on the recently developed concept of holographic regularity. This concept applies to the intrinsic character of regularity and specifies the unique formal status of perceptually relevant regularities. The crucial point is that the two analyses imply the same structure for repetition but a different structure for mirror symmetry. Transformationally, mirror symmetry is an all-or-nothing property, whereas holographically, it is a graded property. This difference pervades the understanding of both perfect regularities and perturbed regularities. Whereas the transformational approach explains hardly any goodness phenomenon, the holographic approach explains a wide variety of goodness phenomena in a coherent way that is ecologically plausible as well.
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paper_title: Higher-order structure in regularity detection

paper_content:

In three experiments a simple Euclidean transformation (reflection, translation, rotation) was applied to collections of twelve dots in such a way that they contained equal lower-order structure, defined on the pairwise grouping of elements with their partner following transformation (e.g. parallel virtual lines), but differed in the presence vs absence of higher-order structure, defined on pairs of pairwise groupings (e.g. virtual quadrangles with correlated angles). Based on the much better performance levels (d′) in the case of additional higher-order structure, we conclude that global regularities are easier to detect when the local correspondences are supported by higher-order ones formed between them. These enable the lower-order groupings to spread out across the whole pattern very rapidly (called bootstrapping). As a preliminary attempt to specify these principles, we proposed a working model with two basic components: first, a function expressing the cost of a perceptual grouping or the lack of regularity, and, secondly, an algorithm based on simulated annealing to minimize the cost function. The simulation results obtained with our current implementation of these principles showed satisfactory qualitative agreement with human regularity detection performance. Finally, the theory was shown to capture the essence of a large number of grouping phenomena taken from diverse domains such as detection of symmetry in dot patterns, global structure in Glass and vector patterns, correspondence in stereoscopic transparency and apparent motion. Therefore, we are convinced that, in principle, the mechanism used by the human visual system to detect regularity incorporates something like bootstrapping based on higher-order structure. We regard this as a promising step towards unraveling the intriguing mechanisms of classic Gestalt phenomena.
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paper_title: Detection of symmetry and repetition in one and two objects. Structures versus strategies.

paper_content:

Symmetry is usually easier to detect within a single object than in two objects (one-object advantage), while the reverse is true for repetition (two-objects advantage). This interaction between regularity and number of objects could reflect an intrinsic property of encoding spatial relations within and across objects or it could reflect a matching strategy. To test this, regularities between two contours (belonging to a single object or two objects) had to be detected in two experiments. Projected three-dimensional (3-D) objects rotated in depth were used to disambiguate figure-ground segmentation and to make matching based on simple translations of the two-dimensional (2-D) contours unlikely. Experiment 1 showed the expected interaction between regularity and number of objects. Experiment 2 used two-objects displays only and prevented a matching strategy by also switching the positions of the two objects. Nevertheless, symmetry was never detected more easily than repetition in these two-objects displays. We conclude that structural coding, not matching strategies, underlies the one-object advantage for symmetry and the two-objects advantage for repetition.
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paper_title: Symmetry and repetition in perspective

paper_content:

Although ecologically relevant, perspective views of symmetries and repetitions have hardly been investigated. Any symmetry or repetition that is not oriented orthogonally to the line of sight yields perspective distortions on the retina. In this study, these distortions are analyzed in terms of first-order structures (i.e., virtual lines between corresponding points) and second-order structures (i.e., correlation quadrangles formed by two virtual lines). In the literature, these structures have been proposed to guide the detection of frontoparallel symmetry and repetition. But what about perspective views? First, the analysis in this study shows that perspective distorts the retinal first-order and second-order structures of symmetry and repetition differently. Second, the results of two experiments on this distortion difference suggest that, in perspective views, symmetry and repetition detection is not preceded by normalization but occurs directly on the basis of the retinal first-order and second-order structures.
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paper_title: Detection of visual symmetries.

paper_content:

—This paper reviews empirical evidence for the detection of visual symmetries and explanatory theories and models of symmetry detection. First, mirror symmetry is compared to other types of symmetry. The idea that symmetry detection is preattentive is then discussed and other roles that attention might play in symmetry detection are considered. The major part of the article consists of a critical examination of the extensive literature about the effects on symmetry detection of several major factors such as the orientation of the symmetry axis, the location of the stimulus in the visual field, grouping, and perturbations. Constraints on plausible models of symmetry detection are derived from this rich database and several proposals are evaluated against it. As a result of bringing this research together, open questions and remaining gaps to be filled by future research are identified.
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paper_title: Detection of symmetry in tachistoscopically presented dot patterns: Effects of multiple axes and skewing

paper_content:

We examined the effects of multiple axes and skewing on the detectability of symmetry in tachistoscopically presented (100-msec) dot patterns to test the role of normal grouping processes based on higher order regularities in element positions. In addition to the first-order regularities of orientational uniformity and midpoint collinearity (Jenkins, 1983), bilateral symmetry (BS) gives rise to second-order relations between two pairs of symmetric elements (represented by correlation quadrangles). We suggest that they allow the regularity (i.e., BS) to emerge simply as a result of the position-based grouping that takes place normally, so that no special symmetry-detection mechanism has to be postulated. In combination with previously investigated variables— number and orientation of axes—we introduced skewing (resulting from orthographic projection of BS) to manipulate the kind and number of higher order regularities. In agreement with our predictions, the data show that the effect of skewing angle (varied at three 15° steps, clockwise and counterclockwise) on the preattentive detectability of symmetry (measured with d’) increases as the number of axes decreases. On the basis of some more specific findings, we suggest that it is not as much the number of correlation quadrangles that determines the saliency of a regularity as it is the degree to which they facilitate or “bootstrap” each other.
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paper_title: The Yin and the Yang of visuo-spatial neglect: A case study

paper_content:

Abstract We report a patient (R.B.) who has shown gross left visuo-spatial neglect over the 3 years since he sustained a right parietal infarct. Although his neglect is severe on such tasks as line bisection, cancellation, and drawing, there are some domains of preserved perceptual performance: he can perceive subjective contours, he can use lateral symmetry as a cue to figure-ground segregation, and he benefits from some forms of global cueing. In a series of five experiments, we show that R.B. has a selective inability to analyse and copy accurately the left contours of geometric nonsense-figures. These results hold even when there is a single vertical contour (to be copied) that divides a rectangle or a circle into two sub-figures; this physically-identical boundary is copied more accurately when it is cued as the right edge of the left sub-figure than when it is cued as the left edge of the right sub-figure. These effects are not influenced by a manipulation in which R.B. is required to trace the outline of the relevant sub-figure with his finger immediately prior to drawing his copy. The results are interpreted in terms of classical Gestalt theories of figure-ground assignment. Pre-attentive (global) figure-ground parsing is basically intact; but when focal attention is demanded, only the right side of an object is coded as figure.
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paper_title: From Interpretation to Segmentation

paper_content:

In visual perception, part segmentation of an object is considered to be guided by image-based properties, such as occurrences of deep concavities in the outer contour. However, object-based properties can also provide information regarding segmentation. In this study, outer contours and interpretations of object configurations were manipulated to examine differences between image-based and object-based segmentation in a visual search task. We found that locating a two-dimensional object configuration with deep concavities in the outer contour depends on the type of outer contour of the surrounding distractors. In addition, locating a three-dimensional object configuration was harder when it was surrounded by object-based-disconnected distractors, as compared with object-based-connected distractors, regardless of image-based connections in these distractors. We conclude that segmentation based on the outer contours of a target facilitates its localization. However, when three-dimensional information is available, segmentation strongly depends on object-based properties, rather than on image-based properties.
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paper_title: Concavities count for less in symmetry perception

paper_content:

We investigated the relative importance of convexities (protrusions) and concavities (indentations) for the perception of shape. On the one hand, it has been suggested that convexities determine the shape of an object, whereas concavities merely act as “perceptual glue” between the convexities. On the other hand, it has been argued that concavities are more salient than convexities. We show that participants find it easier to detect asymmetry in a 2-D silhouette when there is a mismatch between the shapes of convexities on either side of the axis of symmetry than when there is a mismatch between the shapes of concavities. This is the case even when the concavities are closest to the axis of symmetry, and despite the usual bias toward this axis in symmetry perception. We suggest that the actual shape of concavities is less important in symmetry perception, because the main role of concavities is to act as part boundaries in the representation of the shape of objects.
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paper_title: Detection of symmetry and perceptual organization: The way a lock-and-key process works

paper_content:

Abstract We studied the speed with which observers could detect symmetry in drawings that incorporated symmetric contours — related by reflection or translation — within single objects or across different objects. We asked observers to perform a speeded decision whether pairs of contours are the same, i.e., related by reflection or by translation, or different. When the contours belong to a single object, observers are faster to see the relation between contours when they are related by reflection than by translation. When the contours belong to different objects, observers are faster to see the relation between the contours when they are related by translation than by reflection. We tested whether this advantage of translation is due to a lock-and-key process. We first tested our hypothesis by manipulating the correspondence of the features, so as to make matching more difficult. This change did not produce the predicted pattern of results. We performed a second manipulation to change the appearance of the objects: we increased the pragnanz of the objects by changing the type of lines used to connect the contours. Results indicate that perceptual organization can alter the detectability of symmetry.
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paper_title: Mental rotation depends on the number of objects rather than on the number of image fragments

paper_content:

It is often intuitively assumed that disconnected image fragments result in a representation of separate objects. When objects are partly occluded, disconnected image fragments can still result in a representation of a single object, based on visual completion. In a simultaneous matching task, displays showing one object, partly occluded objects, or two objects were compared with each other. When only a translation was required to match pairs of displays, one-object displays were matched faster than both occluded-object and two-object displays, which did not differ significantly from each other. When mental rotation and translation were required, the one-object displays were again matched the fastest. In addition, an advantage for occluded-object displays compared with two-object displays was found. We conclude that when the generation of a mental representation is likely, object-based connectedness determines object matching. Mental rotation then seems to depend on the number of objects rather than on the number of image fragments.
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paper_title: Perception of three-dimensional structure from motion

paper_content:

Abstract The ability to perceive the 3-D shape of objects solely from motion cues is referred to as structure-from-motion perception. Recent experiments indicate how this remarkable perceptual attribute is computed by the brains of primates. This computation proceeds in at least two stages, one in which motion measurements are made and another in which moving surfaces are reconstructed. The middle temporal area (MT) in the macaque monkey appears to play a pivotal role in the latter step and suggests a previously unappreciated function for this well-known cortical region, which had previously been thought to play a more rudimentary role in simply signaling the direction of motion of images.
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paper_title: THE KINETIC DEPTH EFFECT

paper_content:

The problem of how three-dimensional form is perceived in spite of the fact that pertinent stimulation consists only in two-dimensional retinal images has been only partly solved. Much is known about the impressive effectiveness of binocular disparity. However, the excellent perception of threedimensional form in monocular vision has remained essentially unexplained. It has been proposed that some patterns of stimulation on the retina give rise to three-dimensional experiences, because visual processes differ in the spontaneous organization that results from certain properties of the retinal pattern. Rules of organization are supposed to exist according to which most retinal projections of three-dimensional forms happen to produce three-dimensional percepts and most retinal images of flat forms lead to flat forms in experience also. This view has been held mainly by gestalt psychologists. Another approach to this problem maintains that the projected stimulus patterns are interpreted on the basis of previous experience, either visual
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paper_title: Integration of structure-from-motion and symmetry during surface perception

paper_content:

Sinusoidal motion of elements in a random-dot pattern can elicit a striking percept of a rotating volume, a phenomenon known as structure-from-motion (SFM). We demonstrate that if the dots defining the volume are 2D mirror-symmetric, novel 3D interpretations arise. In addition to the classical rotating cylinder, one can perceive mirror-symmetric, flexible surfaces bending along the path of movement. In three experiments, we measured the perceptual durations of the different interpretations in a voluntary control task. The results suggest that motion signals and symmetry signals are integrated during surface interpolation. Furthermore, the competition between the rotating cylinder percept and the symmetric surfaces percept is resolved at the level of surface perception rather than at the level of individual stimulus elements. Concluding, structure-from-motion is an interactive process that incorporates not only motion cues but also form cues. The neurofunctional implication of this is that surface interpolation is not fully completed in its designated neural “engine,” MT/V5, but rather in a higher tier area such as LOC, which receives input from MT/V5 and which is also involved in symmetry detection.
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paper_title: Symmetry versus repetition in cyclopean vision: A microgenetic analysis

paper_content:

In four experiments, participants had to detect symmetries or repetitions distributed over two depth planes, under presentation times of 200-1000 ms. Structurally corresponding elements were placed in different planes (Experiments la and 1b) or in the same plane (Experiments 2a and 2b). Results suggest (a) an ongoing interaction between regularity cues and depth cues, and (b) that efficient detection of symmetry but not of repetition depends on structural correspondences within depth planes. The latter confirms the idea that, to perceptual organization, symmetry is a cue for the presence of one object, whereas repetition is a cue for the presence of multiple objects.
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paper_title: Object-based connectedness facilitates matching

paper_content:

In two matching tasks, participants had to match two images of object pairs. Image-based (IB) connectedness refers to connectedness between the objects in an image. Object-based (OB) connectedness refers to connectedness between the interpreted objects. In Experiment 1, a monocular depth cue (shadow) was used to distinguish different relation types between object pairs. Three relation types were created: IB/OB-connected objects, IB/OB-disconnected objects, and IB-connected/OB-disconnected objects. It was found that IB/OB-connected objects were matched faster than IB/OB-disconnected objects. Objects that were IB-connected/OB-disconnected were matched equally to IB/OB-disconnected objects. In Experiment 2, stereoscopic presentation was used. With relation types comparable to those in Experiment 1, it was again found that OB connectedness determined speed of matching, rather than IB connectedness. We conclude that matching of projections of three-dimensional objects depends more on OB connectedness than on IB connectedness.
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paper_title: Detection of symmetry and repetition in one and two objects. Structures versus strategies.

paper_content:

Symmetry is usually easier to detect within a single object than in two objects (one-object advantage), while the reverse is true for repetition (two-objects advantage). This interaction between regularity and number of objects could reflect an intrinsic property of encoding spatial relations within and across objects or it could reflect a matching strategy. To test this, regularities between two contours (belonging to a single object or two objects) had to be detected in two experiments. Projected three-dimensional (3-D) objects rotated in depth were used to disambiguate figure-ground segmentation and to make matching based on simple translations of the two-dimensional (2-D) contours unlikely. Experiment 1 showed the expected interaction between regularity and number of objects. Experiment 2 used two-objects displays only and prevented a matching strategy by also switching the positions of the two objects. Nevertheless, symmetry was never detected more easily than repetition in these two-objects displays. We conclude that structural coding, not matching strategies, underlies the one-object advantage for symmetry and the two-objects advantage for repetition.
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paper_title: The versatility and absolute efficiency of detecting mirror symmetry in random dot displays

paper_content:

The detection of mirror symmetry has been investigated by measuring discriminability (d') between two populations of dot displays that contain mirror pairs and random dots in different proportions. The difficulty of the task was varied by changing the proportions of paired dots in the two populations, and also by changing the accuracy of positioning the paired dots. Symmetry can be detected in brief exposures, monocularly or binocularly. when the axis is not vertical, and when the axis is not central in the visual field. The mechanism is therefore versatile. Its efficiency can be measured when the pairing is imperfect, for unpaired dots then fall where a pair is expected, thus causing the spurious appearance of a pair. When the pairing has an accuracy of about± 6′ vertically and horizontally an ideal mechanism would achieved′ values about double those attained by subjects; they are thus using 25% of the statistical information available, which is a high figure considering the versatility and complexity of the mechanisms required.
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paper_title: Integration of structure-from-motion and symmetry during surface perception

paper_content:

Sinusoidal motion of elements in a random-dot pattern can elicit a striking percept of a rotating volume, a phenomenon known as structure-from-motion (SFM). We demonstrate that if the dots defining the volume are 2D mirror-symmetric, novel 3D interpretations arise. In addition to the classical rotating cylinder, one can perceive mirror-symmetric, flexible surfaces bending along the path of movement. In three experiments, we measured the perceptual durations of the different interpretations in a voluntary control task. The results suggest that motion signals and symmetry signals are integrated during surface interpolation. Furthermore, the competition between the rotating cylinder percept and the symmetric surfaces percept is resolved at the level of surface perception rather than at the level of individual stimulus elements. Concluding, structure-from-motion is an interactive process that incorporates not only motion cues but also form cues. The neurofunctional implication of this is that surface interpolation is not fully completed in its designated neural “engine,” MT/V5, but rather in a higher tier area such as LOC, which receives input from MT/V5 and which is also involved in symmetry detection.
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paper_title: On the Role of Symmetry in Visual Search

paper_content:

It is known that the efficiency of visual search for a target item among distractor items increases when distractors are similar to each other and decreases when target and distractors are similar. Here we show that symmetry relations between targets and distractors can alter search efficiency. When distractors form a background texture symmetrical about a vertical axis, search is easier than when they do not. In contrast, when some distractors are symmetrical with the target, search is more difficult than when they are not. These results suggest (1) that symmetry relations are processed in parallel and can help to distinguish a target from a distracting background and (2) that stimulus similarity can have several components even for a single feature (here, orientation).
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paper_title: Global Detection of Symmetry

paper_content:

Two experimental approaches examined observers' ability to characterize shape symmetry based upon the information obtained within a single fixation. Exp. I tested observers' ability to discriminate among three levels of symmetry on the basis of a 25-msec. presentation. Results indicated that identification accuracy was higher for symmetrical and asymmetrical shapes than for mixed shapes, which contained both symmetrical and asymmetrical components. Exp. II tested observers' ability to detect a given level of symmetry by means of a signal-detection approach. Symmetrical shapes were detected better than asymmetrical shapes. Detectability of mixed shapes was lower than that for both symmetrical and asymmetrical shapes. The results of Exps. I and II demonstrate that observers can characterize shape symmetry on the basis of information available within a single fixation. The data are supportive of the hypothesis that a global response to the over-all configuration of the shape serves to facilitate form perception.
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paper_title: Detection of symmetry in tachistoscopically presented dot patterns: Effects of multiple axes and skewing

paper_content:

We examined the effects of multiple axes and skewing on the detectability of symmetry in tachistoscopically presented (100-msec) dot patterns to test the role of normal grouping processes based on higher order regularities in element positions. In addition to the first-order regularities of orientational uniformity and midpoint collinearity (Jenkins, 1983), bilateral symmetry (BS) gives rise to second-order relations between two pairs of symmetric elements (represented by correlation quadrangles). We suggest that they allow the regularity (i.e., BS) to emerge simply as a result of the position-based grouping that takes place normally, so that no special symmetry-detection mechanism has to be postulated. In combination with previously investigated variables— number and orientation of axes—we introduced skewing (resulting from orthographic projection of BS) to manipulate the kind and number of higher order regularities. In agreement with our predictions, the data show that the effect of skewing angle (varied at three 15° steps, clockwise and counterclockwise) on the preattentive detectability of symmetry (measured with d’) increases as the number of axes decreases. On the basis of some more specific findings, we suggest that it is not as much the number of correlation quadrangles that determines the saliency of a regularity as it is the degree to which they facilitate or “bootstrap” each other.
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paper_title: Prediction of Human Eye Fixations using Symmetry

paper_content:

Humans are very sensitive to symmetry in visual patterns. Reaction time experiments show that symmetry is detected and recognized very rapidly. This suggests that symmetry is a highly salient feature. Existing computational models of saliency, however, have mainly focused on contrast as a measure of saliency. In this paper, we discuss local symmetry as a measure of saliency. We propose a number of symmetry models and perform an eye-tracking study with human participants viewing photographic images to test the models. The performance of our symmetry models is compared with the contrast-saliency model of Itti, Koch and Niebur (1998). The results show that the symmetry models better match the human data than the contrast model, which indicates that symmetry can be regarded as a salient feature.
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paper_title: The Yin and the Yang of visuo-spatial neglect: A case study

paper_content:

Abstract We report a patient (R.B.) who has shown gross left visuo-spatial neglect over the 3 years since he sustained a right parietal infarct. Although his neglect is severe on such tasks as line bisection, cancellation, and drawing, there are some domains of preserved perceptual performance: he can perceive subjective contours, he can use lateral symmetry as a cue to figure-ground segregation, and he benefits from some forms of global cueing. In a series of five experiments, we show that R.B. has a selective inability to analyse and copy accurately the left contours of geometric nonsense-figures. These results hold even when there is a single vertical contour (to be copied) that divides a rectangle or a circle into two sub-figures; this physically-identical boundary is copied more accurately when it is cued as the right edge of the left sub-figure than when it is cued as the left edge of the right sub-figure. These effects are not influenced by a manipulation in which R.B. is required to trace the outline of the relevant sub-figure with his finger immediately prior to drawing his copy. The results are interpreted in terms of classical Gestalt theories of figure-ground assignment. Pre-attentive (global) figure-ground parsing is basically intact; but when focal attention is demanded, only the right side of an object is coded as figure.
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paper_title: Does symmetry structure facilitate the depth separation between stereoscopically overlapped dot planes

paper_content:

In the present study, we dealt with the problem of whether a symmetrical structure can influence the discrimination of the depth separation of overlapped dot planes. We investigated this problem with the use of both direct and indirect methods. In the direct method, we presented three or two overlapped dot planes consisting of symmetrical or random dots. The subjects were required to discriminate three overlapped from two overlapped planes. In the indirect method, the subjects were required to discriminate the depth positions of a target dot (or a pair of dots) that disappeared during stimulus presentation. Our results, obtained in three experiments, showed that the discrimination performance improved and reached a perfect level in the direct method and a modest plateau level in the indirect method with increasing relative disparity between the two outer planes, irrespective of whether the dot pattern had a symmetrical structure or not. These results suggest that a detection process for symmetry structure on a two-dimensional plane in three-dimensional space will not have a direct or an indirect connection (e.g., via a feedback loop) to a process involved in the depth separation.
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paper_title: Binocular depth perception of computer-generated patterns

paper_content:

The perception of depth involves monocular and binocular depth cues. The latter seem simpler and more suitable for investigation. Particularly important is the problem of finding binocular parallax, which involves matching patterns of the left and right visual fields. Stereo pictures of familiar objects or line drawings preclude the separation of interacting cues, and thus this pattern-matching process is difficult to investigate. More insight into the process can be gained by using unfamiliar picture material devoid of all cues except binocular parallax. To this end, artificial stereo picture pairs were generated on a digital computer. When viewed monocularly, they appear completely random, but if viewed binocularly, certain correlated point domains are seen in depth. By introducing distortions in this material and testing for perception of depth, it is possible to show that pattern-matching of corresponding points of the left and right visual fields can be achieved by first combining the two fields and then searching for patterns in the fused field. By this technique, some interesting properties of this fused binocular field are revealed, and a simple analog model is derived. The interaction between the monocular and binocular fields is also describea. A number of stereo images that demonstrate these and other findings are presented.
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paper_title: Binocular Disappearance of Monocular Symmetry

paper_content:

In an earlier demonstration binocular shapes were produced from monocularly shapeless, random-dot stereo images. A reversal of this phenomenon is demonstrated. A stereo image is devised in which the monocularly apparent shapes of bilateral symmetry disappear when stereoscopically viewed. This phenomenon sharpens the implications of the earlier one.
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paper_title: Integration of structure-from-motion and symmetry during surface perception

paper_content:

Sinusoidal motion of elements in a random-dot pattern can elicit a striking percept of a rotating volume, a phenomenon known as structure-from-motion (SFM). We demonstrate that if the dots defining the volume are 2D mirror-symmetric, novel 3D interpretations arise. In addition to the classical rotating cylinder, one can perceive mirror-symmetric, flexible surfaces bending along the path of movement. In three experiments, we measured the perceptual durations of the different interpretations in a voluntary control task. The results suggest that motion signals and symmetry signals are integrated during surface interpolation. Furthermore, the competition between the rotating cylinder percept and the symmetric surfaces percept is resolved at the level of surface perception rather than at the level of individual stimulus elements. Concluding, structure-from-motion is an interactive process that incorporates not only motion cues but also form cues. The neurofunctional implication of this is that surface interpolation is not fully completed in its designated neural “engine,” MT/V5, but rather in a higher tier area such as LOC, which receives input from MT/V5 and which is also involved in symmetry detection.
---
paper_title: Symmetry versus repetition in cyclopean vision: A microgenetic analysis

paper_content:

In four experiments, participants had to detect symmetries or repetitions distributed over two depth planes, under presentation times of 200-1000 ms. Structurally corresponding elements were placed in different planes (Experiments la and 1b) or in the same plane (Experiments 2a and 2b). Results suggest (a) an ongoing interaction between regularity cues and depth cues, and (b) that efficient detection of symmetry but not of repetition depends on structural correspondences within depth planes. The latter confirms the idea that, to perceptual organization, symmetry is a cue for the presence of one object, whereas repetition is a cue for the presence of multiple objects.
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paper_title: Feature-based activation and suppression during binocular rivalry

paper_content:

In the past decade, effects of pattern coherence have indicated that perception during binocular rivalry does not result solely from reciprocal inhibitory competition between monocular channels. In this study we were interested in feature selectivity both during dominance and during suppression. The first experiment shows that a suppressed stimulus perceptually appears earlier when it shares features with a visible stimulus than when it does not. Subsequently, our second experiment suggests a reversal of this effect when similarity is exhibited with a suppressed stimulus. These findings hint at a role for both selective enhancing (Experiment 1) and selective inhibitory cortical mechanisms (Experiment 2) in causing image rivalry. From a phenomenological perspective these results suggest that we are not only selectively aware but also selectively unaware of specific features in the visual scene.
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paper_title: Symmetry activates extrastriate visual cortex in human and nonhuman primates.

paper_content:

Humans often create and appreciate visual symmetry in their environment, and the underlying brain mechanisms have been a topic of increasing interest. Here, symmetric versus random dot stimuli produced robust functional MRI (fMRI) activity in higher-order regions of human visual cortex (especially areas V3A, V4, V7, and LO) but little activity elsewhere in brain. This fMRI response was found both with and without attention controls. Moreover, it was highly correlated with the psychophysical perception of symmetry. Similar symmetry responses were found by using line-based and dot stimuli and were found at a wide range of stimulus sizes and geometric configurations. Weaker symmetry responses were found in analogous regions of macaque visual cortex by using fMRI techniques with higher sensitivity. This evidence suggests that visual symmetry is specifically enhanced in the human brain, but that the underlying neural mechanisms may nevertheless be resolvable in nonhuman primates.
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paper_title: Symmetry and selective attention: A dissociation between effortless perception and serial search

paper_content:

It is widely assumed that symmetry is an important visual primitive, probably encoded without the need for attention. Julesz’s (1981) definition ofeffortless perception, which states that any stimulus property perceived for exposure durations of 160 msec or less is detected preattentively, contributed greatly to this belief.Single pattern studies confirm that symmetry is detected within this limit. In the present study, however, Julesz’s operationalization is compared with themultiple pattern visual search task, to see whether symmetry as a wholistic property is detected in parallel. The results show that symmetry detection times are highly dependent on the number of distractor patterns. The findings are similar for dot patterns, wire polygons, solid block shapes, and simple parentheses. We conclude that symmetry detection per se requires selective attention, but that some related grouping or segmentation mechanism may operate preattentively.
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paper_title: Attention modulates responses in the human lateral geniculate nucleus

paper_content:

Attentional mechanisms are important for selecting relevant information and filtering out irrelevant information from cluttered visual scenes. Selective attention has previously been shown to affect neural activity in both extrastriate and striate visual cortex. Here, evidence from functional brain imaging shows that attentional response modulation is not confined to cortical processing, but can occur as early as the thalamic level. We found that attention modulated neural activity in the human lateral geniculate nucleus (LGN) in several ways: it enhanced neural responses to attended stimuli, attenuated responses to ignored stimuli and increased baseline activity in the absence of visual stimulation. The LGN, traditionally viewed as the gateway to visual cortex, may also serve as a 'gatekeeper' in controlling attentional response gain.
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paper_title: Grouping with and without attention

paper_content:

The effects of perceptual grouping on a line discrimination task were investigated using Moore and Egeth’s (1997) paradigm. Observers judged which of two lines, presented one above the other over a matrix of spots, was longer. On some trials, larger spots at both ends of the lines formed arrowheads, thereby making possible the Muller-Lyer illusion. When observers attended only to the lines, they were not aware of the arrowheads. Yet their line judgment performance showed that they had succumbed to the illusion. When the observers’ attention was directed to the arrowheads but they nevertheless failed to discern the arrowheads’ orientation, their line judgments were still influenced by the illusion.
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paper_title: Visual attention as a multilevel selection process

paper_content:

Natural visual scenes are cluttered and contain many different objects that cannot all be processed simultaneously. Therefore, attentional mechanisms are needed to select relevant and to filter out irrelevant information. Evidence from functional brain imaging reveals that attention operates at various processing levels within the visual system and beyond. First, the lateral geniculate nucleus appears to be the first stage in the processing of visual information that is modulated by attention, consistent with the idea that it may play an important role as an early gatekeeper in controlling neural gain. Second, areas at intermediate cortical-processing levels, such as V4 and TEO, appear to be important sites at which attention filters out unwanted information by means of receptive field mechanisms. Third, the attention mechanisms that operate in the visual system appear to be controlled by a distributed network of higher order areas in the frontal and parietal cortex, which generate top-down signals that are transmitted via feedback connections to the visual system. And fourth, the pulvinar of the thalamus may operate by integrating and coordinating attentional functions in concert with the fronto-parietal network, although much needs to be learned about its functional properties. The overall view that emerges from the studies reviewed in this article is that neural mechanisms of selective attention operate at multiple stages in the visual system and beyond and are determined by the visual processing capabilities of each stage. In this respect, attention can be considered in terms of a multilevel selection process.
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paper_title: Perceptual organization and attention

paper_content:

It is widely assumed that the grouping of the visual field first described by the Gestalt psychologists and the related phenomenon of texture segregation occur very early in the processing of visual information and involve preattentive processes. All the recent evidence supporting this assumption comes from visual search experiments in which the subject is actively looking for a target and attending to the stimulus. The question at issue is whether these kinds of patterns are perceived under conditions of inattention, i.e., when observers are not searching for them. We performed six experiments to determine whether texture segregation and grouping by similarity or proximity are perceived under conditions of inattention. On the first two trials subjects were asked to report the longer arm of a briefly presented cross which was surrounded by a pattern of ungrouped small elements. On the third trial and subsequent control trials these elements were configured into grouping patterns and subjects queried about them immediately following their line length reports. The results establish that neither texture segregation nor grouping by similarity of lightness or proximity are perceived under conditions of inattention. They support the conclusion that there is an earlier stage of processing than that referred to as preattentive.
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paper_title: Goodness of Regularity in Dot Patterns: Global Symmetry, Local Symmetry, and Their Interactions

paper_content:

Goodness is a classic Gestalt notion defined as salience or perceptual strength of a given pattern. All operational models of goodness have assigned a central role to mirror symmetry but not much attention has been paid to the distinction between global and local mirror symmetry, and their possible interactions. We designed eight different types of dot patterns (all consisting of 80 dots), combining different numbers (0, 1, and 2) and relative orientations (parallel or orthogonal to each other) of local and global axes of symmetry (affecting 50% or 100% of the dots, respectively) at different absolute orientations (vertical and horizontal). Each of 640 trials consisted of a short presentation of a new dot pattern, which subjects had to classify as regular or random. We hypothesised that the overall goodness of patterns is not the simple sum of the amount of regularity present in them but depends on the cooperation and competition between symmetries. The results confirmed our hypothesis, showing that perfo...
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paper_title: Perception without attention: Evidence of grouping under conditions of inattention

paper_content:

Many theories of visual perception assume that before attention is allocated within a scene, visual information is parsed according to the Gestalt principles of organization. This assumption has been challenged by experiments in which participants were unable to identify what Gestalt grouping patterns had occurred in the background of primary-task displays (A. Mack, B. Tang, R. Tuma, S. Kahn, & I. Rock, 1992). In the present study, participants reported which of 2 horizontal lines was longer. Dots in the background, if grouped, formed displays similar to the Ponzo illusion (Experiments 1 and 2) or the Müller-Lyer illusion (Experiment 3). Despite inaccurate reports of what the patterns were, participants' responses on the line-length discrimination task were clearly affected by the 2 illusions. These results suggest that Gestalt grouping does occur without attention but that the patterns thus formed may not be encoded in memory without attention.
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paper_title: Grouping does not require attention

paper_content:

Many theories of visual perception stipulate that Gestalt grouping occurs preattentively. Subjects’ failure to report perceiving even salient grouping patterns under conditions of inattention challenges this assumption (see, e.g., Mack, Tang, Tuma, Kahn, & Rock, 1992), but Moore and Egeth (1997) showed that although subjects are indeed unable to identify grouping patterns outside the focus of attention, effects of these patterns on visual perception can be observed when they are assessed using implicit, rather than explicit, measures. However, this finding, which is the only one to date demonstrating grouping effects without attention, is open to an alternative account. In the present study, we eliminated this confound and replicated Moore and Egeth’s findings, using the Muller-Lyer illusion (Experiments 1 and 2). Moreover, we found converging evidence for these findings with a variant of the flanker task (Experiment 3), when the amount of available attentional resources was varied (Experiments 4 and 5). The results reinforce the idea that, although grouping outside the focus of attention cannot be the object of overt report, grouping processes can occur without attention.
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paper_title: The Effects of Cuing on the Detection of Bilateral Symmetry

paper_content:

Pashler (1990) demonstrated that detection of mirror symmetry can be facilitated by precuing the symmetry axis orientation with a line. In Experiment 1, Pashler's result of a valid pre-cuing benefit was repeated, but it was also shown that invalid cuing produces performance costs, relative to a non-informative cue. Experiment 2 showed that the effect is not purely visual because the letters “V” and “H” can produce the same valid and invalid cuing effects. In Experiments 3Aand 3B, cue and pattern locations were varied, both absolutely and relative to each other. The results support an explanation for Pashler's atypical finding that horizontal symmetry can be detected faster than vertical symmetry. They also showed that the cuing effect is not local, contrary to Pashler's conclusion, but global and hence functionally useful.
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paper_title: Coordinate frame for symmetry detection and object recognition

paper_content:

Can subjects voluntarily set an internal coordinate frame in such a way as to facilitate the detection of symmetry about an arbitrary axis? If so, is this internal coordinate frame the same as that involved in determining perceived top and bottom in object recognition and shape perception? Subjects were required to determine whether dot patterns were symmetric. Cuing the subjects in advance about the orientation of the axis of symmetry produced a substantial speedup in performance (Experiments 1 and 3) and an increase in accuracy with brief displays (Experiment 2). The effects appeared roughly additive, with an overall advantage for vertical symmetry; thus, the vertical axis effect is not due to a tendency to prepare for the vertical axis. The cuing advantage was found to depend upon the subject's knowing in advance the spatial location as well as orientation of the frame of reference (Experiment 4). The fifth experiment provided evidence that the frame of reference responsible for these effects is the same as the one that determines shape perception: Subjects viewed displays containing a letter (at an unpredictable orientation) and a dot pattern, rapidly naming the letter and then determining whether the dots were symmetric about a prespecified axis. When the top-bottom axis of the letter was oriented the same way as the axis of symmetry for the dots, symmetry judgments were significantly more accurate. Thus, the results suggest a single frame of reference for both types of judgment. The General Discussion proposes a theory of how visual symmetry may be computed, which might account for these phenomena and also characterize their relation to "mental rotation" effects. Language: en
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paper_title: Effects of Pattern Orientation and Number of Symmetry Axes on the Detection of Mirror Symmetry in Dot and Solid Patterns

paper_content:

It has been postulated that as the number of axes of symmetry in a pattern increases, so pattern ‘goodness’ increases. Recently, a distinction was made between two different theoretical accounts of regularity or ‘goodness’ in relation to patterns with mirror symmetry: the ‘transformational’ and the ‘holographic’ models. It was argued that the former predicts a ‘goodness’ ordering of four > three > two > one whereas the latter predicts four > two > three > one, where ‘>’ means greater regularity or goodness. In three experiments, we have tested these predictions. In experiment 1, we measured percentage correct and reaction time to dot patterns which had one, two, three, or four axes of symmetry and were flashed for 150 ms. Experiment 2 was identical except that patterns were presented for 2000 ms. In experiment 3, dot patterns were replaced by solid shapes which also had one, two, three, or four axes of symmetry. Although it was found that stimuli with four axes clearly allowed superior performance to that...
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paper_title: Integration of structure-from-motion and symmetry during surface perception

paper_content:

Sinusoidal motion of elements in a random-dot pattern can elicit a striking percept of a rotating volume, a phenomenon known as structure-from-motion (SFM). We demonstrate that if the dots defining the volume are 2D mirror-symmetric, novel 3D interpretations arise. In addition to the classical rotating cylinder, one can perceive mirror-symmetric, flexible surfaces bending along the path of movement. In three experiments, we measured the perceptual durations of the different interpretations in a voluntary control task. The results suggest that motion signals and symmetry signals are integrated during surface interpolation. Furthermore, the competition between the rotating cylinder percept and the symmetric surfaces percept is resolved at the level of surface perception rather than at the level of individual stimulus elements. Concluding, structure-from-motion is an interactive process that incorporates not only motion cues but also form cues. The neurofunctional implication of this is that surface interpolation is not fully completed in its designated neural “engine,” MT/V5, but rather in a higher tier area such as LOC, which receives input from MT/V5 and which is also involved in symmetry detection.
---
paper_title: Binocular depth perception of computer-generated patterns

paper_content:

The perception of depth involves monocular and binocular depth cues. The latter seem simpler and more suitable for investigation. Particularly important is the problem of finding binocular parallax, which involves matching patterns of the left and right visual fields. Stereo pictures of familiar objects or line drawings preclude the separation of interacting cues, and thus this pattern-matching process is difficult to investigate. More insight into the process can be gained by using unfamiliar picture material devoid of all cues except binocular parallax. To this end, artificial stereo picture pairs were generated on a digital computer. When viewed monocularly, they appear completely random, but if viewed binocularly, certain correlated point domains are seen in depth. By introducing distortions in this material and testing for perception of depth, it is possible to show that pattern-matching of corresponding points of the left and right visual fields can be achieved by first combining the two fields and then searching for patterns in the fused field. By this technique, some interesting properties of this fused binocular field are revealed, and a simple analog model is derived. The interaction between the monocular and binocular fields is also describea. A number of stereo images that demonstrate these and other findings are presented.
---
paper_title: Binocular Disappearance of Monocular Symmetry

paper_content:

In an earlier demonstration binocular shapes were produced from monocularly shapeless, random-dot stereo images. A reversal of this phenomenon is demonstrated. A stereo image is devised in which the monocularly apparent shapes of bilateral symmetry disappear when stereoscopically viewed. This phenomenon sharpens the implications of the earlier one.
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paper_title: Symmetry and repetition in perspective

paper_content:

Although ecologically relevant, perspective views of symmetries and repetitions have hardly been investigated. Any symmetry or repetition that is not oriented orthogonally to the line of sight yields perspective distortions on the retina. In this study, these distortions are analyzed in terms of first-order structures (i.e., virtual lines between corresponding points) and second-order structures (i.e., correlation quadrangles formed by two virtual lines). In the literature, these structures have been proposed to guide the detection of frontoparallel symmetry and repetition. But what about perspective views? First, the analysis in this study shows that perspective distorts the retinal first-order and second-order structures of symmetry and repetition differently. Second, the results of two experiments on this distortion difference suggest that, in perspective views, symmetry and repetition detection is not preceded by normalization but occurs directly on the basis of the retinal first-order and second-order structures.
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paper_title: Monocular symmetry is neither necessary nor sufficient for the dichoptic perception of bilateral symmetry

paper_content:

Barlow and Reeves [1979. Vision Research, 19, 783-793] showed that bilateral symmetry detection in dot patterns is about equally efficient whether the displays are viewed monocularly or binocularly. If there is a binocular process which can be stimulated monocularly, this experiment does not indicate whether symmetry detection occurs before or after the site of binocular integration. This is so because the symmetrical patterns would have stimulated both monocular and binocular mechanisms under both viewing conditions. We presented stereoscopic 20-dot patterns, ten dots to each eye, for 150 ms so that 'false fusion' rather than rivalry occurred. Any axis of symmetry in the patterns was oriented at vertical (90 degrees ) or +/-1, 2, 3, or 4 degrees from vertical. The task was to judge whether the axis was tilted left or right of vertical, using the method of constant stimulus differences. Three kinds of pattern were used: SSS patterns were symmetrical in each eye alone and also dichoptically; NNS patterns were random monocularly but dichoptically symmetrical; and SSN patterns were symmetrical monocularly but dichoptically non-symmetrical. Orientation judgements were accurate, and equally so, for SSS and NNS displays but were extremely poor under SSN conditions. A control experiment showed that the poor performance in the SSN condition was not due to the axes of symmetry being eccentric to the fixation point. Thus, monocular symmetry is neither necessary nor sufficient for dichoptic bilateral symmetry perception; and symmetry mechanisms have no access to monocular signals.
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paper_title: Symmetry versus repetition in cyclopean vision: A microgenetic analysis

paper_content:

In four experiments, participants had to detect symmetries or repetitions distributed over two depth planes, under presentation times of 200-1000 ms. Structurally corresponding elements were placed in different planes (Experiments la and 1b) or in the same plane (Experiments 2a and 2b). Results suggest (a) an ongoing interaction between regularity cues and depth cues, and (b) that efficient detection of symmetry but not of repetition depends on structural correspondences within depth planes. The latter confirms the idea that, to perceptual organization, symmetry is a cue for the presence of one object, whereas repetition is a cue for the presence of multiple objects.
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paper_title: The spatial region of integration for visual symmetry detection

paper_content:

Symmetry is a complex image property that is exploited by a sufficiently wide range of species to indicate that it is detected using simple visual mechanisms. These mechanisms rely on measurements made close to the axis of symmetry. We investigated the size and shape of this integration region (IR) by measuring human detection of spatially band–pass symmetrical patches embedded in noise. Resistance to disruption of symmetry (in the form of random phase noise) improves with increasing patch size, and then asymptotes when the embedded region fills the IR. The size of the IR is shown to vary in inverse proportion to spatial frequency; i.e. symmetry detection exhibits scale–invariance. The IR is shown to have rigid dimensions, elongated in the direction of the axis of symmetry, with an aspect ratio of ca. 2:1. These results are consistent with a central role for spatial filtering in symmetry detection.
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paper_title: The role of visible persistence for perception of visual bilateral symmetry1

paper_content:

Abstract: Although the detection of visual bilateral symmetry has been claimed to be highly efficient, the possible involvement and function of visual memory in such efficient mechanisms has rarely been examined. We hypothesized that symmetry perception is rapid, as it can be achieved from rapidly decaying information of visible persistence. To test this hypothesis, we employed a temporal integration paradigm. A symmetric dot pattern was randomly divided into two asymmetric patterns and presented successively with a blank screen presented between patterns. Observers could detect symmetry when the two patterns were presented close in time (Experiment 1), indicating that observers perceived symmetry presumably utilizing visible persistence. In addition, the inverse-intensity effect of visible persistence (Di Lollo & Bischof, 1995) was evident in our temporal integration task of symmetry (Experiment 2). The results of the current study clearly demonstrate that the detection of symmetry can be achieved based on the visible persistence. The large capacity and high spatial precision of visible persistence might be adequate for the rapid and spatially global encoding of visual symmetry.
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paper_title: The versatility and absolute efficiency of detecting mirror symmetry in random dot displays

paper_content:

The detection of mirror symmetry has been investigated by measuring discriminability (d') between two populations of dot displays that contain mirror pairs and random dots in different proportions. The difficulty of the task was varied by changing the proportions of paired dots in the two populations, and also by changing the accuracy of positioning the paired dots. Symmetry can be detected in brief exposures, monocularly or binocularly. when the axis is not vertical, and when the axis is not central in the visual field. The mechanism is therefore versatile. Its efficiency can be measured when the pairing is imperfect, for unpaired dots then fall where a pair is expected, thus causing the spurious appearance of a pair. When the pairing has an accuracy of about± 6′ vertically and horizontally an ideal mechanism would achieved′ values about double those attained by subjects; they are thus using 25% of the statistical information available, which is a high figure considering the versatility and complexity of the mechanisms required.
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paper_title: Foundations of Cyclopean Perception

paper_content:

This classic work on cyclopean perception has influenced a generation of vision researchers, cognitive scientists, and neuroscientists and has inspired artists, designers, and computer graphics pioneers. In Foundations of Cyclopean Perception (first published in 1971 and unavailable for years), Bela Julesz traced the visual information flow in the brain, analyzing how the brain combines separate images received from the two eyes to produce depth perception. Julesz developed novel tools to do this: random-dot stereograms and cinematograms, generated by early digital computers at Bell Labs. These images, when viewed with the special glasses that came with the book, revealed complex, three-dimensional surfaces; this mode of visual stimulus became a paradigm for research in vision and perception. This reprint edition includes all 48 color random-dot designs from the original, as well as the special 3-D glasses required to view them.Foundations of Cyclopean Perception has had a profound impact on the vision studies community. It was chosen as one of the one hundred most influential works in cognitive science in a poll conducted by the University of Minnesota's Center for Cognitive Sciences. Many copies are "permanently borrowed" from college libraries; used copies are sought after online. Now, with this facsimile of the 1971 edition, the book is available again to cognitive scientists, neuroscientists, vision researchers, artists, and designers.
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paper_title: Global Detection of Symmetry

paper_content:

Two experimental approaches examined observers' ability to characterize shape symmetry based upon the information obtained within a single fixation. Exp. I tested observers' ability to discriminate among three levels of symmetry on the basis of a 25-msec. presentation. Results indicated that identification accuracy was higher for symmetrical and asymmetrical shapes than for mixed shapes, which contained both symmetrical and asymmetrical components. Exp. II tested observers' ability to detect a given level of symmetry by means of a signal-detection approach. Symmetrical shapes were detected better than asymmetrical shapes. Detectability of mixed shapes was lower than that for both symmetrical and asymmetrical shapes. The results of Exps. I and II demonstrate that observers can characterize shape symmetry on the basis of information available within a single fixation. The data are supportive of the hypothesis that a global response to the over-all configuration of the shape serves to facilitate form perception.
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paper_title: Detection of visual symmetries.

paper_content:

—This paper reviews empirical evidence for the detection of visual symmetries and explanatory theories and models of symmetry detection. First, mirror symmetry is compared to other types of symmetry. The idea that symmetry detection is preattentive is then discussed and other roles that attention might play in symmetry detection are considered. The major part of the article consists of a critical examination of the extensive literature about the effects on symmetry detection of several major factors such as the orientation of the symmetry axis, the location of the stimulus in the visual field, grouping, and perturbations. Constraints on plausible models of symmetry detection are derived from this rich database and several proposals are evaluated against it. As a result of bringing this research together, open questions and remaining gaps to be filled by future research are identified.
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paper_title: Component processes in the perception of bilaterally symmetric dot textures

paper_content:

If a random-dot texture is reflected about a given axis, the resulting bilateral symmetry is immediately detected. In order to account for this ability, it has been suggested that the visual system detects reflection in these dot textures because of the existence of a symmetric neural organization, centered about the fovea, which performs a point-by-point analysis. As yet, there is no evidence of such an organization in the human visual system. An alternative description of a bilaterally symmetric texture, that of a two-dimensional distribution of uniformly oriented point-pair elements, of nonuniform size and with collinear midpoints, is more consistent with known mammalian visual-system neurophysiology. Experiments were conducted in order to determine whether the human visual system is sensitive to the orientational uniformity of otherwise nonuniform point-pair elements and to their midpoint collinearity. The results indicate that there are three processes involved in the perception of bilaterally symmetric dot textures: the detection of orientational uniformity of the different sized point-pair elements; the fusion of salient element point-pairs into a salient feature; the detection of the symmetry of the resulting feature. This component-process hypothesis eliminates the necessity to postulate the existence of a symmetrical neural organization centered about the fovea.
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paper_title: Symmetry detection across the visual field

paper_content:

Humans are extremely sensitive to symmetry when it is foveated but sensitivity drops as a symmetrical region of a fixed size is moved into the periphery. A psychophysical study was undertaken to determine if eccentricity dependent sensitivity loss could be overcome by magnifying stimuli at each eccentricity ( E ) by a factor F = 1 + E/E2 , where E 2 indicates the eccentricity at which the size of a stimulus must be doubled, relative to a foveal standard, to achieve equivalent performance. The psychophysical task required subjects to decide on each trial in which of two intervals a symmetrical stimulus had been presented. Stimuli were presented at a range of sizes and eccentricities (0 to 8°) and the probability of a correct discrimination was computed for each condition. In Experiment 1, thresholds were measured with stimuli set to maximum available contrast and, in Experiment 2, stimuli were presented at a constant multiple of contrast detection threshold. In both experiments, a single scaling function removed most of the eccentricity dependent variation from the data. However, the E 2 value recovered for one subject tested in both experiments was larger by about 65% when stimuli were not equated for visibility. We conclude that symmetry detection can be equated across a range of eccentricities by scaling stimuli with an E 2 in the range of 0.88 to 1.38°. Failure to equate for visibility across all viewing conditions may result in an inflated estimate of E 2 .
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paper_title: The Salience of Vertical Symmetry

paper_content:

It has long been accepted that amongst patterns which are bilaterally symmetrical, those which have their axis of symmetry vertical are more saliently symmetrical than patterns whose axis of symmetry is at some other orientation. The evidence regarding the relative salience of other orientations of axis of symmetry is somewhat more equivocal. In experiment 1, subjects were required to discriminate between symmetric or random-dot patterns when the axis of symmetry was at one of eighteen different orientations, spaced 10° apart, both clockwise and counterclockwise of vertical to horizontal. The data indicated that vertical was most salient, then horizontal but that, unlike in the classical oblique effect for contrast sensitivity, performance for precisely diagonal axes was better than that for surrounding axis orientations. Additional data (from experiments 2 and 3) also showed that the salience of vertical and horizontal axes of symmetry can be manipulated extensively by varying the range of stimuli presen...
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paper_title: Perception of symmetry in infancy: The salience of vertical symmetry and the perception of pattern wholes

paper_content:

Abstract Four experiments were conducted to assess converging aspects of 4-month-old infants' perception of symmetry in visual patterns. Experiments 1 and 2 manipulated the structure and orientation of comparable patterns in order to evaluate the specialty of vertical symmetry. Infants showed no preference among vertically symmetrical, vertically repeated, and obliquely symmetrical patterns, but they processed vertically symmetrical patterns more efficiently than either vertically repeated patterns or obliquely symmetrical patterns. Experiment 3 manipulated the spatial separation of pattern components in order to determine the ability of young infants to integrate and coalesce information in visual patterns that is distributed in space. Infants processed vertically symmetrical patterns whose components were contiguous or nearly contiguous about the vertical axis (0 to 2.5° separations) more efficiently than discotiguous patterns (5 and 10° separations). Thus, extreme spatial separation about the vertical meridian caused infants to lose the advantage for vertical symmetry, and by inference their holistic perception of the visual pattern. Experiment 4 manipulated the organization of individual components of a vertical pattern in order to examine further infants' sensitivity to perceptual organization and synthesis of pattern form. Infants discriminated vertically symmetrical patterns from asymmetrical patterns with a vertical organization, thereby demonstrating sensitivity to the symmetrical organization of the pattern above their perception of components in the pattern. The results of these four experiments together corroborate and extend previous findings that vertical symmetry has a special status in early perceptual development and that infants can perceive pattern wholes.
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paper_title: Coordinate frame for symmetry detection and object recognition

paper_content:

Can subjects voluntarily set an internal coordinate frame in such a way as to facilitate the detection of symmetry about an arbitrary axis? If so, is this internal coordinate frame the same as that involved in determining perceived top and bottom in object recognition and shape perception? Subjects were required to determine whether dot patterns were symmetric. Cuing the subjects in advance about the orientation of the axis of symmetry produced a substantial speedup in performance (Experiments 1 and 3) and an increase in accuracy with brief displays (Experiment 2). The effects appeared roughly additive, with an overall advantage for vertical symmetry; thus, the vertical axis effect is not due to a tendency to prepare for the vertical axis. The cuing advantage was found to depend upon the subject's knowing in advance the spatial location as well as orientation of the frame of reference (Experiment 4). The fifth experiment provided evidence that the frame of reference responsible for these effects is the same as the one that determines shape perception: Subjects viewed displays containing a letter (at an unpredictable orientation) and a dot pattern, rapidly naming the letter and then determining whether the dots were symmetric about a prespecified axis. When the top-bottom axis of the letter was oriented the same way as the axis of symmetry for the dots, symmetry judgments were significantly more accurate. Thus, the results suggest a single frame of reference for both types of judgment. The General Discussion proposes a theory of how visual symmetry may be computed, which might account for these phenomena and also characterize their relation to "mental rotation" effects. Language: en
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paper_title: Detection of mirror symmetry in random dot patterns at different eccentricities

paper_content:

Abstract Differences between central and eccentric vision in the detection of mirror symmetry were investigated using patterns consisting of small dots. In each trial, a dot pattern was flashed for 140 msec and the subject had to decide whether the upper and lower parts of the dot pattern contained mirror symmetric pairs or whether the dots were distributed totally randomly. Detectability of mirror symmetry declined with increasing eccentricity when the retinal size of the dot patterns was constant at different eccentricities and when the size of the patterns in eccentric vision was size-scaled by the cortical magnification factor derived from the frequency of ganglion cells ( M-scaling ). The drop in detectability was more rapid for constant-size patterns than for M-scaled patterns. The results seem to support the notion that the encoding of positional information in eccentric vision is inferior to that of central vision even when the test patterns are M-scaled .
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paper_title: The Effects on Bilateral-Symmetry Detection of Multiple Symmetry, near Symmetry, and Axis Orientation:

paper_content:

Palmer and Hemenway (1978 Journal of Experimental Psychology: Human Perception and Performance4 691–702) reported that shapes with multiple axes of symmetry are processed faster than those with single symmetry even when trials are blocked so that the subject knows that any symmetry axis will be vertical. Because their model of symmetry detection postulated a two-stage process in which all orientations are searched crudely at first, in no particular order, followed by second-stage scrutiny, the continued salience of multiple over single symmetry with blocking could not be explained. They claimed that stimuli with multiple axes of symmetry have an additional ‘goodness’.Four experiments are reported in which it is demonstrated that both sensitivity (d′) and response bias (β) vary considerably in symmetry detection, not just as a function of the positive (symmetrical) stimuli used but also as a function of the negative or conjugate instances selected. Although stimuli with multiple axes of symmetry may well h...
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paper_title: The versatility and absolute efficiency of detecting mirror symmetry in random dot displays

paper_content:

The detection of mirror symmetry has been investigated by measuring discriminability (d') between two populations of dot displays that contain mirror pairs and random dots in different proportions. The difficulty of the task was varied by changing the proportions of paired dots in the two populations, and also by changing the accuracy of positioning the paired dots. Symmetry can be detected in brief exposures, monocularly or binocularly. when the axis is not vertical, and when the axis is not central in the visual field. The mechanism is therefore versatile. Its efficiency can be measured when the pairing is imperfect, for unpaired dots then fall where a pair is expected, thus causing the spurious appearance of a pair. When the pairing has an accuracy of about± 6′ vertically and horizontally an ideal mechanism would achieved′ values about double those attained by subjects; they are thus using 25% of the statistical information available, which is a high figure considering the versatility and complexity of the mechanisms required.
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paper_title: Ideal observer and absolute efficiency of detecting mirror symmetry in random images.

paper_content:

The problem of detecting symmetry has been studied by using digitally generated images with random pixel values. The statistical efficiency of humans and a computerized observer, the cross correlator of the image halves, has been evaluated. The efficiency of humans is approximately 100% when the image comprises only a few pixels and is notably better than that of the cross correlator. When the number of pixels in the image is increased, the detectability of symmetry gets better. For human observers detectability saturates, however, on a level corresponding to a modest number of pixels. Human efficiency in detecting symmetry is thus low when the image matrix size is large.
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paper_title: Scale invariance is driven by stimulus density

paper_content:

Scale invariance refers to aspects of visual perception that remain constant with changes in viewing distance. Previously, Dakin and Herbert [Proc. Roy. Soc. B. 265 (1397) (1998) 659] reported that the spatial integration region (IR) for mirror symmetry in bandpass noise is scale invariant because its dimensions scale with the inverse of peak spatial frequency. In bandpass noise, however, peak spatial frequency covaries with stimulus numerosity (i.e. the total number of information samples) and density (i.e. the total number of information samples per unit area). In this study, we report four experiments that decoupled properties of the retinal image affected by viewing distance––spatial frequency, numerosity, size, and density––and measured their effect on IR size. Stimuli consisted of bandpass microelements with vertically mirror-symmetric but otherwise random positions, and we measured observer resistance to random jitter imposed on microelement position. Results show that jitter resistance and IR size vary with the inverse of stimulus density but are unaffected by changes in stimulus spatial frequency, numerosity, or size. We found the IR has a 2:1 heightto-width aspect ratio and integrates information from � 18 microelements regardless of their spatial separation. Our results reveal that stimulus density plays a central role in the visual system’s implementation of scale invariance. Using an ideal-observer, we demonstrate that scale invariance reflects genuine neural scale selection rather than a physical limitation on the stimulus’ information content. Our findings that jitter resistance and IR size vary with the inverse of density challenge current models of spatial vision but can be reconciled with a model that compares the output of bandpass non-Fourier mechanisms to select spatial scales that match stimulus density. � 2002 Elsevier Science Ltd. All rights reserved.
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paper_title: The spatial region of integration for visual symmetry detection

paper_content:

Symmetry is a complex image property that is exploited by a sufficiently wide range of species to indicate that it is detected using simple visual mechanisms. These mechanisms rely on measurements made close to the axis of symmetry. We investigated the size and shape of this integration region (IR) by measuring human detection of spatially band–pass symmetrical patches embedded in noise. Resistance to disruption of symmetry (in the form of random phase noise) improves with increasing patch size, and then asymptotes when the embedded region fills the IR. The size of the IR is shown to vary in inverse proportion to spatial frequency; i.e. symmetry detection exhibits scale–invariance. The IR is shown to have rigid dimensions, elongated in the direction of the axis of symmetry, with an aspect ratio of ca. 2:1. These results are consistent with a central role for spatial filtering in symmetry detection.
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paper_title: The role of pattern outline in bilateral symmetry detection with briefly flashed dot patterns

paper_content:

—Experiment 1 demonstrates that, while the outline shapes of bilaterally symmetrical dot patterns play a role in symmetry detection, the removal of the outline by a surrounding random-dot annulus merely reduces performance by a fixed amount. It does not affect the relative salience of different symmetry-axis orientations. The converse is also true: performance is almost as good when the symmetrical dot pattern is confined to the surrounding annulus but is disrupted similarly when the central area is filled with random dots (Experiment 2). In Experiment 3, any one or more of three areas — a central circular area and two surrounding annuli — could be filled with vertically symmetrical or random dots and symmetry was detected reliably only when the central circular area contained the symmetrical dots. A new paradigm was explored in Experiment 4: subjects judged the orientation — left or right of vertical — of 20-dot symmetrical patterns oriented 1-4 deg left or right of vertical and with or without surrounding random-outline masks. Surprisingly, the orientation judgments were extremely precise, with JNDs of the order of 1 deg or less, and outline masking dots made no difference. Experiment 5 showed that performance was even better with just two dots and it made no difference whether these were separated by just under 4 deg or just over 20 deg. It was concluded that while pattern outline plays some role in dot symmetry detection, the major mechanisms are located near the fovea. It is suggested that the relative salience of vertical and horizontal symmetry only in central vision is related to the preponderance of foveal cells tuned to those orientations (Mansfield, Science 186, 1133-1135, 1974; Mansfield and Ronner, Brain Res. 149, 229-234, 1978) but that attentional factors and scanning strategies also boost the salience of oblique symmetry and the salience of vertical over horizontal symmetry (Wenderoth, Perception 23, 221-236, 1994).
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paper_title: The functional role of oriented spatial filters in the perception of mirror symmetry — psychophysics and modeling

paper_content:

We investigated human sensitivity to vertical mirror symmetry in noise patterns filtered for narrow bands of variable orientations. Sensitivity is defined here as the amount of spatial phase randomization corresponding to 75% correct performance in a 2AFC detection task. In Experiment 1, sensitivity was found to be high for tests patterns of all orientations except those parallel to the axis of symmetry. This implies that corresponding mirror-orientations (e.g. 45 and 45°) are combined prior to symmetry detection. In Experiment 2, observers detected symmetry in tests of variable orientation in the presence of either non-symmetric or symmetric masks filtered for orientations either parallel or perpendicular to the axis. Observers were found to be primarily affected by masks of the same orientation as the test, thus suggesting that symmetry is computed separately in distinct mirror-orientation channels. In Experiment 3, observers detected a symmetric test of variable height and width embedded in random noise. Data revealed that mirror symmetry is computed over a spatial integration region (IR) that remains approximately constant in area but whose height-to-width aspect ratio changes from 20:1 to 2:1 as orientation is varied from parallel to perpendicular to the axis. We compare human data against that of an ideal observer to identify key factors that limit visual performance and discuss the implications for the functional architecture of symmetry perception. We also propose a multi-channel model of symmetry detection that combines the output of oriented spatial filters in a simple and physiologically plausible manner. Particular emphasis is placed on the notion that changes in the shape of the IR with orientation compensate for changes in information density and partially equate performance across orientations. © 2000 Elsevier Science Ltd. All rights reserved.
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paper_title: The versatility and absolute efficiency of detecting mirror symmetry in random dot displays

paper_content:

The detection of mirror symmetry has been investigated by measuring discriminability (d') between two populations of dot displays that contain mirror pairs and random dots in different proportions. The difficulty of the task was varied by changing the proportions of paired dots in the two populations, and also by changing the accuracy of positioning the paired dots. Symmetry can be detected in brief exposures, monocularly or binocularly. when the axis is not vertical, and when the axis is not central in the visual field. The mechanism is therefore versatile. Its efficiency can be measured when the pairing is imperfect, for unpaired dots then fall where a pair is expected, thus causing the spurious appearance of a pair. When the pairing has an accuracy of about± 6′ vertically and horizontally an ideal mechanism would achieved′ values about double those attained by subjects; they are thus using 25% of the statistical information available, which is a high figure considering the versatility and complexity of the mechanisms required.
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paper_title: The spatial mechanisms mediating symmetry perception

paper_content:

Abstract This paper examines the role of spatial frequency and orientation tuned channels in the perception of visual symmetry. Subjects discriminated between band-pass filtered, white noise textures that either did or did not contain vertical bilateral symmetry (VBS, i.e., around a vertical midline) as a function of the spatial phase disruption imposed on the images. Resistance to phase noise is largely scale-invariant for isotropically filtered images, but horizontally filtered images are consistently more noise-resistant than vertical. However, when stimuli are rotated through 90 deg ( horizontal bilateral symmetry, HBS) performance is better with vertically filtered images suggesting a general advantage for orientations orthogonal to the axis of symmetry. At these orientations symmetry may be signaled directly by clusters of features along the axis. Our data further suggest that the established disadvantage for HBS may be attributable to an over-reliance on the output of horizontal filters. We compare models which exploit feature clustering around the axis by measuring the co-alignment in the output of oriented filters. Models using filters oriented orthogonal to the axis of symmetry predict the psychophysical performance for isotropic patterns and for patterns filtered orthogonal to the axis. For patterns filtered parallel to the axis, our data suggest that visual attention may play a role.
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paper_title: Higher-order structure in regularity detection

paper_content:

In three experiments a simple Euclidean transformation (reflection, translation, rotation) was applied to collections of twelve dots in such a way that they contained equal lower-order structure, defined on the pairwise grouping of elements with their partner following transformation (e.g. parallel virtual lines), but differed in the presence vs absence of higher-order structure, defined on pairs of pairwise groupings (e.g. virtual quadrangles with correlated angles). Based on the much better performance levels (d′) in the case of additional higher-order structure, we conclude that global regularities are easier to detect when the local correspondences are supported by higher-order ones formed between them. These enable the lower-order groupings to spread out across the whole pattern very rapidly (called bootstrapping). As a preliminary attempt to specify these principles, we proposed a working model with two basic components: first, a function expressing the cost of a perceptual grouping or the lack of regularity, and, secondly, an algorithm based on simulated annealing to minimize the cost function. The simulation results obtained with our current implementation of these principles showed satisfactory qualitative agreement with human regularity detection performance. Finally, the theory was shown to capture the essence of a large number of grouping phenomena taken from diverse domains such as detection of symmetry in dot patterns, global structure in Glass and vector patterns, correspondence in stereoscopic transparency and apparent motion. Therefore, we are convinced that, in principle, the mechanism used by the human visual system to detect regularity incorporates something like bootstrapping based on higher-order structure. We regard this as a promising step towards unraveling the intriguing mechanisms of classic Gestalt phenomena.
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paper_title: The Effects on Bilateral-Symmetry Detection of Multiple Symmetry, near Symmetry, and Axis Orientation:

paper_content:

Palmer and Hemenway (1978 Journal of Experimental Psychology: Human Perception and Performance4 691–702) reported that shapes with multiple axes of symmetry are processed faster than those with single symmetry even when trials are blocked so that the subject knows that any symmetry axis will be vertical. Because their model of symmetry detection postulated a two-stage process in which all orientations are searched crudely at first, in no particular order, followed by second-stage scrutiny, the continued salience of multiple over single symmetry with blocking could not be explained. They claimed that stimuli with multiple axes of symmetry have an additional ‘goodness’.Four experiments are reported in which it is demonstrated that both sensitivity (d′) and response bias (β) vary considerably in symmetry detection, not just as a function of the positive (symmetrical) stimuli used but also as a function of the negative or conjugate instances selected. Although stimuli with multiple axes of symmetry may well h...
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paper_title: Effects of Pattern Orientation and Number of Symmetry Axes on the Detection of Mirror Symmetry in Dot and Solid Patterns

paper_content:

It has been postulated that as the number of axes of symmetry in a pattern increases, so pattern ‘goodness’ increases. Recently, a distinction was made between two different theoretical accounts of regularity or ‘goodness’ in relation to patterns with mirror symmetry: the ‘transformational’ and the ‘holographic’ models. It was argued that the former predicts a ‘goodness’ ordering of four > three > two > one whereas the latter predicts four > two > three > one, where ‘>’ means greater regularity or goodness. In three experiments, we have tested these predictions. In experiment 1, we measured percentage correct and reaction time to dot patterns which had one, two, three, or four axes of symmetry and were flashed for 150 ms. Experiment 2 was identical except that patterns were presented for 2000 ms. In experiment 3, dot patterns were replaced by solid shapes which also had one, two, three, or four axes of symmetry. Although it was found that stimuli with four axes clearly allowed superior performance to that...
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paper_title: Detection of symmetry in tachistoscopically presented dot patterns: Effects of multiple axes and skewing

paper_content:

We examined the effects of multiple axes and skewing on the detectability of symmetry in tachistoscopically presented (100-msec) dot patterns to test the role of normal grouping processes based on higher order regularities in element positions. In addition to the first-order regularities of orientational uniformity and midpoint collinearity (Jenkins, 1983), bilateral symmetry (BS) gives rise to second-order relations between two pairs of symmetric elements (represented by correlation quadrangles). We suggest that they allow the regularity (i.e., BS) to emerge simply as a result of the position-based grouping that takes place normally, so that no special symmetry-detection mechanism has to be postulated. In combination with previously investigated variables— number and orientation of axes—we introduced skewing (resulting from orthographic projection of BS) to manipulate the kind and number of higher order regularities. In agreement with our predictions, the data show that the effect of skewing angle (varied at three 15° steps, clockwise and counterclockwise) on the preattentive detectability of symmetry (measured with d’) increases as the number of axes decreases. On the basis of some more specific findings, we suggest that it is not as much the number of correlation quadrangles that determines the saliency of a regularity as it is the degree to which they facilitate or “bootstrap” each other.
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paper_title: Detection of symmetry and anti-symmetry

paper_content:

To assess the role of second-order channels in symmetry perception we measured the effects of check size, spatial frequency content, eccentricity and grey scale range on the detection of symmetrical and anti-symmetrical patterns. Thresholds for symmetrical stimuli were only moderately affected by these manipulations. Anti-symmetrical stimuli composed of large black and white checks elicited low thresholds. However, anti-symmetry became essentially undetectable at small check sizes. Removing low frequencies from large-check-size, anti-symmetrical stimuli had little effect on thresholds whereas removing high frequencies had a pronounced effect. Moving the stimuli from fixation to 8� eccentricity caused a dramatic increase in thresholds for anti-symmetrical stimuli but not symmetrical stimuli. When the grey scale range was increased anti-symmetry was undetectable at any check size whereas symmetry was easily seen at all. We argue that these results and others in the literature suggest that anti-symmetry is only detected under conditions favourable to selective attention. � 2005 Elsevier Ltd. All rights reserved.
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paper_title: Scale invariance is driven by stimulus density

paper_content:

Scale invariance refers to aspects of visual perception that remain constant with changes in viewing distance. Previously, Dakin and Herbert [Proc. Roy. Soc. B. 265 (1397) (1998) 659] reported that the spatial integration region (IR) for mirror symmetry in bandpass noise is scale invariant because its dimensions scale with the inverse of peak spatial frequency. In bandpass noise, however, peak spatial frequency covaries with stimulus numerosity (i.e. the total number of information samples) and density (i.e. the total number of information samples per unit area). In this study, we report four experiments that decoupled properties of the retinal image affected by viewing distance––spatial frequency, numerosity, size, and density––and measured their effect on IR size. Stimuli consisted of bandpass microelements with vertically mirror-symmetric but otherwise random positions, and we measured observer resistance to random jitter imposed on microelement position. Results show that jitter resistance and IR size vary with the inverse of stimulus density but are unaffected by changes in stimulus spatial frequency, numerosity, or size. We found the IR has a 2:1 heightto-width aspect ratio and integrates information from � 18 microelements regardless of their spatial separation. Our results reveal that stimulus density plays a central role in the visual system’s implementation of scale invariance. Using an ideal-observer, we demonstrate that scale invariance reflects genuine neural scale selection rather than a physical limitation on the stimulus’ information content. Our findings that jitter resistance and IR size vary with the inverse of density challenge current models of spatial vision but can be reconciled with a model that compares the output of bandpass non-Fourier mechanisms to select spatial scales that match stimulus density. � 2002 Elsevier Science Ltd. All rights reserved.
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paper_title: Parallel computation of symmetry but not repetition within single visual shapes

paper_content:

Abstract Visual symmetry is highly salient to human observers. Indeed, Mach (1885) observed that symmetry is more salient than repetition in the contours of a shape. We find that symmetry within a single shape can be detected in parallel, whereas repetition is apparently detected by a serial process. Subjects were required to judge whether a pseudorandom block-shape was symmetrical (Experiment I) or had repeated contours (Experiment 2). When present, these relations arose around either vertical or horizontal axes of elongation, which were unpredictably intermingled. In both cases, symmetry judgements were scarcely affected by the number of discontinuities along the contours to be compared, whereas repetition judgements showed substantial delays when there were more discontinuities. These results are consistent with parallel encoding of a part-description for shapes, in accordance with Hoffman and Richards' (1984) curvature-minima rule.
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paper_title: VEPs elicited by local correlations and global symmetry: Characteristics and interactions

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Abstract Psychophysical and fMRI studies have indicated that visual processing of global symmetry has distinctive scaling properties, and proceeds more slowly than analysis of contrast, spatial frequency, and texture. We therefore undertook a visual evoked potential (VEP) study to directly compare the dynamics of symmetry and texture processing, and to determine the extent to which they interact. Stimuli consisted of interchange between structured and random black-and-white checkerboard stimuli. For symmetry, structured stimuli were colored with 2-fold symmetry (horizontal or vertical mirror), 4-fold symmetry (both mirror axes), and 8-fold symmetry (oblique mirror axes added). For texture, structured stimuli were colored according to the “even” isodipole texture [Julesz, B., Gilbert, E. N., & Victor, J. D. (1978). Visual discrimination of textures with identical third-order statistics. Biological Cybernetics, 31 , 137–140]. Thus, all stimuli had the same contrast, and check size, but differed substantially in correlation structure. To separate components of the VEP related to symmetry and texture from components that could be generated by local luminance and contrast changes, we extracted the odd-harmonic components of the VEP (recorded at C z – O z , C z – O 1 , C z – O 2 , C z – P z ) elicited by structured–random interchange. Responses to symmetry were largest for the 8-fold patterns, and progressively smaller for 4-fold, vertical, and horizontal symmetry patterns. Eightfold patterns were therefore used in the remainder of the study. The symmetry response is shifted to larger checks and lower temporal frequencies compared to the response to texture, and its temporal tuning is broader. Processing of symmetry makes use of neural mechanisms with larger receptive fields, and slower, more sustained temporal tuning characteristics than those involved in the analysis of texture. Sparse stimuli were used to dissociate check size and check density. VEP responses to sparse symmetry stimuli showed that there is no difference between first- and second-order symmetry for densities less than 12.5%. We discuss these findings in relation to local and global visual processes.
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paper_title: The effects of the contrast polarity of dot-pair partners on the detection of bilateral symmetry.

paper_content:

Detection of vertical bilateral symmetry has previously been studied in patterns composed of black or white dots on a grey background under four conditions: (a) same contrast (black or white) for all dots (called BB or WW, for 'all black or all white'); (b) half of the dots black and half white with positive correspondence between symmetrical dot pairs (called MA for 'matched'); (c) half of the dots black and half white with negative correspondence between symmetrical dot pairs (called OPP for 'opposite'); and (d) black (white) dots on one side of the axis and white (black) dots on the other (called BW for 'one side black the other white'). It was found that performance was ordered BB (or WW) = MA > OPP = BW, where > indicates better performance. That experiment was repeated here in experiment 1 with symmetry axes not only at vertical but also at horizontal and the two diagonals. It was found overall that BB = MA > OPP, BW. However, OPP > BW when random trials were included in the analysis but when they were excluded BW > OPP. This was due to a very high false-alarm rate in condition BW which could be accounted for if grouping by colour occurs prior to symmetry detection. In experiment 2 it was shown that vertical-symmetry salience over other orientations remained about the same as OPP patterns progressively changed into BB patterns by varying the percentage same polarity between 0% and 100% in 12%-13% steps. Thus, dot-pair polarity affects performance without affecting relative axis salience, as was also found recently when dot pattern outlines were masked. All of the data indicate that although opposite dot polarity does reduce performance slightly, the symmetry-detection mechanism is remarkably resilient to such perturbation. The high false-alarm rate in the BW condition of experiment 1 may be accounted for by extremely salient global grouping of dots by luminance which effectively creates an integral stimulus which is perceptually difficult to break down into its component dot pairs, prohibiting the required point-by-point matching necessary to reject symmetry detection. The small detrimental effect of nonmatched polarity might be due to the polarity differences masking the grouping of dots into 'clumps' on either side of the axis, a process for which there is a great deal of independent evidence.
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paper_title: Detection of symmetry and repetition in one and two objects. Structures versus strategies.

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Symmetry is usually easier to detect within a single object than in two objects (one-object advantage), while the reverse is true for repetition (two-objects advantage). This interaction between regularity and number of objects could reflect an intrinsic property of encoding spatial relations within and across objects or it could reflect a matching strategy. To test this, regularities between two contours (belonging to a single object or two objects) had to be detected in two experiments. Projected three-dimensional (3-D) objects rotated in depth were used to disambiguate figure-ground segmentation and to make matching based on simple translations of the two-dimensional (2-D) contours unlikely. Experiment 1 showed the expected interaction between regularity and number of objects. Experiment 2 used two-objects displays only and prevented a matching strategy by also switching the positions of the two objects. Nevertheless, symmetry was never detected more easily than repetition in these two-objects displays. We conclude that structural coding, not matching strategies, underlies the one-object advantage for symmetry and the two-objects advantage for repetition.
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paper_title: Symmetry versus repetition in cyclopean vision: A microgenetic analysis

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In four experiments, participants had to detect symmetries or repetitions distributed over two depth planes, under presentation times of 200-1000 ms. Structurally corresponding elements were placed in different planes (Experiments la and 1b) or in the same plane (Experiments 2a and 2b). Results suggest (a) an ongoing interaction between regularity cues and depth cues, and (b) that efficient detection of symmetry but not of repetition depends on structural correspondences within depth planes. The latter confirms the idea that, to perceptual organization, symmetry is a cue for the presence of one object, whereas repetition is a cue for the presence of multiple objects.
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paper_title: Higher-level mechanisms detect facial symmetry

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The role of symmetry detection in early visual processing and the sensitivity of biological visual systems to symmetry across a wide range of organisms suggest that symmetry can be detected by low-level visual mechanisms. However, computational and functional considerations suggest that higher-level mechanisms may also play a role in facial symmetry detection. We tested this hypothesis by examining whether symmetry detection is better for faces than comparable patterns, which share low-level properties with faces. Symmetry detection was better for upright faces than for inverted faces (experiment 1) and contrast-reversed faces (experiment 2), implicating high-level mechanisms in facial symmetry detection. In addition, facial symmetry detection was sensitive to spatial scale, unlike low-level symmetry detection mechanisms (experiment 3), and showed greater sensitivity to a 45° deviation from vertical than is found for other aspects of face perception (experiment 4). These results implicate specialized, higher-level mechanisms in the detection of facial symmetry. This specialization may reflect perceptual learning resulting from extensive experience detecting symmetry in faces or evolutionary selection pressures associated with the important role of facial symmetry in mate choice and ‘mind-reading’ or both.
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paper_title: Detection of Bilateral Symmetry in Complex Biological Images

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The recognition of bilateral symmetry in simple dot patterns is reliably influenced by orientation. Performance is best when the axis of symmetry is vertical. We conducted two experiments to determine whether stimulus orientation also affects detection of the low levels of naturally occurring asymmetry in complex biological images. University students judged whether colour images displayed on a computer monitor possessed perfect bilateral symmetry. Stimuli were generated from high-resolution plan-view images of crabs and insects. In experiment 1, the asymmetric stimuli were the original animals, displayed on a standard black background. Symmetrical versions of each natural image were generated by sectioning the shape at the midline, copying and reflecting one side, and then fusing the two halves together. To facilitate comparison of results with those obtained in earlier studies, we also presented dot patterns based upon both the slightly asymmetric and perfectly symmetrical natural images. Experiment 2 w...
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paper_title: Facial symmetry detection ability changes across the menstrual cycle

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The effects of menstrual cycle phase and hormones on women's visual ability to detect symmetry and visual preference for symmetry were examined. Participants completed tests of symmetry detection and preference for male facial symmetry at two of three menstrual cycle phases (menses, periovulatory, and luteal). Women were better at detecting facial symmetry during the menses than luteal phase of their cycle. A trend indicated the opposite pattern for dot symmetry detection. Similarly, change in salivary progesterone levels across the cycle was negatively related to change in facial symmetry detection scores. However, there was no clear evidence of a greater preference for facial symmetry at any cycle phase, despite an overall preference for facial symmetry across phases. These findings suggest a menses phase advantage and a low progesterone advantage in women's ability to detect facial symmetry. The results are discussed in the context of hormonal, evolutionary mate selection, and functional neurocognitive theories.
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paper_title: Orientational effects and component processes in symmetry detection

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In previous research on symmetry detection, factors contributing to orientational effects (axis and virtual lines connecting symmetrically positioned dots) and component processes (axis selection and pointwise evaluation) have always been confounded. The reason is the restriction to bilateral symmetry (BS), with pointwise correspondences being orthogonal to the axis of symmetry. In our experiments, subjects had to discriminate random dot patterns from symmetries defined by combining 12 axis orientations (every 15°) with seven reflection angles (0°, yielding BS, and three clockwise and counterclockwise 15° steps, yielding skewed symmetry, SS). In Experiment 1, with completely randomized trial order, a significant interaction between axis and skewing angle was obtained, indicating that classically observed orientational effects are restricted to BS and that the orientation of the pointwise correspondences is important. These basic findings were replicated in three subsequent experiments, which differed in t...
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paper_title: The importance of symmetry and virtual views in three-dimensional object recognition

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Abstract Background: Human observers can recognize three-dimensional objects seen in novel orientations, even when they have previously seen only a relatively small number of different views of the object. How our visual system does this is a key problem in vision research. Recent theories and experiments suggest that the human visual system might store a relatively small number of sample two-dimensional views of a three-dimensional object, and recognize novel views by a process of interpolation between the stored sample views. These sample views may be collected during a training phase as the visual system familiarizes itself with the object. Results Here, we investigate whether constraints on the shapes of objects commonly encountered in the real world can reduce the number of training views required for recognition of three-dimensional objects. We are particularly concerned with the constraint of object symmetry. We show that if an object is bilaterally symmetrical, then additional ‘virtual views' can automatically be generated from one sample view by symmetry transformations. These virtual views should make it more easy to recognize novel views of a symmetric than an asymmetric object, when a single sample view has been seen. Recognition should be particularly facilitated when the novel views are close to the virtual view. We present psychophysical results that bear out these predictions. Conclusion Our results show that the human visual system can indeed exploit symmetry to facilitate object recognition, and support the model for object recognition in which a small number of two-dimensional views are remembered and combined to recognize novel views of the same object. These results raise questions about how symmetry is recognized, and symmetry transformations implemented, in real, biological neural networks.
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paper_title: Symmetry detection through local skewed symmetries

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We explore how global symmetry can be detected prior to segmentation and under noise and occlusion. The definition of local symmetries is extended to affine geometries by considering the tangents and curvatures of local structures, and a quantitative measure of local symmetry known as symmetricity is introduced, which is based on Mahalanobis distances from the tangent-curvature states of local structures to the local skewed symmetry state-subspace. These symmetricity values, together with the associated local axes of symmetry, are spatially related in the local skewed symmetry field (LSSF). In the implementation, a fast, local symmetry detection algorithm allows initial hypotheses for the symmetry axis to be generated through the use of a modified Hough transform. This is then improved upon by maximizing a global symmetry measure based on accumulated local support in the LSSF ― a straight active contour model is used for this purpose. This produced useful estimates for the axis of symmetry and the angle of skew in the presence of contour fragmentation, artifacts and occlusion
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paper_title: Perception of surface slant from oriented textures

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When a surface covered with a regular texture is viewed in perspective, the projected texture provides a number of cues to 3D surface orientation. For oriented textures, one cue is perspective convergence: symmetry lines that are parallel along the surface project to lines that vary systematically in orientation. We investigated the contribution of perspective convergence to perception of 3D slant and tested whether slant from convergence depends on oriented spectral components. Subjects judged the sign of slant about a vertical axis of rotation. Textures were composed of filled circles in three spatial arrangements: a hex grid with symmetry lines at 0 and T60 deg relative to the tilt direction (aligned condition), a hex grid with symmetry lines at 90 and T30 deg (perpendicular condition), and random arrangements with similar average spacing (isotropic condition). The two hex grid textures differed in the amount of spectral energy present in the tilt direction (horizontal) but were otherwise closely matched. Slant discrimination thresholds for monocular stimuli were higher for isotropic textures than for either of the two hex grid textures and were higher for the perpendicular texture than for the aligned texture. In a second experiment, we measured the weight given to texture relative to binocular slant information for cue conflict stimuli (T5 deg). Weights were found to agree with individual subjects’ monocular thresholds, in accordance with optimal estimation theory. We conclude that the visual system uses perspective convergence to perceive slant and that effective use of convergence requires the presence of spectral components aligned with the tilt direction.
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paper_title: Representation and recognition of the spatial organization of three-dimensional shapes

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The human visual process can be studied by examining the computational problems associated with deriving useful information from retinal images. In this paper, we apply this approach to the problem of representing three-dimensional shapes for the purpose of recognition. 1. Three criteria, accessibility, scope and uniqueness, and stability and sensitivity, are presented for judging the usefulness of a representation for shape recognition. 2. Three aspects of a representation9s design are considered, (i) the representation9s coordinate system, (ii) its primitives, which are the primary units of shape information used in the representation, and (iii) the organization the representation imposes on the information in its descriptions. 3. In terms of these design issues and the criteria presented, a shape representation for recognition should: (i) use an object-centred coordinate system, (ii) include volumetric primitives of varied sizes, and (iii) have a modular organization. A representation based on a shape9s natural axes (for example the axes identified by a stick figure) follows directly from these choices. 4. The basic process for deriving a shape description in this representation must involve: (i) a means for identifying the natural axes of a shape in its image and (ii) a mechanism for transforming viewer-centred axis specifications to specifications in an object-centred coordinate system. 5. Shape recognition involves: (i) a collection of stored shape descriptions, and (ii) various indexes into the collection that allow a newly derived description to be associated with an appropriate stored description. The most important of these indexes allows shape recognition to proceed conservatively from the general to the specific based on the specificity of the information available from the image. 6. New constraints supplied by a conservative recognition process can be used to extract more information from the image. A relaxation process for carrying out this constraint analysis is described.
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paper_title: A computational model that recovers the 3D shape of an object from a single 2D retinal representation

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Human beings perceive 3D shapes veridically, but the underlying mechanisms remain unknown. The problem of producing veridical shape percepts is computationally difficult because the 3D shapes have to be recovered from 2D retinal images. This paper describes a new model, based on a regularization approach, that does this very well. It uses a new simplicity principle composed of four shape constraints: viz., symmetry, planarity, maximum compactness and minimum surface. Maximum compactness and minimum surface have never been used before. The model was tested with random symmetrical polyhedra. It recovered their 3D shapes from a single randomly-chosen 2D image. Neither learning, nor depth perception, was required. The effectiveness of the maximum compactness and the minimum surface constraints were measured by how well the aspect ratio of the 3D shapes was recovered. These constraints were effective; they recovered the aspect ratio of the 3D shapes very well. Aspect ratios recovered by the model were compared to aspect ratios adjusted by four human observers. They also adjusted aspect ratios very well. In those rare cases, in which the human observers showed large errors in adjusted aspect ratios, their errors were very similar to the errors made by the model.
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paper_title: Human Symmetry Perception and Its Computational Analysis

paper_content:

Contents: Part I:Introduction. C.W. Tyler, Human Symmetry Perception. Part II:Empirical Evaluation of Symmetry Perception. J. Wagemans, Detection of Visual Symmetries. P. Wenderoth, The Role of Pattern Outline in Bilateral Symmetry Detection With Briefly Flashed Dot Patterns. K.E. Higgins, A. Arditi, K. Knoblauch, Detection and Identification of Mirror-Image Letter Pairs in Central and Peripheral Vision. P.T. Quinlan, Evidence for the Use of Scene-Based Frames of Reference in Two-Dimensional Shape Recognition. G. Leone, M. Lipshits, J. McIntyre, V. Gurfinkel, Independence of Bilateral Symmetry Detection From a Gravitational Reference Frame. J.P. Szlyk, I. Rock, C.B. Fisher, Level of Processing in the Perception of Symmetrical Forms Viewed From Different Angles. S. Hong, M. Pavel, Determinants of Symmetry Perception. C.W. Tyler, L. Hardage, Mirror Symmetry Detection: Predominance of Second-Order Pattern Processing Throughout the Visual Field. P.J. Passmore, A. Johnston, Human Discrimination of Surface Slant in Fractal and Related Textured Images. Part III:Theoretical Issues in Symmetry Analysis. S.C. Dakin, R.J. Watt, Detection of Bilateral Symmetry Using Spatial Filters. C. Latimer, W. Joung, C. Stevens, Modelling Symmetry Detection With Back-Propagation Networks. M.A. Kurbat, A Network Model for Generating Differential Symmetry Axes of Shapes Via Receptive Fields. I. Rentschler, E. Barth, T. Caelli, C. Zetzsche, M. Juttner, On the Generalization of Symmetry Relations in Visual Pattern Classification. F. Labonte, Y. Shapira, P. Cohen, J. Faubert, A Model for Global Symmetry Detection in Dense Images. H. Zabrodsky, D. Algom, Continuous Symmetry: A Model for Human Figural Perception. Y. Bonneh, D. Reisfeld, Y. Yeshurun, Quantification of Local Symmetry: Application to Texture Discrimination. J.S. Joseph, J.D. Victor, A Continuum of Non-Gaussian Self-Similar Image Ensembles With White Power Spectra. L.L. Kontsevich, Symmetry as a Depth Cue. T. Vetter, T. Poggio, Symmetric 3D Objects Are an Easy Case for 2D Object Recognition. L. Matin, W. Li, Mirror Symmetry and Parallelism: Two Opposite Rules for the Identity Transform in Space Perception and Their Unified Treatment by the Great Circle Model. J.R. Pani, The Generalized Cone in Human Spatial Organization.
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paper_title: Using Bilateral Symmetry To Improve 3D Reconstruction From Image Sequences

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Abstract In previous applications, bilateral symmetry of objects was used either as a descriptive feature in domains such as recognition and grasping or as a way to reduce the complexity of structure from motion. In this paper we demonstrate how bilateral symmetry can be used to improve the accuracy in 3D reconstruction. The symmetry property is used to “symmetrize” data before and after reconstruction. We first show how to compute the closest symmetric 2D and 3D configurations given noisy data. This gives us a symmetrization procedure, which we apply to images before reconstruction, and which we apply to the 3D configuration after reconstruction. We demonstrate a significant improvement obtained with real images. We demonstrate the relative merits of symmetrization before and after reconstruction using simulated and real data.
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paper_title: Higher-order structure in regularity detection

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In three experiments a simple Euclidean transformation (reflection, translation, rotation) was applied to collections of twelve dots in such a way that they contained equal lower-order structure, defined on the pairwise grouping of elements with their partner following transformation (e.g. parallel virtual lines), but differed in the presence vs absence of higher-order structure, defined on pairs of pairwise groupings (e.g. virtual quadrangles with correlated angles). Based on the much better performance levels (d′) in the case of additional higher-order structure, we conclude that global regularities are easier to detect when the local correspondences are supported by higher-order ones formed between them. These enable the lower-order groupings to spread out across the whole pattern very rapidly (called bootstrapping). As a preliminary attempt to specify these principles, we proposed a working model with two basic components: first, a function expressing the cost of a perceptual grouping or the lack of regularity, and, secondly, an algorithm based on simulated annealing to minimize the cost function. The simulation results obtained with our current implementation of these principles showed satisfactory qualitative agreement with human regularity detection performance. Finally, the theory was shown to capture the essence of a large number of grouping phenomena taken from diverse domains such as detection of symmetry in dot patterns, global structure in Glass and vector patterns, correspondence in stereoscopic transparency and apparent motion. Therefore, we are convinced that, in principle, the mechanism used by the human visual system to detect regularity incorporates something like bootstrapping based on higher-order structure. We regard this as a promising step towards unraveling the intriguing mechanisms of classic Gestalt phenomena.
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paper_title: Symmetry and repetition in perspective

paper_content:

Although ecologically relevant, perspective views of symmetries and repetitions have hardly been investigated. Any symmetry or repetition that is not oriented orthogonally to the line of sight yields perspective distortions on the retina. In this study, these distortions are analyzed in terms of first-order structures (i.e., virtual lines between corresponding points) and second-order structures (i.e., correlation quadrangles formed by two virtual lines). In the literature, these structures have been proposed to guide the detection of frontoparallel symmetry and repetition. But what about perspective views? First, the analysis in this study shows that perspective distorts the retinal first-order and second-order structures of symmetry and repetition differently. Second, the results of two experiments on this distortion difference suggest that, in perspective views, symmetry and repetition detection is not preceded by normalization but occurs directly on the basis of the retinal first-order and second-order structures.
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paper_title: Locating and modelling a flat symmetric object from a single perspective image

paper_content:

Abstract A new approach for finding the axis projection, under the perspective view assumption, in an image of a symmetric two-dimensional pattern is proposed. Using the convex hull provides its rough location. This location is then improved using the cross-ratio properties. The second part of this paper shows that an object of this class can be located up to a translation and modelled up to a scaling factor from one perspective image of its contour. The method is tested on real images.
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paper_title: Detection of visual symmetries.

paper_content:

—This paper reviews empirical evidence for the detection of visual symmetries and explanatory theories and models of symmetry detection. First, mirror symmetry is compared to other types of symmetry. The idea that symmetry detection is preattentive is then discussed and other roles that attention might play in symmetry detection are considered. The major part of the article consists of a critical examination of the extensive literature about the effects on symmetry detection of several major factors such as the orientation of the symmetry axis, the location of the stimulus in the visual field, grouping, and perturbations. Constraints on plausible models of symmetry detection are derived from this rich database and several proposals are evaluated against it. As a result of bringing this research together, open questions and remaining gaps to be filled by future research are identified.
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paper_title: Detection of symmetry in tachistoscopically presented dot patterns: Effects of multiple axes and skewing

paper_content:

We examined the effects of multiple axes and skewing on the detectability of symmetry in tachistoscopically presented (100-msec) dot patterns to test the role of normal grouping processes based on higher order regularities in element positions. In addition to the first-order regularities of orientational uniformity and midpoint collinearity (Jenkins, 1983), bilateral symmetry (BS) gives rise to second-order relations between two pairs of symmetric elements (represented by correlation quadrangles). We suggest that they allow the regularity (i.e., BS) to emerge simply as a result of the position-based grouping that takes place normally, so that no special symmetry-detection mechanism has to be postulated. In combination with previously investigated variables— number and orientation of axes—we introduced skewing (resulting from orthographic projection of BS) to manipulate the kind and number of higher order regularities. In agreement with our predictions, the data show that the effect of skewing angle (varied at three 15° steps, clockwise and counterclockwise) on the preattentive detectability of symmetry (measured with d’) increases as the number of axes decreases. On the basis of some more specific findings, we suggest that it is not as much the number of correlation quadrangles that determines the saliency of a regularity as it is the degree to which they facilitate or “bootstrap” each other.
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paper_title: Determining the orientation of depth-rotated familiar objects.

paper_content:

How does the human visual system determine the depth-orientation of familiar objects? We examined reaction times and errors in the detection of 15° differences in the depth orientations of two simultaneously presented familiar objects, which were the same objects (Experiment 1) or different objects (Experiment 2). Detection of orientation differences was best for 0° (front) and 180° (back), while 45° and 135° yielded poorer results, and 90° (side) showed intermediate results, suggesting that the visual system is tuned for front, side and back orientations. We further found that those advantages are due to orientation-specific features such as horizontal linear contours and symmetry, since the 90° advantage was absent for objects with curvilinear contours, and asymmetric object diminished the 0° and 180° advantages. We conclude that the efficiency of visually determining object orientation is highly orientation-dependent, and object orientation may be perceived in favor of front-back axes.
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paper_title: Spatial-scale contribution to the detection of mirror symmetry in fractal noise

paper_content:

We investigated how the detection of mirror symmetry depends on the distribution of contrast energy across spatial scales. Stimuli consisted of vertically symmetric noise patterns with fractal power spectra defined by 1/fβ slopes (-2≤β≤5). While overall rms contrast remained fixed at 25%, symmetry-detection thresholds were obtained by corrupting the signal with variable amounts of noise with identical spectral characteristics. A first experiment measured thresholds as a function of spectral slope, and performance was found to be substantially facilitated in images with power spectra that characterize natural scenes (1.2≤β≤3.2). In a second experiment, symmetry was removed from randomly chosen octave bands and replaced by noise with the same spectral profile. Results revealed that only in images with 1/f2 spectra does performance decrease by constant amounts across all frequency bands. Together, the results imply that symmetry mechanisms extract equal amounts of information from constant-octave frequency bands but lack the ability to whiten stimuli whose spectral slopes differ from those of natural scenes. Results are qualitatively well predicted by a multichannel model that (1) relies on spatial filters with equal-volume point-spread functions and constant-octave frequency bandwidths and (2) restricts the computation of symmetry to spatial regions whose dimensions are proportional to the filters’ spatial scale. These findings are also consistent with the notion that mechanisms that mediate the perception of form exploit the ability of early vision to reduce second-order redundancy in natural scenes.
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paper_title: Descriptive and evaluative judgment processes: Behavioral and electrophysiological indices of processing symmetry and aesthetics

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Descriptive symmetry and evaluative aesthetic judgment processes were compared using identical stimuli in both judgment tasks. Electrophysiological activity was recorded while participants judged novel formal graphic patterns in a trial-by-trial cuing setting using binary responses (symmetric, not symmetric; beautiful, not beautiful). Judgment analyses of a Phase 1 test and main experiment performance resulted in individual models, as well as group models, of the participants’ judgment systems. Symmetry showed a strong positive correlation with beautiful judgments and was the most important cue. Descriptive judgments were performed faster than evaluative judgments. The ERPs revealed a phasic, early frontal negativity for the not-beautiful judgments. A sustained posterior negativity was observed in the symmetric condition. All conditions showed late positive potentials (LPPs). Evaluative judgment LPPs revealed a more pronounced right lateralization. It is argued that the present aesthetic judgments engage a two-stage process consisting of early, anterior frontomedian impression formation after 300 msec and right-hemisphere evaluative categorization around 600 msec after onset of the graphic patterns.
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paper_title: Symmetry activates extrastriate visual cortex in human and nonhuman primates.

paper_content:

Humans often create and appreciate visual symmetry in their environment, and the underlying brain mechanisms have been a topic of increasing interest. Here, symmetric versus random dot stimuli produced robust functional MRI (fMRI) activity in higher-order regions of human visual cortex (especially areas V3A, V4, V7, and LO) but little activity elsewhere in brain. This fMRI response was found both with and without attention controls. Moreover, it was highly correlated with the psychophysical perception of symmetry. Similar symmetry responses were found by using line-based and dot stimuli and were found at a wide range of stimulus sizes and geometric configurations. Weaker symmetry responses were found in analogous regions of macaque visual cortex by using fMRI techniques with higher sensitivity. This evidence suggests that visual symmetry is specifically enhanced in the human brain, but that the underlying neural mechanisms may nevertheless be resolvable in nonhuman primates.
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paper_title: Binocular depth perception of computer-generated patterns

paper_content:

The perception of depth involves monocular and binocular depth cues. The latter seem simpler and more suitable for investigation. Particularly important is the problem of finding binocular parallax, which involves matching patterns of the left and right visual fields. Stereo pictures of familiar objects or line drawings preclude the separation of interacting cues, and thus this pattern-matching process is difficult to investigate. More insight into the process can be gained by using unfamiliar picture material devoid of all cues except binocular parallax. To this end, artificial stereo picture pairs were generated on a digital computer. When viewed monocularly, they appear completely random, but if viewed binocularly, certain correlated point domains are seen in depth. By introducing distortions in this material and testing for perception of depth, it is possible to show that pattern-matching of corresponding points of the left and right visual fields can be achieved by first combining the two fields and then searching for patterns in the fused field. By this technique, some interesting properties of this fused binocular field are revealed, and a simple analog model is derived. The interaction between the monocular and binocular fields is also describea. A number of stereo images that demonstrate these and other findings are presented.
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paper_title: Scale invariance is driven by stimulus density

paper_content:

Scale invariance refers to aspects of visual perception that remain constant with changes in viewing distance. Previously, Dakin and Herbert [Proc. Roy. Soc. B. 265 (1397) (1998) 659] reported that the spatial integration region (IR) for mirror symmetry in bandpass noise is scale invariant because its dimensions scale with the inverse of peak spatial frequency. In bandpass noise, however, peak spatial frequency covaries with stimulus numerosity (i.e. the total number of information samples) and density (i.e. the total number of information samples per unit area). In this study, we report four experiments that decoupled properties of the retinal image affected by viewing distance––spatial frequency, numerosity, size, and density––and measured their effect on IR size. Stimuli consisted of bandpass microelements with vertically mirror-symmetric but otherwise random positions, and we measured observer resistance to random jitter imposed on microelement position. Results show that jitter resistance and IR size vary with the inverse of stimulus density but are unaffected by changes in stimulus spatial frequency, numerosity, or size. We found the IR has a 2:1 heightto-width aspect ratio and integrates information from � 18 microelements regardless of their spatial separation. Our results reveal that stimulus density plays a central role in the visual system’s implementation of scale invariance. Using an ideal-observer, we demonstrate that scale invariance reflects genuine neural scale selection rather than a physical limitation on the stimulus’ information content. Our findings that jitter resistance and IR size vary with the inverse of density challenge current models of spatial vision but can be reconciled with a model that compares the output of bandpass non-Fourier mechanisms to select spatial scales that match stimulus density. � 2002 Elsevier Science Ltd. All rights reserved.
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paper_title: The spatial region of integration for visual symmetry detection

paper_content:

Symmetry is a complex image property that is exploited by a sufficiently wide range of species to indicate that it is detected using simple visual mechanisms. These mechanisms rely on measurements made close to the axis of symmetry. We investigated the size and shape of this integration region (IR) by measuring human detection of spatially band–pass symmetrical patches embedded in noise. Resistance to disruption of symmetry (in the form of random phase noise) improves with increasing patch size, and then asymptotes when the embedded region fills the IR. The size of the IR is shown to vary in inverse proportion to spatial frequency; i.e. symmetry detection exhibits scale–invariance. The IR is shown to have rigid dimensions, elongated in the direction of the axis of symmetry, with an aspect ratio of ca. 2:1. These results are consistent with a central role for spatial filtering in symmetry detection.
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paper_title: C.: Temporal dynamics of the human response to symmetry

paper_content:

Symmetry is a highly salient feature of animals, plants, and the constructed environment. Although the perceptual phenomenology of symmetry processing is well understood, little is known about the underlying neural mechanisms. Here we use visual evoked potentials to measure the time course of neural events associated with the extraction of symmetry in random dot fields. We presented sparse random dot patterns that were symmetric about both the vertical and horizontal axes. Symmetric patterns were alternated with random patterns of the same density every 500 msec, using new exemplars of symmetric and random patterns on each image update. Random/random exchanges were used as a control. The response to updates of random patterns was multiphasic, consisting of P65, N90, P110, N140 and P220 peaks. The response to symmetric/random sequences was indistinguishable from that for random/random sequences up to about 220 msec, after which the response to symmetric patterns became relatively more negative. Symmetry in random dot patterns thus appears to be extracted after an initial response phase that is indifferent to configuration. These results are consistent with the hypothesis (Lee, Mumford, Romero, & Lamme, 1998; Tyler & Baseler, 1998) that the symmetry property is extracted by processing in extrastriate cortex. Keywords: evoked potentials, shape, form
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paper_title: Electrophysiological indices of processing aesthetics: Spontaneous or intentional processes?

paper_content:

Processes underlying aesthetic appreciation of formal graphic black and white patterns were investigated. In previous EEG studies on aesthetic and symmetry judgments, an early frontocentral negativity has been observed for not beautiful judgments, and interpreted as reflecting an impression formation. In addition, a lateralized late positivity, more pronounced in the aesthetic than in the symmetry judgment task, has been interpreted as reflecting evaluative categorization; and a sustained posterior negativity for not symmetric judgments, has been interpreted as reflecting a prolonged symmetry analysis. Here, we investigated whether these processes occur spontaneously, i.e. independent of an aesthetics task instruction or a judgment task demand. Participants were randomly assigned to two group conditions. In the Viewing condition, participants were instructed to view graphic patterns, and to detect a probe. In the Contemplation condition, participants were instructed to contemplate the beauty of the patterns, and to detect a probe. No aesthetics-related response was required in either condition. ERP results suggest that symmetry analysis occurred spontaneously. Evaluative categorization, reflected by a late positivity, required an aesthetics instruction and did not occur spontaneously. This process was elicited without an overt aesthetic judgment. An early frontocentral negativity for not beautiful patterns, interpreted as reflecting impression formation, did not occur (in contrast to previous studies that required an overt aesthetic judgment). Given the present data, aesthetic appreciation of graphic patterns requires different sub-processes. Aesthetic contemplation is reflected by a lateralized late positivity, whilst an aesthetic judgment is additionally reflected by an early frontocentral negativity. Aesthetic appreciation of beauty appears to require intention and is not spontaneous in character.
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paper_title: The effects of stimulus symmetry on landmark judgments in left and right visual fields

paper_content:

Line bisection impairment is greater following right compared to left hemisphere damage, suggesting that some of the underlying visuo-spatial mechanisms may be lateralised. One important perceptual component of line bisection is estimating stimulus midpoint. Here, we used a modified version of the perceptual landmark task to examine, in healthy individuals, how the midpoint of a stimulus is apprehended, and if the cerebral hemispheres are equally as efficient in performing such a task. We show that the right, relative to the left, hemisphere is both faster and more accurate at apprehending prebisected lines, but no better at apprehending misbisected lines. We then demonstrate that the right hemisphere advantage stems from a specialisation in detecting stimulus symmetry; by associating prebisected lines with the presence of display symmetry, transect location can be inferred without having to explicitly calculate the midpoint of lines. The findings provide a further reason why right hemisphere damage is so deterimental to perceptual line bisection. In addition, the data indicate that the detection of visual symmetry is preferentially lateralised to the right hemisphere.
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paper_title: Evidence that both area V1 and extrastriate visual cortex contribute to symmetry perception

paper_content:

Abstract Bilateral symmetry is common in nature and most animals seem able to perceive it. Many species use judgements of symmetry in various behaviours, including mate selection [1–3]. Originally, however, symmetry perception may have developed as a tool for generating object-centered, rather than viewer-centered, descriptions of objects, facilitating recognition irrespective of position or orientation [4]. There is evidence that the visual system treats the orientation of axes-of-symmetry in the same way it treats the orientation of luminance-defined contours [5], suggesting that axes-of-symmetry act as ‘processing tokens' [6]. We have investigated the characteristics of neural mechanisms giving rise to the perceived orientation of axes-of-symmetry. We induced tilt aftereffects with symmetrical dot patterns, eliciting perceived angle expansion and contraction effects like those usually observed with luminance-defined contours [7,8]. Induction of aftereffects during binocular rivalry resulted in a reduction of the magnitude of these effects, consistent with the aftereffects being mediated in extrastriate visual cortex, probably between visual areas V2 and MT [9]. In a second experiment in which the aftereffects were induced monocularly, their magnitudes were measured in the unadapted eye. Contraction effects transferred completely, suggesting that they are mediated by binocular cells. Expansion effects did not transfer completely, consistent with their having a monocular component. These data suggest that information about the orientation of axes-of-symmetry may be available as early as area V1, but that processing continues in extrastriate cortex.
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paper_title: VEPs elicited by local correlations and global symmetry: Characteristics and interactions

paper_content:

Abstract Psychophysical and fMRI studies have indicated that visual processing of global symmetry has distinctive scaling properties, and proceeds more slowly than analysis of contrast, spatial frequency, and texture. We therefore undertook a visual evoked potential (VEP) study to directly compare the dynamics of symmetry and texture processing, and to determine the extent to which they interact. Stimuli consisted of interchange between structured and random black-and-white checkerboard stimuli. For symmetry, structured stimuli were colored with 2-fold symmetry (horizontal or vertical mirror), 4-fold symmetry (both mirror axes), and 8-fold symmetry (oblique mirror axes added). For texture, structured stimuli were colored according to the “even” isodipole texture [Julesz, B., Gilbert, E. N., & Victor, J. D. (1978). Visual discrimination of textures with identical third-order statistics. Biological Cybernetics, 31 , 137–140]. Thus, all stimuli had the same contrast, and check size, but differed substantially in correlation structure. To separate components of the VEP related to symmetry and texture from components that could be generated by local luminance and contrast changes, we extracted the odd-harmonic components of the VEP (recorded at C z – O z , C z – O 1 , C z – O 2 , C z – P z ) elicited by structured–random interchange. Responses to symmetry were largest for the 8-fold patterns, and progressively smaller for 4-fold, vertical, and horizontal symmetry patterns. Eightfold patterns were therefore used in the remainder of the study. The symmetry response is shifted to larger checks and lower temporal frequencies compared to the response to texture, and its temporal tuning is broader. Processing of symmetry makes use of neural mechanisms with larger receptive fields, and slower, more sustained temporal tuning characteristics than those involved in the analysis of texture. Sparse stimuli were used to dissociate check size and check density. VEP responses to sparse symmetry stimuli showed that there is no difference between first- and second-order symmetry for densities less than 12.5%. We discuss these findings in relation to local and global visual processes.
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paper_title: The functional role of oriented spatial filters in the perception of mirror symmetry — psychophysics and modeling

paper_content:

We investigated human sensitivity to vertical mirror symmetry in noise patterns filtered for narrow bands of variable orientations. Sensitivity is defined here as the amount of spatial phase randomization corresponding to 75% correct performance in a 2AFC detection task. In Experiment 1, sensitivity was found to be high for tests patterns of all orientations except those parallel to the axis of symmetry. This implies that corresponding mirror-orientations (e.g. 45 and 45°) are combined prior to symmetry detection. In Experiment 2, observers detected symmetry in tests of variable orientation in the presence of either non-symmetric or symmetric masks filtered for orientations either parallel or perpendicular to the axis. Observers were found to be primarily affected by masks of the same orientation as the test, thus suggesting that symmetry is computed separately in distinct mirror-orientation channels. In Experiment 3, observers detected a symmetric test of variable height and width embedded in random noise. Data revealed that mirror symmetry is computed over a spatial integration region (IR) that remains approximately constant in area but whose height-to-width aspect ratio changes from 20:1 to 2:1 as orientation is varied from parallel to perpendicular to the axis. We compare human data against that of an ideal observer to identify key factors that limit visual performance and discuss the implications for the functional architecture of symmetry perception. We also propose a multi-channel model of symmetry detection that combines the output of oriented spatial filters in a simple and physiologically plausible manner. Particular emphasis is placed on the notion that changes in the shape of the IR with orientation compensate for changes in information density and partially equate performance across orientations. © 2000 Elsevier Science Ltd. All rights reserved.
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paper_title: Detection of bilateral symmetry using spatial filters

paper_content:

When bilaterally symmetric images are spatially filtered and thresholded, a subset of the resultant 'blobs' cluster around the axis of symmetry. Consequently, a quantitative measure of blob alignment can be used to code the degree of symmetry and to locate the axis of symmetry. Four alternative models were tested to examine which components of this scheme might be involved in human detection of symmetry. Two used a blob-alignment measure, operating on the output of either isotropic or oriented filters. The other two used similar filtering schemes, but measured symmetry by calculating the correlation of one half of the pattern with a reflection of the other. Simulations compared the effect of spatial jitter, proportion of matched to unmatched dots and width or location of embedded symmetrical regions, on models' detection of symmetry. Only the performance of the oriented filter + blob-alignment model was consistent with human performance in all conditions. It is concluded that the degree of feature co-alignment in the output of oriented filters is the cue used by human vision to perform these tasks. The broader computational role that feature alignment detection could play in early vision is discussed, particularly for object detection and image segmentation. In this framework, symmetry is a consequence of a more general-purpose grouping scheme.
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paper_title: Binocular Disappearance of Monocular Symmetry

paper_content:

In an earlier demonstration binocular shapes were produced from monocularly shapeless, random-dot stereo images. A reversal of this phenomenon is demonstrated. A stereo image is devised in which the monocularly apparent shapes of bilateral symmetry disappear when stereoscopically viewed. This phenomenon sharpens the implications of the earlier one.
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paper_title: Monocular symmetry is neither necessary nor sufficient for the dichoptic perception of bilateral symmetry

paper_content:

Barlow and Reeves [1979. Vision Research, 19, 783-793] showed that bilateral symmetry detection in dot patterns is about equally efficient whether the displays are viewed monocularly or binocularly. If there is a binocular process which can be stimulated monocularly, this experiment does not indicate whether symmetry detection occurs before or after the site of binocular integration. This is so because the symmetrical patterns would have stimulated both monocular and binocular mechanisms under both viewing conditions. We presented stereoscopic 20-dot patterns, ten dots to each eye, for 150 ms so that 'false fusion' rather than rivalry occurred. Any axis of symmetry in the patterns was oriented at vertical (90 degrees ) or +/-1, 2, 3, or 4 degrees from vertical. The task was to judge whether the axis was tilted left or right of vertical, using the method of constant stimulus differences. Three kinds of pattern were used: SSS patterns were symmetrical in each eye alone and also dichoptically; NNS patterns were random monocularly but dichoptically symmetrical; and SSN patterns were symmetrical monocularly but dichoptically non-symmetrical. Orientation judgements were accurate, and equally so, for SSS and NNS displays but were extremely poor under SSN conditions. A control experiment showed that the poor performance in the SSN condition was not due to the axes of symmetry being eccentric to the fixation point. Thus, monocular symmetry is neither necessary nor sufficient for dichoptic bilateral symmetry perception; and symmetry mechanisms have no access to monocular signals.
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paper_title: Symmetry Perception and Spatial-Frequency Channels:

paper_content:

It is known that the sum of a random-dot array with vertical bilateral symmetry and one with horizontal bilateral symmetry appears as a random array. Here we show that if the vertically and horizontally symmetrical arrays are spatially filtered, so that their respective spectra are 2 octaves apart, then their superposition does not appear random, but both symmetries can be simultaneously perceived. The low-band array has a stronger perceptual weight than the high-band array. These demonstrations give further evidence that frequency channels are before symmetry perception.
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paper_title: Predominantly extra-retinotopic cortical response to pattern symmetry

paper_content:

Abstract Symmetry along one or more axes is a key property of objects and biological organisms. We report on a bilateral visual region of occipital cortex that responds strongly to the presence of multiple symmetries in the viewed image. The stimuli consisted of random dots organized in fourfold and onefold mirror-symmetric patterns, against random control stimuli. The contrast between symmetric and random patterns produced negligible or inconsistent activation of the primary visual projection area V1 or of other medial occipital projection areas. However, there was strong symmetry-specific activation in extra-retinotopic lateral occipital cortex. The high level of activation in this region of cortex may represent part of a general class of computations that require integration of information across a large span of the visual field.
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paper_title: Goodness of visual regularities: A non-transformational approach

paper_content:

Until recently, the transformational approach provided the only available formal analysis of visual regularities like repetition and mirror symmetry. This theoretical study presents a new analysis, based on the recently developed concept of holographic regularity. This concept applies to the intrinsic character of regularity and specifies the unique formal status of perceptually relevant regularities. The crucial point is that the two analyses imply the same structure for repetition but a different structure for mirror symmetry. Transformationally, mirror symmetry is an all-or-nothing property, whereas holographically, it is a graded property. This difference pervades the understanding of both perfect regularities and perturbed regularities. Whereas the transformational approach explains hardly any goodness phenomenon, the holographic approach explains a wide variety of goodness phenomena in a coherent way that is ecologically plausible as well.
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paper_title: The spatial region of integration for visual symmetry detection

paper_content:

Symmetry is a complex image property that is exploited by a sufficiently wide range of species to indicate that it is detected using simple visual mechanisms. These mechanisms rely on measurements made close to the axis of symmetry. We investigated the size and shape of this integration region (IR) by measuring human detection of spatially band–pass symmetrical patches embedded in noise. Resistance to disruption of symmetry (in the form of random phase noise) improves with increasing patch size, and then asymptotes when the embedded region fills the IR. The size of the IR is shown to vary in inverse proportion to spatial frequency; i.e. symmetry detection exhibits scale–invariance. The IR is shown to have rigid dimensions, elongated in the direction of the axis of symmetry, with an aspect ratio of ca. 2:1. These results are consistent with a central role for spatial filtering in symmetry detection.
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paper_title: The versatility and absolute efficiency of detecting mirror symmetry in random dot displays

paper_content:

The detection of mirror symmetry has been investigated by measuring discriminability (d') between two populations of dot displays that contain mirror pairs and random dots in different proportions. The difficulty of the task was varied by changing the proportions of paired dots in the two populations, and also by changing the accuracy of positioning the paired dots. Symmetry can be detected in brief exposures, monocularly or binocularly. when the axis is not vertical, and when the axis is not central in the visual field. The mechanism is therefore versatile. Its efficiency can be measured when the pairing is imperfect, for unpaired dots then fall where a pair is expected, thus causing the spurious appearance of a pair. When the pairing has an accuracy of about± 6′ vertically and horizontally an ideal mechanism would achieved′ values about double those attained by subjects; they are thus using 25% of the statistical information available, which is a high figure considering the versatility and complexity of the mechanisms required.
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paper_title: Simplicity versus likelihood in visual perception: from surprisals to precisals

paper_content:

The likelihood principle states that the visual system prefers the most likely interpretation of a stimulus, whereas the simplicity principle states that it prefers the most simple interpretation. This study investigates how close these seemingly very different principles are by combining findings from classical, algorithmic, and structural information theory. It is argued that, in visual perception, the two principles are perhaps very different with respect to the viewpoint-independent aspects of perception but probably very close with respect to the viewpoint-dependent aspects which, moreover, seem decisive in everyday perception. This implies that either principle may have guided the evolution of visual systems and that the simplicity paradigm may provide perception models with the necessary quantitative specifications of the often plausible but also intuitive ideas provided by the likelihood paradigm.
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paper_title: Scale invariance is driven by stimulus density

paper_content:

Scale invariance refers to aspects of visual perception that remain constant with changes in viewing distance. Previously, Dakin and Herbert [Proc. Roy. Soc. B. 265 (1397) (1998) 659] reported that the spatial integration region (IR) for mirror symmetry in bandpass noise is scale invariant because its dimensions scale with the inverse of peak spatial frequency. In bandpass noise, however, peak spatial frequency covaries with stimulus numerosity (i.e. the total number of information samples) and density (i.e. the total number of information samples per unit area). In this study, we report four experiments that decoupled properties of the retinal image affected by viewing distance––spatial frequency, numerosity, size, and density––and measured their effect on IR size. Stimuli consisted of bandpass microelements with vertically mirror-symmetric but otherwise random positions, and we measured observer resistance to random jitter imposed on microelement position. Results show that jitter resistance and IR size vary with the inverse of stimulus density but are unaffected by changes in stimulus spatial frequency, numerosity, or size. We found the IR has a 2:1 heightto-width aspect ratio and integrates information from � 18 microelements regardless of their spatial separation. Our results reveal that stimulus density plays a central role in the visual system’s implementation of scale invariance. Using an ideal-observer, we demonstrate that scale invariance reflects genuine neural scale selection rather than a physical limitation on the stimulus’ information content. Our findings that jitter resistance and IR size vary with the inverse of density challenge current models of spatial vision but can be reconciled with a model that compares the output of bandpass non-Fourier mechanisms to select spatial scales that match stimulus density. � 2002 Elsevier Science Ltd. All rights reserved.
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paper_title: Using relational structure to detect symmetry: A Voronoi tessellation based model of symmetry perception

paper_content:

Numerous models of symmetry perception have been proposed in recent years. Unfortunately, it is difficult to assess the relative utility of these models as little effort has been made to directly compare them. This paper outlines a new model of symmetry perception based upon the relational structure revealed by Voronoi tessellation. The model has been developed in response to evidence suggesting that the human visual system is generating a Voronoi-like representation at an early stage in processing. Bayesian model selection is employed to compare the performance of the Voronoi model to that of five previously published models across six empirical datasets. The results indicate that the Voronoi model provides a more likely account of the data than the five alternative models.
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paper_title: Higher-order structure in regularity detection

paper_content:

In three experiments a simple Euclidean transformation (reflection, translation, rotation) was applied to collections of twelve dots in such a way that they contained equal lower-order structure, defined on the pairwise grouping of elements with their partner following transformation (e.g. parallel virtual lines), but differed in the presence vs absence of higher-order structure, defined on pairs of pairwise groupings (e.g. virtual quadrangles with correlated angles). Based on the much better performance levels (d′) in the case of additional higher-order structure, we conclude that global regularities are easier to detect when the local correspondences are supported by higher-order ones formed between them. These enable the lower-order groupings to spread out across the whole pattern very rapidly (called bootstrapping). As a preliminary attempt to specify these principles, we proposed a working model with two basic components: first, a function expressing the cost of a perceptual grouping or the lack of regularity, and, secondly, an algorithm based on simulated annealing to minimize the cost function. The simulation results obtained with our current implementation of these principles showed satisfactory qualitative agreement with human regularity detection performance. Finally, the theory was shown to capture the essence of a large number of grouping phenomena taken from diverse domains such as detection of symmetry in dot patterns, global structure in Glass and vector patterns, correspondence in stereoscopic transparency and apparent motion. Therefore, we are convinced that, in principle, the mechanism used by the human visual system to detect regularity incorporates something like bootstrapping based on higher-order structure. We regard this as a promising step towards unraveling the intriguing mechanisms of classic Gestalt phenomena.
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paper_title: The versatility and absolute efficiency of detecting mirror symmetry in random dot displays

paper_content:

The detection of mirror symmetry has been investigated by measuring discriminability (d') between two populations of dot displays that contain mirror pairs and random dots in different proportions. The difficulty of the task was varied by changing the proportions of paired dots in the two populations, and also by changing the accuracy of positioning the paired dots. Symmetry can be detected in brief exposures, monocularly or binocularly. when the axis is not vertical, and when the axis is not central in the visual field. The mechanism is therefore versatile. Its efficiency can be measured when the pairing is imperfect, for unpaired dots then fall where a pair is expected, thus causing the spurious appearance of a pair. When the pairing has an accuracy of about± 6′ vertically and horizontally an ideal mechanism would achieved′ values about double those attained by subjects; they are thus using 25% of the statistical information available, which is a high figure considering the versatility and complexity of the mechanisms required.
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paper_title: Component processes in the perception of bilaterally symmetric dot textures

paper_content:

If a random-dot texture is reflected about a given axis, the resulting bilateral symmetry is immediately detected. In order to account for this ability, it has been suggested that the visual system detects reflection in these dot textures because of the existence of a symmetric neural organization, centered about the fovea, which performs a point-by-point analysis. As yet, there is no evidence of such an organization in the human visual system. An alternative description of a bilaterally symmetric texture, that of a two-dimensional distribution of uniformly oriented point-pair elements, of nonuniform size and with collinear midpoints, is more consistent with known mammalian visual-system neurophysiology. Experiments were conducted in order to determine whether the human visual system is sensitive to the orientational uniformity of otherwise nonuniform point-pair elements and to their midpoint collinearity. The results indicate that there are three processes involved in the perception of bilaterally symmetric dot textures: the detection of orientational uniformity of the different sized point-pair elements; the fusion of salient element point-pairs into a salient feature; the detection of the symmetry of the resulting feature. This component-process hypothesis eliminates the necessity to postulate the existence of a symmetrical neural organization centered about the fovea.
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paper_title: Scale invariance is driven by stimulus density

paper_content:

Scale invariance refers to aspects of visual perception that remain constant with changes in viewing distance. Previously, Dakin and Herbert [Proc. Roy. Soc. B. 265 (1397) (1998) 659] reported that the spatial integration region (IR) for mirror symmetry in bandpass noise is scale invariant because its dimensions scale with the inverse of peak spatial frequency. In bandpass noise, however, peak spatial frequency covaries with stimulus numerosity (i.e. the total number of information samples) and density (i.e. the total number of information samples per unit area). In this study, we report four experiments that decoupled properties of the retinal image affected by viewing distance––spatial frequency, numerosity, size, and density––and measured their effect on IR size. Stimuli consisted of bandpass microelements with vertically mirror-symmetric but otherwise random positions, and we measured observer resistance to random jitter imposed on microelement position. Results show that jitter resistance and IR size vary with the inverse of stimulus density but are unaffected by changes in stimulus spatial frequency, numerosity, or size. We found the IR has a 2:1 heightto-width aspect ratio and integrates information from � 18 microelements regardless of their spatial separation. Our results reveal that stimulus density plays a central role in the visual system’s implementation of scale invariance. Using an ideal-observer, we demonstrate that scale invariance reflects genuine neural scale selection rather than a physical limitation on the stimulus’ information content. Our findings that jitter resistance and IR size vary with the inverse of density challenge current models of spatial vision but can be reconciled with a model that compares the output of bandpass non-Fourier mechanisms to select spatial scales that match stimulus density. � 2002 Elsevier Science Ltd. All rights reserved.
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paper_title: Periodicity of striate-cortex-cell receptive fields

paper_content:

If striate cells had the simple bipartite or tripartite receptive fields (RF’s) classically attributed to them, they should be quite broadly tuned for spatial frequency. Most striate-cortex cells, however, are fairly narrowly tuned and would be expected to have more-periodic RF’s. We have examined this question in recordings of the responses of cat and monkey striate-cortex cells to gratings of increasingly large number of cycles, all centered on the cells’ RF’s. Simple cells narrowly tuned for spatial frequency were found to increase their responses with increasing numbers of stimulus cycles beyond the 1½ cycles expected from the classical RF shape. Broadly tuned simple cells were found to have less-periodic RF’s. Whereas narrowly tuned complex cells were also found to respond maximally to many stimulus cycles, other more broadly tuned complex cells did as well (possibly reflecting summation across many broadly tuned simple cells without regard to phase). A suppressive region was often seen just outside the excitatory two-dimensional spatial-frequency region, at off orientations and/or off spatial frequencies and around the whole RF in space. Most striate cells can thus be described as having periodic RF’s in the space domain such that they fire just to patterns whose local spatial-frequency spectra fall within a compact, restricted, roughly circular two-dimensional spatial-frequency region, with an encircling suppressive region in both the space and the frequency domains.
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paper_title: A biologically plausible model of human shape symmetry perception.

paper_content:

Symmetry is usually computationally expensive to encode reliably, and yet it is relatively effortless to perceive. Here, we extend F. J. A. M. Poirier and H. R. Wilson's (2006) model for shape perception to account for H. R. Wilson and F. Wilkinson's (2002) data on shape symmetry. Because the model already accounts for shape perception, only minimal neural circuitry is required to enable it to encode shape symmetry as well. The model is composed of three main parts: (1) recovery of object position using large-scale non-Fourier V4-like concentric units that respond at the center of concentric contour segments across orientations, (2) around that recovered object center, curvature mechanisms combine multiplicatively the responses of oriented filters to encode object-centric local shape information, with a preference for convexities, and (3) object-centric symmetry mechanisms. Model and human performances are comparable for symmetry perception of shapes. Moreover, with some improvement of edge recovery, the model can encode symmetry axes in natural images such as faces.
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paper_title: Detection of bilateral symmetry using spatial filters

paper_content:

When bilaterally symmetric images are spatially filtered and thresholded, a subset of the resultant 'blobs' cluster around the axis of symmetry. Consequently, a quantitative measure of blob alignment can be used to code the degree of symmetry and to locate the axis of symmetry. Four alternative models were tested to examine which components of this scheme might be involved in human detection of symmetry. Two used a blob-alignment measure, operating on the output of either isotropic or oriented filters. The other two used similar filtering schemes, but measured symmetry by calculating the correlation of one half of the pattern with a reflection of the other. Simulations compared the effect of spatial jitter, proportion of matched to unmatched dots and width or location of embedded symmetrical regions, on models' detection of symmetry. Only the performance of the oriented filter + blob-alignment model was consistent with human performance in all conditions. It is concluded that the degree of feature co-alignment in the output of oriented filters is the cue used by human vision to perform these tasks. The broader computational role that feature alignment detection could play in early vision is discussed, particularly for object detection and image segmentation. In this framework, symmetry is a consequence of a more general-purpose grouping scheme.
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paper_title: Bilateral symmetry embedded in noise is detected accurately only at fixation

paper_content:

Bilateral or mirror symmetry is a ubiquitous feature of biological forms that the visual system could exploit for segmenting an object from a cluttered background. If this is so, the visual system may be prepared to detect symmetry at all retinal locations in parallel. Indeed, a biologically plausible model that responds optimally at axes of symmetry is quite easy to construct. Our data show, however, that if such a mechanism exists, it works with high efficiency only at the fovea. The detection of vertical bilateral symmetry embedded in random noise is very poor unless the axis of symmetry is very close to the point of fixation. This leads to the conclusion that symmetry does not play an important role in image segmentation and that it is important to the visual system only after it is fixated. © 1998 Elsevier Science Ltd. All rights reserved.
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paper_title: Spatial frequency adaptation can enhance contrast sensitivity

paper_content:

Abstract Adaptation to a high-contrast sinusoidal luminance grating produces a temporary, band limited loss in sensitivity centered around the adaptation frequency. The decrease appears to be both narrower and more symmetrical than earlier reports suggest. The effect falls to zero by f ± 1 octave and is not reliably present from f ± 1 octave to f ± 2 octaves. Enhancement of contrast sensitivity occurs for frequencies further removed, peaking at about f ± 2 built 34 to 3 octaves. This suggests mutual inhibitory interactions among spatial-frequency-selective units of varying filter characteristics. Longterm practice produces significantly higher contrast sensitivity functions and narrower bandwidths of the adaptational sensitivity loss.
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paper_title: Visual pattern analyzers

paper_content:

PART I: INTRODUCTION 1. Neurophysiology and Psychophysics 2. Some Mathematics PART II: ADAPTION 3. Models of Selective Effects PART III: SUMMATION 4. Models for Far-Apart Values 5. Far-Apart Values on Spatial Dimensions 6. Close Values on Spatial Dimensions PART IV: UNCERTAINTY 7. Extrinsic Uncertainty and Summation Revisited 8. Intrinsic Uncertainty and Transducer Functions PART V: IDENTIFICATION 9. Discrimination 10. Three More Paradigms and Transducer Functions PART VI: MULTIPLE DIMENSIONS 11. Some General Considerations 12. Results of Analyzer-Revealing Experiments 13. Results of Parametric Experiments PART VII: EPILOGUE 14. The Assumptions Revisited
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paper_title: Symmetry detection by categorization of spatial phase, a model

paper_content:

Bilateral symmetry of patterns or ornaments is attractive to animals as diverse as birds choosing mates and insects searching for food. Although symmetry detection seems to be widespread the mechanisms remain obscure. It has been suggested that this is a more complex task than establishing the co-linearity of a row of dots, requiring matching of points in the two halves of the image, and is perhaps a corollary of the ability to recognize objects regardless of orientation or position. Here I show that axes of bilateral symmetry can be found by one class of local feature detector. For a mechanism that identifies edges and lines by classifying relative phases in spatial harmonics an axis resembles a line with no contrast. Because asymmetries modify spatial phases they will degrade the signal making the mechanism inherently sensitive to fluctuating asymmetry.
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paper_title: Psychophysical studies of monkey Vision-III. Spatial luminance contrast sensitivity tests of macaque and human observers

paper_content:

Abstract The detectability of luminance modulated gratings of different spatial frequencies was determined at five different adaptation levels for three macaque monkeys and five normal human observers. The human and macaque observers gave results which were identical in form and similar in absolute values. Both species showed optimal contrast sensitivity in the middle spatial frequency range of about 3–5 c/deg with both low and high frequency attenuation, at high light levels. Contrast sensitivity to high frequencies dropped rapidly as adaptation levels were lowered, with a resulting shift in peak sensitivity to lower spatial frequencies. At the lowest adaptation level studied, neither macaque nor human observers showed any low frequency attenuation in the spatial luminance contrast sensitivity function.
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paper_title: Modelling symmetry detection with back-propagation networks

paper_content:

This paper reports experimental data and results of network simulations in a project on symmetry detection in small 6 x 6 binary patterns. Patterns were symmetrical about the vertical, horizontal, positive-oblique, or negative-oblique axis, and were viewed on a computer screen. Encouraged to react quickly and accurately, subjects indicated axis of symmetry by pressing one of four designated keys. Detection times and errors were recorded. Back-propagation networks were trained to categorize the patterns on the basis of axis of symmetry, and, by employing cascaded activation functions on their output units, it was possible to compare network performance with subjects' detection times. Best correspondence between simulated and human detection-time functions was observed after the networks had been given significantly more training on patterns symmetrical about the vertical and the horizontal axes. In comparison with no pre-training and pre-training with asymmetric patterns, pre-training networks with sets of single vertical, horizontal, positive-oblique or negative-oblique bars speeded subsequent learning of symmetrical patterns. Results are discussed within the context of theories suggesting that faster detection of symmetries about the vertical and horizontal axes may be due to significantly more early experience with stimuli oriented on these axes.
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paper_title: Foundations of Cyclopean Perception

paper_content:

This classic work on cyclopean perception has influenced a generation of vision researchers, cognitive scientists, and neuroscientists and has inspired artists, designers, and computer graphics pioneers. In Foundations of Cyclopean Perception (first published in 1971 and unavailable for years), Bela Julesz traced the visual information flow in the brain, analyzing how the brain combines separate images received from the two eyes to produce depth perception. Julesz developed novel tools to do this: random-dot stereograms and cinematograms, generated by early digital computers at Bell Labs. These images, when viewed with the special glasses that came with the book, revealed complex, three-dimensional surfaces; this mode of visual stimulus became a paradigm for research in vision and perception. This reprint edition includes all 48 color random-dot designs from the original, as well as the special 3-D glasses required to view them.Foundations of Cyclopean Perception has had a profound impact on the vision studies community. It was chosen as one of the one hundred most influential works in cognitive science in a poll conducted by the University of Minnesota's Center for Cognitive Sciences. Many copies are "permanently borrowed" from college libraries; used copies are sought after online. Now, with this facsimile of the 1971 edition, the book is available again to cognitive scientists, neuroscientists, vision researchers, artists, and designers.
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paper_title: Perception of mirror symmetry reveals long-range interactions between orientation-selective cortical filters.

paper_content:

We investigated perceptual interactions between orientation selective cortical filters using a task in which the observer was to detect mirror symmetry in briefly flashed visual patterns composed of oriented Gabor elements. On each trial, the Gabor patches were randomly placed in one half of the stimulus region, and symmetry was generated by reflecting the positions of the patch centers across the vertical axis. A prespecified proportion of patches were in mirror symmetrical positions with the remaining patches placed at random positions. The perception of mirror symmetry was measured for three stimulus conditions: (1) same orientation (i.e. all the local Gabor elements were either vertical or horizontal), (2) mixed matching (i.e. the orientations could be randomly both vertical and horizontal with the constraint that the orientations in a mirror symmetrical pair were matching), and (3) mixed opposing (i.e. the orientations were both vertical and horizontal, but in a mirror symmetrical pair they were always orthogonal). We found that the perception of global symmetry was poorer (thresholds were elevated) when the local orientations of feature pairs were orthogonal than when they were matched. This result is consistent with the properties of the neurons in the corpus callosum, which selectively interconnect cortical filters with identical orientation specificity.
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paper_title: A biologically plausible model of human shape symmetry perception.

paper_content:

Symmetry is usually computationally expensive to encode reliably, and yet it is relatively effortless to perceive. Here, we extend F. J. A. M. Poirier and H. R. Wilson's (2006) model for shape perception to account for H. R. Wilson and F. Wilkinson's (2002) data on shape symmetry. Because the model already accounts for shape perception, only minimal neural circuitry is required to enable it to encode shape symmetry as well. The model is composed of three main parts: (1) recovery of object position using large-scale non-Fourier V4-like concentric units that respond at the center of concentric contour segments across orientations, (2) around that recovered object center, curvature mechanisms combine multiplicatively the responses of oriented filters to encode object-centric local shape information, with a preference for convexities, and (3) object-centric symmetry mechanisms. Model and human performances are comparable for symmetry perception of shapes. Moreover, with some improvement of edge recovery, the model can encode symmetry axes in natural images such as faces.
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paper_title: Detection of bilateral symmetry using spatial filters

paper_content:

When bilaterally symmetric images are spatially filtered and thresholded, a subset of the resultant 'blobs' cluster around the axis of symmetry. Consequently, a quantitative measure of blob alignment can be used to code the degree of symmetry and to locate the axis of symmetry. Four alternative models were tested to examine which components of this scheme might be involved in human detection of symmetry. Two used a blob-alignment measure, operating on the output of either isotropic or oriented filters. The other two used similar filtering schemes, but measured symmetry by calculating the correlation of one half of the pattern with a reflection of the other. Simulations compared the effect of spatial jitter, proportion of matched to unmatched dots and width or location of embedded symmetrical regions, on models' detection of symmetry. Only the performance of the oriented filter + blob-alignment model was consistent with human performance in all conditions. It is concluded that the degree of feature co-alignment in the output of oriented filters is the cue used by human vision to perform these tasks. The broader computational role that feature alignment detection could play in early vision is discussed, particularly for object detection and image segmentation. In this framework, symmetry is a consequence of a more general-purpose grouping scheme.
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paper_title: Bilateral symmetry embedded in noise is detected accurately only at fixation

paper_content:

Bilateral or mirror symmetry is a ubiquitous feature of biological forms that the visual system could exploit for segmenting an object from a cluttered background. If this is so, the visual system may be prepared to detect symmetry at all retinal locations in parallel. Indeed, a biologically plausible model that responds optimally at axes of symmetry is quite easy to construct. Our data show, however, that if such a mechanism exists, it works with high efficiency only at the fovea. The detection of vertical bilateral symmetry embedded in random noise is very poor unless the axis of symmetry is very close to the point of fixation. This leads to the conclusion that symmetry does not play an important role in image segmentation and that it is important to the visual system only after it is fixated. © 1998 Elsevier Science Ltd. All rights reserved.
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Title: Behind the Looking-Glass: A Review on Human Symmetry Perception

Section 1: Motivation
Description 1: This section explains the historical context and the reasons why research into human symmetry perception is important.

Section 2: The Symmetry of Nature
Description 2: This section discusses how symmetry is prevalent in nature and artificial environments, and its significance to human perception.

Section 3: The Nature of Symmetry
Description 3: This section describes the geometrical and perceptual aspects of symmetry, focusing particularly on bilateral symmetry and its importance.

Section 4: The Role of Symmetry Processing in Perceptual Organization
Description 4: This section explores how symmetry detection is an automatic visual process integral to perceptual organization, grouping, and segmentation.

Section 5: Object Formation
Description 5: This section delves into how symmetry processing aids in the perceptual grouping and segmentation of visual input, supporting object formation.

Section 6: Automatic Processing
Description 6: This section provides evidence that symmetry detection is automatic and does not rely on cognitive control.

Section 7: The Relationship between Symmetry Processing and Cognition
Description 7: This section discusses how higher cognitive processes, such as attention and awareness, interact with symmetry detection.

Section 8: Functional Characteristics
Description 8: This section details various functional properties of symmetry detection, including spatial, temporal characteristics, noise resistance, and the processing of symmetry axes.

Section 9: Models of Symmetry Processing
Description 9: This section reviews different models of symmetry perception, including representational, process, spatial filtering, and neural models.

Section 10: Neural Implementation
Description 10: This section addresses the neural basis of symmetry perception and the specific brain areas involved.

Section 11: Discussion and Conclusions
Description 11: This section summarizes key findings, discusses the complexity of symmetry perception, and suggests areas for future research.