The dynamic-stimulus advantage of visual symmetry perception

It has been speculated that visual symmetry perception from dynamic stimuli involves mechanisms different from those for static stimuli. However, previous studies found no evidence that dynamic stimuli lead to active temporal processing and improve symmetry detection. In this study, four psychophysical experiments investigated temporal processing in symmetry perception using both dynamic and static stimulus presentations of dot patterns. In Experiment 1, rapid successive presentations of symmetric patterns (e.g., 16 patterns per 853 ms) produced more accurate discrimination of orientations of symmetry axes than static stimuli (single pattern presented through 853 ms). In Experiments 2-4, we confirmed that the dynamic-stimulus advantage depended upon presentation of a large number of unique patterns within a brief period (853 ms) in the dynamic conditions. Evidently, human vision takes advantage of temporal processing for symmetry perception from dynamic stimuli.     

Identification of symmetry: Effects of stimulus orientation and head position

It has been argued that the perceptual advantage of symmetry depends upon the essentially symmetrical properties of the visual system. According to this explanation, the ease of identification of symmetries about different axes of orientation should decrease with increasing distance from the vertical: Reaction times to vertical symmetry should be faster than those to diagonal symmetry, which in turn should be faster than those to horizontal symmetry. Previous research demonstrating this pattern of responding employed stimuli with linear axes. In the present study, the subjects viewed tachistoscopically presented symmetrical and asymmetrical dot patterns (which had no explicit axes) in one of three head positions: upright, 45 deg left, and 45 deg right. The subjects’ performance failed to support the structural explanation: Identification of symmetry is equivalently fast for vertical and horizontal; vertical and horizontal show strong advantages over obliques, and this general advantage follows retinal coordinates. Findings are discussed in light of alternative theories of symmetry processing.     

Detection of symmetry in tachistoscopically presented dot patterns: Effects of multiple axes and skewing

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.     

Detection of symmetry in tachistoscopically presented dot patterns: effects of multiple axes and skewing.

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 degrees 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.     

Goodness of regularity in dot patterns: global symmetry, local symmetry, and their interactions

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 performance in this regularity-detection task did not increase in a linear way when some symmetries were added to other symmetries.     

Detection of bilateral symmetry in complex biological images

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 was designed to assess whether symmetry detection was dependent upon the markings and patterns on the body and appendages of the animals. The natural images were converted to silhouettes and tested against matched dot patterns. In both studies, images were presented in a random sequence with the axis of symmetry vertical, horizontal, oblique left, and oblique right. Performance with the biological images was consistently better than with the dot patterns. Abolishing fine detail did not appreciably reduce this effect. A pronounced vertical advantage was apparent with all stimuli, demonstrating that this phenomenon is robust despite considerable variation in image complexity. The implications of orientation effects for perception of natural structures are discussed.     

Floral guidance of learning a preference for symmetry by bumblebees

This study examines the mechanism underlying one way in which bumblebees are known to develop a preference for symmetric patterns: through prior non-differential reinforcement on simple patterns (black discs and white discs). In three experiments, bees were given a choice among symmetric and asymmetric black-and-white non-rewarding patterns presented at the ends of corridors in a radial maze. Experimental groups had prior rewarded non-discrimination training on white patterns and black patterns, while control groups had no pre-test experience outside the colony. No preference for symmetry was obtained for any of the control groups. Prior training with circular patterns highlighting a horizontal axis of symmetry led to a specific subsequent preference for horizontal over vertical symmetry, while training with a vertical axis abolished this effect. Circles highlighting both axes created a general avoidance of asymmetry in favour of symmetric patterns with vertical, horizontal or both axes of symmetry. Training with plain circles, but not with deformed circles, led to a preference for symmetry: there was no evidence that the preference emerged just by virtue of having attention drawn away from irrelevant pattern differences. Our results point to a preference for symmetry developing gradually through first learning to extract an axis of symmetry from simple patterns and subsequently recognizing that axis in new patterns. They highlight the importance of continued learning through non-differential reinforcement by skilled foragers. Floral guides can function not only to guide pollinators to the source of reward but also to highlight an axis of symmetry for use in subsequent floral encounters.     

Effects of asynchrony on symmetry perception

The effect of temporal image segmentation on symmetry perception was investigated by means of stimuli composed of one part surrounding another. The two parts could be presented synchronously or with a temporal offset (20–100 ms), and each part could be either symmetrical or random. The task was to discriminate completely symmetrical (S) stimuli (in Experiment 1) or completely random (R) stimuli (in Experiment 2) from partially symmetrical (PS) stimuli in which one part was symmetrical and the other random. The R stimuli showed an asynchrony effect but the S stimuli did not. Furthermore, in both experiments, the PS stimuli showed an asynchrony effect when the symmetrical part was presented last but not when the symmetrical part was presented first (independent of whether it was the surrounded part or the surrounding part). Both results suggest that symmetry is strong enough to override this kind of temporal image segmentation.     

The force of symmetry revisited: symmetry-to-noise ratios regulate (a)symmetry effects

Freyd and Tversky's [Am. J. Psychol. 97 (1984) 109] data suggested that human observers tend to overestimate relatively high levels of symmetry (symmetry effect), and tend to underestimate relatively low levels of symmetry (asymmetry effect). However, on the basis of their holographic approach to visual regularity, van der Helm and Leeuwenberg [Psychol. Rev. 103(3) (1996) 429] predicted that, at any level of symmetry, both symmetry and asymmetry effects may occur as a consequence of correct estimates of symmetry-to-noise ratios. This prediction was tested in two experiments, with tasks and stimuli similar to those in Freyd and Tversky's study. First, subjects had to judge whether a noisy symmetry is more similar to a slightly more symmetrical variant or to a slightly less symmetrical variant. Second, for every pair of stimuli in such a triadic comparison, subjects had to judge which stimulus is the more symmetrical one. The results from both experiments show that the occurrence of (a)symmetry effects indeed depends on symmetry-to-noise ratios.     

Complexity and goodness of dot patterns varying in symmetry

Summary Two experiments were performed to specify stimulus determinants of pattern complexity and pattern goodness. Dot patterns distributed in 3×3 and 4×4 matrices with a rectilinear frame were used in Experiment 1, and dot patterns in hexagonal frameworks with a circular frame were used in Experiment 2. The patterns were invariant for transformations of rotation or reflection, and formed symmetry groups of different orders, i.e., cyclic and dihedral groups. The complexity and goodness of the patterns depended upon such stimulus variables as follows: (1) complexity decreased with the order of symmetry groups with equal weights for cyclic and dihedral groups, whereas goodness increased with the order of both symmetry groups with different weights; (2) the simplicity and goodness of patterns with a vertical axis were greater than those with a horizontal axis and those with an oblique one; (3) the complexity of the patterns that had collinear elements with equal length was rated the simplest; (4) pattern goodness increased as a function of the number of dots and the concentrations of dot to rotation/reflection axis in 3×3 and 4 × 4 matrices. Thus, complexity and goodness of pattern differed with respect to these stimulus variables.     

The effect of vertical and horizontal symmetry on memory for tactile patterns in late blind individuals

Visual stimuli that exhibit vertical symmetry are easier to remember than stimuli symmetric along other axes, an advantage that extends to the haptic modality as well. Critically, the vertical symmetry memory advantage has not been found in early blind individuals, despite their overall superior memory, as compared with sighted individuals, and the presence of an overall advantage for identifying symmetric over asymmetric patterns. The absence of the vertical axis memory advantage in the early blind may depend on their total lack of visual experience or on the effect of prolonged visual deprivation. To disentangle this issue, in this study, we measured the ability of late blind individuals to remember tactile spatial patterns that were either vertically or horizontally symmetric or asymmetric. Late blind participants showed better memory performance for symmetric patterns. An additional advantage for the vertical axis of symmetry over the horizontal one was reported, but only for patterns presented in the frontal plane. In the horizontal plane, no difference was observed between vertical and horizontal symmetric patterns, due to the latter being recalled particularly well. These results are discussed in terms of the influence of the spatial reference frame adopted during exploration. Overall, our data suggest that prior visual experience is sufficient to drive the vertical symmetry memory advantage, at least when an external reference frame based on geocentric cues (i.e., gravity) is adopted.     

Effects of test-mask similarity on forward and backward masking of patterns by patterns

Summary Effects of test-mask similarity on the masking function were examined in two experiments. In Experiment 1, random bar patterns were used as test and mask stimuli. Bars were oriented in 135° oblique direction in test stimuli, and in 135° or 45° oblique direction in mask stimuli. The SOA was varied from 0 to 100 ms (backward masking). In Experiment 2, red and blue random dot patterns were used as both test and mask stimuli, with SOAs of –100 to 100 ms (forward and backward masking). The subject was asked to report the number of bars or dots as quickly as possible. The results of four subjects in one experiment and five in the other indicated that masking effects were generally greater when the test and mask stimuli were the same in orientation or color than when they were different. Slightly asymmetrical U-shaped functions were obtained both in the same and in different (orientation or color) conditions. A two-factor model with a similarity-related symmetrical integration process and a similarity-unrelated asymmetrical interuption process was considered.Experiment 1 was conducted by the first and third authors at Chiba University, and Experiment 2 was performed by the first and second authors at the University of Tokyo     

Spontaneous transitions and symmetry: Pattern dynamics in human four-limb coordination

Transitions between the coordinative patterns of rhythmically moving human arms and legs were studied to test the predictions of a four-component model (Schöner, Jiang and Kelso, 1990). Based upon results from previous two-component experiments (Kelso and Jeka, 1992), three assumptions were made about the four-limb system: (1) all limb pairs produce stable in-phase and anti-phase patterns; (2) the coupling between homologous limbs (i.e., right and left arms or right and left legs) is appreciably stronger than the coupling between nonhomologous limbs (i.e., arm and leg); and (3) right-left symmetry. An analysis of a four-component model (Jeka, Kelso and Kiemel, 1993) led to the prediction of four attracting invariant circles, each with two stable patterns in the state space of four-limb dynamics. In an experiment to test this prediction, subjects were required to cycle all four limbs in one of the eight patterns to the beat of an auditory metronome whose frequency was systematically increased. All subjects demonstrated spontaneous transitions corresponding to pathways along the invariant circles. Pre-transition relative phase variability increased with required frequency up to the transition, suggesting that loss of pattern stability induced the observed transitions. Thus, despite a large number of potential transitions, differential coupling between limb pairs and symmetry of the pattern dynamics restricts the behavior of the human four-limb system to a limited area of its state space.     

State and complexity-dependent symmetry identification of 2-dimensional patterns and evoked potentials

To analyse the influence of structural complexity of visual patterns and of an operationally defined cognitive state on evoked potentials some on--line closed--loop experiments were carried out. Symmetrical checkerboard patterns generated by means of Walsh functions were used as stimuli. The inherent symmetry should be recognized by the subjects. The state was defined on the basis of the spectral power density distribution of the EEG measured in the time interval of one second before the stimulus onset. The two state values were labeled by the state of alpha wave dominance and the state of non alpha wave dominance. According to the definition for the state of alpha wave dominance 70% of the whole spectral power must be contained in the frequency range from 8 Hz until 13 Hz at least. Otherwise the prestimulus EEG are labeled by the concept of non alpha wave state. The influence of the cognitive state and of the structural complexity on the evoked potentials has been verified experimentally. Significantly higher amplitudes of the evoked potentials in the time range of 140 ms until 200 ms after stimulus onset are due to higher complexity of the stimuli. The state of alpha wave dominance led to significantly stronger negativity of the evoked potentials in the range of 280 ms until 400 ms after stimulus onset.     

Two-dimensional tilt illusions induced by orthogonal plaid patterns: effects of plaid motion, orientation, spatial separation, and spatial frequency

Tilt illusions occur when a drifting vertical test grating is surrounded by a drifting plaid pattern composed of orthogonal moving gratings. The angular function of this illusion was measured as the plaid orientation (and therefore its drift direction) varied over a 180 degrees range. This was done when the test and inducing stimuli abutted and had the same spatial frequency, and when the test and inducing stimuli either differed in frequency by an octave, or were spatially separated by a 2 deg blank annulus, or both differed in frequency and were also separated by the annulus (experiments 1-4). The obtained angular function was virtually identical to that obtained previously with the rod and frame effect and other cases involving orthogonal inducing components, with evidence for illusions induced both by real-line components and by virtual axes of symmetry. Although the magnitude of the illusion was very similar in all four experiments, there was evidence to suggest that largest real-line effects occurred in the abutting same-frequency condition, with a pattern of results similar to that obtained previously with the simple one-dimensional tilt illusion. On the other hand, virtual-axis effects were more prominent with gaps between test and inducing stimuli. A fifth, repeated-measures, experiment confirmed this pattern of results. It is suggested that this pattern-induced tilt effect reflects both striate and extrastriate mechanisms and that the apparent influence of spatially distal virtual axes of symmetry upon perceived orientation implies the existence of AND-gate mechanisms, or conjunction detectors, in the orientation domain.     

Effects of surface pre-presentation on symmetry detection on a 3-D bumpy surface

Abstract:  The aim of this study was to investigate the visual detection mechanism of mirror symmetrical dot patterns drawn on a 3-D bumpy surface (i.e., 3-D noisy curved surface). The focus of this investigation was whether symmetry detection on the bumpy surface is associated with structure recovery of the surface. In Experiment 1, we confirmed that the human visual system can distinguish the bumpy surface from a distorted dot pattern on a transparent bumpy surface. In Experiment 2, we required participants to discriminate between a symmetrical pattern on a transparent (non-visible) bumpy surface and an opaque (visible) bumpy surface for the same stimuli as in Experiment 1. Finally, in Experiment 3, we examined the effect of pre-presentation of the opaque bumpy surface on pattern discrimination. The results showed that pre-presentation of the opaque surface facilitated the detection of a diagonal symmetry, but not in the case of the detection of a cardinal symmetry. These results suggested that diagonal symmetry involves the process of surface recovery, whereas cardinal symmetry does not.     

Coordinate frame for symmetry detection and object recognition

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.     

The perception of complex patterns by touch

Two experiments are reported on matching Braille characters in dot pattern and outline shape formats by congenitally blind subjects. In a third experiment subjects' drawings of Braille shapes were analysed. Experiment 1 showed that normal and retarded readers differed significantly when outline shapes 'cued' identical dot patterns, but did not differ when the dot patterns preceded outlines. However, normal as well as retarded readers were faster and more accurate in judging identical pairs in dot-pattern format than in any other condition. In experiment 2 dot patterns and outline shapes were matched at three levels of reading proficiency. Faster readers made fewer errors in matching identical pairs, but all subjects were more accurate and faster with dot patterns than with outline shapes. Experiment 3 showed that blind subjects' drawing of outline shapes is not affected by reading proficiency. Most common were errors of alignment, including 'rotation' from vertical to horizontal axes, suggesting that sources of confusion were spatial position of dots and major axes of alignment rather than mirror-image reversals. It is argued that the results are not compatible with the hypothesis that Braille letters are perceived as global outline shapes by faster readers.     

Visual symmetry recognition by pigeons

Summary 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.     

Mirror symmetry opposes splitting of chromatically homogeneous surfaces

Chromatically homogeneous surfaces can be seen as single figures but also as two or more overlapping figures. Local factors such as relatability have been proposed in order to explain perception of two or more figures (Kellman and Shipley, 1991 Cognitive Psychology 23 141-221). However, even when these factors are at work, there are conditions favouring the perception of a single figure, which have not been explored so far. Here we propose that one such factor is the mirror symmetry of the surface. Three experiments were designed to test: (a) the main hypothesis, that mirror symmetry enhances perception of a single figure; (b) the role of orientation; (c) the effect of the number of axes of symmetry. The results show that (i) there is a good general correlation between mirror symmetry and perception of a single figure; (ii) vertical and horizontal axes of symmetry are the most effective; and (iii) the more axes of symmetry a surface has, the more likely is the perception of a single figure. These results suggest that mirror symmetry is an important factor in the perception of chromatically homogeneous displays. Some explanations are discussed, particularly one based on the rejection-of-coincidence principle [Rock, 1983 The Logic of Perception (Cambridge, MA: MIT Press)], and a version of the minimum principle in which the strength of the global solution depends on symmetry, whereas the strength of the splitting solution depends on the strength of local factors. In brief, global and local factors compete in determining the perceptual outcome in chromatically homogeneous surfaces.