On the perception of symmetrical and repeated patterns

Four experiments investigated rapid perceptual judgments about tachistoscopically presented patterns that were either symmetrical about or repeated across a vertical axis. The same patterns were presented under two different instructional conditions; some Ss were to judge the two halves of each pattern “same” or “mirror,” others were to judge each pattern as a whole “symmetrical” or “asymmetrical.” With dot patterns, RTs were faster for symmetrical than for repeated patterns when the two halves were close together, but not when they were separated, regardless of instructions. With simpler patterns made up of arrowheads and C-shapes, however, “same” RTs were faster than “mirror,” but “asymmetrical” RTs were marginally slower than “symmetrical,” regardless of spatial separation. The advantage of “same” over “mirror” did not seem to be simply a labeling effect. The results suggest that left-right symmetry is perceptually more salient than left-right repetition when the patterns are perceived holistically. By contrast, distinct patterns can be matched more rapidly when they are the same than when they are left-right mirror images.     

Long-term repetition priming with symmetrical polygons and words

In two different tasks, subjects were asked to make lexical decisions (word or nonword) and symmetry judgments (symmetrical or nonsymmetrical) about two-dimensional polygons. In both tasks, every stimulus was repeated at one of four lags (0, 1, 4, or 8 items interposed between the first and second stimulus presentations). This paradigm, known as repetition priming, revealed comparable short-term priming (Lag 0) and long-term priming (Lags 1, 4, and 8) both for symmetrical polygons and for words. A shorter term component (Lags 0 and 1) of priming was observed for nonwords, and only very short-term priming (Lag 0) was observed for nonsymmetrical polygons. These results indicate that response facilitation accruing from repeated exposure can be observed for stimuli that have no preexisting memory representations and suggest that perceptual factors contribute to repetition-priming effects.     

The influence of visual symmetry on the encoding of objects

Two experiments examined how symmetry affects the visual encoding of simple flat objects (lamellae). Experiment 1 showed that subjects encode a lamella's shape as both a facsimile and its enantiomorph. In Experiment 2 the errors made when responding to symmetrical and asymmetrical stimuli showed that there were three factors affecting the reproduction of a symmetrical stimulus. These are, in order of decreasing influence, (i) the orientation of the axis of symmetry, (ii) the presence of overall symmetry (irrespective of orientation), and (iii) identity of the orientation of the elements of the response in relation to those of the stimulus. They also show that symmetry is likely to be reproduced even where the reproduction is not of the same shape as the original stimulus. The relevance of these results to representation of objects is discussed.     

Perception of symmetry in infancy: the salience of vertical symmetry and the perception of pattern wholes

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 degrees separations) more efficiently than discontiguous patterns (5 and 10 degrees 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.     

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.     

Symmetry perception in bamboo sharks (Chiloscyllium griseum) and Malawi cichlids (Pseudotropheus sp.)

Several species have been shown to perceive symmetry as a measure of superior genetic quality, useful for assessing potential mates or mediating other visual activities such as the selection of food sources. The current study assessed whether Pseudotropheus sp. and Chiloscyllium griseum, two fish species from distantly related groups, possess symmetry perception. In alternative two choice experiments, individuals were tested for spontaneous preferences and trained to discriminate between abstract symmetrical and asymmetrical stimulus pairs. Pair discriminations were followed by extensive categorization experiments. Transfer tests elucidated whether bilaterally symmetrical and rotationally symmetrical stimuli could be distinguished. Sharks were also tested for the degree of dissimilarity between two symbols that could still be detected. While sharks showed both a spontaneous preference for symmetry as well as remarkable discrimination abilities by succeeding in all of the presented tasks, cichlids showed no spontaneous preference, had difficulties in discriminating between symbols and performed poorly in the categorization experiments. Sharks distinguished between bilaterally and rotationally symmetrical stimuli and easily differentiated between a four-armed cross (all arms 90° apart) and a cross where one of the arms was only 45° spaced from the one next to it. Performance did not decline when the separation was extended to 70°, but was significantly reduced at an 80° separation. Results indicate that the ability for symmetry perception varies across fish species and individuals, whereby some can detect even subtle differences in this respect.     

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.     

Effects of pattern orientation and number of symmetry axes on the detection of mirror symmetry in dot and solid patterns

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 of stimuli with one axis, results obtained with stimuli with two and three axes were almost identical and in between those obtained with one and four axes. The data thus support the suggestion that extra axes add 'goodness' to symmetrical patterns but not in a monotonic fashion.     

Symmetry and transitivity assumptions about a nonspecified logical relation

Twenty-five subjects were presented with eight problems involving a non-specified relation, devoid of its concrete content. This relation was signified by the symbol (--), thus logically precluding any knowledge about the properties of the relation. The problems were so designed that the truth evaluation of their solution statements reflected assumptions about the symmetry and transitivity properties of the relation. Six subjects assumed that the relation was both symmetrical and transitive, and 12 subjects assumed that it was symmetrical only. When these same 18 subjects were presented with problems which lent themselves to only one of these assumptions, all assumed that the relation was symmetrical rather than transitive. The remaining seven subjects made neither of these two assumptions in any of the problems. Examples of logical relations, given as part of the problems, and varying in their properties of symmetry and transitivity, had no effect on the subjects' assumptions. It is proposed that symmetrical and transitive relations are conceptual good figures which predisposed subjects to perceive the nonspecified relation as symmetrical or as transitive. The stronger tendency towards symmetry assumptions than towards transitivity assumptions suggests that symmetrical relations are better figures than transitive relations.     

Do muscles matter for coordinated action?

This article investigates coordination stability when 2 fingers of each hand periodically tap together. The main question concerns the functional origin of the symmetry tendency, which has widely been conceived as a bias toward coactivation of homologous fingers and homologous muscular portions. In Experiment 1, the symmetry tendency was independent of finger combination. In Experiment 2, virtually identical stability characteristics were revealed under full vision and no vision. In Experiment 3, symmetrical and parallel visual labels on the fingers neither stabilized nor destabilized symmetrical and parallel tapping patterns. In Experiment 4, in which the relative position of the hands was varied, it revealed that the observed stability characteristics are to be defined in a hand-centered reference frame. Because the symmetry tendency was always independent of finger combination, the authors suggest that it is not a bias toward coactivation of homologous muscle portions but instead originates on a more abstract, functional level.     

The Goldmeier effect in adults and children: environmental, retinal, and phenomenal influences on judgments of visual symmetry

Adults judge that patterns symmetrical about the vertical axis are more similar to standard patterns symmetrical about both major orthogonal axes than are patterns which are symmetrical only about the horizontal axis (the Goldmeier effect). Thus, symmetry about the vertical axis is more salient for adults than symmetry about the horizontal axis. Two experiments are reported in which subjects from three age groups (preschool, 8 years old, and adult) were given Goldmeier problems under different conditions. In experiment 1 three head-tilt conditions were used (0 degrees, 45 degrees, 90 degrees); in experiment 2 there were four conditions defined by head orientation (0 degrees, 90 degrees) and phenomenal instructions (top of figure at 0 degrees or at 90 degrees). In both experiments, increasing head tilt from 0 degrees decreased the consistency with which the environmentally vertical pattern was chosen. Noncorrespondence between the three spatial frameworks (environmental, retinal, and phenomenal) failed to produce biases in favor of either retinal-egocentric or phenomenal systems. For rotated adult subjects in experiment 2, 0 degrees phenomenal instructions strengthened an environmental bias, and 90 degrees phenomenal instructions shifted responses toward a retinal bias. These findings provide strong refutation of explanations for symmetry perception that are based solely upon the anatomical symmetry of the visual system. The data also fail to support arguments for environmental or phenomenal frameworks as singular influences. The results are best explained in terms of failure of constancy mechanisms to coordinate environmental and retinal information as a function of degree of head rotation and stimulus complexity.     

Associative symmetry by pigeons after few-exemplar training

The present experiment investigated whether pigeons can show associative symmetry on a two-alternative matching-to-sample procedure. The procedure consisted of a within-subject sequence of training and testing with reinforcement, and it provided (a) exemplars of symmetrical responding, and (b) all prerequisite discriminations among test samples and comparisons. After pigeons had learned two arbitrary-matching tasks (A-B and C-D), they were given a reinforced symmetry test for half of the baseline relations (B1-A1 and D1-C1). To control for the effects of reinforcement during testing, two novel, nonsymmetrical responses were concurrently reinforced using the other baseline stimuli (D2-A2 and B2-C2). Pigeons matched at chance on both types of relations, thus indicating no evidence for symmetry. These symmetrical and nonsymmetrical relations were then directly trained in order to provide exemplars of symmetry and all prerequisite discriminations for a second test. The symmetrical test relations were now B2-A2 and D2-C2 and the nonsymmetrical relations were D1-A1 and B1-C1. On this test, 1 pigeon showed clear evidence of symmetry, 2 pigeons showed weak evidence, and 1 pigeon showed no evidence. The previous training of all prerequisite discriminations among stimuli, and the within-subject control for testing with reinforcement seem to have set favorable conditions for the emergence of symmetry in nonhumans. However, the variability across subjects shows that methodological variables still remain to be controlled.     

Memory confusions for real and imagined completions of symmetrical visual patterns

In Experiment 1, subject ratings indicated that it was easier to imaginally complete half of a symmetrical form when the form was symmetrical about the vertical axis than when the form was rotated so that it was symmetrical about the horizontal axis. In Experiment 2, new subjects saw these same forms, some presented as wholes and some presented as halves. Compared with controls, subjects who were instructed to imagine the vertically symmetrical half forms as complete had more difficulty remembering which forms had been presented as wholes and which had been presented as halves. Imagery and control groups did not differ in ability to discriminate half from whole horizontally symmetrical forms. The results are consistent with predictions from Johnson and Raye’s (1981) reality monitoring model that discriminating memories of imagined and perceived events should be a function of the amount of cognitive operations included in the memory.     

Cerebral Asymmetry and Decision Strategies in Mental Rotation: A Psychophysical Analysis

The accuracy with which observers judged the parity of pairs of rotated images in the two visual fields was determined from receiver operating characteristic (ROC) analysis of confidence ratings. In one experiment, observers judged whether pairs of letters were of the same parity (that is, both normal or both backwards) or of different parities (one normal and one backwards). A small right visual field advantage in the observers' accuracy was found in this mental rotation task. In a second experiment, observers judged whether pairs of pictures were of the same parity or of different parities. Unlike the first experiment, no evidence of a consistent visual field advantage was found in this mental rotation task. The decision strategy adopted by the observers in making same-different judgements about rotated stimuli was examined. The symmetrical shape of the ROCs obtained was consistent with the adoption of the likelihood-ratio decision strategy, a result which supplemented previous evidence that this decision strategy is adopted when same-different judgements are made about multidimensional stimuli.     

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.     

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.     

物体相似性对空间表征的影响：来自眼动的证据

以三维场景图片为实验材料,采用眼动追踪技术,通过两个实验考察了对称场景中物体相似性对空间表征的影响。结果表明：（1）无相似物体条件下,场景本身的内在结构对空间表征有重要影响,对称轴方向可以作为空间表征参照方向;（2）存在部分相似物体条件下,物体的相似性会影响空间表征参照方向的选择,并且相似物体方向也是空间表征的参照方向之一。     

Conditioned reinforcement dynamics in three-link chained schedules.

In two experiments rats were trained on three-link concurrent-chains schedules of reinforcement. In Experiment 1, additional entries to one terminal link were added during one of the middle links to a baseline schedule that was otherwise equal for the two chains, and, depending on the condition, these additional terminal-link presentations ended either in food or in no food. When food occurred, preference was always in favor of the chain with the additional terminal-link presentations (which also entailed a higher rate of reinforcement). When no food occurred at the end of the additional terminal links, the outcome depended on the nature of the stimuli associated with these additional terminal links. When stimuli different from the reinforced baseline terminal links were used for the no-food terminal links, preference was against the choice alternative that led to the extra periods of extinction. When the same stimulus was used for the two kinds of terminal links, preference was near indifference, that is, significantly greater than when different stimuli were used. In Experiment 2, rats learned repeated reversals of a simultaneous discrimination under a three-link concurrent-chains schedule, in which the food or no-food choice outcomes were delayed until the end of the chain. Different conditions were defined by the point in the chain at which differential stimuli occurred. When the middle and terminal links provided no differential stimuli, discrimination was acquired more slowly than when differential stimuli occurred in both links. When differential stimuli occurred in the middle but not the terminal links, acquisition rates were intermediate. Both experiments together show that the effects of stimuli in a chain schedule are due partly to the time to food correlated with the stimuli and partly to the time to the next conditioned reinforcer in the sequence.     

Can certain stimulus characteristics influence the hemispheric differences in global and local processing?

Hemispheric processing of global and local form was examined in two experiments in which the size of hierarchical visual stimuli was manipulated in divided-attention tasks. In experiment 1, the subjects were instructed to decide whether or not a symmetrical target (T) was in the visual object presented. In experiment 2, the target to be detected was nonsymmetrical (L). In both studies, global precedence was found depending on stimulus size. When the stimuli subtended about 3 degrees vertically, global dominance was found, but it was not detected when the stimuli subtended about 10 degrees. Experiments 1 and 2 provided evidence against the analytic/holistic dichotomy, presenting the same performance for both hemispheres: the global analysis was much better than the local analysis. When the target was in the global form, both the LH and the RH analyzed the 3 degrees stimuli more efficiently, while both analyzed the 10 degrees stimuli with greater efficiency when the target was in the local form.     

Transfer of contextual stimulus function via equivalence class development

In a conditional discrimination, 6 college students arranged six Cyrillic letters into groups of three based upon which of two additional Cyrillic letters (contextual stimuli) was present. All subjects demonstrated symmetry and transitivity within each class of equivalent stimuli. In a second conditional discrimination, two more Cyrillic letters were related to each contextual stimulus. Testing of symmetrical and transitive relations between the original contextual stimulus and the two new ones confirmed the development of two three-member classes of contextual stimuli. Subsequent tests demonstrated that the new contextual stimuli controlled the previously trained sample-comparison relations for all subjects.