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.     

Orientational Effects and Component Processes in Symmetry Detection

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 that they used blocks containing patterns with the same axis (Experiment 2), virtual lines orientation (Experiment 3), or their combination (Experiment 4). Based on a comparison between the results obtained by these manipulations, we suggest a possible reason for the failure of preattentive symmetry detection in the case of dot patterns with SS.     

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.     

Regularity of symmetry verticality guides perceptual judgments of objects

Previous research indicated that most salient, real-world objects possess natural regularities that observers commonly assume in perceptual judgments of figural orientation and interpretation. Regularities include 3-dimensionality, bilateral symmetry, and the tendency for object tops to possess more salient information than bottoms. Thus, when observers interpret randomly shaped figures, they reliably impose volume, bilateral symmetry, and top and front orientation directions, even when figures are 2-dimensional and asymmetric. We confirmed generalizability for observers to assume these regularities with stimuli that vary in complexity, and we found evidence supporting another regularity, that of symmetry verticality (symmetry about a vertical axis). Findings support use of a family of perceptual heuristics corresponding to natural regularities that constrain stimulus indeterminacy and help guide judgment of object orientation and interpretation.     

Interactions between constituent single symmetries in multiple symmetry

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

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.     

The role of axes of elongation and symmetry in rotated object naming

Many theorists have postulated that axes of elongation and/or symmetry play an important role in the recognition of objects. In this paper, evidence is presented that mitigates this claim from independent assessments of the effects of axes of elongation or symmetry on the time to name rotated line drawings of common objects. This conclusion was further supported in a stronger test in which both of these variables were orthogonally controlled, the aspect ratio of elongation was manipulated,and only objects that were completely geometrically symmetrical or asymmetrical were used. In all the experiments, objects were named for several blocks to determine the influence of these variables on effects of orientation with practice. Symmetry was found to diminish the effects of orientation after practice in naming the object set, and the effects of the most extreme orientation tested (120 degrees from upright) were diminished when both axes defined the same orientation, relative to when they defined different orientations. Contrary to many theories, these findings relegate the axes of symmetry and elongation to relatively minor roles during object identification.     

Symmetry and repetition in perspective

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 fron to parallel 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.     

Perceived shape regularity does not depend on regularities along the contour

In four experiments we investigated whether human observers are able to use certain regularities in polygons when they have to indicate which polygon they perceive as the more regular in a paired comparison task. From our results we conclude that regularities that are restricted to the contour do not play a role in judgments of regularity. For instance, equilateral polygons are not considered to be more regular than entirely random polygons. Only bilaterally symmetric polygons are consistently judged as regular. However, we show that this is caused by regularities across the polygon. These results are at odds with approaches that assume that regularities along the contour play an important part in visual perception.     

Occlusion, symmetry, and object-based attention: reply to Saiki (2000)

J. Saiki (2000) argued that, because the stimuli used by M. Behrmann, R. S. Zemel, and M. C. Mozer (1998) were confounded by symmetry, conclusions about whether amodally completed objects can benefit from object-based attention are unwarranted. Here, the authors examine J. Saiki's claim further and expand on their view of the mechanisms underlying object-based attention, suggesting that perceptual organization is the process whereby features from a single object are selectively attended. In light of this, they claim that heuristics such as symmetry and collinearity play an important role in the facilitation of features from a single object. In support of this claim, they present data from a further experiment using displays that exploit common fate, another grouping heuristic, and show that, under these conditions, the hallmark of object-based attention, a single-object advantage, is obtained for the occluded (amodally completed) shapes.     

Perceived orientation of contour quadrangles

One hundred subjects ranked the apparent tilt of ten quadrangles. A scale of perceived orientation was derived from a pair-comparison treatment of these data. The main characteristic determining estimated orientation of the quadrangles was the axis from which the sum of the squared distances to each point of the figure was minimal (the LS-axis). Judgements were also influenced by the orientation of an 'axis of balance', which ran through the centre of gravity and the lowermost apex of the quadrangle. Quadrangles with parallel LS-axes were systematically judged as differently tilted according to the difference in the orientation of their axes of balance. Both the LS-axis and the axis of balance are physical characteristics of an object that are of great importance for the optimal control of human action through vision.     

The role of symmetry in determining perceived centers within shapes

This study was designed to assess the effects of symmetry and plane of presentation on the determination of the perceptual center of flat figures. Experiment 1 demonstrates the existence of effects in improving center determination, both in the number of sides of the shape and in rotational and reflective symmetry (confounded in the experiment). Experiment 2 shows that the presentation plane has no effect on center determination. In Experiment 3, we divide the effects of the two symmetry types, showing that rotational symmetry alone is as effective as the presence of both symmetry types—that is, the presence of symmetry axes is not very useful in finding perceived centers.     

The role of symmetry in determining perceived centers within shapes.

This study was designed to assess the effects of symmetry and plane of presentation on the determination of the perceptual center of flat figures. Experiment 1 demonstrates the existence of effects in improving center determination, both in the number of sides of the shape and in rotational and reflective symmetry (confounded in the experiment). Experiment 2 shows that the presentation plane has no effect on center determination. In Experiment 3, we divide the effects of the two symmetry types, showing that rotational symmetry alone is as effective as the presence of both symmetry types--that is, the presence of symmetry axes is not very useful in finding perceived centers.     

Serial processing of visual spatial patterns in a search paradigm

Previous experiments in this laboratory employing a search paradigm have found highly significant differences in the detectability of a briefly exposed target pattern as a function of the spatial location of the target when it is presented simultaneously with a number of discriminably different nontarget patterns. These detectability differences, at loci equidistant from the fovea, could not be accounted for by any known variation in retinal spatial resolution or by differential lateral masking effects of the target by nearby nontarget patterns. These observations led to the hypothesis that the target in these experiments was detected by a serial mechanism which "scanned" a persisting but rapidly degrading neural representation of the visual scene with increasing detection failures the later in time the scan processed the location occupied by the target. If this hypothesis is correct, then target detectability should vary inversely with the number of stimuli which must be examined. The present experiment confirmed this expectation. A mathematical model of such a serial scanning process also predicts other, less obvious, effects on target detectability which were observed when the number of nontarget patterns was changed.     

Regularity Theories Reassessed

For a long time, regularity accounts of causation have virtually vanished from the scene. Problems encountered within other theoretical frameworks have recently induced authors working on causation, laws of nature, or methodologies of causal reasoning – as e.g. May (Kausales Schliessen. Eine Untersuchung über kausale Erklärungen und Theorienbildung. Ph.D. thesis, Universität Hamburg, Hamburg, 1999), Ragin (Fuzzy-set social science. Chicago: University of Chicago Press, 2000), Graßhoff and May (Causal regularities. In W. Spohn, M. Ledwig, &; M. Esfeld (Eds.), Current issues in causation (pp. 85–114). Paderborn: Mentis, 2001), Swartz (The concept of physical law (2nd ed.). http://www.sfu.ca/philosophy/physical-law/, 2003), Halpin (Erkenntnis, 58, 137–168, 2003) – to direct their attention back to regularity theoretic analyses. In light of the latest proposals of regularity theories, the paper at hand therefore reassesses the criticism raised against regularity accounts since the INUS theory of causation of Mackie (The cement of the universe. A study of causation. Oxford: Clarendon Press, 1974). It is shown that most of these objections target strikingly over-simplified regularity theoretic sketches. By outlining ways to refute these objections it is argued that the prevalent conviction as to the overall failure of regularity theories has been hasty.     

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.     

多目标追踪中基于运动信息的分组效应

本研究旨在探讨运动信息对多目标追踪的影响, 具体为考察多目标追踪中是否存在基于运动信息的分组效应, 以及不同类型表面特征(颜色和形状)对这一效应的影响。实验1发现多目标追踪中存在基于运动信息的分组效应, 并且这一分组效应是自动化的。实验2和实验3分别在不同颜色和不同形状组合条件下考察了基于运动信息的分组效应的稳定性, 结果都表明不同表面特征的组合不会干扰基于运动信息的分组效应的形成, 但其效应量都因表面特征的出现而缩减。整体而言, 多目标追踪中存在基于运动信息的自动化分组效应, 并且这一效应是格式塔法则中共同命运律的具体表现, 能稳定存在于不同表面特征组合之间。     

La percepción del habla durante el primer año de vida

Language acquisition involves a number of complex skills that evolve in correlation with each other, thus making it possible for learners of their first spoken language —or sign language— to achieve the best results with minimal effort, as long as they do so within the appropriate period of time. In this regard, it is proposed that early speech perception has a primary role in language acquisition. In order to provide an overview of the current scientific knowledge as to the capabilities of children under the age of one to perceive spoken language, this paper presents the results of the most relevant research on discrimination of classes and types of words, interidiomatic and prosodic discrimination, phonological and phonotactic discrimination, as well as recognition of distributional regularities amongst the elements of the speech signal.