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.     

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.     

Natural laws and the problem of provisos

Hempel and Giere contend that the existence of provisos poses grave difficulties for any regularity account of physical law. However, Hempel and Giere rely upon a mistaken conception of the way in which statements acquire their content. By correcting this mistake, I remove the problem Hempel and Giere identify but reveal a different problem that provisos pose for a regularity account — indeed, for any account of physical law according to which the state of affairs described by a law-statement presupposes a Humean regularity. These considerations suggest a normative analysis of law-statements. On this view, law-statements are not distinguished from accidental generalizations by the kind of Humean regularities they describe because a law-statement need not describe any Humean regularity. Rather, a law-statement says that in certain contexts, one ought to regard the assertion of a given type of claim, if made with justification, as a proper way to justify a claim of a certain other kind.     

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.     

Spatial Nonuniformities in Visual Search

Previous search experiments in this laboratory have been concerned with the marked differences in target detectability as a function of its location in the visual field—differences we have called a detectability gradient—when subjects were required to detect a vertically oriented “target” among a number of distractor items having different orientations. This gradient was characterized by a marked right visual field superiority as well as differences in the shape of the gradient in the two half fields. A scanning model was proposed to account for these robust phenomena. The present experiments, using reaction time methods with vertical, horizontal, and colored targets have revealed marked differences in both reaction time and detectability as a function of target location and have isolated some of the spatial nonuniformities in the visual system which influence the shape of these gradients. The results reported here have forced us to abandon the scanning hypothesis in favor of a model in which attention is efficiently guided to the target.     

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.     

Methods of item validation and abacs for item-test correlation and critical ratio of upper-lower difference

It is shown that by making the assumption that the knowledge of the test-item and the knowledge of the entire test are both distributed normally, the correlation coefficient between any item and the entire test can be expressed as a function solely of two proportions — the percentage of a high-scoring group passing the item and the percentage of a low-scoring group passing the item. This function is expressed graphically as a family of curves for each of two conditions — where the high-scoring and low-scoring groups are samples of the highest and the lowest quarters respectively, and where they are samples from the upper and lower halves. It is shown, moreover, that two other common measures of item validity, the upper-lower difference and the critical ratio of the upper-lower difference, may be drawn on the same coordinate axes.     

Prior knowledge does not facilitate the perceptual organization of dynamic random-dot patterns

Three classes of models for the origins of perceptual organization—linear independence, cognitive facilitation, and self-organization—were tested by evaluating the effects of stimulus unccrtainty and pattern coherence on the detection of coherent motion in dynamic random-dot patterns. Stimulus patterns consisted of two successive frames of randomly positioned dots in which motion was perceived when the dot positions in successive frames were correlated and displaced. The number of alternative directions axed locations of motion and the degree of coherences correlation) between the two successive frames were manipulated. The effects of stimulus uncertainty were less than predicted by cognitive facilitation models and were less than predicted by one linear independence model Ichoice theory), although similar to the predictions of another linear model (the Peterson, Birdsall, & Fox, 1954, approximation of the optimum Gaussian model). Small, but significant, tendencies toward self-organization rather than linear independence of perceived motion in neighboring locations were indicated by a nonlinear effect of coherence on detection accuracy and by the superior detectability of the direction as compared with the location of motion.     

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.     

Children's Ideas About What Can Really Happen: The Impact of Age and Religious Background

Five- to 11-year-old U.S. children, from either a religious or secular background, judged whether story events could really happen. There were four different types of stories: magical stories violating ordinary causal regularities; religious stories also violating ordinary causal regularities but via a divine agent; unusual stories not violating ordinary causal regularities but with an improbable event; and realistic stories not violating ordinary causal regularities and with no improbable event. Overall, children were less likely to judge that religious and magical stories could really happen than unusual and realistic stories although religious children were more likely than secular children to judge that religious stories could really happen. Irrespective of background, children frequently invoked causal regularities in justifying their judgments. Thus, in justifying their conclusion that a story could really happen, children often invoked a causal regularity, whereas in justifying their conclusion that a story could not really happen, they often pointed to the violation of causal regularity. Overall, the findings show that children appraise the likelihood of story events actually happening in light of their beliefs about causal regularities. A religious upbringing does not impact the frequency with which children invoke causal regularities in judging what can happen, even if it does impact the type of causal factors that children endorse.     

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.     

An algebra of human concept learning

An important element of learning from examples is the extraction of patterns and regularities from data. This paper investigates the structure of patterns in data defined over discrete features, i.e. features with two or more qualitatively distinct values. Any such pattern can be algebraically decomposed into a spectrum of component patterns, each of which is a simpler or more atomic “regularity.” Each component regularity involves a certain number of features, referred to as its degree. Regularities of lower degree represent simpler or more coarse patterns in the original pattern, while regularities of higher degree represent finer or more idiosyncratic patterns. The full spectral breakdown of a pattern into component regularities of minimal degree, referred to as its power series, expresses the original pattern in terms of the regular rules or patterns it obeys, amounting to a kind of “theory” of the pattern. The number of regularities at various degrees necessary to represent the pattern is tabulated in its power spectrum, which expresses how much of a pattern's structure can be explained by regularities of various levels of complexity. A weighted mean of the pattern's spectral power gives a useful numeric summary of its overall complexity, called its algebraic complexity. The basic theory of algebraic decomposition is extended in several ways, including algebraic accounts of the typicality of individual objects within concepts, and estimation of the power series from noisy data. Finally some relations between these algebraic quantities and empirical data are discussed.     

Insights into sleep's role for insight: Studies with the number reduction task

In recent years, vibrant research has developed on “consolidation” during sleep: To what extent are newly experienced impressions reprocessed or even restructured during sleep? We used the number reduction task (NRT) to study if and how sleep does not only reiterate new experiences but may even lead to new insights. In the NRT, covert regularities may speed responses. This implicit acquisition of regularities may become explicitly conscious at some point, leading to a qualitative change in behavior which reflects this insight. By applying the NRT at two consecutive sessions separated by an interval, we investigated the role of sleep in this interval for attaining insight at the second session. In the first study, a night of sleep was shown to triple the number of participants attaining insight above the base rate of about 20%. In the second study, this hard core of 20% discoverers differed from other participants in their task-related EEG potentials from the very beginning already. In the third study, the additional role of sleep was specified as an effect of the deep-sleep phase of slow-wave sleep on participants who had implicitly acquired the covert regularity before sleep. It was in these participants that a specific increase of EEG during slow-wave sleep in the 10-12 Hz band was obtained. These results support the view that neuronal memory reprocessing during slow-wave sleep restructures task-related representations in the brain, and that such restructuring promotes the gain of explicit knowledge.     

Developmental trends in the salience of meaning versus structural attributes of written words

Summary This study was designed to evaluate Gibson's contention that maximum sensitivity to the meanings of printed words does not occur until the individual has become a fluent reader. Also of interest was the degree to which reading ability would significantly influence the developmental course. These questions were evaluated by means of a sorting task which allowed subjects to group printed words on the basis of either semantic-syntactic (meaning) or graphic-phonologic (structural) attributes, and differential grouping tendencies along the age/grade continuum were the dependent measures specifically evaluated. Subjects consisted of normal and poor readers from grades 1–6, as well as ninth graders and college sophomores. The study was quasi-longitudinal in that available subjects from grades 2–5 were retested a year later to evaluate the reliability of developmental trends.Results were consistent with Gibson's theory. Sensitivity to word meanings was much more stable in fluent readers than it was in less fluent readers, although there was considerable individual variability noted at all levels. Poor readers were inclined to place words they could identify more often in meaning than in structural categories. However, structural categories that were utilized, were often idiosyncratic, suggesting that poor readers are less atuned to orthographic regularities than are normal readers.     

Children's comprehension of grammatical structures in context

Children from nursery school, kindergarten, and first grade were asked to select pictures which correctly represented the propositional content of six grammatical structures-active, passive, cleft-agent, cleft-patient, prepositional beneficiary, indirect object presented under three context conditions-appropriate, inappropriate, isolation. In the appropriate-context condition the relationship between the target structure and its prior context sentence followed known discourse regularities about the allocation of given and new information, while in the inappropriate-context condition the relationship between the target structure and prior context violated these discourse regularities. Comprehension of two of the grammatical structures tested—the passive and the cleft-patient—was better under the appropriate-context treatment than under the inappropriate-context treatment, indicating that young children are in fact sensitive to discourse regularities about the allocation of given and new information.The research reported herein was part of Gourley's Ph.D. dissertation for Cornell University, which was directed by Catlin. An earlier version of this article was presented by Gourley at the 1974 Summer Meeting of the Linguistic Society of America at Amherst, Massachusetts.Deceased.     

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。