Area perception in simple geometrical figures

The results of experiments on visual perception of area of circles and squares are reported. Pairs of geometrical figures were presented simultaneously on an oscilloscope screen. While one of them was fixed, the other one was controlled by an experimental subject. The task of the subject was to match the area of the variable figure to the area of the fixed one. The obtained data show underestimation of the area of circle when compared with square. A mathematical model designed to explain this phenomenon is proposed here. The image function defined as a low-pass filtered (blurred) version of the figure is employed for this purpose. Then, instead of the position of the image function maxima, the position of a threshold value is used for area computation.     

Some experiments on spacial position as a factor in children's perception and reproduction of simple figures

Summary It has appeared in our experiments that certain absolute spacial directions play a dominant r?le in the drawings even of young children, but that frequently the dominant directions are not determined by absolute position but by their significance in a given form.

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Zusammenfassung In unseren Versuchen hat sich ergeben, da? gewisse absolute Raumrichtungen schon bei jungen Kindern ausgezeichnet sind, da? aber andererseits die Bestimmung der Hauptrichtung oft nicht absolut, sondern durch ihre Rolle innerhalb einer gegebenen Form gegeben ist.

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From the Research Laboratory of Smith College

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With 10 Figures     

The recency effect in the perception of ambiguous figures

After a failure to obtain a recency effect in the perception of ambiguous figures three experiments were carried out to determine the conditions which govern the effect. It was found that the duration of the stimulus which precedes the ambiguous figure (the most recent stimulus) was important. Also of importance was the interval between the next-to-most-recent stimulus and the ambiguous figure. The effect of manipulating these variables was such that sometimes no recency effect was obtained, implying that their state is sometimes critical for the effect. Variations in the duration of the ambiguous stimulus did not cause the recency effect to vary. Recommendations are made for the demonstration of a reliable recency effect.     

Simultaneous perception of both interpretations of ambiguous figures

When viewing ambiguous figures like the classic duck/rabbit, people alternately perceive one interpretation and then the other, but not both interpretations at once. When two identical ambiguous figures appear together, the majority of observers perceive them as identical, and they typically alternate in unison. Just as most observers cannot see a single figure as both a duck and a rabbit, most cannot see one figure in a pair as a duck and the other as a rabbit even though the two figures and their features are spatially distinct. Is this inability to see both interpretations an inherent limitation of the visual system or is it just due to differences in top-down processing? We show that a simple prompt immediately allows people to see both interpretations, to their own surprise.     

The role of discontinuities in the perception of subjective figures

Recently we proposed a theory of visual interpolation (Kellman & Shipley, in press) that addresses a variety of unit formation phenomena, including the perception of partly occluded objects and subjective figures. A basic notion of the theory is that discontinuities in the first derivative of projected edges are the initiating conditions for interpolation of boundaries that are not physically specified. In this paper, we report four experiments in which this claim was tested in the domain of subjective figures. Experiments 1 and 2 demonstrate that discontinuities in the first derivative of the edges of inducing elements have a clear effect on the frequency of report and the perceived clarity of simple subjective figures. Similar effects are found when unfamiliar subjective figures and inducing elements are used (Experiment 3). Experiment 4 rules out the possibility that the discontinuities in the first derivative merely add to the clarity of subjective figures. These experiments suggest that first-order discontinuities play a central role in unit formation.     

Attentional biases in geometric form perception

This paper reports the operation of robust attentional bias to the top and right during perception of small, single geometric forms. Same/different judgements of successively presented standard and comparison forms are faster when local differences are located at top and right rather than in other regions of the forms. The bias persists when form size is reduced to approximately one degree of visual angle, and it is unaffected by saccadic eye movements and by instructions to attend to other reliably differentiating regions of the forms. Results lend support in various degrees to two of the possible explanations of the bias: (1) a static, skewed distribution of attentional resources around eye fixation; and (2) biased, covert scanning that commences invariably at the top and right of stim ulus forms. Origins of the bias in terms of possible left-hemispheric capacity for constructing representations of visual stimuli from parts, as well as in terms of reading experience and prevailing optic flow during locomotion through space are considered. Recent investigations of conditions under which the bias can be maintained or reduced are mentioned.     

Ambiguity and structural information in the perception of reversible figures

The perspective reversals elicited by a set of drawings based on the Mach truncated pyramid are examined. We obtained each pattern of the set from the previous one by adding to it some graphic cues, which were easily integrated into one of the two competing interpretations, thus reducing step by step the ambiguity of the basic pattern. The phenomenological model, proposed to link the mean times of both alternative interpretations with their complexities, is in close agreement with our experimental data. Furthermore, different aspects of such data are well described by the model equations: The measure of the prevalence of the supported interpretation is well correlated with the difference in complexity between the two alternative interpretations; the two different trends of the mean time of the unfavored interpretation, found in the data obtained from different observers as a function of the various patterns of the set, are well fitted by the model without the need for any specific additional hypothesis.     

Holistic processes in the perception and transformation of disoriented figures

Two experiments tested whether mental rotation of complex, hierarchical stimuli occurs holistically or separately at global and local levels of structure. Large (global) letters were constructed from spatial arrangements of small (local) letters. Reflection conditions (normal vs. reflected) were produced by varying the two levels independently. The task was structured so that subjects could rotate one level of the stimulus in some conditions but had to rotate both levels in other conditions. Experiment 1 showed that rotation rate was not affected by the number of levels that had to be rotated to make a reflection decision. This result implies that the rotation of global and local levels occurred together rather than sequentially. Experiment 2 showed that the rotation of the two levels was holistic as opposed to parallel and independent. The results also demonstrate that global information is processed faster than local information regardless of whether or not a rotation is performed. These findings are discussed in relation to theories of mental rotation and global precedence.     

A hierarchical model of temporal perception

Temporal perception comprises subjective phenomena such as simultaneity, successiveness, temporal order, subjective present, temporal continuity and subjective duration. These elementary temporal experiences are hierarchically related to each other. Functional system states with a duration of 30 ms are implemented by neuronal oscillations and they provide a mechanism to define successiveness. These system states are also responsible for the identification of basic events. For a sequential representation of several events time tags are allocated, resulting in an ordinal representation of such events. A mechanism of temporal integration binds successive events into perceptual units of 3 s duration. Such temporal integration, which is automatic and presemantic, is also operative in movement control and other cognitive activities. Because of the omnipresence of this integration mechanism it is used for a pragmatic definition of the subjective present. Temporal continuity is the result of a semantic connection between successive integration intervals. Subjective duration is known to depend on mental load and attentional demand, high load resulting in long time estimates. In the hierarchical model proposed, system states of 30 ms and integration intervals of 3 s, together with a memory store, provide an explanatory neuro-cognitive machinery for differential subjective duration.     

A model of empty duration perception

An attempt to construct a general theory of duration perception is presented. First, four experiments are reported in which the supplement hypothesis, on the relation between two or three empty durations, was examined: the subjective duration of a subjectively empty time interval is directly proportional to its physical duration plus a constant of approximately 80 ms. This hypothesis could be applied to the ratio judgments of auditorily marked empty durations between 40 and 600 ms given serially. It could also explain the discrepancies between musically notated rhythms and the corresponding physical performed rhythms in very simple rhythm patterns consisting of three tones. Next, three earlier experiments on discriminations of empty durations marked by sound bursts were also reanalyzed. Within the range 40-600 ms, the absolute just noticeable difference of an empty duration was almost directly proportional to the standard duration plus a constant of about 80 ms. If the supplement hypothesis is accepted, this means that the relative just noticeable difference of the subjective duration was constant. Finally, the processing time hypothesis is presented: subjective duration is directly proportional to the physical time required to process the given empty duration. This processing is considered to begin with the detection of the first marker, and to end approximately 80 ms after the detection of the second marker.