Local spatial distortion caused by simple geometrical figures

Dynamic distortion of the visual field has been shown to affect perceptual judgment of visual dimensions such as size, length, and distance. Here, we report four experiments demonstrating that the different aspects of a triangle differently influence judgments of distance. Specifically, when the base of the triangle faces the centre of the display, participants consistently underestimate and overestimate the distance of a small dot from the unmarked centre of the display relative to conditions in which the vertex of the triangle faces the centre. When the dot is close to the figure, the distance of the dot to the centre is underestimated. Conversely, when the dot is close to the figure, the distance to the centre is overestimated. The effect is replicated when the internal distances are equalized and when ellipses are used instead of triangles. These results support a ripple model of spatial distortion in which local curvature acts to attract or repel objects. In conclusion, we suggest some implications of our findings for theories of perceptual organization.     

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.     

Emotional triangles: a test of emotion-based attentional capture by simple geometric shapes

Previous work has proposed that simple geometric shapes, carrying the features present within negative or threatening faces are especially effective at capturing or guiding attention. Here we test this account and provide converging evidence for a threat-based attentional advantage. Experiment 1 found that downward-pointing triangles continue to be detected more efficiently than upward-pointing triangles when: (i) both overall RT and search slope measures are obtained; and (ii) when the set size is varied and the stimuli are presented in random configurations. Experiment 2 tested and ruled out an alternative account of the selection advantage, based on differences between triangle shape consistencies with scene perspective cues. Overall, the data provide converging evidence that simple geometric shapes, which might be particularly important in providing emotional signals in faces, can also attract attention preferentially even when presented outside of a face context.     

Emotional triangles: A test of emotion-based attentional capture by simple geometric shapes

Previous work has proposed that simple geometric shapes, carrying the features present within negative or threatening faces are especially effective at capturing or guiding attention. Here we test this account and provide converging evidence for a threat-based attentional advantage. Experiment 1 found that downward-pointing triangles continue to be detected more efficiently than upward-pointing triangles when: (i) both overall RT and search slope measures are obtained; and (ii) when the set size is varied and the stimuli are presented in random configurations. Experiment 2 tested and ruled out an alternative account of the selection advantage, based on differences between triangle shape consistencies with scene perspective cues. Overall, the data provide converging evidence that simple geometric shapes, which might be particularly important in providing emotional signals in faces, can also attract attention preferentially even when presented outside of a face context.     

Prototype formation from imaged, kinesthetically, and visually presented geometric figures

The issue of prototype formation from simple geometric figures presented in various modes was studied in four conditions. Base figures and their exemplars were scaled in terms of their physical similarity, which was considered to reflect cognitive similarity. Geometric exemplars were visually presented, imaged by the subject, and kinesthetically presented. Following initial presentation, a recognition task was given in which some old items, some new items, and the prototype (also a new item) were presented in the same modality as originally perceived. The results indicate that prototype formation spans a wide class of human experiences and that internal representations of geometric figures derived from experiences with one modality tend to be second-order isomorphic with similar experiences derived from another modality.     

Selective changes of sensitivity after adaptation to simple geometrical figures

Using simple geometrical figures, the effect of adaptation upon sensitivity to figures of the same or different form was investigated. The adapting stimuli (blank white field, contour triangles, or circles) were presented for 1, 5, 30, or 60 sec. The test stimuli were always triangles, presented for a short exposure time at .1, .2, .4, .8, and 1.2 sec after the offset of the adapting pattern. The threshold duration of the test stimuli was measured. It was found that both adapting patterns raised the threshold above that measured for adaptation with the blank white field. But it wss only for the pair “adapting triangles-test triangles” that an increase of the time of adaptation beyond 5 sec resulted in an increase of this effect. This suggests that selective lowering in sensitivity during prolonged viewing of some figures may develop. The effect disappeared after about 1.2 sec following an exponential curve.     

Implications for phonetic symbolism: The relationship between pure tones and geometric figures

In studies of phonetic symbolism, the most commonly cited attribute of speech relevant to the phenomenon has been frequency. The present study was conducted in order to examine the relationship between pure tone frequencies and geometric figures. A pure tone oscillator was constructed which produced tones in a continuous sweep from 40–12,250 Hz. Six geometric shapes were employed and varied along three binary dimensions (size, complexity, and density) producing a total of 48 stimulus figures. Twelve male and twelve female subjects adjusted pure tone frequencies until they best fit the visually presented geometric figure in a complete within-subject, block-randomization design of 48 trials. There was consistency in the assignment of pure tone frequencies to the dimensions of the geometric figures. Round figures (circles and ellipses) generally received lower frequency assignments than other figures, and the shape by size interaction was also found to be statistically significant. The results are interpreted in light of recent research in psycholinguistics and in particular to the hypothesis of a universal phonetic symbolism.This research was a portion of a Master's thesis submitted to the University of Nevada, Las Vegas, by Michael W. O'Boyle, who is now at the University of Southern California.     

Perception of simple figures: implicit-shape constancy and mental rotation.

Adults were shown simple figures either drawn on their own or on a face of a depicted cube. Under each of these conditions they were required to find identical figures in an array of stimuli of either the first or the second type. The response chosen determined the next stimulus used, the figures in both being identical. Four chains of 10 responses were thus obtained. Comparison of the choices reveals that the set consisting of 'plain' responses to 'cube' stimuli diverges significantly from the other three sets. This result is discussed in the context of other studies of implicit-shape constancy.     

Negative triangles: simple geometric shapes convey emotional valence

It has been suggested that downward pointing triangles convey negative valence, perhaps because they mimic an underlying primitive feature present in negative facial expressions (Larson, Aronoff, and Stearns, 2007). Here, we test this proposition using a flanker interference paradigm in which participants indicated the valence of a central face target, presented between two adjacent distracters. Experiment 1 showed that, compared with face flankers, downward pointing triangles had little influence on responses to face targets. However, in Experiment 2, when attentional competition was increased between target and flankers, downward pointing triangles slowed responses to positively valenced face targets, and speeded them to negatively valenced targets, consistent with valence-based flanker compatibility effects. These findings provide converging evidence that simple geometric shapes may convey emotional valence.     

Strategies used by children when solving simple subtractions

Ten children, 9–11 years old, solved all subtraction problems in the form of M?N=…, where 0 ? M ? 13, 0 ? N ? 13 and M ? N. The solution times were analysed and used for the formulation of a process model for subtraction. The model involves memory processes on two different levels, called reproductive and reconstructive respectively. When M=N, N=1, and M=2N the answers were quickly retrieved in reproductive memory processes. The reconstructive processes were found to be analogous to one of two counting procedures, viz. counting up and counting down. In general, the counting process starts either on N (when M < 2N) and counts up to reach the answer, or on M (when M > 2N) and counts down to reach the answer. This may reflect an effort to minimize the number of steps to be counted. However, when M > 10 and N < 10 a problem is always solved in a decrementing counting process. When M=10 many subtractions are solved in a reproductive memory process and the number 10 is also important as a point of reference for solving subtractions when M > 10 and N < 10.