Judgment of angle size: An experimental appraisal

Maclean, Iain E.; Stacey, Barrie

doi:10.3758/bf03208965

Cited by 26 publications

(14 citation statements)

References 5 publications

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“…This is a reasonable first approximation for design. Research on the psychophysics of angle judgments indicates that observers tend to overestimate acute angles and underestimate obtuse angles (Fisher, 1969;Maclean & Stacey, 1971;MacRae & Loh, 1981). Thus, the design of present displays (which provided a larger change in angle size with larger angles and vice versa) is consistent with these findings.…”

Section: Contourssupporting

confidence: 81%

Contours and borders in animated mimic displays

Bennett

Madigan

1994

International Journal of Human-Computer Interaction

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Previous research has indicated that ambiguities in apparent motion (e.g., direction, rate) can result when color table techniques are used to produce animation in mimic displays. Two experiments were conducted to investigate alternative display designs in which contours (angled vs. straight) and borders (explicit vs. implicit) were varied. In Experiment 1, contours, borders, and temporal frequency interacted. At 5 Hz angled contours improved accuracy significantly. At 10 Hz explicit borders improved accuracy significantly with angled contours but degraded accuracy significantly with straight contours. In Experiment 2, the design of the angled contours was changed to convey less information and an additional border condition was added. Once again, borders and contours interacted: The widest explicit border degraded accuracy with straight contours. Angled contours also improved latency performance. The results suggest that angled contours can reduce ambiguity and improve the effectiveness of animated mimic displays by providing a redundant encoding of rate information. However, this benefit must be weighed against the associated computational costs. A secondary finding was that when contours are straight the borders should be implicit, not explicit. Alternative design solutions for animated mimic displays are also discussed.

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Section: Contourssupporting

confidence: 81%

Contours and borders in animated mimic displays

Bennett

Madigan

1994

International Journal of Human-Computer Interaction

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“…Pies may be subject to two kinds of bias-differential sensitivity to angles depending on orientation, in addition to the bias associated with the use ofthe ends and middle as points of reference. Maclean and Stacey (1971) have shown that the perception of the size of an angle is dependent on its orientation. Since in our study, the shaded segment always started at 12 o'clock, the angles in the pie slices are completely confounded with orientation.…”

Section: "mentioning

confidence: 99%

Children's Perception of Proportion in Graphs

Spence

Krizel

1994

Child Development

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Children ranging in age from 9 to 13 years made judgments of proportion with a variety of graphical elements in 2 experiments. Younger children can be misled by irrelevant dimensions of objects used to portray magnitudes and proportions, but older children make their judgments like adults, ignoring or accommodating the extra dimensions. Although the psychophysical function for older children and adults is approximately linear, closer inspection reveals a complex pattern of bias that is not captured by traditional psychophysical models. A characteristic pattern of over-and underestimation was observed and also turns out to be present, but previously unnoticed, in judgments made by adults. The pattern of bias is consistent with the view that the visual system extracts real or virtual axes of symmetry and that subjects use these, in addition to the object boundaries, as points of reference when making their judgments. A model that assumes repulsion of judgments away from these reference points is described and fitted to the children's data. The model is motivated by both neurophysiological and cognitive considerations.

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“…These 19th century investigations were, however, descriptive rather than experimental, and the interpretations, speculative. Despite numerous modern studies (5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15), the phenomenon of angle misperception has never been explained.…”

mentioning

confidence: 99%

Why are angles misperceived?

Nundy

Lotto²,

Coppola³

et al. 2000

Proc. Natl. Acad. Sci. U.S.A.

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Although it has long been apparent that observers tend to overestimate the magnitude of acute angles and underestimate obtuse ones, there is no consensus about why such distortions are seen. Geometrical modeling combined with psychophysical testing of human subjects indicates that these misperceptions are the result of an empirical strategy that resolves the inherent ambiguity of angular stimuli by generating percepts of the past significance of the stimulus rather than the geometry of its retinal projection.T he fact that the subtense of any acute angle is seen as being somewhat larger than the measured angle of the stimulus, whereas the subtense of any obtuse angle is seen as being somewhat smaller, was first reported by Wundt (1) and subsequently by both Hering (2) and Helmholtz (3), all of whom surmised that these distortions might underlie some of the classical geometrical illusions (4). These 19th century investigations were, however, descriptive rather than experimental, and the interpretations, speculative. Despite numerous modern studies (5-15), the phenomenon of angle misperception has never been explained.Here we provide evidence that the systematic misperception of angle subtense is the consequence of a radically empirical strategy of perception in which the angle seen is determined by the relative frequency of the possible sources of angle projections that observers have experienced. The biological rationale for this strategy is a solution to the problem posed by the inevitable ambiguity of angular stimuli. The inability of an angle projected onto a plane to specify uniquely the source is illustrated in Fig. 1. Indeed, because space is divisible without limit, the number of possible real-world sources underlying a given retinal projection is infinite.Because the well being of an observer depends on appropriate interactions with the sources of visual stimuli, the ambiguity of retinal images has long been regarded as a central problem in vision (16). Recent studies of simultaneous brightness contrast (17,18), Mach bands (19,20),, and the perception of color (22) have all suggested that this dilemma is solved by an empirical strategy in which retinal activation triggers associations (percepts) determined by the relative frequencies of the possible sources of the stimulus in past experience. A limitation in validating this concept of vision has been the practical difficulty of quantifying the frequency distribution of the real-world sources underlying the various categories of visual experience. (This problem has also been an obstacle to psychologists who have sought to model perception in terms of Bayes' decision theorem; see ref. 23 for a recent review.) Examining the perception of oriented lines circumvents this obstacle in that the frequency distribution of the possible sources of a given retinal projection-for example, the subtense of the typical source of a given angle projected on the retina-can be computed by geometrical principles, thus providing a more concrete basis for predicting perceptual...

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Judgment of angle size: An experimental appraisal

Cited by 26 publications

References 5 publications

Contours and borders in animated mimic displays

Contours and borders in animated mimic displays

Children's Perception of Proportion in Graphs

Why are angles misperceived?

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