Bias in proportion judgments: the cyclical power model.

When participants make part-whole proportion judgments, systematic bias is commonly observed. In some studies, small proportions are overestimated and large proportions underestimated; in other studies, the reverse pattern occurs. Sometimes the bias pattern repeats cyclically with a higher frequency (e.g., overestimation of proportions less than .25 and between .5 and .75; underestimation otherwise). To account for the various bias patterns, a cyclical power model was derived from Stevens' power law. The model proposes that the amplitude of the bias pattern is determined by the Stevens exponent, beta (i.e., the stimulus continuum being judged), and that the frequency of the pattern is determined by a choice of intermediate reference points in the stimulus. When beta < 1, an over-then-under pattern is predicted; when beta > 1, the under-then-over pattern is predicted. Two experiments confirming the model's assumptions are described. A mixed-cycle version of the model is also proposed that predicts observed asymmetries in bias patterns when the set of reference points varies across trials.

Image velocity magnitudes and perception of heading.

Most theoretical approaches to perception of heading rely on the directions of image velocity vectors as the primary source of heading information. The research described in this article examined an additional source of information for determining heading: distributions of image velocity magnitudes. Displays simulated observer motion relative to rigid three-dimensional environments. Depth was distributed nonuniformly such that image velocity magnitudes provided, for some display conditions, conflicting heading information relative to the radial directions of the flow field. Results indicated that image velocity magnitudes influenced heading performance, suggesting that the perception of heading is not based solely on the radial structure of the directions of image flow.

Perceptual similarity of shapes generated from Fourier descriptors.

A metric representation of shape is preserved by a Fourier analysis of the cumulative angular bend of a shape's contour. Three experiments examined the relationship between variation in Fourier descriptors and judgments of perceptual shape similarity. Multidimensional scaling of similarity judgments resulted in highly ordered solutions for matrices of shapes generated by a Fourier synthesis of a few frequencies. Multiple regression analyses indicated that particular Fourier components best accounted for the recovered dimensions. In addition, variations in the amplitude and the phase of a given frequency, as well as the amplitudes of 2 different frequencies, produced independent effects on perceptual similarity. These results suggest that a Fourier representation is consistent with the perceptual similarity of shapes, at least for the relatively low-dimensional Fourier shapes considered.

Spatial orientation from optic flow in the central visual field.

Previous research has shown that stimulation of the central visual field with radial flow patterns (produced by forward motion) can induce perceived self-motion, but has failed to demonstrate effects on postural stability of either radial flow patterns or lamellar flow patterns (produced by horizontal translation) in the central visual field. The present study examined the effects of lamellar and radial flow on postural stability when stimulation was restricted to the central visual field. Displays simulating observer motion through a volume of randomly positioned points were observed binocularly through a window that limited the field of view to 15 degrees. The velocity of each display varied according to the sum of four sine functions of prime frequencies. Changes in posture were used to measure changes in perceived spatial orientation. A frequency analysis of postural sway indicated that increased sway occurred at the frequencies of motion simulated in the display for both lamellar and radial flow. These results suggest that both radial and lamellar optic flow are effective for determining spatial orientation when stimulation is limited to the central visual field.