The apparent length of rotating arcs under conditions of dark adaptation

The apparent contraction of a rotating light arc occurred during the first 20 rain, but not after 25 min, of dark adaptation. Estimates of length obtained after 25 min were affected by the level of luminance of the arc but not by its speed of rotation, by dark gaps in the arc, or by instructions to estimate its length in terms of a brighter region. There was no tendency for a rotating dark arc to appear shorter at any stage of adaptation.     

Apparent brightness of a rotating arc-line as a function of speed of rotation

52 Ss were required to adjust the brightness of a center fixation line to equal that of the apparent brightness of an arc line viewed at a distance from the fixation point subtending an angle of 12° to the eye. Adjustments were made when the arc-line was stationary and rotating at speeds of 30, 45, 60 and 75 rpm. It was found that brightness enhancement occurred with increase in speed. This result was interpreted as supporting Ansbacher's account of distortion in the perception of moving arc-lines.     

Exposure-time and spatial-frequency effects in the tilt illusion

The exposure durations of a vertical test line and a tilted inducing grating were varied and the tilt illusion thus generated was found to change as a function of this variation. Significant direct effects (acute-angle expansion) and indirect effects (acute-angle contraction) were found to occur at times consistent with Andrew's estimate of the time course of inhibition in the visual system when the inducing grating had a spatial frequency of 10 cycles deg-1. However, a 2.71 cycles deg-1 grating gave significant effects at exposure durations of 10 as well as 1000 ms, while in a further experiment a 10.91 cycles deg-1 grating gave significant effects at 1000 ms only. These results seem to suggest that orientation interactions thought to be due to inhibition (direct effect) and disinhibition (indirect effect) may occur within both sustained and transient channels with concomitant differences in time constants.     

Assessment of apparent length and angle explanations of the Poggendorff effect

Explanations of the Poggendorff effect were assessed by comparing the degree of angular distortion induced by modified and traditional configurations. Assimilation theory predicted that the traditional effect would be reversed in modified configurations. Analysis showed that the effect, although reduced in magnitude, was not reversed. Comparison of the degree of the effect induced by modified and traditional configurations indicated that a substantial portion of the Poggendorff effect was due to processing of areas between the long vertical lines of the display. This finding is not consistent with theories based on subjective distortion of angles. It was concluded that a theory of the Poggendorff effect must include processing of internal areas of the configuration.     

The apparent length of a line as a function of its inclination

In the first of two experiments reported here, subjects adjusted the length of a variable line until it appeared to be as long as a standard line. There were two sizes of standard line, 3 and 6 inches, and each was shown vertically for some trials and horizontally for others. The variable line was presented in each of the 10° positions from 0° (horizontal), through 90° (vertical), to 170°. The principal results of the first experiment are:

(1) Vertical lines look longer than horizontal lines of the same length, but lines tilted 20°-30° to the left of vertical look longer than lines in any other orientation. The results are asymmetrical, because lines tilted to the right of vertical do not look as long as those tilted to the left of vertical.

(2) The variability of the settings increases as the angle increases between the standard and variable lines.

(3) When they are expressed in percentage terms, the data obtained with the 3-and 6-inch standards are virtually identical, i.e. the data for the 3-inch standard can be made to match those for the 6-inch standard simply by doubling the former.

(4) There are enormous differences among subjects in the patterns of settings made at the various angles. A few subjects apparently experienced no illusory effects since they adjusted the variable line to about the same physical length irrespective of its orientation. Other subjects showed exaggerated overestimations of the variable line for vertical and near-vertical positions.

In the first experiment, the variable line was always to the left of the standard, and it was natural to assume that this position effect had somehow produced the asymmetry noted in paragraph 1 above. This hypothesis was tested in the second experiment which alternatively showed the variable line above, below, to the right of, and to the left of the standard line. The results of this experiment generally confirm the data of the first experiment in showing that lines tilted 20°-30° to the left of vertical look longer than lines tilted to any other position. In addition, the second experiment shows that this asymmetry in the results is not a function of the relative positions of the variable and standard lines. In general, however, overestimations of length are smaller when the two lines are one above the other, greater when the two lines are side by side.     

Examination of apparent extent as an explanation of the Poggendorff effect

The explanation of apparent misalignment in the Poggendorff figure, based on underestimation of the intertransversal distance, was investigated in two experiments. In Experiment 1, subjects judged the intertransversal distance in the traditional Poggendorff figure and two of its variants. The size of the acute angle and the intertransversal distance were manipulated. Half of the subjects made the judgments with the method used by Wilson and Pressey (1976) and the other half made their judgments with the method used by Greist-Bousquet and Schiffman (1981). The results indicated that perceived intertransversal distance was greater with the former method. In Experiment 2, subjects adjusted the transversals to apparent collinearity in the same displays as were used in Experiment 1. The collinearity judgments were transformed to allow comparison with the results of Experiment 1. Comparison of the collinearity judgments with the distance judgments indicated that they did not follow similar trends. For each Poggendorff variant, proportional distance judgments increased as the size of the acute angle increased, and decreased as the intertransversal distance increased. Collinearity judgments did not vary as a function of intertransversal distance. As the size of the acute angle increased, collinearity judgments increased for two of the Poggendorff variants but decreased for the third. It was concluded that the findings did not support the explanation of apparent misalignment based on underestimation of the intertransversal distance.     

The maintenance of apparent luminance of an object.

Results from luminance discriminations with objects defined by apparent motion suggest an object-specific temporal integration of luminance. Further experiments suggested that this integration is weighted to favor the initial display of an object and involves the percept of surface reflectance (lightness). These results are consistent with the object-file metaphor suggested by D. Kahneman, A. Treisman, and B. Gibbs (1992), in which an object's perceived initial surface reflectance is assigned and maintained in an object file. A strategy is proposed in which the intrinsic properties of an object are assumed not to change over time. As intrinsic properties are generally invariant and possibly difficult to compute, this strategy would have the advantage of relatively high accuracy at relatively low computational cost.     

The apparent size of the path traversed by a rotating target during saccadic and smooth pursuit: New data on the shrinking circle illusion

Twelve subjects attempted to visually track a continuously or discretely moving target as it rotated through a path 20° in diameter at velocities ranging from .18 to 5.2 cps. Tracking error, resulting from the eye tracking a path inside that of the target, was an increasing function of velocity from .18 to 1.13 cps. Higher velocity targets could not be tracked consistently. Apparent path diameter and the tracking diameter of the eye were both a decreasing function of velocity (through 1.13 cps) in the condition requiring smooth pursuit of a continuously moving target. Tracking diameter was also a decreasing function of velocity for the condition requiring saccadic pursuit of a discretely moving target, but this was not associated with a corresponding decrease in apparent size. These results suggest that the retinal position error generated by undertracking the target is processed during saccadic, but not during smooth, pursuit.     

The effect of luminance variation on the apparent position of an edge

A gray outline against a white (or black) ground appears to deviate when one of the divided regions turns into black (white). The direction of shift is not predictable on the basis of luminance profile and polarity contrast of this part of contour, called gray edge (to indicate a stepwise gradient from black to gray and from gray to white). Rather, it appears to depend on the luminance profiles of the collinear regions: A gray edge shifts toward the dark side whenever collinear with a gray line traversing a white ground. The same gray edge takes the opposite direction whenever it extends against a black ground. This rule proved to be successful in predicting the illusory convergence of the sides of a square that formed the stimuli of the first experiment, but the magnitude of the phenomenon was affected by luminance ratios and polarity contrasts of the gray edges, in agreement with the findings of the experiments on gray or blurred edge misalignment. A second experiment tested some hypotheses predicting the combined effects of two or more distorting sources. These hypotheses, suggested by the physical theory of vector sum, were partially disproved. A new model is proposed that assumes different ways of integrating local distortions. The third experiment tested predictions of how distorting pulses in opposite directions combine. The illusory misplacement of edge studied in this experiment is proposed as the underlying phenomena of the café wall illusion, the hollow square illusion, and other illusory phenomena observed with blurred areas. A connection with the induction grid phenomena is hypothesized.