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.     

Gaze angle explanations of the induced effect.

Mayhew and Longuet-Higgins formulated a computational explanation of the induced effect which successfully predicts the conditions under which the induced effect will occur. Underlying their theories are the assumptions that disparity information is separated into horizontal and vertical components and that the vertical disparities are used to calculate the gaze angles. An implementation of the fusional explanation introduced by Petrov makes similar predictions for the induced effect, but does not depend on these two assumptions.     

The role of apparent distance in the Poggendorff illusion

This study was designed to test the hypothesis that apparent shrinkage of the distance between the oblique lines is responsible for the Poggendorff illusion. The results from one experiment, which provided an indirect test by increasing the length of the oblique arm, supported the shrinkage hypothesis. However, a second experiment, in which apparent distance was measured directly, did not support the hypothesis. Instead, the distance between the oblique lines appeared longer than a control distance. It was concluded that the argument, made by assimilation theory, that the Poggendorff illusion is caused by changes in the apparent distance between oblique lines must be reassessed.     

Modulation of the rod and frame effect: Retinal angle vs apparent size

Summary Two rod and frame displays, constructed in a 3:1 linear ratio, were used to assess the apparent vertical. When viewed at the common distance of 1.5 m, the larger-appearing frame also produced the greater retinal angle. With the small frame at .5 m and the large one at 4.5 m, the smaller-appearing frame produced the greater retinal angle. In both cases the rod and frame effect increased with increasing retinal size, rather than with the apparent size of the frame.This research was supported by NIH Grant EY 02264 from the National Eye Institute to the first author.     

The Poggendorff illusion: Apparent misalignment which is not attributable to apparent orientation of the transversals

Subjects while looking down were required to adjust a horizontal field of parallel lines (Experiment I) or a single line (Experiment II) to the apparent sagittal direction with and without a superimposed rectangle in the centre of a circular field. The rectangle was tilted at 20, 30 or 40° to the parallels and at 20° to the line. For the 20° condition the parallel lines were apparently oriented at about half a degree compared with the field without a rectangle but in the direction opposite to that necessary to account for the Poggendorff misalignment effect. For the 30 and 40° conditions the lines did not change in apparent orientation. The orientation of the single line did not change. Almost all subjects readily reported an apparent misalignment between the collinear parallels and line separated by the oblique rectangle. It is concluded that the Poggendorff misalignment illusion occurs without apparent regression of the lines to right angles with the figure.     

Reduction of the Poggendorff effect by the motion of oblique lines

The magnitude of the Poggendorff illusion was measured when the test lines were moved up or down and tracked by subjects. The difference between test lines and inducing lines caused by motion of the test lines significantly reduced the magnitude of illusion (60%). Supplementary experiments seemed to indicate that location of test lines, perceptual shrinkage of space in the vertical dimension, and effective display time were not the main factors contributing to the reduction in illusion magnitude. Instead, it seems that some reduction in interaction between test and inducing lines was the main cause of the reduction. The rising curve of the reduction was very steep with velocity, and the reduction magnitude was almost constant over most of the range of velocities studied. The current evidence seems to suggest that moving and stationary figures are processed by separate channels and that, therefore, the interaction between them is reduced.     

Exposure-time and the apparent length of an illuminated rotating arc-line

Eighteen male Ss made estimates of the apparent length of an illuminated arc-line rotating at 75 rpm. Two arc-lengths (6 and 12 cm) were exposed for 200, 100 and 40 msec. Apparent shrinkage occurred for both arc-lengths at 200 msec, but not at the other exposures. This result was interpreted as indicating that stimulation of a certain proportion of retinal units during a specific time interval is a necessary condition for the contraction effect to occur.     

The effect of retinal location on the magnitude of the Poggendorff illusion

The effect of retinal locus on the magnitude of the Poggendorff illusion was investigated. A significant illusion was found to occur in the fovea and in undiminished magnitude at the peripheral locations horizontally displaced from the fovea. No significant illusion was induced at the vertically displaced positions. It is suggested that the results obtained at the positions displaced from the fovea may be attributable to the refracting surfaces of the cornea, and that these findings lend support to an account of the Poggendorff illusion which emphasizes the significant involvement of peripheral mechanisms.     

The effect of a moving dot transversal on the Poggendorff illusion

In attempting to derive the minimal component of the Poggendorff figure which would still produce an illusion, responses to three types of transversal were measured. One was the customary solid line type; a second type presented the two segments sequentially, alternating between them; and the third consisted of a moving dot which traveled the transversal path. Each transversal was shown with and without verticals, for a total of six conditions. Ten subjects in each condition adjusted the luminous transversal until the segments appeared to be collinear. Figures with verticals present showed a greater magnitude of illusion than those without, and discrepancies for moving dot transversals were greater than those for comparable solid line figures. Since alternating transversals were not significantly larger than solid line figures, it was concluded that the magnitude of the moving dot effect could not be attributed to temporal sequence. An eyemovement hypothesis was suggested instead.     

The effects of the motion path and the length of the variable segment in the Poggendorff illusion without parallels

Previous studies have shown that small, but consistent, errors in an alignment task occur for oblique lines when the variable stimulus is a line segment but not when it is a dot. This discrepancy could have been due to the structure of the variable stimulus or its path of motion. These alternative hypotheses were tested in two experiments. The results indicated that motion path is irrelevant but that errors generally occur when extended line segments are adjusted and do not occur in the adjustment of very short line segments (“dots”).     

Sex differences in the Poggendorff illusion: identifying the locus of the effect

Extensive research has identified individual differences associated with sex in a range of visual task performances, including susceptibility to visual illusions. The aim of this study was to identify the locus of sex differences within the context of the Poggendorf illusion. 79 women and 79 men participated within a mixed factorial design. Analyses indicated that sex differences were only present in the stimulus context with the full inducing element present. This finding replicates recent research and provides qualifying evidence as to the locus of the effect. The findings are discussed within the functional framework of perceptual processes involved in extrapolating 3-dimensional characteristics from 2-dimensional visual stimuli.     

Pictorial depth and the Poggendorff illusion

An informal demonstration is offered, which strongly supports previous contentions that, when the elements of a Poggendorff display appear to be arranged in pictorial space such that the two critical line segments are at different heights, an illusory impression of misalignment may occur. A second pair of demonstrations shows, however, that such a height difference is neither a necessary nor a sufficient cause of the illusion. In addition, the harmful effect of adding certain pictorial elements to the standard Poggendorff pattern requires a new understanding.     

Subjective contours and the Poggendorff illusion

Poggendorff illusions were generated by real edges, subjective contours, and various control patterns. Using both magnitude estimation and reproduction measures of illusion strength, it was found that subjective contours produced a reliable Poggendorff illusion. This clarifies previous reports which could not demonstrate a subjective contour-based illusion.     

The relative contribution of contact and target lines in the magnitude of the Poggendorff effect

It is well known that a set of parallel lines can cause misperception of the projected path of an oblique. Most studies of this effect have emphasized either the proximal or the distal stimulus components--the line with which the oblique makes contact, or the line that serves as the target of the projection. An experiment is reported in which the relative contribution of the contact and target lines was examined. The results indicate that rotation of either line can determine the magnitude of the projection error.     

Visual angle and apparent size of objects in peripheral vision

Measurements of apparent size were obtained by distance adjustment of a peripherally viewed stimulus to produce a match to a foveally viewed standard. As eccentricity increased, the peripheral stimulus was adjusted at distances of progressively greater visual angle, indicating that a continuous diminution in apparent size occurs with increased eccentricity. This effect was found to be stable for several conditions of illumination and for changes in the light adaptive state of S. Apparent size diminution and apparent distance increase were also found for familiar objects viewed in an open field.