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.     

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 Poggendorff illusion: consider all the angles

In the Poggendorff display, which consists of parallel lines interrupting a transversal, one of the two transversal segments was replaced by a dot lying along the parallel. The angle between the remaining transversal segment and the parallels was varied in 15 degree increments, as was the orientation of the transversal with respect to the subject. Subjects set the dot to appear collinear with the transversal. Judgmental errors can be partitioned into additive components, one linearly related to the size of the obtuse angle between transversal and parallels and the other a sinusoidal function of transversal and parallels and the other a sinusoidal function of transversal orientation (collinearity settings err toward the horizontal or vertical, whichever is closer), plus a meridional effect, an interaction term that magnifies the errors of a given obtuse angle as the transversal approaches an oblique orientation.     

Spatial context affects the Poggendorff illusion

The Poggendorffillusion has often been explainedas purely an interactionbetween the parallels and the transversals. The present study demonstrates that additional spatial context exerts an influence on this illusion. In Experiment 1, we examined the effects of a surrounding tilted frame (complete and degraded versions) on collinearity adjustments iatheuprightandrotatedPoggendorfffigures. The frame’s orientation was always oblique. Relative to the no-frame condition, frames decreased error in collinearity adjustments in the upright-Poggendorff figure, and increased error in the rotated Poggendorfffigure. In Experiment 2, a circumscribing circle did not cause an orientation-inhibition effect (Ebenholtz & Utrie, 1982, 1983), suggestingthat the effect ofthe frame on the Poggendorif illusion may not be closely related to the rod-and-frame effect. In Experiment 3, orientation of a central texture modulated the magnitude ofthe illusion. The results do not serve to explain the mechanisms behind the Poggendorffillusion, but they do demonstrate the importance of visual reference frames in understanding perceived misalignment.     

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.     

Some puzzling results on the Poggendorff illusion

Results obtained by Weintraub and Krantz on the Poggendorff illusion were critically evaluated. It was also shown that the assimilation theory of the Poggendorff illusion adequately predicted the form of the function that results from rotating one of the oblique arms.     

The Poggendorff illusion with obtuse and acute angles

The Poggendorff misalignment illusion with the conventional figure and its obtuse- and acute-angle variants was investigated in five experiments. The method of adjustment was used in Experiments I–IV, and in Experiment V compared with a forced-choice procedure. The first experiment showed that the 45-deg acute-angle illusion is positive but smaller than those from the other two figures, the second that it is the same size as that with two 45-deg oblique lines without parallels, and the third that the 30-deg acute-angle illusion is also positive but smaller than that for the other two patterns. In the fourth experiment, the 30-deg acute-angle illusion was insignificant under the same condition in which it was positive in Experiment III, but significantly positive for a reversed contrast (white on black) figure. The results from the last experiment were paradoxical; the 45-deg acute-angle figure again gave a significantly positive illusion with the method of adjustment, but mainly reports of a negative illusion with a forced-choice technique. A possible basis for this difference is discussed in terms of psychophysical procedures and special features of the acute-angle pattern. The weakness of the 30-deg acute-angle illusion is also considered along with other issues.     

A new explanation for the Poggendorff illusion

Kanizsa (1972, 1974) has observed that the surface upon which a figure is amodally completed undergoes shrinkage. That observation is investigated here as a possible explanation of the Poggendorff illusion, on the assumption that the shrinkage of the surface behind the surface defined by the two vertical parallel lines results in displacement of the two visible segments of the oblique line. The first two experiments attempted to quantify the shrinkage of the amodal surface by measuring the enlargement of the vertical strip required to achieve perceived collinearity; the oblique lines intercepted the vertical strip at 45- and 30-deg angles. In both cases, the enlargement required to counterbalance the assumed amodal shrinkage was approximately 30%. In the third experiment, the oblique line was rotated to the horizontal, and again the perceived shrinkage of the amodal surface was approximately 30%. The application of this explanation to the Poggendorff illusion is discussed, as well as the relevance of this explanation to the common experimental finding that magnitude of the illusion is dependent upon the slope of the oblique line.     

3-D processing in the Poggendorff illusion

In the Poggendorff illusion two collinear oblique lines, separated by two vertical lines, appear to be misaligned. 3-D processing of the oblique but not the vertical lines is considered to cause this apparent misalignment. We investigated whether more explicitly triggering 2-D versus 3-D interpretations of the different parts of Poggendorff-like displays would influence the apparent misalignment. In Experiment 1, we found that compared to 2-D controls, 3-D interpretations of the vertical parts did not influence apparent misalignment, while for the oblique parts 3-D processing resulted in more apparent misalignment than 2-D controls. In Experiment 2, the amount of contour convergence of the oblique parts was manipulated resulting in the 3-D blocks, but not the 2-D line patterns, to be perceived as receding in depth. Now, apparent misalignment increased the more the 3-D blocks were perceived as receding in depth. We conclude that apparent misalignment in Poggendorff-like displays can be influenced by different interpretations of its separate parts, while keeping the local junctions between the different elements the same.     

Influence of the Poggendorff illusion on manual pointing

The results of recent studies indicate that certain visuomotor actions, such as grasping and pointing, are unaffected by visual size illusions. The present study investigated whether the Poggendorff illusion of alignment influences pointing to a target's location. 15 subjects pointed with their unseen hands to the apparent location of the extension of the oblique line onto the target line of a version of the Poggendorff illusion. Analysis indicated the pointing action was influenced by the Poggendorff illusion. The implications of this finding for the claim that different cortical streams of visual processing subserve visuomotor actions and conscious visual perception are discussed.     

A depth processing theory of the Poggendorff illusion

The Poggendorff illusion is attributed to the processing of the oblique lines of the Poggendorff figure as receding horizontal lines with their inner ends equidistant because of attachment to a frontal plane (defined by the parallel lines of the figure). Collinearity in three-dimensional space is inconsistent with such equidistance; one line must lie on a higher horizontal plane than the other. This necessarily noncollinear resolution of the lines in depth processing (which is inferred irrespective of the O’s consciousness of depth) is assumed to influence apparent projective relationships within the figure, thus accounting for the illusion. Predictions from the theory, involving manipulations of the plane defined by the parallels, were confirmed experimentally. In addition, the theory is shown to account very well for the effects of amputations and rotations of the figure, which other theories of the illusion cannot handle.     

The Poggendorff illusion in Descent from the Cross by Rubens

A comparison of the painting Descent from the Cross by Rubens with the earlier oil sketch reveals that Rubens discovered the Poggendorff illusion.     

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.     

Sex differences in susceptibility to the Poggendorff illusion

This study presents experimental results indicating that there are sex differences in the susceptibility to a geometric optical illusion. Participants (57 male and 39 female undergraduate students) performed 3 trials on a test involving the Poggendorff illusion. Analysis indicated that the magnitude of the illusion diminished significantly with each trial and that the percent perceived error was significantly larger for women than for men. This finding is consistent with the numerous studies which have indicated better visuospatial abilities for men than for women.     

The influence of optical aberrations on the magnitude of the Poggendorff illusion

The amount of blurring of the retinal image can be reduced by proper selection of an artificial pupil and a chromatic filter. Reduction of the amount of blurring due to optical aberrations by viewing through a 1-mm artificial pupil and an interference filter in the eye, results in a concomitant reduction in the magnitude of the Poggendorff illusion. The magnitude of the reduction is smaller, however, than would be expected if the illusion was predominantly determined by blur due to optical aberration.