The orientation of a parallel-line texture between the verticals can modify the strength of the Poggendorff illusion.

In the present experiments, we attempted to evaluate the modification of the strength of the Poggendorff illusion as a function of the different orientation of a parallel-line texture filling the space between the vertical lines. In Experiment 1, the standard version of the Poggendorff configuration was tested against four different parallel-line textures oriented at 0 degrees, 45 degrees, 90 degrees, and 135 degrees with respect to the obliques. The results showed that the illusory effect was a linear function of the progressive discrepancy between the angle of the lines of the texture and that of the obliques. In Experiment 2, we tested the same textures used in Experiment 1 after the elimination of the two vertical lines. The data obtained approximated a linear function, as in the previous experiment, but the alignment errors were consistently lower. The statistical analysis performed on the data of all eight experimental conditions shows that both factors--texture and presence/absence of verticals--were significant, but most of the effect was due to the texture factor. The results may be interpreted through the "perceptual compromise hypothesis," originally proposed for the bisection forms of the Poggendorff illusion, but with important modifications. The data are also discussed in terms of their implications for other theories proposed for the Poggendorff illusion.     

Modifications of the Poggendorff effect as a function of random dot textures between the verticals

In the present research, we investigated the modification of the strength of the Poggendortf illusion as a function of different densities ofrandom dot textures failing the space between the verticals. The results ofExperiment 1 show that the illusory effect is a nonlinear function ofthe texture parameterr, the ratio of black pixels to white and black pixels, with a minimum forr=0.5, approximately, and a maximum forr=0 andr=1. The results may be interpreted by an analytical model of perceptual space dynamics, in which the effect dependson the amount of interaction between points of different light intensity. A computer simulation performed by applying the analytical model to different values ofr shows a good agreement between the predictions and the experimental data. To test the hypothesis underlying the model, a second experiment was carried out to measure the magnitude of the expansion ofthe space between the verticals as a function of the parameterr. The results are consistent with the hypothesis of the model. The overall data are discussed in terms of their implications on various theories proposed for the Poggeadorff illusion.     

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.     

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.     

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 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.     

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.     

Lack of evidence for a tactual Poggendorff illusion

Lucca, Dellantonio, and Riggio (1986) reported large distortions in a tactual analogue of the visual Poggendorff illusion. They also reported large effects in the direction opposite to the visual illusion, which they termed "inversions." However, their evidence for such effects is questionable; they used what we consider to be inappropriate measurement and analysis procedures. In attempting to replicate their experiment, and in conducting four additional experiments, we found no evidence at all for their alleged tactual analogue of the visual Poggendorff effect. Instead, we demonstrated that "inversions" are likely due to the use of a raised stimulus display that causes artifactual mistracking, which is totally unrelated to normal mechanisms of alignment judgment. We also discuss the possible role of intersensory factors in the generation of tactual illusions.     

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 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.     

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.