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 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.     

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 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 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 parallel-less Poggendorff: Virtual contours put the illusion down but not out

Four versions of Poggendorff displays were compared: (1) the conventional display of a transversal interrupted by parallel lines, (2) a transversals-only display, (3) a virtual-contour display where the parallels were suggested (but not drawn) via “good continuation” and “c1osure, ” and (4) the profile display, a degraded version of the virtual-contour display that retained many of its borders but did not suggest parallels. Each display was drawn with transversal tilted at 45 and 51 deg from vertical. All displays produced significant illusions at both tilts. By comparison with the illusion magnitudes of the conventional display, the effects for the other displays were small. The outcome supports the existence of two salient illusion-producing factors: the necessity for actual contours to form the subtended angle and assimilation of the transversal toward O’s horizontal.     

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.     

Sighting-down and the Poggendorff illusion: a mystery within a mystery.

As reported before, sighting-down one of the diagonal lines on a typical Poggendorff pattern will reduce the illusion even if that situation is only pictorial. But here it is also argued that sighting-down itself requires further understanding.     

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.     

Illusion decrement and transfer of illusion decrement in obtuse- and acute-angle variants of the Poggendorff illusion

Illusion-decrement and transfer-of-illusion-decrement procedures were used to examine the contribution of the obtuse- and acute-angle components of the Poggendorff pattern to the standard Poggendorff illusion. In the first four experiments, subjects were required to scan between the oblique lines of the Poggendorff pattern during the inspection phase of the decrement procedure. However, because of a possible confound associated with this procedure, a different decrement technique was used in Experiment 5. The results of Experiment 5 confirm and extend MacKay and Newbigging's (1977) finding that similar amounts of transfer to the standard pattern are obtained from the obtuse- and acute-angle patterns as from the standard pattern itself: In showing that the acute- and obtuse-angle components both contribute to the illusion, these findings question the plausibility of those theories of the Poggendorff illusion which do not assign any significant role to the acute-angle component. Furthermore, the potential confound associated with the decrement procedure of Experiments 1-4 suggests that the results of other studies obtained with similar procedures need to be reevaluated.     

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.     

Modal completion in the Poggendorff illusion: support for the depth-processing theory

The Poggendorff illusion is one of the most prominent geometrical-optical illusions and has attracted enduring interest for more than a hundred years. Most modern theories explain the illusion by postulating various kinds of distortion of the "test" component of the figure by the context or the inducing component. They make no reference to the importance of processes involved in three-dimensional scene perception for understanding the illusion. We measured the strength of the Poggendorff illusion in configurations containing solid inducing surfaces as opposed to the usual parallel lines. The surface, oblique-line, and background luminances were manipulated separately to create configurations consistent with modal completion of the obliques in front of the surface. The marked decrease in the size of the illusion in conditions favoring modal completion is consistent with claims that perceived spatial layout is a major determinant of the Poggendorff illusion.