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.     

Visual illusions with acute and obtuse angles: Configurational effects and observer strategies

In three experiments, it is demonstrated that the negative Poggendorff illusions that Restle (1969) and others have reported are a special case, that, in general, acute- and obtuse-angle effects are the same, that there are additional special cases which modulate the illusion, but only slightly, and that these special cases derive from particular configurations which impose other effects, including observer strategies, on the basic illusion. These additional effects do not bear necessarily upon the fundamental explanation of the illusion. The experiments also show that effects obtained with amputated illusory figures are not linearly additive. Recent experiments that have measured apparent oblique separation in the Poggendorff figure and have found large obtuse-angle but small, or negative, acute-angle effects are also discussed. It is argued that these experiments have not demonstrated that the two dependent variables-alignment and length judgments-are correlated, or that one error causes the other; and it is argued that uinaHolland’s theory of parallel attraction to explain the illusion is not tenable.     

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.     

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.     

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.     

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.     

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.     

The Poggendorff illusion: Amputations,rotations, and other perturbations

Studies of the Poggendorff illusion (a transversal interrupted by parallel lines) showed that illusory effects increased linearly with increasing separation between the parallels, increased in inverse proportion to the tangent of the angle of intersection between transversal and parallels, decreased whenever line segments (other than a transversal segment) were omitted, decreasing to zero when the segment of a parallel forming the obtuse angle with the transversal was omitted, and varied systematically with the tilt of the whole display, approaching zero when the transversal was oriented in a horizontal or vertical position. Hypothesis: The Poggendorff illusion involves at least three kinds of effects on the perceived orientation of a segment: distortion by other segments (especially a segment intersecting at an obtuse angle), stability of vertical and Horizontal orientations, and assimilation towards vertical or horizontal.     

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.     

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.     

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.