Factors affecting perceived orientation of the Poggendorff transversal

The Poggendorff figure was simplified by removing the right transversal segment. When Ss judged the distance between a dot located on the right parallel and the imagined point where the left transversal, if extended, would intersect the right parallel, the error was independent of dot location. This result is consistent with the idea that the Poggendorff figure is processed asymmetrically by (mis)projecting one of the transversals across to the opposite parallel. Systematically omitting line segments reduced (and sometimes reversed) illusory effects. The most critical Poggendorff feature was the obtuse angle formed between transversal and parallel. Ss vertically adjusted one of two dots to apparent collinearity with an implied transversal, the tip of an intervening vertical line and the other (stationary) dot. Which dot was stationary proved critical. This primitive Poggendorff display generated no illusion unless the implied transversal, defined by the stationary dot, was the one that formed an obtuse angle with the vertical line. This result also strongly supports asymmetric active processing ideas. Perceived orientation is a property of directed line segments.     

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.     

The Poggendorff Illusion and estimates of transverse extent.

The underestimation of transverse extent relative to longitudinal extent, in the Poggendorff Illusion, was tested by varying oblique line orientation, interparallel line distance, and presence or absence of obliques. 20 subjects made estimates of the transverse extent on both a longitudinal and transverse extent. The results indicated that, although underestimation was found for some stimulus conditions, overestimation was found for others. It was argued that even though presence of obliques affected judgmental error the longitudinal-transverse illusion could not form a basis for the Poggendorff Illusion.     

The role of angles in inducing misalignment in the poggendorff figure

Much experimental evidence has been put forward against the idea that angles are necessary for the occurrence of the Poggendorff illusion. We show that five separate alignment illusions can be demonstrated in the Poggendorff figure according to its orientation, length of the parallels, and so on. In one of these (angle-caused misalignment) angles are a necessary component. The main source of the belief that angles are not necessary is the alignment illusion (attraction-caused misalignment), which is due to the action of the distant parallel on the transversal that does not abut it. We show finally that it is unlikely that the angle-caused misalignment illusion is due to a change in the apparent size of the angle.     

Angular induction as a function of contact and target orientation

The Poggendorff effect is seen as misalignment of two obliques, or misprojection of one, when the obliques are placed outside a set of parallel lines. To understand better the mechanisms behind this effect, the orientation of the lines which are normally parallel was systematically manipulated. The results indicate that projection bias is affected by the orientation of either line, is at a minimum where the line is orthogonal to the oblique, and is maximal at small angles. This is in line with classic theories which attribute the illusion to misperception of angular size. However, such explanations presuppose that in order to be effective the induction line must be proximal to the oblique so that an angle can be formed. Results are reported which show that the angle formed by the oblique and a line placed at a distance from the oblique, serving as the target of the projection, follows an angular rule of effectiveness similar to what is seen when the line is placed directly in contact with the oblique. The underlying process is described as 'angular induction'.     

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°, 45°,90°, and 135° 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.     

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 with subjective contours

Gregory (1972) has claimed that the Poggendorff misalignment effect occurs when the collinear obliques are separated by subjective rather than real contours. He used two figures to demonstrate this variant of the illusion. Two experiments to test the claim are reported. The first showed that apparent misalignment in one of the two original figures is no greater than that with two obliques alone (the oblique line effect), but misalignment in the other is greater than with two oblique lines and than with a control without subjective contours. The second experiment showed that apparent misalignment in the second figure was less than in two control figures without subjective contours. Since this reduced effect was probably due to the nature of the intersection between the oblique and a semi-circular element, the role of subjective contours remains unsettled.     

Poggendorff and Müller-Lyer illusions: common effects

Previous investigations have shown that the magnitude of the Müller-Lyer illusion is a function of the linear and angular dimensions of the figure. If the Müller-Lyer and Poggendorff illusions share a common basis, then the magnitude of the Poggendorff illusion should similarly be a function of the analogous configural dimensions. A study is reported in which changes were made in the dimensions of the Poggendorff figure that are analogous to the dimensions of the Müller-Lyer figure: the length of the parallel components (analogous to the wings of the Müller-Lyer figure); the length of the intertransversal extent (analogous to Müller-Lyer shaft length); and the angle formed between the parallel components and the intertransversal extent (analogous to the angle of wing attachment in the Müller-Lyer figure). The relationship between the magnitude of the illusion and the dimensions of the Poggendorff figure was found to be generally in line with previous findings relating to the Müller-Lyer illusion. Adaptation-level theory and the positive-context model accommodate the major findings of the present study.     

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.     

Slope and the Zöllner illusion

Informal observation suggests that the magnitude of the Z?llner illusion is reduced when the figure is viewed on a sloping plane. The hypothesis that this effect derives from the enlargement of the acute angle of intersection between the obliques and the verticals in the figure when it is viewed on a sloping plane is here investigated. The magnitude of the Z?llner illusion was measured with the use of a visual analogue scale. The results show that the change in the magnitude of the Z?llner effect as a function of the slope of the figure is different from that for corresponding figures, with enlarged angles of intersection between the obliques and the verticals, presented vertically. It is concluded that the enlargement of the angles of intersection can only partly account for the reduction of the Z?llner effect when the figure is viewed under slope, and that some other factor must be involved. An alternative hypothesis is evaluated whereby the effects result from the diminution in the contrast of the obliques when the figure is viewed under slope. Data are also presented to show that observers are able to perceive the enlarged or foreshortened angles of intersection veridically.     

On the common stimulus condition and explanation of the Müller‐Lyer,Poggendorff and Zöllner illusions: The basis for a class of geometrical illusions

Although the Müller‐Lyer, Poggendorff and Zöllner figures and the illusions with which they are associated– those of length, misalignment and non‐parallelism, respectively – are quite different, all three are attributable to the same basic effect, that of the difference in the apparent length of equal lines forming acute and obtuse angles. The role of this basic affect, reported originally by Müller‐Lyer but overlooked by him and others as a possible cause of the three illusions, is identified and discussed. It is suggested that the demonstration of a basic stimulus condition (acute and obtuse angles) and its associated illusion (difference in apparent length) generating a class of “higher order” geometric illusions has implications not only for a closer understanding of the three illusions under consideration but for other classes of illusory phenomena that might also share a common basis.     

Alignment errors to both ends of acute- and obtuse-angle arms

It has been reported that errors which occur in attempts to align the arms of two acute angles differ in size and direction from errors which occur when the angles are obtuse (Restle, 1969). Other experiments have qualified this conclusion, and it has been suggested that Restle’s result was dependent on the use of a forced-choice method with a dual-angle display (Day, 1973). Data are reported here on dot-to-line misalignments using staircase techniques both at the free end and at the vertex end of single acute or obtuse angles. The results essentially agree with Day’s method-of-adjustment results, thus implicating the display rather than the method as the cause of the original negative acute-angle effect. However, Day found no difference between the acute-angle effect and the parallelless Poggendorff illusion, while we did obtain a difference under some conditions. Consideration of the magnitudes and directions of errors at both ends of the angles’ arms gives pause to any possible accounts of the errors in terms of simple or single whole-of-line effects.     

Illusion decrement and transfer of illusion decrement in real- and subjective-contour Poggendorff figures

The reduction in illusion magnitude with visual inspection and the transfer of such illusion decrement to a noninspected figure were examined in real- and subjective-contour Poggendorff figures. For both types of figures, illusion magnitude decreased significantly, and in a similar manner, during a 5-min inspection period. Postinspection tests showed that inspecting either a real- or subjective-contour figure resulted in a reduction in illusion magnitude for the other, noninspected figure. These findings suggest that real- and subjective-contour Poggendorff figures share a similar global organization and are thus probably processed in a similar manner. These characteristics make subjective-contour figures a useful tool for separating illusion-producing mechanisms into structural and strategy components.     

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.     

Acute angles and the poggendorff illusion

Burns and Pritchard's (1971) explanation of the Poggendorff illusion is criticized. An experiment was designed to determine whether the acute angle plays any role in the perception of the illusion. The results showed that (i) an inducing line which crossed a test-line was highly effective in altering the apparent orientation of the test line, (ii) an inducing line forming an acute angle with a test-line had a small effect in changing the apparent orientation of the test-line, and (iii) an acute angle which formed part of the Poggendorff configuration produced an effect opposite to that predicted by the view that acute angles are perceptually enlarged.     

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 corner Poggendorff

With the classic Poggendorff illusion a set of parallel 'induction lines' will cause a set of oblique line segments to look misaligned even though they are collinear. A different kind of misalignment can be produced by placing the induction lines so that they form a corner. Under these conditions the obliques will appear to be angled slightly, one relative to the other. The effects are small, but can be seen and reliably reported by a group of naive subjects. The influence of the induction lines drops sharply as their relative position is moved from parallel to orthogonal, but there is a small residual influence which may be called the corner Poggendorff effect.     

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 effect of line-figure information on the magnitude of the dot forms of the Poggendorff and Müller-Lyer illusions

The magnitudes of the dot and line forms of the Poggendorff illusion and the Brentano version of the Müller-Lyer illusion were assessed in two groups of subjects: the informed group was given information about the implied figure configuration in the dot pattern, the uninformed group was not. The informed group produced a significantly greater dot illusion than the uninformed group, and there was no difference between the two groups in the magnitudes of the line illusions. The experiments are discussed in the context of Coren and Porac's proposal that illusion-inducing mechanisms can be divided into structural and cognitive components. The results suggest that about 64% of the magnitude of the Poggendorff illusion and about 54% of the Müller-Lyer illusion can be attributed to the involvement of cognitive factors.