The Poggendorff illusion: an illusion of linear extent?

The development of the Poggendorff illusion in typically developing children

We examined how the strength of the Poggendorff illusion changes with age in typically developing children. To this end, we recruited children aged 6 to 14 years and quantified the degree to which they experienced the illusion. The illusion was strongest in the youngest children and decreased with age logarithmically-reaching adult levels (as established by an earlier study) by 21.6 years, as determined by nonlinear interpolation. We also measured the ability to align two lines together in a nonillusory condition, receptive language, and abstract reasoning to determine whether changes in illusion strength were also associated with these factors. Alignment-matching abilities, receptive language, and abstract reasoning increased with age. However, only receptive language and abstract reasoning were correlated with illusion strength. Abilities in alignment matching were not related to illusion strength and reached adult levels (as established by a previous study) earlier at 14.7 years, as determined by nonlinear interpolation. A multiple regression analysis further revealed that receptive language and abstract reasoning did not contribute beyond their shared variance with age. Based on these findings, we suggest that the illusion is exaggerated in early development and attenuates as low-level and high-level processes mature. The theoretical implications of these findings are discussed.

Spatial Alignment and Response Hand in Geometric and Motion Illusions

Perception of visual illusions is susceptible to manipulation of their spatial properties. Further, illusions can sometimes affect visually guided actions, especially the movement planning phase. Remarkably, visual properties of objects related to actions, such as affordances, can prime more accurate perceptual judgements. In spite of the amount of knowledge available on affordances and on the influence of illusions on actions (or lack of thereof), virtually nothing is known about the reverse: the influence of action-related parameters on the perception of visual illusions. Here, we tested a hypothesis that the response mode (that can be linked to action-relevant features) can affect perception of the Poggendorff (geometric) and of the Vanishing Point (motion) illusion. We explored the role of hand dominance (right dominant versus left non-dominant hand) and its interaction with stimulus spatial alignment (i.e., congruency between visual stimulus and the hand used for responses). Seventeen right-handed participants performed our tasks with their right and left hands, and the stimuli were presented in regular and mirror-reversed views. It turned out that the regular version of the Poggendorff display generates a stronger illusion compared to the mirror version, and that participants are less accurate and show more variability when they use their left hand in responding to the Vanishing Point. In summary, our results show that there is a marginal effect of hand precision in motion related illusions, which is absent for geometrical illusions. In the latter, attentional anisometry seems to play a greater role in generating the illusory effect. Taken together, our findings suggest that changes in the response mode (here: manual action-related parameters) do not necessarily affect illusion perception. Therefore, although intuitively speaking there should be at least unidirectional effects of perception on action, and possible interactions between the two systems, this simple study still suggests their relative independence, except for the case when the less skilled (non-dominant) hand and arguably more deliberate responses are used.

Biases and sensitivities in the Poggendorff effect when driven by subjective contours

PURPOSE

A consensus in the existing literature suggests that the Poggendorff effect (a perceptual misalignment of two collinear transversal segments when separated by a pair of parallel contours) persists when the parallels are defined by Kanizsa-like subjective contours. However, previous studies have often been complicated by a lack of quantitative measures of effect size, statistical tests of significance, appropriate measures of baseline and control biases, or stringent definition of subjective contours. The aim of this study was thus to determine whether subjective contours are capable of driving the Poggendorff effect once other factors are accounted for.

METHODS

Twenty participants were tested on a number of test and control figures incorporating first-order (luminance-defined) and subjective parallels using the method of adjustment. All figures were tested at two different orientations, and observer sensitivities and observer biases were assessed.

RESULTS

A systematic response bias (in the direction of the classical effect) was found for Poggendorff figures that incorporated subjective parallels. The effect was highly significant and greater than for control figures. There was no concomitant change in judgment sensitivity (positional certainty). Finally, there was a positive correlation between the effect size for figures incorporating first-order and subjective parallels.

CONCLUSIONS

The findings reported demonstrate conclusively that true Kanizsa-like subjective contours are capable of driving the Poggendorff effect. Further, the data are consistent with a growing body of evidence that suggests both first-order and subjective contours are processed at early loci in the visual pathways when position is encoded.

The Poggendorff illusion: effect of distance between the parallel lines

43 subjects observed Poggendorff figures with transverse line segments at a constant distance while the parallels were positioned closer or farther apart. At closer distances, no illusion occurred; at farther distances, the illusion diminished. The illusion no longer occurred when the parallels were located beyond the outside end of the transverse lines. Since illusions occurred only when the parallels physically touched the transverse line, this research emphasizes the importance of the intersection of figural elements in the production of 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 Poggendorff illusion as a function of different densities of random dot textures filling the space between the verticals. The results of Experiment 1 show that the illusory effect is a nonlinear function of the texture parameter r, the ratio of black pixels to white and black pixels, with a minimum for r = 0.5, approximately, and a maximum for r = 0 and r = 1. The results may be interpreted by an analytical model of perceptual space dynamics, in which the effect depends on the amount of interaction between points of different light intensity. A computer simulation performed by applying the analytical model to different values of r 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 of the space between the verticals as a function of the parameter r. 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 Poggendorff illusion.

Collinearity judgment as a function of induction angle

The misalignment which is seen in the Poggendorff illusion can be studied with better control by using a configuration which has only two line segments. Two experiments were conducted in which subjects judged collinearity of a test segment, this judgment being subjected to a biasing influence from a second (induction) segment. Exp. 1 held the test segment at one of three orientations relative to the observer (30 degrees, 45 degrees, and 60 degrees) and systematically varied the orientation of the induction segment in 15 degrees increments through the range of possible positions. The orientation of the page relative to the observer was varied as well. Exp. 2 varied the test segment through a greater range of angles and sampled more levels of induction segment orientation. Analysis indicated that projection errors follow orderly rules similar in kind to but different in magnitude from those observed for the Tilt Illusion, most notably, (a) misprojection is greatest when the orientation of the interfering line is similar to that of the line segment being projected and (b) the strength of this influence decreases as the relative angle becomes orthogonal. Also, the orientation of the segment being projected relative to the observer serves to modulate the strength of the basic induction effect. These perceptual interactions are discussed in relation to neural models for orientation selectivity.

Spatial context affects the Poggendorff illusion

The Poggendorff illusion has often been explained as purely an interaction between 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 in the upright and rotated Poggendorff figures. 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 Poggendorff figure. In Experiment 2, a circumscribing circle did not cause an orientation-inhibition effect (Ebenholtz & Utrie, 1982, 1983), suggesting that the effect of the frame on the Poggendorff illusion may not be closely related to the rod-and-frame effect. In Experiment 3, orientation of a central texture modulated the magnitude of the illusion. The results do not serve to explain the mechanisms behind the Poggendorff illusion, but they do demonstrate the importance of visual reference frames in understanding perceived misalignment.

The logic of misperceived distance (or location) theories of the Poggendorff illusion

For the Poggendorff display (transversal interrupted by parallel lines), the typical distance-misperception theory postulates that a particular linear distance extending across the empty space between parallels is underestimated; examples are the intertransversal slant distance defined by the closest ends of the transversal segments (a "wings-in Müller-Lyer like" underestimation) or the perpendicular distance between parallels (parallels "attract"). Distance misperception by itself, however, can neither establish that perceived transversal misalignment exists for a Poggendorff display nor specify the perceived-location condition(s) that will produce perceptual collinearity. The perceptual displacement vector is introduced as a means of specifying fully the perceptual mislocation (displacement) of one transversal segment with respect to the other. Given this vector information (direction as well as distance), the logical soundness of theories postulating distance or location misperception were evaluated, and they were compared on the basis of extant data. Such vector information can be used to evaluate other classes of theories as well.

The Poggendorff illusion and apparent interparallel extents

An explanation of the Poggendorff misalignment effect in terms of apparent contraction of interparallel extent resulting from the Müller-Lyer illusion was tested in three experiments. Three of the eight stimulus figures had oblique transversals outside the parallels in the usual way, three had them inside, and two were controls consisting of the transversals only. Müller-Lyer forms were differently delineated between the parallels for the inside-transversal and outside-transversal figures, and were not delineated in the control figures. In the first experiment apparent misalignment occurred in four of the six parallel-line figures and in neither of the controls. In the second experiment oblique extent between the parallels was underestimated in six of the eight figures and right-angle extent was overestimated in all of them. The results of the third experiment showed that right-angle (horizontal) extent between the parallels without transversals is estimated without significant error. The data from the three experiments do not support the interparallel-extent explanation of apparent misalignment. Instead, the results are interpreted in terms of independent perceptual compromises, one involving alignment of the transversals and the other the distance between them.

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.

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.

How far can attraction-caused misalignment account for the Morinaga misalignment effect?

When a line (the pointer) is collinear with a dot, the addition of a second line (the induction line) contiguous with the dot or near it may cause the pointer to appear to be collinear with a point further along or nearer to the induction line. The geometrical relations upon which this effect (which we call attraction-caused misalignment) depends, have been studied with the Obonai and Wundt-Loeb (Hotopf, 1981; Hotopf & Brown, 1988) figures. Drawing upon the studies of misalignment in the Morinaga figure carried out by Restle (1976), Day, Bellamy, and Norman (1983), and Day and Kasperczyk (1985), as well as upon two new experiments, we show that misalignment in the Morinaga figure is also attraction-caused misalignment, as previously defined. We conclude with a discussion of a number of theories that aim at accounting for attraction misalignment.

Examination of apparent extent as an explanation of the Poggendorff effect

The explanation of apparent misalignment in the Poggendorff figure, based on underestimation of the intertransversal distance, was investigated in two experiments. In Experiment 1, subjects judged the intertransversal distance in the traditional Poggendorff figure and two of its variants. The size of the acute angle and the intertransversal distance were manipulated. Half of the subjects made the judgments with the method used by Wilson and Pressey (1976) and the other half made their judgments with the method used by Greist-Bousquet and Schiffman (1981). The results indicated that perceived intertransversal distance was greater with the former method. In Experiment 2, subjects adjusted the transversals to apparent collinearity in the same displays as were used in Experiment 1. The collinearity judgments were transformed to allow comparison with the results of Experiment 1. Comparison of the collinearity judgments with the distance judgments indicated that they did not follow similar trends. For each Poggendorff variant, proportional distance judgments increased as the size of the acute angle increased, and decreased as the intertransversal distance increased. Collinearity judgments did not vary as a function of intertransversal distance. As the size of the acute angle increased, collinearity judgments increased for two of the Poggendorff variants but decreased for the third. It was concluded that the findings did not support the explanation of apparent misalignment based on underestimation of the intertransversal distance.

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.

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.

Assessment of apparent length and angle explanations of the Poggendorff effect

Explanations of the Poggendorff effect were assessed by comparing the degree of angular distortion induced by modified and traditional configurations. Assimilation theory predicted that the traditional effect would be reversed in modified configurations. Analysis showed that the effect, although reduced in magnitude, was not reversed. Comparison of the degree of the effect induced by modified and traditional configurations indicated that a substantial portion of the Poggendorff effect was due to processing of areas between the long vertical lines of the display. This finding is not consistent with theories based on subjective distortion of angles. It was concluded that a theory of the Poggendorff effect must include processing of internal areas of the configuration.