Assessing Poggendorff effects via collinearity, perpendicularity, parallelism, and Oppel (distance) experiments

Light Refraction by Water as a Rationale for the Poggendorff Illusion

The Poggendorff illusion in its classical form of parallel lines interrupting a transversal is viewed from the perspective of being related to the everyday experience of observing the light refraction in water. It is argued that if one considers a transversal to be a light ray in air and the parallel lines to form an occluding strip of a medium with the refractive index being between that of air and water, then one should be able to account, both qualitatively and quantitatively, for most of the features associated with the Poggendorff illusion. Statistical treatment of the visual experiments conducted with seven participants, each analyzing 50 configurations having different intercepting angles and strip widths, resulted in the effective refractive index of the occluding strip N = 1.13 ± 0.15, which is sufficiently close to the average (between that of water and air) refractive index of ∼1.17. It is further argued that the same mechanism can also be employed to account for many variants of the Poggendorff illusion, including the corner-Poggendorff pattern, as well as for the Hering illusion.

Applying Emmert's Law to the Poggendorff illusion

The Poggendorff illusion was approached with a novel perspective, that of applying Emmert's Law to the situation. The extensities between the verticals and the transversals happen to be absolutely equal in retinal image size, whereas the registered distance for the verticals must be smaller than that of the transversals due to the fact that the former is assumed to occlude the latter. This combination of facts calls for the operation of Emmert's Law, which results in the shrinkage of the occluding space between the verticals. Since the retinal image shows the transversals to be in contact with the verticals, the shrinkage must drag the transversals inwards in the cortical representation in order to eliminate the gaps. Such dragging of the transversals produces the illusory misalignment, which is a dictation of geometry. Some of the consequences of this new explanation were tested in four different experiments. In Experiment 1, a new illusion, the tilting of an occluded continuation of an oblique line, was predicted and achieved. In Experiments 2 and 3, perceived nearness of the occluding entity was manipulated via texture density variations and the predicted misalignment variations were confirmed by using a between-subjects and within-subjects designs, respectively. In Experiment 4, tilting of the occluded segment of the transversal was found to vary in the predicted direction as a result of being accompanied by the same texture cues used in Experiments 2 and 3.

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 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.

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.

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.

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.

The Poggendorff illusion: an illusion of linear extent?

In the standard version of the Poggendorff figure a transversal intersects two parallel verticals and the segment of the transversal between the two intersection points, A and B, is not shown. The two portions of the transversal outside the parallels then seem to be misaligned. Besides this illusion of direction, there is also an illusion of size, the distance AB being underestimated in the standard figure. The influence of configural components in determining this spatial distortion of the Poggendorff figure was examined by having subjects reproduce the inner oblique (at 45 degrees) extent AB in variations of the figure. This distance was found to be underestimated in Poggendorff variations which contained parallel (vertical) components that formed an acute angle with AB; and the underestimation increased as the number of these components present in the figure increased. The distance AB was found not be significantly distorted in figures which contained only those parallel (vertical) components that formed an obtuse angle with AB, yet their presence in the figure tended to counteract the underestimation. When the transversals were omitted, the underestimation was found to increase. The findings are interpreted in support of an explanation that reduces the Poggendorff effect to those factors which mediate the Müller-Lyer illusion.

The locus of maximum weighting within attentive fields: an empirical investigation

Fixation within a modified Poggendorff display was used to assess Pressey's hypothesized construct of attentive fields. In Experiment I the results for fixating near the bottom of the display supported the predictions based on Pressey's construct; however, results from fixating near the top of the display were more easily explained by a tilt effect noted by Zajac (1957).

Experiment II and III replicated the first experiment and obtained independent measures of the tilt effect. After the tilt effect was subtracted from the Poggendorff scores, the prediction based upon the attentive field construct was supported in the top fixation condition; however, only Experiment II provided support for the prediction in the bottom fixation condition.