Contour displacements and tracking errors: Probing ’twixt Poggendorff parallels

Testing the Tilt-Constancy Theory of Visual Illusions

Prinzmetal and Beck (2001) Journal of Experimental Psychology: Human Perception and Performance27 206–217) argued that a subset of visual illusions is caused by the same mechanisms that are responsible for the perception of vertical and horizontal—a theory they referred to as the tilt-constancy theory of visual illusions. They argued that these illusions should increase if the observer's head or head and body are tilted because extra reliance would then be placed on the illusion-inducing local visual context. Exactly that result had previously been reported in the case of the tilted-room and the rod-and-frame illusions. Prinzmetal and Beck reported similar increases in the tilt illusion (TI), as well as the Zöllner, Poggendorff, and Ponzo illusions. In two experiments, we re-examined the effect of head tilt on the TI. In experiment 1, we used more conventional TI stimuli, more standard experimental methods, and a more complete experimental design than Prinzmetal and Beck, and additionally extended the investigation to attraction as well as repulsion effects. Experiment 2 more closely replicated the Prinzmetal and Beck stimuli. Although we found that head tilt did increase TIs in both experiments, the increases were of the order of 1°–2°, more modest than the 7° reported by Prinzmetal and Beck. Significantly, the TI increase was larger when inducing tilts and head tilts were in the same direction than when they were in opposite directions, suggesting that the tilt-constancy theory may be oversimplified. In addition, because previous evidence renders unlikely the claim that the Poggendorff illusion can be explained simply in terms of misperceived orientation of the transversals, the question arises whether there might be some other explanation for the increase in the Zöllner, Poggendorff, and Ponzo illusions with body tilt that Prinzmetal and Beck reported.

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.

Real and virtual borders in the Poggendorff illusion

The strength of the Poggendorff illusion has been determined by a nulling method for the classical as well as other configurations of the central inducing region. Compared to a uniform field, an inducing rectangle with very low contrast produces a marked illusion, which saturates at a Michelson contrast of about 0.1. With virtual borders of the Kanizsa type there is a weak illusion and this effect is attenuated when the 'pacman' sectors are occluded. Texture borders without luminance contrast induce a stronger illusion. These results are discussed in relation to earlier data for contrast dependence of Vernier acuity and for the orientation discrimination and tilt illusion with real and virtual borders.

Evaluating the decay gradient for collinearity bias with lateral displacement from the axis of induction

The misperception of alignment which is found in many geometric illusions can be quantified using relatively simple stimulus configurations. Perceived collinearity of one segment (designated as the test segment) is biased by a second segment (designated as the induction segment), with the size of effect being a function of the relative angle between the two segments. The process can be described as angular induction. The strength of bias is greatest when the induction segment is centered at the tip of the test segment. Tong and Weintraub have reported that lateral displacement from the tip, i.e., at right angles to the axis of the induction segment, produces a sharp drop in the strength of effect. This decline is described as a "decay gradient" for the angular induction. One experiment replicates and provides better quantification of this "decay gradient". Two other experiments examine the decay gradient using a pair of induction segments, one on each side of the tip of the test segment. Displacement of the segments (either in the same direction or in opposite directions) produces substantially the same gradient of effect. Therefore, previous evidence of "tandem boosting" of effect for segment pairs does not depend on collinearity among the stimulus components. Finally, a fourth experiment finds that an induction segment which is at a fixed position and orientation differentially affects the influence of a variable induction segment. At some angles the influence of the variable segment is augmented, and at others it is suppressed. These findings are discussed in a neuroreductionist context, and a simple model for angular induction is presented.

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.

How the range effect contaminates control scores in studies of visual illusions

The relationship between mean control scores and mean experimental scores in 23 experiments on alignment illusions has been examined. Evidence is presented to show that, through the operation of the range effect, control scores are biased to a significant degree in the direction of experimental scores. The implications of this are considered, not only as regards the value of control scores in psychophysical studies, but also as further evidence of the dangers of within-subjects experimental designs when issues depend upon the values of extreme points in a range of values.

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 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.

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.

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 role of the second oblique in the Poggendorff illusion

It has been observed previously in the classic Poggendorff illusion figure that the end of the oblique line which abuts onto the vertical parallel appears more misaligned than its free end. Various theories suggest that angular distortions are largest at the point of abutment. Two experiments are reported which, however, suggest that, compared to displays in which a single dot is aligned with an oblique line, the introduction of a second, parallel oblique segment does not increase errors more at the abutting tip than at the free end, but, rather, reduces them more at the free end. These results not only cast doubt on the relative importance of angular effects alone in the classic Poggendorff display, but also emphasise the complexity of that figure as a tool in the investigation of visual processing.

A comparison of visual tilt illusions measured by the techniques of verticle setting, parallel matching, and dot alignment

The tilt illusion (TI) was investigated by using both short (19 min) and long (2 deg 6 min) test lines, at three angles of test line-inducing line separation (15 degrees, 45 degrees, and 75 degrees). Three groups of ten observers each provided data under one of three task conditions: vertical judgment, parallel matching, and dot alignment on a common visual display. The main result was that both the vertical judgment and the parallel matching task provided similar, classic TI angular functions with the means ordered 15 degrees greater than 45 degrees greater than 75 degrees and with small attraction effects at 75 degrees in three of the four relevant functions. The third task, dot alignment, yielded results different from the average of the other two: no attraction effects occurred and, with the short test line, the obtained mean illusion at 45 degrees exceeded those at the other intersect angles. These results are consistent with alignment data reported by others. One explanation is that the inducing line produces an apparent bowing of the test line which would be reflected in dot alignments but not in vertical setting or in parallel matching. However, direct evidence does not support this hypothesis. An alternate hypothesis, for which independent evidence exists, is that alignment errors reflect perceptual mistracking but that the origin of these errors is not the tip of the test line but within it. Although this does not explain dot alignment errors, it highlights their complexity and the need to interpret them with caution.

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.