Misalignment effects in 3-D versions of Poggendorff displays

Strong misalignment effects are found in three-dimensional (3-D) versions of Poggendorff displays viewed binocularly. The components of the standard 2-D Poggendorff figure—the parallels and the oblique segments—were presented in 3-D depth as a flat rectangular object with occluding edges and an oblique line situated behind the object. Three experiments investigated the misalignment effects under three different observation instructions: Subjects were told to look at the oblique (Experiment 1), at the rectangle (Experiment 2), or at the background (Experiment 3). Experiments 1 and 2 examined the effects on judgments of alignment of varying the distance in depth that separates the oblique from the rectangle. Experiment 3 examined the effects of varying the distance between the fixated background and the 3-D Poggendorff figure. Both standard and reversed misalignment effects were obtained. When the viewing condition produces crossed disparity for the oblique, perceived misalignment occurs in the usual Poggendorff direction, but it is reversed with uncrossed disparity. Moreover, the amount of misalignment is related to the amount of disparity, and it can be much stronger than is usual in the 2-D versions of the Poggendorff. The misalignment effects can be explained by binocular integration to produce a single cyclopean image.     

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: 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.     

On apparent misalignment of collinear edges and boundaries

In two experiments, subjects adjusted various pairings of the top and bottom boundaries of two obliquely oriented outline bars (Experiment 1) and those of two similarly oriented complete and incomplete squares (Experiment 2) to apparent alignment. The data from the first experiment showed that the misalignment effects were determined jointly by the directional properties of the bar ends (vertical, oblique, and semicircular) and the pair of boundaries that were aligned (both top boundaries, top of upper bar with bottom of lower bar, bottom of upper bar with top of lower bar). The results from the second experiment showed that the misalignment effects were the same for the oblique boundaries of solid and outline squares and persisted when the squares were reduced to two parallel lines. The effect was undiminished when the ends of the parallels were aligned, but was markedly reduced when pairs of parallels themselves were aligned. The outcomes of the two experiments are explained in terms of the apparentpositions of the oblique boundaries. It is proposed that these vary with the positions of the elements (bar or square) relative to the visual field, the position of the boundaries relative to the stimulus elements, and the positions of the boundaries relative to axes that are delineated by the parallel adjacent ends of bars and sides of squares. This relative-position basis for apparent misalignment is held to be the basis of misalignment effects in other figures.     

The effect of edge orientation and movement direction on the apparent misalignment of collinear bars

Four experiments on apparent misalignment of oblique collinear bars are reported. The data from the first three experiments showed that the misalignment was slight but significant when no direction other than that of the bars themselves was delineated and about double when the vertical was delineated by movements of the adjustable bar. When the vertical was delineated by both these movements and the ends of the bars (or by vertical parallel lines), the misalignment was more than six times greater. Conversely, it was reduced when the bar ends delineated the vertical and bar movements delineated the direction at right angles to the bars. The data from a fourth experiment showed that the inner pair of edges were closely involved in apparent misalignment and that the outer ends were not. The relationship between the misalignment effect with bars and the Poggendorif figure (oblique lines separated by parallels), the delineation of direction by edges and movement, and the implications of these data for an explanation are discussed.     

The oblique line illusion: The poggendorff effect without parallels

The apparent misalignment of two oblique collinear lines was investigated in two experiments. In the first the effect with the lines at 45° to the median plane was compared with that for the same two lines separated by the conventional parallels of the Poggendorff figure. The illusion with the two lines was consistent and significant but about one-third the magnitude of that with the parallels. The two illusions were significantly correlated. In the second experiment the angle of the two oblique, collinear lines was varied in 15° steps. The misalignment illusion was maximal at 45° and smaller but significant at 60 and 75°. There was no significant effect at 15 and 30°.     

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.     

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.     

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.     

A stereo disadvantage for recognizing rotated familiar objects

We tested recognition of familiar objects in two different conditions: mono, where stimuli were displayed as flat, 2-D images, and stereo, where objects were displayed with stereoscopic depth information. In three experiments, participants performed a sequential matching task, where an object was rotated by up to 180° between presentations. When the 180° rotation resulted in large changes in depth for object components, recognition performance in the mono condition showed better performance at 180° rotations than at smaller rotations, but stereo presentations showed a monotonic increase in response time with rotation. However, 180° rotations that did not result in much depth variation showed similar patterns of results for mono and stereo conditions. These results suggest that in some circumstances, the lack of explicit 3-D information in 2-D images may influence the recognition of familiar objects when they are depicted on flat computer monitors.     

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

By adjusting the orientation of, and separation between, two free-standing dots, Ss indicated directions and distances associated with the Poggendorff display (a transversal interrupted by parallel lines). Judged distance between parallels (with transversal absent) increased slightly when additional interior parallels were added; this Oppel effect can be interpreted as contour repulsion. Errors in judging the orientation of an actual transversal segment were too small to account for the Poggendorff effect. The usual large errors occurred for estimates of the orientation of the missing transversal segment between the parallel lines. Cognitive mistracking adequately describes the Poggendorff effect. Mistracking is a function of the angle subtended between transversal and parallels, and of the orientation of the entire display.     

Angular subtense effects on perception of polar and parallel projections of cubes

Many authors contend that the perception of 2-D drawings of a 3-D object is governed by polar projective geometry. A problem for this position is that observers accept parallel projections, which are not produced with polar projective geometry, as accurate representations of 3-D objects. In Experiments 1 and 2, we used two different standards of comparison to study the perceptions of three line drawings of cubes—correct polar projections of cubes with subtenses of 15° and 35°, and a parallel projection—at five different angular subtenses. In Experiment 1, 14 observers judged each drawing when it subtended about 35°, 15°, 5°, 4°, and 2° in width. Subjects used an 8-point rating scale to compare each drawing with a correct polar projection of a cube subtending 35°, viewed with the drawing subtending 15°. As predicted, both polar projections had their highest ratings at their correct vantage points. Ratings for the parallel projection were highest at small angular subtenses and decreased when it subtended 35°. These findings were supported by a second experiment in which the 15° polar projection was set at a 5° viewing angle as a standard. In Experiment 3, 15 observers compared the three drawings, viewed at a second set of angular subtenses (30°, 35°, 40°, 45°, and 50°), with a standard, the 35° polar set at 45°. Ratings fell with increases in viewing angle, and the parallel projection was rated lowest. The results indicate that parallel projections are assessed as polar projections that are correct for objects at a small angular subtense. Furthermore, projections at a small angular subtense are robust; that is, they are acceptable over a wide range of angular subtenses. We suggest that robustness can be explained by the modest variability in the proportions of pictures of cubes subtending small angles.     

Spatial distortions within the Poggendorff fig are and its variants: A parametric analysis

Angle size and horizontal separation of the Poggendorff figure and three components (acute angles, obtuse angles, and obliques) were varied parametrically. Two adult trained observers judged the distance between the obliques of the test figure relative to a pair of comparison dots during 250-msec tachistoscopic presentations. Results indicated: (1) the Poggendorff effect is created by an underestimation of intercontour distance, resulting in apparent misalignment; (2) only the obtuse angles can serve as a significant predictor of the classical illusion; (3) the parallel lines play an important contributory role in the Poggendorff illusion when they are present. Findings tended to support a theoretical explanation based on contour interactions.     

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.     

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.     

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 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.     

The morinaga misalignment effect: Reduction and reversal by modification of figural extremities

Summary In three experiments straight lines varying in length were added to the physically aligned apexes of asymmetrically arranged angles (Experiment 1) and the ends of similarly arranged parallel lines (Experiments 2 and 3). Compared with the condition without added lines, apparent misalignment of the aligned apexes (Morinaga effect) was markedly reduced by the shorter lines and reversed in direction by the longer ones. Apparent misalignment of the ends of parallels was also reduced but not reversed by collinear and right-angle lines. Reduction was greater with the longer collinear lines and with right-angle lines that crossed the parallels a short distance from their ends. These outcomes are interpreted as implicating processes associated with the extremities of figural elements (apexes, ends, and edges) rather than the configuration formed by the elements.     

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.     

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.