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: 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.     

Modulations of the processing of line discontinuities under selective attention conditions?

We examined whether the processing of discontinuities involved in figure-ground segmentation, like line ends, can be modulated under selective attention conditions. Subjects decided whether a gap in collinear or parallel lines was located to the right or left. Two stimuli were displayed in immediate succession. When the gaps were on the same side, reaction times (RTs) for the second stimulus increased when collinear lines followed parallel lines, or the reverse, but only when the two stimuli shared the same orientation and location. The effect did not depend on the global form of the stimuli or on the relative orientation of the gaps. A frame drawn around collinear elements affected the results, suggesting a crucial role of the "amodal" orthogonal lines produced when line ends are aligned. Including several gaps in the first stimulus also eliminated RT variations. By contrast, RT variations remained stable across several experimental blocks and were significant for interstimulus intervals from 50 to 600 msec between the two stimuli. These results are interpreted in terms of a modulation of the processing of line ends or the production of amodal lines, arising when attention is selectively drawn to a gap.     

Constant errors in judgements of collinearity due to the presence of neighbouring objects

If a line (the pointer) is aligned with a dot (the target) that stands on another line (the induction line) which is at an angle to the pointer, the pointer and the dot may no longer appear collinear. Whether they do or not depends upon the angle formed by the pointer with the induction line: the smaller the angle, the greater the misalignment effect. Misalignment is always in the direction of the induction line, which is why this alignment illusion is called attraction-caused misalignment (attraction misalignment for short). Three experiments are described in which this illusion is explored further. In the first it is shown that the induction line can exert its influence even when not contiguous with the target, though the size of the effect varies inversely with the distance of the induction line from the target. In the second experiment it is demonstrated that a dot as well as a line can induce attraction misalignment and that similarity between the induction and target items increases misalignment. Evidence in support of the theory that the termination of the induction line, as well as the part contiguous with the target dot, may induce attraction misalignment is provided in the third experiment.     

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.     

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 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 perceivedlocation conditions) 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.     

Focused attention is not enough to activate discontinuities in lines, but scrutiny is

We distinguish between the roles played by spatial attention and conscious intention in terms of their impact on the processing of segmentation signals, like discontinuities in lines, associated with the act of scrutinizing. We showed previously that the processing of discontinuities in lines can be activated. This is evidenced by an impairment in the detection of a gap between parallel elements when it follows a gap between collinear elements in the same location and orientation. This effect is no longer observed if attention is divided between two gaps in the first stimulus. The results from this study show that focusing attention on a gap between collinear elements is not enough to observe a modulation, consistently with the need to integrate, rather than to separate, collinear elements in usual conditions. The modulation is sensitive to the conscious expectations of subjects, suggesting that an intention can trigger modulations that spatial attention cannot.     

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.     

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

Summary 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.     

Apparent misalignment of oblique coplanar bars in depth

Following preliminary observations of apparent misalignment of coplanar surfaces in a three-dimensional (3-D) form of the Poggendorff Figure viewed in depth, the effect was investigated in five experiments and compared with the 2-D Poggendorff effect in the same object in a sixth. The effect in depth occurred with the complete object when it was viewed binocularly but did not do so with the oblique bars alone or when the object was viewed monocularly. The effect did not vary with oblique-parallel angles of 30°, 45°, and 60° and was absent when the angle was 90°. It varied as a function of the distance between the parallels, but was unaffected by a regular pattern on the oblique bars. A smaller 2-D Poggendorff effect occurred when the upper edges of the object were viewed from above. Although the depth effect was robust, its variance was high compared with that of the 2-D effect, indicating that acuity for misalignments of oblique elements in depth is poor. An explanation of apparent misalignment of oblique elements in 2-D and 3-D space in terms of a perceptual compromise between alignment in an oblique axis and separation relative to the axes of the parallels is proposed.     

Determinants of the Bourdon effect

The Bourdon illusion is the apparent inward bending of straight, collinear edges in a solid figure consisting of two elongated triangles meeting at their apexes. This effect was investigated in five experiments. In the first and third experiments, it was shown that the apparent bending is greatest when the apical angles are about 12 deg and the axis of the figure is oriented at about 22 deg from the vertical. The second experiment was a control involving visual acuity for angular departures of two lines from collinearity and served as a basis of selection for subjects in Experiments 3, 4, and 5. Experiments 4 and 5 showed that the illusion occurs strongly in a solid (“filled in”) figure but is notably smaller in outline figures of the same size and shape. It tends to be negative in outline figures with boundaries formed by continuous and broken lines. The relationship between the Bourdon illusion and the “negative” Zöllner illusion is considered.     

The Poggendorff illusion: consider all the angles

In the Poggendorff display, which consists of parallel lines interrupting a transversal, one of the two transversal segments was replaced by a dot lying along the parallel. The angle between the remaining transversal segment and the parallels was varied in 15 degree increments, as was the orientation of the transversal with respect to the subject. Subjects set the dot to appear collinear with the transversal. Judgmental errors can be partitioned into additive components, one linearly related to the size of the obtuse angle between transversal and parallels and the other a sinusoidal function of transversal and parallels and the other a sinusoidal function of transversal orientation (collinearity settings err toward the horizontal or vertical, whichever is closer), plus a meridional effect, an interaction term that magnifies the errors of a given obtuse angle as the transversal approaches an oblique orientation.     

How configurations of binocular disparity determine whether stereoscopic slant or stereoscopic occlusion is seen

A partially occluded contour and a slanted contour may generate identical binocular horizontal disparities. We investigated conditions promoting an occlusion resolution indicated by an illusory contour in depth along the aligned ends of horizontally disparate line sets. For a set of identical oblique lines with a constant width added to one eye's view, strength, depth, and stability of the illusory contour were poor, whereas for oblique lines of alternating orientations the illusory contours were strong, indicating a reliance on vertical size disparities rather than vertical positional disparities in generating perceived occlusion. For horizontal lines, occlusion was seen when the lines were of different lengths and absolute width disparity was invariant across the set. In all line configurations, when the additional length was on the wrong eye to be attributed to differential occlusion, lines appeared slanted consistent with their individual horizontal disparities. This rules out monocular illusory contours as the determining factor.     

The relation between color spreading and illusory contours

In the present study, we examine the relation between neon color spreading (Redies & Spillmann, 1981) and illusory contours. In Experiment 1, the effects of misalignment between the line elements on the illusory contours in the Ehrenstein figure and in the Redies-Spillmann figure were examined. The remarkable overlap of the two curves for the likelihood of perceiving illusory contours in the Ehrenstein figure and in the Redies-Spillmann figure suggests that the illusory contours surrounding brightness enhancement (Ehrenstein, 1941) and those surrounding neon color spreading are caused by the same mechanism. We further examined both the effects of the interposed grids seen either in front of or behind the figures (Experiment 2) and the effects of misalignment (Experiment 3) on the illusory contours and range of color spreading, and found a high correlation between the appearance/disappearance of illusory contours and global/local color spreading. In Experiment 4, we added new lines to induce illusory contours to the line elements inducing local color spreading. We found that global color spreading was seen to cover the area surrounded by the illusory contours. On the basis of these findings, we suggest that there is an interaction between illusory contours and local color spreading.     

The Poggendorff illusion with obtuse and acute angles

The Poggendorff misalignment illusion with the conventional figure and its obtuse- and acute-angle variants was investigated in five experiments. The method of adjustment was used in Experiments I–IV, and in Experiment V compared with a forced-choice procedure. The first experiment showed that the 45-deg acute-angle illusion is positive but smaller than those from the other two figures, the second that it is the same size as that with two 45-deg oblique lines without parallels, and the third that the 30-deg acute-angle illusion is also positive but smaller than that for the other two patterns. In the fourth experiment, the 30-deg acute-angle illusion was insignificant under the same condition in which it was positive in Experiment III, but significantly positive for a reversed contrast (white on black) figure. The results from the last experiment were paradoxical; the 45-deg acute-angle figure again gave a significantly positive illusion with the method of adjustment, but mainly reports of a negative illusion with a forced-choice technique. A possible basis for this difference is discussed in terms of psychophysical procedures and special features of the acute-angle pattern. The weakness of the 30-deg acute-angle illusion is also considered along with other issues.     

Aggregation and unit formation in the perception of moving collinear lines

The degree to which collinear lines are treated as a unit in resolving rotary motion in depth was investigated with the use of parallel projection to make direction of motion ambiguous. The proportion of time that the collinear lines appeared to rotate in the same direction was used as an index of their perceptual coherence. When the gap between the lines was small, there was strong grouping of the lines with respect to direction of motion as well as appearance of rigidity for the configuration. For larger gaps the grouping for direction of motion was maintained, but the lines appeared to have different axes of rotation leading to an appearance of nonrigidity. It is concluded that line elements can be aggregated for the resolution of certain properties without constituting a unit in any general sense.     

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.