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 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 tactual horizontal-vertical illusion depends on radial motion of the entire arm

Wesought to clarify the causes of the tactual horizontal-vertical illusion, where vertical lines are overestimated as compared with horizontals in Land inverted-T figures. Experiment 1 did not use L or inverted-T figures, but examined continuous or bisected horizontal and vertical lines. It was expected that bisected lines would be perceived as shorter than continuous lines, as in the inverted-T figure in the horizontal-vertical illusion. Experiment 1 showed that the illusion could not be explained solely by bisection, since illusory effects were similar for continuous and bisected vertical and horizontal lines. Experiments 2 and 3 showed that the illusory effects were dependent upon stimulus size and scanning strategy. Overestimation of the vertical was minimal or absent for the smallest patterns, where it was proposed that stimuli were explored by finger movement, with flexion at the wrist. Larger stimuli induce whole-arm motions, and illusory effects were found in conditions requiring radial arm motion. The illusion was weakened or eliminated in Experiment 4 when subjects were forced to examine stimuli with finger-and-hand motion alone, that is, their elbows were kept down on the table surface, and they were prevented from making radial arm motions. Whole-arm motion damaged performance and induced perceptual error. The experiments support the hypothesis that overestimation of the vertical in the tactual horizontal-vertical illusion derives from radial scanning by the entire arm.     

Anomalous induction of brightness and surface qualities: a new illusion due to radial lines and chromatic rings

When a chromatic (eg light-blue) annulus surrounds the central gap of an Ehrenstein figure so as to connect the inner ends of the radial lines, a striking new lightness effect emerges: the central white disk has both a self-luminous quality (brighter than in the regular Ehrenstein figure) and a surface quality (dense, paste-like). Self-luminous and surface qualities do not ordinarily appear co-extensively: hence, the brightness induction is called anomalous. In experiment 1, subjects separately scaled self-luminous and surface properties, and in experiment 2, brightness was nulled by physically darkening the central gap. Experiments 3 and 4 were designed to evaluate the importance of chromatic versus achromatic properties of the annulus; other aspects of the annulus (width or the inclusion of a thin black ring inside or outside the chromatic annulus) were tested in experiments 5-7. In experiments 8-12, subjects rated the brightness of modified Ehrenstein figures varying the radial lines (number, length, width, contrast, arrangement). Variation of these parameters generally affected brightness enhancement in the Ehrenstein figure and anomalous brightness induction in a similar manner, but was stronger for the latter effect. On the basis of these results, anomalous brightness induction is attributed to a surface induction process triggered by an interaction between illusory brightness enhancement (due to the radial lines) and border ownership (due to the blue annulus).     

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.     

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.     

Illusory figures based on local kinematics.

A new type of motion-induced illusory figure determined by local kinematic information is investigated. The new figure is induced by radial line patterns subjected to either figure motion (the lines change as if they were stationary and a triangle was rotating in front of them) or background motion (the lines change as if they were being rotated behind a stationary triangle). Although the two kinds of motion are equivalent from the viewpoint of relative displacements, perceptually they yield very different results. With background motion, observers tend to perceive rigid figures that have a triangular shape. With figure motion, observers report seeing deforming figures with shapes that vary depending on the number of lines in the display. We consider two alternative accounts for this asymmetry which we term the background superiority effect (BSE). The first account proposes that the effect is due to retinal persistence and to figure stability. Against this line of explanation, we demonstrate that observers also see rigid triangular shapes in displays where both the figure and the radial lines rotate (double motion displays). The second account proposes that the effect depends on the availability of local kinematic information constraining contour orientation. This second line of explanation is consistent with observers' reports of bowed edges in double motion displays rotating in phase or in counterphase. Candidate mechanisms for extracting local kinematic information are discussed.     

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.     

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 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 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.     

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 object-detection effect: configuration enhances perception.

Line drawings used by Weisstein and Harris (1974) are seen as box-like three-dimensional figures if the lines are arranged properly. A flat two-dimensional pattern is seen when these same lines are disarranged. A target line contained within the three-dimensional figure is identified more readily than is the same line contained within a two-dimensional figure. This finding was extended in the present experiments: The three-dimensional stimulus was detected more quickly than the two-dimensional stimulus, under conditions of visual backward masking. Three-dimensional stimuli were also classified more quickly than two-dimensional stimuli. Just as with the face-detection effect and the word-detection effect, object detection can be affected by the form of the visual stimulus.     

The object-detection effect: Configuration enhances perception

Line drawings used by Weisstein and Harris (1974) are seen as box-like three-dimensional figures if the lines are arranged properly. A flat two-dimensional pattern is seen when these same lines are disarranged. A target line contained within the three-dimensional figure is identified more readily than is the same line contained within a two-dimensional figure. This finding was extended in the present experiments: The three-dimensional stimulus was detected more quickly than the two-dimensional stimulus, under conditions of visual backward masking. Three-dimensional stimuli were also classified more quickly than two-dimensional stimuli. Just as with the face-detection effect and the word-detection effect, object detection can be affected by the form of the visual stimulus.     

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.     

Asymmetric priming effects in visual processing of occlusion patterns

In three experiments, we examined the effect of temporal context in amodal completion of partly occluded nontarget figures. In a primed same-different task, test pairs were preceded by a sequence of two primes, one of which was a single, the other a composite figure. Single figures reappeared in the composite ones, which also contained a square that could be viewed, alternatively, as an occluder or as yielding a mosaic fit to the other shape. To measure context influences between single and composite figures, both of which were nontargets, we studied their combined effect as primes on the test pairs of the same-different task, expecting that congruency between both primes should lead to a superadditive priming effect on the task. We found that single figures presented first provided facilitatory context for local and global occlusion as well as for mosaic interpretations of subsequently presented composite figures. These effects occurred only when the composite figure was presented briefly (50 msec). No superadditive facilitation occurred when composite figures were presented first and single figures followed them. The restriction of the effect to short presentations and its temporal asymmetry were taken as evidence that prior context biases possible occlusion interpretations during the process of completion, rather than afterward.     

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.     

The spacing illusion: a spatial aperture problem?

A geometrical illusion in which the horizontal spacing between adjacent parallel lines in a row is underestimated when the lines are tilted away from vertical in a chevron configuration was investigated in two experiments. The perceived spacing was found to decrease as the tilt angle increased, consistent with the idea that separation judgements are influenced by the normal spacing between lines ie at right angles to the line orientation. It is proposed that this illusion reveals an analogue in spatial perception to the well-known aperture problem in motion perception. In establishing the separation of nearby or overlapping shapes in an image, the visual system cannot only rely upon the normal separation of contours belonging to each shape (as would be visible through small spatial apertures or receptive fields), since this varies with contour orientation. The system is therefore faced with a spatial aperture problem. The spacing illusion may arise because information usually available to solve the problem is absent in the illusion figure, or it may reflect a bias in favour of the orthogonal, which is adopted in the face of the ambiguity.     

Perceived curvature of arcs and dot patterns as a function of curvature, arc length, and instructions

Arcs of circles, with six arc lengths and four radii of curvature, and an equivalent set of figures composed of three dots were used as stimuli. Subjects in Group I imagined the circle from which an arc or dot triplet was taken and indicated the centre of the circle. Group II subjects estimated the location of the point that was equidistant from the middle and ends of an arc, or equidistant from the three dots of a triplet. The results from arcs showed, in Group I, an underestimation of curvature that decreased as a function on the length of the arc. In Group II, however, overestimation of the curvature of most arcs occurred, indicating a strong influence of the difference in the perceptual task on the results. The effect of instructions was similar with the dot figures but, in general, more errors resembling overestimation of curvature occurred with these figures.     

Focusing attention on overlapping and non-overlapping figures with subjective contours

In a series of five experiments we investigated whether observers could focus attention on a restricted visual area that was demarcated by Kanizsa-like subjective contours, and whether this effect also occurred in the case of overlapping figures. The task was a simple reaction time to a luminance increment and the basic finding was that reaction time was faster when the imperative stimulus fell inside the focus of attention than when it fell outside. The first two experiments showed that the extent of the attentional focus could be adapted to a region that was demarcated by subjective contours, thus extending the results of previous studies that used regions demarcated by real contours. The last three experiments showed that, regardless of the type of margins, focusing was more efficient for the figure that was perceived as lying in front in a pair of overlapping figures. Received: 21 December 1999  / Accepted: 23 August 2000