The parallel-less Poggendorff: Virtual contours put the illusion down but not out

The Poggendorff illusion driven by real and illusory contour: Behavioral and neural mechanisms

The Poggendorff illusion refers to the phenomenon that the human brain misperceives a diagonal line as being apparently misaligned once the diagonal line is interrupted by two parallel edges, and the size of illusion is negatively correlated with the angle of interception of the oblique, i.e. the sharper the oblique angle, the larger the illusion. This optical illusion can be produced by both real and illusory contour. In this fMRI study, by parametrically varying the oblique angle, we investigated the shared and specific neural mechanisms underlying the Poggendorff illusion induced by real and illusory contour. At the behavioral level, not only the real but also the illusory contours were capable of inducing significant Poggendorff illusion. The size of illusion induced by the real contour, however, was larger than that induced by the illusory contour. At the neural level, real and illusory contours commonly activated more dorsal visual areas, and the real contours specifically activated more ventral visual areas. More importantly, examinations on the parametric modulation effects of the size of illusion revealed the specific neural mechanisms underlying the Poggendorff illusion induced by the real and the illusory contours, respectively. Left precentral gyrus and right middle occipital cortex were specifically involved in the Poggendorff illusion induced by the real contour. On the other hand, bilateral intraparietal sulcus (IPS) and right lateral occipital complex (LOC) were specifically involved in the Poggendorff illusion induced by the illusory contour. Functional implications of the above findings were further discussed.

Horizontal-vertical illusion in mental imagery: quantitative evidence

The present study had two main goals: (1) to investigate the difference between perception and mental imagery using a visual illusion as a stimulus; (2) to inspect gender related differences in perception and imagery. Our main hypothesis, that there would be no differences between perception and mental imagery, was motivated by previous neuroimaging data. Unlike these neuroimaging studies that demonstrate great similarity between the two processes, results obtained in behavioral studies have not always been consistent. We assumed that this inconsistency was a consequence of methodological differences. Hence, we explored the two processes with a modified behavioral procedure. The additional exploration of gender differences was motivated by the discrepancy between our findings and the existing literature. In two experiments, participants estimated the lines constituting the horizontal-vertical illusion, either in perception or imagery task. Results confirmed that there was no significant difference between perception and imagery: the illusion was equally strong in both tasks. In the second experiment, an additional factor was tested, stimulus size. The results showed that, although there was no significant difference in illusion strength, there was a gender difference in the size of mental image for medium and large stimuli. While male subjects performed equally in the two tasks, female subjects tended to underestimate size in the imagery task. This tendency intensified as the stimulus size increased. Our results not only inform us about the status of illusions in imagery but also offer some answers about the spatial nature of mental representations. We hope that such precise measurements of mental representation might provide better understanding of reasoning that uses mental images.

The Poggendorff illusion affects manual pointing as well as perceptual judgements

Pointing movements made to a target defined by the imaginary intersection of a pointer with a distant landing line were examined in healthy human observers in order to determine whether such motor responses are susceptible to the Poggendorff effect. In this well-known geometric illusion observers make systematic extrapolation errors when the pointer abuts a second line (the inducer). The kinematics of extrapolation movements, in which no explicit target was present, where similar to those made in response to a rapid-onset (explicit) dot target. The results unambiguously demonstrate that motor (pointing) responses are susceptible to the illusion. In fact, raw motor biases were greater than for perceptual responses: in the absence of an inducer (and hence also the acute angle of the Poggendorff stimulus) perceptual responses were near-veridical, whilst motor responses retained a bias. Therefore, the full Poggendorff stimulus contained two biases: one mediated by the acute angle formed between the oblique pointer and the inducing line (the classic Poggendorff effect), which affected both motor and perceptual responses equally, and another bias, which was independent of the inducer and primarily affected motor responses. We conjecture that this additional motor bias is associated with an undershoot in the unknown direction of movement and provide evidence to justify this claim. In conclusion, both manual pointing and perceptual judgements are susceptible to the well-known Poggendorff effect, supporting the notion of a unitary representation of space for action and perception or else an early locus for the effect, prior to the divergence of processing streams.

Characterisation of the misalignment and misangulation components in the Poggendorff and corner-Poggendorff illusions

In the Poggendorff illusion, two colinear segments abutting obliquely on an intervening configuration (often consisting of two long parallel lines) appear misaligned. We report here the results of a component analysis of the illusion and several of its variants, including in particular the 'corner-Poggendorff' illusion, and variants with a single arm. Using a nulling method, we determined an 'orientation profile' of each configuration, that is, how the illusions varied as the configuration was rotated in the plane of the display. We were able to characterise a pure-misalignment component (having peaks and dips around the +/- 22.5 degrees and +/- 67.5 degrees orientations of the arms) and a pure misangulation component of constant sign, having peaks at the +/- 45 degrees orientations of the arms. Both these components were present in both the classic and the corner-Poggendorff configurations. Thus, the misangulation component appears clearly in the classic Poggendorff illusion, once the misalignment component is partitioned out. Similarly, the corner-Poggendorff configuration, which essentially estimates a misangulation component, contains a misalignment component which becomes apparent once the misangulation is nulled. While our analysis accounts for much of the variability in the shapes of the profiles, additional assumptions must be made to explain the relatively small misangulation measured in the corner-Poggendorff configuration (1.5 degrees, on average, at peak value), and the relatively large illusion measured in the configurations with a single arm (above 6 degrees, on average, at peak values). We invoke the notion that parallelism and colinearity detectors provide counteracting cues, the first class reducing misangulation in the corner-Poggendorff configuration, and the second class reducing the illusion in the Poggendorff configurations with two arms.

Hierarchical organisation in perception of orientation

According to Rock [1990, in The Legacy of Solomon Asch (Hillsdale, NJ: Lawrence Erlbaum Associates)], hierarchical organisation of perception describes cases in which the orientation of an object is affected by the immediately surrounding elements in the visual field. Various experiments were performed to study the hierarchical organisation of orientation perception. In most of them the rod-and-frame-illusion (RFI: change of the apparent vertical measured on a central rod surrounded by a tilted frame) was measured in the presence/absence of a second inner frame. The first three experiments showed that, when the inner frame is vertical, the direction and size of the illusion are consistent with expectancies based on the hierarchical organisation hypothesis. An analysis of published and unpublished data collected on a large number of subjects showed that orientational hierarchical effects are independent from the absolute size of the RFI. In experiments 4 to 7 we examined the perceptual conditions of the inner stimulus (enclosure, orientation, and presence of luminance borders) critical for obtaining a hierarchical organisation effect. Although an inner vertical square was effective in reducing the illusion (experiment 3), an inner circle enclosing the rod was ineffective (experiment 4). This indicates that definite orientation is necessary to modulate the illusion. However, orientational information provided by a vertical or horizontal rectangle presented near the rod, but not enclosing it, did not modulate the RFI (experiment 5). This suggests that the presence of a figure with oriented contours enclosing the rod is critical. In experiments 6 and 7 we studied whether the presence of luminance borders is important or whether the inner upright square might be effective also if made of subjective contours. When the subjective contour figure was salient and the observers perceived it clearly, its effectiveness in modulating the RFI was comparable to that observed with luminance borders.

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.

Phenomena of illusory form: can we bridge the gap between levels of explanation?

The study of illusory brightness and contour phenomena has become an important tool in modern brain research. Gestalt, cognitive, neural, and computational approaches are reviewed and their explanatory powers are discussed in the light of empirical data. Two well-known phenomena of illusory form are dealt with, the Ehrenstein illusion and the Kanizsa triangle. It is argued that the gap between the different levels of explanation, bottom-up versus top-down, creates scientific barriers which have all too often engendered unnecessary debate about who is right and who is wrong. In this review of the literature we favour an integrative approach to the question of how illusory form is derived from stimulus configuration which provide the visual system with seemingly incomplete information. The processes that can explain the emergence of these phenomena range from local feature detection to global strategies of perceptual organisation. These processes may be similar to those that help us restore partially occluded objects in everyday vision. To understand better the Ehrenstein and Kanizsa illusions, it is proposed that different levels of analysis and explanation are not mutually exclusive, but complementary. Theories of illusory contour and form perception must, therefore, take into account the underlying neurophysiological mechanisms and their possible interactions with cognitive and attentional processes.

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 degrees, 45 degrees, and 60 degrees and was absent when the angle was 90 degrees. 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.

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.

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 Poggendorff illusion and apparent interparallel extents

An explanation of the Poggendorff misalignment effect in terms of apparent contraction of interparallel extent resulting from the Müller-Lyer illusion was tested in three experiments. Three of the eight stimulus figures had oblique transversals outside the parallels in the usual way, three had them inside, and two were controls consisting of the transversals only. Müller-Lyer forms were differently delineated between the parallels for the inside-transversal and outside-transversal figures, and were not delineated in the control figures. In the first experiment apparent misalignment occurred in four of the six parallel-line figures and in neither of the controls. In the second experiment oblique extent between the parallels was underestimated in six of the eight figures and right-angle extent was overestimated in all of them. The results of the third experiment showed that right-angle (horizontal) extent between the parallels without transversals is estimated without significant error. The data from the three experiments do not support the interparallel-extent explanation of apparent misalignment. Instead, the results are interpreted in terms of independent perceptual compromises, one involving alignment of the transversals and the other the distance between them.

Subjective contours 1900-1990: research trends and bibliography

A bibliography on subjective contours and a brief summary of trends in research on this problem are presented. The bibliography covers the years 1900-1990 and contains 445 entries, each briefly annotated with a code that indicates the general content and theoretical orientation of the item.

Three-dimensional Müller-Lyer illusion

Three-dimensional (3-D) variants of the Müller-Lyer pattern were created to address the question of where along the path of information flow in the visual system the illusion might occur. These variants, which yielded a robust illusion, included dihedral angles in place of the arrowheads of the classical pattern. The enormous difference in the shape of the resulting retinal image, compared with that of the classical pattern, makes it difficult to explain the present illusion by resorting to image-processing theories such as selective filtering (Ginsburg, 1984, 1986) or depth processing (Gregory, 1963, 1966, 1968). It was also shown that this 3-D illusion is homologous with the classical illusion, and that the two may thus share a common causal mechanism. A new type of 3-D figure, which yielded the same retinal image as did the classical pattern, was then employed. However, since the figure was 3-D, its shape in spatial coordinates was very different compared to that of the classical pattern. The magnitude of the illusion obtained with this figure was half that of the classical pattern. This finding suggests that the illusion might be caused by processes that occur after the computation of depth. All three experiments indicated that the illusion may be produced later in the processing stream than has previously been suggested.

Similar processing of real- and subjective-contour Poggendorff figures by men and women

Measures of illusion magnitude for a real-contour and two subjective-contour Poggendorff figures were obtained from 42 men and 42 women. Although magnitudes of illusion differed as a function of figure type, male-female differences in magnitude of illusion did not vary across figures or judgment orders. Also, correlations among the illusions observed for three types of figures did not differ for men and women. These data are consistent with the view that real- and subjective-contour Poggendorff figures evoke similar processing strategies and that sex differences, when observed, are probably the result of differences in cognitive-judgmental strategy rather than differences in the optical and neural properties of the visual system.

Illusion decrement and transfer of illusion decrement in real- and subjective-contour Poggendorff figures

The reduction in illusion magnitude with visual inspection and the transfer of such illusion decrement to a noninspected figure were examined in real- and subjective-contour Poggendorff figures. For both types of figures, illusion magnitude decreased significantly, and in a similar manner, during a 5-min inspection period. Postinspection tests showed that inspecting either a real- or subjective-contour figure resulted in a reduction in illusion magnitude for the other, noninspected figure. These findings suggest that real- and subjective-contour Poggendorff figures share a similar global organization and are thus probably processed in a similar manner. These characteristics make subjective-contour figures a useful tool for separating illusion-producing mechanisms into structural and strategy components.

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.

Visual imagery selectively reduces vernier acuity

Mental imagery interferes with perception. This, an example of the 'Perky effect', was studied for vernier acuity. Mean accuracy for reporting the offset of vertical line targets declined from 80% to 65% when subjects were requested to imagine vertical lines near fixation. Images of horizontal lines or of a grey mist in the fixation region lowered accuracy to a similar extent. However, accuracy was barely affected when the image was requested 1.5 deg or more from the target. The Perky effect remained strong for at least 4 s after an instruction to 'clear' the image away. The results were not due to imagery-induced changes in fixation, pupil diameter, or accommodation, or (at least primarily) to central attentional or decisional factors. Rather, imagery produces a local, pattern-insensitive, and relatively long-lasting reduction in visual sensitivity. The sensitivity loss may be mimicked by a 0.24 log unit reduction in target energy.

Flicker haloes observed with subjective borders

Subjective borders are known to behave quite similarly to real borders when the stimulus presents fragments of visually meaningful forms. There is less information on whether this also applies to unfamiliar stimulus elements. Thus, if a dark/bright stimulus border is presented intermittently at certain frequencies below flicker fusion, the bright border enhancement band increases greatly in width and takes on a textured appearance, resembling a halo streaming from the border. The percept is spontaneous and unlike anything experienced in real life. Preliminary observations showed that the effect occurs also at subjective borders. The extent of the halo from the border was measured for various flicker frequencies and compared with similar measurements obtained with real borders. It was found that the extent varies with frequency in an identical manner for real and virtual borders. Also, the halo was judged equal in qualitative appearance for both kinds of border. The striking similarity between virtual and real effects in this respect is best explained in terms of physiological border perception processes, possibly instigated by a cognitive mechanism.

The effects of illumination level and retinal size on the depth stratification of subjective contour figures

The apparent stratification in depth of subjective contour figures over their backgrounds was investigated as a function of illumination level, figure size, and viewing distance. Magnitude estimation, with a real contour figure serving as the modulus, was used to measure the stratification in depth of a subjective contour figure over its background. Illumination level and retinal size both had significant effects on the depth stratification of the subjective contour figures. The greatest apparent depth differences were obtained for figures of small retinal size under low levels of illumination. These results paralleled previous findings for judgments of subjective contour strength. Consequently, both contour clarity and depth stratification of subjective contour figures are affected in similar ways by illumination level, figure size, and viewing distance. The implications of this response coupling are discussed in terms of current theories of subjective contours.

Orientation masking and the tilt illusion with subjective contours

Exposure to one edge renders another edge less visible as a function of relative orientation. Experiment 1 showed that orientation-selective masking occurs between phenomenal edges located at sites where the visual display is homogeneous (subjective contours) as well as between edges defined in terms of luminance discontinuity (real edges). In addition, real contours can be masked by subjective contours, and vice-versa. In experiment 2 it was found that the tilt illusion (apparent expansion of the angle formed by intersecting lines) can be induced with subjective as well as with real contours. These results suggest that it is inappropriate to attribute the perception of real and subjective contours to fundamentally different processes.

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°.