Angular induction as a function of contact and target orientation

Biases and sensitivities in the Poggendorff effect when driven by subjective contours

PURPOSE

A consensus in the existing literature suggests that the Poggendorff effect (a perceptual misalignment of two collinear transversal segments when separated by a pair of parallel contours) persists when the parallels are defined by Kanizsa-like subjective contours. However, previous studies have often been complicated by a lack of quantitative measures of effect size, statistical tests of significance, appropriate measures of baseline and control biases, or stringent definition of subjective contours. The aim of this study was thus to determine whether subjective contours are capable of driving the Poggendorff effect once other factors are accounted for.

METHODS

Twenty participants were tested on a number of test and control figures incorporating first-order (luminance-defined) and subjective parallels using the method of adjustment. All figures were tested at two different orientations, and observer sensitivities and observer biases were assessed.

RESULTS

A systematic response bias (in the direction of the classical effect) was found for Poggendorff figures that incorporated subjective parallels. The effect was highly significant and greater than for control figures. There was no concomitant change in judgment sensitivity (positional certainty). Finally, there was a positive correlation between the effect size for figures incorporating first-order and subjective parallels.

CONCLUSIONS

The findings reported demonstrate conclusively that true Kanizsa-like subjective contours are capable of driving the Poggendorff effect. Further, the data are consistent with a growing body of evidence that suggests both first-order and subjective contours are processed at early loci in the visual pathways when position is encoded.

Modal completion in the Poggendorff illusion: support for the depth-processing theory

The Poggendorff illusion is one of the most prominent geometrical-optical illusions and has attracted enduring interest for more than a hundred years. Most modern theories explain the illusion by postulating various kinds of distortion of the "test" component of the figure by the context or the inducing component. They make no reference to the importance of processes involved in three-dimensional scene perception for understanding the illusion. We measured the strength of the Poggendorff illusion in configurations containing solid inducing surfaces as opposed to the usual parallel lines. The surface, oblique-line, and background luminances were manipulated separately to create configurations consistent with modal completion of the obliques in front of the surface. The marked decrease in the size of the illusion in conditions favoring modal completion is consistent with claims that perceived spatial layout is a major determinant of the Poggendorff illusion.

The tilt-constancy theory of visual illusions

The authors argue that changes in the perception of vertical and horizontal caused by local visual cues can account for many classical visual illusions. Because the perception of orientation is influenced more by visual cues than gravity-based cues when the observer is tilted (e.g., S. E. Asch & H. A. Witkin, 1948), the authors predicted that the strength of many visual illusions would increase when observers were tilted 30 degrees. The magnitude of Zöllner, Poggendorff, and Ponzo illusions and the tilt-induction effect substantially increased when observers were tilted. In contrast, the Müller-Lyer illusion and a size constancy illusion, which are not related to orientation perception, were not affected by body orientation. Other theoretical approaches do not predict the obtained pattern of results.

The Ponzo illusion and the perception of orientation

A new theory, called the tilt constancy theory, claims that the Ponzo illusion is caused by the misperception of orientation induced by local visual cues. The theory relates the Ponzo illusion-along with the Zöllner, Poggendorff, Wündt-Hering, and cafe wall illusions-to the mechanisms that enable us to perceive stable orientations despite changes in retinal orientation or body orientation. In Experiment 1, the magnitude of the misperception of orientation was compared with the magnitude of the Ponzo illusion. In Experiment 2, predictions of the tilt constancy theory were compared with accounts based on (1) low spatial frequencies in the image, (2) memory comparisons (pool-and-store model), and (3) relative sizejudgments. In Experiment 3, predictions of the tilt constancy theory were tested against predictions of the assimilation theory of Pressey and his colleagues. In the final experiment, the orientation account was compared with theories based on linear perspective and inappropriate size constancy. The results support the tilt constancy theory.

A test of the gravity lens theory

Naito and Cole [1994, in Contributions to Mathematical Psychology: Psychometrics and Methodology Eds G H Fischer and D Laming (New York: Springer)] provide a configuration which they describe as the Gravity Lens illusion. In this configuration, four small dots are presented in proximity to four large disks, and one is asked to compare the slope of an imaginary line which connects one pair of dots with the slope of a line which connects the other pair. In fact the slopes are the same, i.e. their axes are parallel, but because of the positioning of the large disks they appear to be at different orientations. Naito and Cole propose that the perceptual bias is analogous to the effects of gravity on the metrics of physical space, such that mental projections in the vicinity of a disk (or an open circle) are distorted just as the path of light is bent as it passes a massive body such as a star. Here we provide a simple test of this concept by having subjects judge alignments of dots which lie near tangents to a circle. Subjects were asked to project straight lines through pairs of stimulus dots, selecting and marking points in open space which were collinear with each pair. As would be predicted by the Gravity Lens theory, the locations selected by subjects were displaced from straight lines. However, the error magnitudes were substantially larger for judgments of dot pairs which had an oblique alignment, as compared with dot pairs which were aligned with a cardinal axis. This differential of effect as a function of stimulus orientation is not predicted by the gravity concept.

Classical geometric illusion effects with nonclassical stimuli: angular induction from decomposing lines into point arrays

Angular induction is the process by which one line segment can bias judgment of orientation and/or collinearity of another segment, and it has been established that the magnitude of error is a determinate function of the relative angle between the two. We examined how these known relationships are affected by decomposing the induction segment into an array of scattered points. The bias that was produced by such arrays was found to be consistent with a formal model of angular induction, with the strength of the effect decreasing as the scatter among the points was increased. This decline in strength was almost linear with a logarithmic transform of the dimensions of the stimulus array. We also evaluated the hypothesis that the induction stimulus is detected by one or more channels--for example, neurons--for which the sensitivity profiles are modeled as Gabor wavelets. The change in induction strength with increasing point scatter was not predicted by a single width of channel. However, the combined activity of an ensemble of channels that differed in width did match the perceptual effects if one also stipulated that each channel would respond maximally to a fine-line stimulus.

Angular induction as a function of the length and position of segments and gaps

The perceptual distortions which are manifested in the Poggendorff illusion can be studied with the use of a more restricted set of stimulus elements. Experiments were designed in which angular induction effects between two line elements, known respectively as the test segment and induction segment, were evaluated. In some stimulus configurations the induction 'segment' consisted of a tandem pair of segments. Previous studies had shown that the induction segment will bias operant judgments of collinearity for a test segment, this effect being a function of the relative angle between the two. Six experiments are reported, in which the length and position of segments in relation to the tip of the test segment were varied. It was found that substantial induction is produced by a very short segment, and that this can bias judgment even when its displacement spans more than 10 deg of visual angle. Several aspects of the data suggest that the strength of effect is a log-linear function of segment position. However, the results from displacement of single or tandem segments do not conform to predictions based on length/response summation, and thus do not support a linear-systems approach. Neural substrates for these interactions are given brief attention.

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.

Collinearity judgment as a function of induction angle

The misalignment which is seen in the Poggendorff illusion can be studied with better control by using a configuration which has only two line segments. Two experiments were conducted in which subjects judged collinearity of a test segment, this judgment being subjected to a biasing influence from a second (induction) segment. Exp. 1 held the test segment at one of three orientations relative to the observer (30 degrees, 45 degrees, and 60 degrees) and systematically varied the orientation of the induction segment in 15 degrees increments through the range of possible positions. The orientation of the page relative to the observer was varied as well. Exp. 2 varied the test segment through a greater range of angles and sampled more levels of induction segment orientation. Analysis indicated that projection errors follow orderly rules similar in kind to but different in magnitude from those observed for the Tilt Illusion, most notably, (a) misprojection is greatest when the orientation of the interfering line is similar to that of the line segment being projected and (b) the strength of this influence decreases as the relative angle becomes orthogonal. Also, the orientation of the segment being projected relative to the observer serves to modulate the strength of the basic induction effect. These perceptual interactions are discussed in relation to neural models for orientation selectivity.

Anomalous and luminance contours produce similar angular induction effects

One can shear a pattern of lines to produce an anomalous contour which has a perceptual influence similar to that of a straight line segment. Illusion effects have been found with configurations which contain these anomalous contours, as well as cross adaptation with respect to luminance contours. We have found that sheared-line contours will bias judgment of collinearity, ie perceived alignment, of a luminance contour. The angular induction effects are similar to those reported for interactions between luminance contours, and the same equation can be used to model both kinds of data. The results of this experiment support the neuroreductionist view that anomalous and luminance contours are processed at the same level of the nervous system. Additionally, we suggest that with both types of contour the perceptual system registers and responds to the alignment of local brightness differentials.

Angular induction is modulated by the orientation of the test segment but not its length

Angular induction is the basic process by which the orientation of line segments can affect the perceived orientation of other segments as well as their alignment. In this laboratory, we have found that the effect on alignment follows approximately linear rules, with the inducing segment having its greatest influence when its orientation is near to that of the segment being judged. Other laboratories, however, have reported peak effects when the relative angle between the two is at 45 degrees, and with the inducing segment being aligned with one of the cardinal axes of the observer. It has been said that the length of the test segment being judged is a critical factor, but the first experiment of the present study shows a similar linear decline of induction strength irrespective of test segment length. The second experiment indicates that the orientation of the test segment relative to the observer modulates the induction to determine the location of peak effects. A two-factor linear model predicts the observed pattern of results.

Both tilt and misalignment are manifestations of angular induction

With a Poggendorff configuration one sees two obliques as being misaligned, and with a Judd configuration one sees them as having different tilts, i.e., as being misoriented. It has been suggested that these are separate illusory effects. I submit, however, that one can see misorientation in the double Poggendorff and misalignment with a Judd-like configuration. It seems likely that both perceptual effects are manifestations of the same process.

Use of segment arrays to evaluate the strength of angular induction

The contribution of local and global influence on angular induction was evaluated by varying the orientation of individual segments that were organized into an array. It was found that some of the misprojection of an oblique is determined by the orientation of the individual segments, and some by the overall configuration of the segments into two parallel bands. These results are integrated into a model that views angular induction as a lateral bias among orientation-sensitive neurons, with global influence differing from local influence only as a matter of scale.