Acute angles and the Poggendorff illusion

Light Refraction by Water as a Rationale for the Poggendorff Illusion

The Poggendorff illusion in its classical form of parallel lines interrupting a transversal is viewed from the perspective of being related to the everyday experience of observing the light refraction in water. It is argued that if one considers a transversal to be a light ray in air and the parallel lines to form an occluding strip of a medium with the refractive index being between that of air and water, then one should be able to account, both qualitatively and quantitatively, for most of the features associated with the Poggendorff illusion. Statistical treatment of the visual experiments conducted with seven participants, each analyzing 50 configurations having different intercepting angles and strip widths, resulted in the effective refractive index of the occluding strip N = 1.13 ± 0.15, which is sufficiently close to the average (between that of water and air) refractive index of ∼1.17. It is further argued that the same mechanism can also be employed to account for many variants of the Poggendorff illusion, including the corner-Poggendorff pattern, as well as for the Hering illusion.

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.

Applying Emmert's Law to the Poggendorff illusion

The Poggendorff illusion was approached with a novel perspective, that of applying Emmert's Law to the situation. The extensities between the verticals and the transversals happen to be absolutely equal in retinal image size, whereas the registered distance for the verticals must be smaller than that of the transversals due to the fact that the former is assumed to occlude the latter. This combination of facts calls for the operation of Emmert's Law, which results in the shrinkage of the occluding space between the verticals. Since the retinal image shows the transversals to be in contact with the verticals, the shrinkage must drag the transversals inwards in the cortical representation in order to eliminate the gaps. Such dragging of the transversals produces the illusory misalignment, which is a dictation of geometry. Some of the consequences of this new explanation were tested in four different experiments. In Experiment 1, a new illusion, the tilting of an occluded continuation of an oblique line, was predicted and achieved. In Experiments 2 and 3, perceived nearness of the occluding entity was manipulated via texture density variations and the predicted misalignment variations were confirmed by using a between-subjects and within-subjects designs, respectively. In Experiment 4, tilting of the occluded segment of the transversal was found to vary in the predicted direction as a result of being accompanied by the same texture cues used in Experiments 2 and 3.

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.

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.

Assessment of apparent length and angle explanations of the Poggendorff effect

Explanations of the Poggendorff effect were assessed by comparing the degree of angular distortion induced by modified and traditional configurations. Assimilation theory predicted that the traditional effect would be reversed in modified configurations. Analysis showed that the effect, although reduced in magnitude, was not reversed. Comparison of the degree of the effect induced by modified and traditional configurations indicated that a substantial portion of the Poggendorff effect was due to processing of areas between the long vertical lines of the display. This finding is not consistent with theories based on subjective distortion of angles. It was concluded that a theory of the Poggendorff effect must include processing of internal areas of the configuration.