An extension of assimilation theory to illusions of size,area, and direction

Two postulates, one concerning assimilation and the other concerning attentive fields, are employed to explain the Ponzo, Poggendorff, Wundt, and Hering illusions. Several new configurations are predicted from the theory. In addition, changes in the magnitude or direction of illusion which result from alterations of the basic illusion are explained.     

A descriptive model for perception of optical illusions

The apparent curves of stable geometrical illusions of angle are modeled by a first-order differential equation depending on a single parameter, called the strength of the illusion. The model is based on Brentano's theory that the human visual system tends to overestimate acute angles. It is mathematically equivalent to Hoffman's Lie-theoretic model (SIAM Review, 13 (1971), pp. 169–184) except for some deficiencies of detail in Hoffman's approach which are noted and corrected. By reversing the sign of the strength parameter, “correction” curves may be plotted which cause the illusion to “disappear,” thereby demonstrating the effectiveness and accuracy of the model. The method is illustrated with the classical illusions of Poggendorff, Zöllner, Hering, Orbison, Ponzo, and Müller-Lyer.     

The case for misapplied constancy scaling: depth associations elicited by illusion configurations

It has been suggested that many visual-geometric illusions arise from inappropriate evocation of size-constancy by depth cues implicit in illusion configurations. Observers gave free association responses while viewing illusion figures. Analysis of these responses provides weak but consistent evidence for the elicitation of depth in the Sander parallelogram, Mueller-Lyer, Zoellner, and Ehrenfels variant of the Ponzo illusion. No evidence for depth is found in the normal form of the Ponzo, Poggendorff, and horizontal-vertical illusions, and the evidence is ambiguous in the Orbison configurations. These results indicate that depth processing may be evoked by some, but not all, classical illusion forms.     

A Mueller-Lyer illusion induced by selective attention

Subjects estimated the length of a horizontal line which was flanked by oblique angles pointing both inside and outside (this figure would be created by superimposing the wings-in and wings-out figures of the Mueller-Lyer illusion). Ignoring the outside wings resulted in an underestimation of the line length of comparable magnitude to that obtained for the wings-in Mueller-Lyer figure. Ignoring the inside wings caused an overestimation of the line length only when the inner and outer wings were of non-corresponding orientations. These results emphasize the role of cognitive factors in the Mueller-Lyer illusion.     

A new explanation for the Poggendorff illusion

Kanizsa (1972, 1974) has observed that the surface upon which a figure is amodally completed undergoes shrinkage. That observation is investigated here as a possible explanation of the Poggendorff illusion, on the assumption that the shrinkage of the surface behind the surface defined by the two vertical parallel lines results in displacement of the two visible segments of the oblique line. The first two experiments attempted to quantify the shrinkage of the amodal surface by measuring the enlargement of the vertical strip required to achieve perceived collinearity; the oblique lines intercepted the vertical strip at 45- and 30-deg angles. In both cases, the enlargement required to counterbalance the assumed amodal shrinkage was approximately 30%. In the third experiment, the oblique line was rotated to the horizontal, and again the perceived shrinkage of the amodal surface was approximately 30%. The application of this explanation to the Poggendorff illusion is discussed, as well as the relevance of this explanation to the common experimental finding that magnitude of the illusion is dependent upon the slope of the oblique line.     

Curved movement paths and the Hering illusion: Positions or directions?

When trying to move in a straight line to a target, participants produce movement paths that are slightly (but systematically) curved. Is this because perceived space is curved, or because the direction to the target is systematically misjudged? We used a simple model to investigate whether continuous use of an incorrect judgement of the direction to the target could explain the curvature. The model predicted the asymmetries that were found experimentally when moving across a background of radiating lines (the Hering illusion). The magnitude of the curvature in participants' movements was correlated with their sensitivity to the illusion when judging a moving dot's path, but not with their sensitivity when judging the straightness of a line. We conclude that a misjudgement of direction causes participants to perceive a straight path of a moving dot as curved and to produce curved movement paths.     

认知方式、视错觉及其关系的跨文化研究

运用测验法研究了藏、回、汉族小学三年级、五年级、初二、高二共1032名儿童认知方式的特点,考察了不同认知方式与视错觉之间的关系。结果表明:1)认知方式的民族、居住环境和年龄差异显著,藏族儿童、居住在草原上的儿童、低年级儿童倾向于场依存性,汉族和回族儿童、生活在城市和山村的儿童、高年级儿童倾向于场独立性;2)视错觉的文化差异显著,居住环境和年龄是影响视错觉的重要变量;3)认知方式对视错觉有影响,场独立性者错觉量小,场依存性者错觉量大。     

Influence of the Poggendorff illusion on manual pointing

The results of recent studies indicate that certain visuomotor actions, such as grasping and pointing, are unaffected by visual size illusions. The present study investigated whether the Poggendorff illusion of alignment influences pointing to a target's location. 15 subjects pointed with their unseen hands to the apparent location of the extension of the oblique line onto the target line of a version of the Poggendorff illusion. Analysis indicated the pointing action was influenced by the Poggendorff illusion. The implications of this finding for the claim that different cortical streams of visual processing subserve visuomotor actions and conscious visual perception are discussed.     

The role of structural components in the Mueller-Lyer illusion

In order to assess the role of the structural components of the Mueller-Lyer illusion, subjects reproduced the central extent of standard Mueller-Lyer figures and configural variations. Illusory magnitude of the underestimated wings-in and overestimated wings-out figures was examined with selective amputations of the oblique wings and central line segment (shaft). Variations were presented at 0, 45, 90, and 135 deg from vertical. Orientation had no reliable effect on illusory magnitude. Elimination of the shaft effected a decrease in the apparent extent for all variations, presumably due to the addition of the filled-unfilled space illusory effect to the standard Mueller-Lyer effect. A second study corroborated this finding The decrease in apparent extent consequent to shaft removal occurred independently of any response factor. Selective wing removal differentially decreased the illusory magnitude of the standard Mueller-Lyer figures; this was discussed with regard to a dual-illusion hypothesis. Finally, variations that contained no intersecting lines produced a significant illusion in the direction of the standard Mueller-Lyer figures, suggesting the involvement of higher level, nonperipheral distortion mechanisms.     

Poggendorff and Müller-Lyer illusions: common effects

Previous investigations have shown that the magnitude of the Müller-Lyer illusion is a function of the linear and angular dimensions of the figure. If the Müller-Lyer and Poggendorff illusions share a common basis, then the magnitude of the Poggendorff illusion should similarly be a function of the analogous configural dimensions. A study is reported in which changes were made in the dimensions of the Poggendorff figure that are analogous to the dimensions of the Müller-Lyer figure: the length of the parallel components (analogous to the wings of the Müller-Lyer figure); the length of the intertransversal extent (analogous to Müller-Lyer shaft length); and the angle formed between the parallel components and the intertransversal extent (analogous to the angle of wing attachment in the Müller-Lyer figure). The relationship between the magnitude of the illusion and the dimensions of the Poggendorff figure was found to be generally in line with previous findings relating to the Müller-Lyer illusion. Adaptation-level theory and the positive-context model accommodate the major findings of the present study.     

Perception: A HyperCard stack for demonstrating visual perceptual phenomena

Perception is a HyperCard stack that allows users to explore visual illusions and other perceptual phenomena on the Apple Macintosh. The stack contains over 20 demonstrations of intersecting line illusions, size and shape illusions, subjective contours, color assimilation, and so forth. As a presentation tool for classroom or laboratory demonstrations, Perception offers three unique features for displaying visual phenomena: (1) the capability to “dissolve” the inducing elements of an illusion in order to show the objective state of affairs, (2) the ability to quickly reverse the inducing elements of an illusion and therefore the effects of the distortion, and (3) animation of the various components of an illusion to produce continuous distortions in-real time. These features are illustrated with use of the Orbison, Titchener, Hering, and Wundt illusions. Use of the stack reveals two interesting and unanticipated findings: (1) an apparent size distortion in the central square of the Orbison illusion as it moves back and forth across the background of concentric rings, and (2) perceptual aftereffects that arise when the inducing elements of the Titchener, Hering, or Wundt illusion is dissolved.     

The effect of line-figure information on the magnitude of the dot forms of the Poggendorff and Müller-Lyer illusions

The magnitudes of the dot and line forms of the Poggendorff illusion and the Brentano version of the Müller-Lyer illusion were assessed in two groups of subjects: the informed group was given information about the implied figure configuration in the dot pattern, the uninformed group was not. The informed group produced a significantly greater dot illusion than the uninformed group, and there was no difference between the two groups in the magnitudes of the line illusions. The experiments are discussed in the context of Coren and Porac's proposal that illusion-inducing mechanisms can be divided into structural and cognitive components. The results suggest that about 64% of the magnitude of the Poggendorff illusion and about 54% of the Müller-Lyer illusion can be attributed to the involvement of cognitive factors.     

The orientation of a parallel-line texture between the verticals can modify the strength of the Poggendorff illusion.

In the present experiments, we attempted to evaluate the modification of the strength of the Poggendorff illusion as a function of the different orientation of a parallel-line texture filling the space between the vertical lines. In Experiment 1, the standard version of the Poggendorff configuration was tested against four different parallel-line textures oriented at 0 degrees, 45 degrees, 90 degrees, and 135 degrees with respect to the obliques. The results showed that the illusory effect was a linear function of the progressive discrepancy between the angle of the lines of the texture and that of the obliques. In Experiment 2, we tested the same textures used in Experiment 1 after the elimination of the two vertical lines. The data obtained approximated a linear function, as in the previous experiment, but the alignment errors were consistently lower. The statistical analysis performed on the data of all eight experimental conditions shows that both factors--texture and presence/absence of verticals--were significant, but most of the effect was due to the texture factor. The results may be interpreted through the "perceptual compromise hypothesis," originally proposed for the bisection forms of the Poggendorff illusion, but with important modifications. The data are also discussed in terms of their implications for other theories proposed for the Poggendorff illusion.     

Acute angles and the poggendorff illusion

Burns and Pritchard's (1971) explanation of the Poggendorff illusion is criticized. An experiment was designed to determine whether the acute angle plays any role in the perception of the illusion. The results showed that (i) an inducing line which crossed a test-line was highly effective in altering the apparent orientation of the test line, (ii) an inducing line forming an acute angle with a test-line had a small effect in changing the apparent orientation of the test-line, and (iii) an acute angle which formed part of the Poggendorff configuration produced an effect opposite to that predicted by the view that acute angles are perceptually enlarged.     

Reduction of the Zöllner illusion with motion of inducing figure

The magnitude of the Zöllner illusion was measured when the inducing lines moved rightward or leftward and were tracked by subjects. Motion of the inducing lines significantly reduced the magnitude of illusion, as in the Poggendorff illusion. Increasing velocity markedly increased the reduction, and, again, this effect was not significantly different from that obtained with the Poggendorff illusion. The current evidence seems to support the suggestion outlined earlier in relation to the Poggendorff illusion, that is, moving and stationary figures are processed by separate channels and, therefore, the interaction between them is reduced.     

A depth processing theory of the Poggendorff illusion

The Poggendorff illusion is attributed to the processing of the oblique lines of the Poggendorff figure as receding horizontal lines with their inner ends equidistant because of attachment to a frontal plane (defined by the parallel lines of the figure). Collinearity in three-dimensional space is inconsistent with such equidistance; one line must lie on a higher horizontal plane than the other. This necessarily noncollinear resolution of the lines in depth processing (which is inferred irrespective of the O’s consciousness of depth) is assumed to influence apparent projective relationships within the figure, thus accounting for the illusion. Predictions from the theory, involving manipulations of the plane defined by the parallels, were confirmed experimentally. In addition, the theory is shown to account very well for the effects of amputations and rotations of the figure, which other theories of the illusion cannot handle.     

Morinaga’s paradox and figure-ground organization

Morinaga’s paradox of displacement is constructed by setting several copies of the two Mueller-Lyer figures one above the other. The Mueller-Lyer illusion is that the wings pointing out seem farther apart than wings pointing in, and Morinaga’s paradox is that when one looks down a column of wings pointing alternately one way and the other, they appear misaligned but in the opposite direction from the Mueller-Lyer illusion. The hypothesis of this paper is that the subject, under instructions to align the vertical array of wings, sets up a vertical figure-ground organization different from that used in judging the horizontal distance between wings, and that the two illusions are contingent upon the two organizations. The experiment showed that Morinaga’s paradox occurs when only one column of wings is shown, in agreement with the figure-ground hypothesis, and also shows that Morinaga’s paradox disappears when short line segments are introduced which disrupt the vertical figure-ground organization.     

Mistracking in alignment illusions

A number of anomalies have been pointed out in opposition to attempts to account for the Poggendorff illusion in terms of the expansion of small or medium-sized acute angles. A principle under which these anomalies could be subsumed was proposed and subjected to experimental testing using simplified displays. The following theory emerged from these experiments. If a straight line (the pointer) is aligned with a do (the target) situated at the end of a second line (the induction line) and lying in a different orientation from the pointer, then (depending on the angle between pointer and induction line) the pointer will appear to be aligned with a point further along the induction line. The amount of misalignment varies inversely with increase in size, up to about 135 degrees, of the angle formed by the pointer with the induction line, after which there is no displacement attributable to the induction line. The effect appears not to be due to neural interaction. An explanation in terms of eye movement is discussed.     

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.     

The orientation of a parallel-line texture between the verticals can modify the strength of the Poggendorff illusion

In the present experiments, we attempted to evaluate the modification of the strength of the Poggendorff illusion as a function of the different orientation of a parallel-line texture filling the space between the vertical lines. In Experiment 1, the standard version of the Poggendorff configuration was tested against four different parallel-line textures oriented at 0°, 45°,90°, and 135° with respect to the obliques. The results showed that the illusory effect was a linear function of the progressive discrepancy between the angle of the lines of the texture and that of the obliques. In Experiment 2, we tested the same textures used in Experiment 1 after the elimination of the two vertical lines. The data obtained approximated a linear function, as in the previous experiment, but the alignment errors were consistently lower. The statistical analysis performed on the data of all eight experimental conditions shows that both factors—texture and presence/absence of verticals—were significant, but most of the effect was due to the texture factor. The results may be interpreted through the “perceptual compromise hypothesis,” originally proposed for the bisection forms of the Poggendorff illusion, but with important modifications. The data are also discussed in terms of their implications for other theories proposed for the Poggendorff illusion.