A comparison of five methods of illusion measurement

The relative efficiency of five techniques of illusion measurement were tested on parametric variations of the Mueller-Lyer and Ebbinghaus figures. The methods of average error, reproduction, and selection from a graded series all showed significant effects of configurational variations. The subjective scaling techniques each failed to measure adequately changes in illusion magnitude for one illusion configuration. The suitability of the tested measures for group administration is also discussed.     

Length illusions in conventional and single-wing Müller-Lyer stimuli

Warren and Bashford (1977) reported that eliminating one of the wing components from the conventional (i.e., two-wing) Müller-Lyer figures had no appreciable effect on the magnitude of the acute-angle (contraction) illusion but substantially reduced the magnitude of the obtuse-angle (expansion) illusion. In addition, they found that whereas the contractionary effects of the acute-angle components tended to be confined to the region of the shaft adjacent to the angles, the expansionary effects of the obtuse-angle components were more uniformly distributed across the shaft. Since these findings challenge many theories of the Müller-Lyer illusion, the purpose of the present investigation was to evaluate further Warren and Bashford's work with four experiments. Experiments 1 and 2 assessed length illusion magnitudes by requiring subjects to adjust either the length of a plain comparison line to match the length of the Müller-Lyer test figures (Experiment 1) or the length of comparison Müller-Lyer figures to match the length of plain test lines (Experiment 2). Experiments 3 and 4 used a bisection task to assess whether the illusory effects of the angle components are confined mainly to regions of the shaft adjacent to the angles. Consistent with most theories of the Müller-Lyer illusion, eliminating one of the wing components reduced both forms of the Müller-Lyer length illusion to a similar extent. In addition, the acute- and obtuse-angle forms yielded similar patterns of bisection errors, with substantial errors for regions of the shaft adjacent to the angles and negligible errors for regions of the shaft distant from the angles.     

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.     

The reversed Müller-Lyer illusion in conventional and in wing-amputated Müller-Lyer figures

Summary When the wings of the conventional or four-wing Müller-Lyer figures are displaced away from the shaft, the apparent elongation of the wings-out figure decreases and the apparent contraction of the wings-in figure changes to apparent elongation. Worrall and Firth (1974) reported a different pattern of illusion change for two-wing Müller-Lyer figures containing wings at only one end of the shaft. Whereas moving the wings away from the shaft decreased the magnitude of the wings-in illusion, it changed the wings-out illusion from apparent elongation to apparent contraction. The effect of wing displacement upon the Müller-Lyer illusion was measured in three experiments. Illusion magnitude was assessed by obtaining judgments of either the length (Experiment 1) or the apparent midpoint (Experiments 2 and 3) of the shaft of four-wing (Experiment 1), two-wing (Experiments 1–3), and one-wing (Experiments 1 and 2) Müller-Lyer figures. Both measures of the illusion showed that displacement of the wings away from the shaft had similar effects on the four and two-wing Müller-Lyer figures. The results are discussed in the context of assimilation theories of the Müller-Lyer illusion, and a possible reason for the apparent inconsistency between Worrall and Firth's conclusions and the present findings is outlined.     

Wings in the intershaft space contribute to the Mueller-Lyer illusion

The interference of the wings of the wings-in part of the Mueller-Lyer figure was examined for the version of the illusion in which one part of the figure is placed above the other. Wings were removed in pairs from either above or below the shaft of one of the two parts of the figure. Subjects indicated the apparent difference between the lengths of the shafts of the two parts of the figure. Removal of the wings between the shafts of the wings-in part of the figure reduced the amount of the illusion more than removal of the wings from outside the shafts. Removing wings from the wings-out part of the figure reduced the amount of illusion, but it made no difference whether the wing removal occurred between or outside the shafts.     

The assessment of components involved in illusion formation using a long-term decrement procedure

Available evidence seems to indicate that illusion decrement represents reorganization of cognitive components involved in visual-geometric illusions. Observers viewed one of the two forms of the Mueller-Lyer illusion, containing differential opportunities for peripheral structural interactions, for a 10-min test session on each of 5 successive days. The magnitude of the distortion decreased to a different asymptotic level in each of the two configurations with the form, with more opportunity for structural interactions showing the higher asymptote. Thus, this asymptote probably represents the structural or physiological contribution to the illusory distortion.     

Spatial range of illusory effects in Müller-Lyer figures

The spatial range of the illusory effects in Müller-Lyer (M-L) figures was examined in three experiments. Experiments 1 and 2 assessed the pattern of bisection errors along the shaft of the standard or double-angle (experiment 1) and the single-angle (experiment 2) M-L figures: Subjects bisected the shaft and the resulting two half-segments of the shaft to produce apparently equal quarters, and then each of the quarters to produce eight equal-appearing segments. The bisection judgments of each segment were referenced to the segment's physical midpoints. The expansion or wings-out and the contraction or wings-in figures yielded similar patterns of bisection errors. For the standard M-L figures, there were significant errors in bisecting each half, and each end-quarter, but not the two central quarters of the shaft. For the single-angle M-L figures, there were significant errors in bisecting the length of the shaft, the half-segment, and the quarter, of the shaft adjacent to the vertex but not the second quarter from the vertex nor in dividing the half of the shaft at the open end of the figure into four equal intervals. Experiment 3 assessed the apparent length of the half-segment of the shaft at the open end of the single-angle figures. Length judgments were unaffected by the vertex at the opposite end of the shaft. Taken together, the results indicate that the length distortions in both the standard and single-angle M-L figures are not uniformly distributed along the shaft but rather are confined mainly to the quarters adjacent to the vertices. The present findings imply that theories of the M-L illusion which assume uniform expansion or contraction of the shafts are incomplete. Received: 15 December 2000 / Accepted: 5 June 2001     

Altering Mueller-Lyer illusion magnitude using figural additions at the wing-shaft intersections

The Mueller-Lyer (ML) illusion has been used to study the way in which perceived length is affected by processes of information extraction when a visual target of interest (the ML shaft) is surrounded by other nontarget figural elements (inward-or outward-turning wings). It is argued that the perception of length is computed in terms of the center of gravity or centroid of figural elements at the wing-shaft intersection. The outward-turning wings shift the computational centroid away from the shaft end, giving rise to an erroneous overestimation of shaft length, while the inward-turning wings have the opposite effect. In three experiments, we observed that figural changes, which theoretically shifted the center of gravity of figural elements at the wing-shaft intersection, also increased or decreased the magnitude of the ML illusion.     

Depth separation and the Ponzo illusion

The Ponzo illusion refers to an apparent change in length of objectively equal parallel lines induced by enclosure within an acute angle. The present study investigated this illusory change in stimulus extent as a function of the relative depth positions of the parallel lines and the inducing angle. To permit facile and unconfounded manipulation of apparent depth, the stimuli comprising the Ponzo configuration were stereoscopic contours formed from dynamic random-element stereograms. The main results were: (1) apparent depth separation exerted a strong influence on illusion magnitude; (2) this influence was asymmetrical in that illusion magnitude decreased when the inducing angle appeared in depth behind the parallel lines and increased when the inducing angle appeared in depth in front of the lines. These data are consistent with a general theory of space perception that assumes that information about depth position is processed prior to information about stimulus characteristics.     

The role of apparent depth and context in the perception of the Ponzo illusion

The role of apparent depth features and the proximity of the test lines to the adjacent contours in the actuation of the Ponzo illusion was examined. Six versions of the Ponzo figure were employed: a standard Ponzo figure and five modified figures in which the test lines varied in orientation (horizontal or vertical) and in location (inside or outside the converging contours). Both manipulations resulted in a significant decrease in the magnitude of the illusion in comparison to the standard Ponzo figure. The results suggest that the Ponzo illusion is significantly affected by contextual factors.     

Relative spatial expansion and contraction within the Müller-Lyer and Judd illusions

The shaft portions of Müller-Lyer (M-L) figures, one-ended M-L figures, Judd figures, and their respective control (tails-up) figures were divided by subjects into eight equal-appearing intervals by means of successive bisections. For most of the control stimuli the length of the left half of the shaft tended to be overestimated relative to the length of the right side. For the tails-out version of the M-L figure, there was relative overestimation of segments of the shaft adjacent to the tails, while for the tails-in version there was relative underestimation of these segments. These results indicate that the distortion of perceived length in the M-L illusion is not distributed evenly along the shaft. For the one-ended M-L figures the apparent overestimations and underestimations extended further along the shaft than for the standard figures. For the Judd figure perceived length varied systematically along the length of the shaft from underestimation near the tails-in end of the figure to overestimation near the tails-out end. These results are contradictory to the hypothesis that the M-L illusion results from inappropriate size scaling produced through the operation of size-constancy mechanisms, since this conjecture would predict uniform expansion or contraction. The results are compared with findings that localization responses are accurate for M-L figures but biased for one-ended M-L figures and Judd figures.     

Further developments in the assimilation theory of geometric illusions: The adjacency,principle

It is argued that the parallel lines illusion is the basic model for many visual distortions that are produced by geometric patterns. An experiment assessed the effect of moving the contextual contour away from the standard contour in two directions—away from the center of the attentive field and toward the center of the attentive field. The degree of illusion declined as the contextual magnitude moved away from the standard magnitude, but the rate of decline was more rapid when the contextual stimulus was moved away from the center of the attentive field. The results necessitated the addition of a new postulate for the assimilation theory of geometric illusions. This postulate states that the effectiveness of a contextual magnitude decreases as the distance between the contextual magnitude and the standard magnitude increases. The postulate was translated into a mathematical form in a manner analogous to the way in which the “attentive field” postulate was quantified. The new formula was successful in predicting both the pattern of means and the pattern of variances found in this study. The formula was cross-validated with data from the Ponzo and reversed Mueller-Lyer illusions.     

A mathematical theory of optical illusions and figural aftereffects

If it is assumed that spurious enhancement of receptive field excitations near the intersection of image lines on the retina contributes to the cortical determination of the geometry of two-dimensional figures, an equation based on the least-squares fit of data points to a straight line-can be obtained to represent theapparent line. Such a fit serves as anextreemum on the precision with which a data set can be represented by a straight line. The disparity between theapparent line and the actual line that occurs in the case of peripheral (and to a lesser degree in more central regions of the retina) vision is sufficient to produce the perceptual errors that occur in the Poggendorff, Hering, and Mueller-Lyer illusions. The magnitude of the Poggendorff illusion as a function of the line angle is derived and experimentally tested. Blakemore, Carpenter, and Georgeson’s (1970) experimental data on angle perception are shown to fit this same function. Theapparent curve is derived for the Hering illusion. The Mueller-Lyer illusion is found to be a variation of the Poggendorff illusion. The equations are further developed and used to derive Pollack’s (1958) experimental results on figural aftereffects. The results involve onlyone experimentally determined coefficient that can be evaluated, within the limits of experimental error, in terms of physiological data. The use of these concepts provides a foundation for the abstract modeling of the initial phases of the central nervous system data reduction processes, including receptive field structure, that is consistent with the physiological limitations of the retina as a source of visual data, as well as with the findings of Hubel and Wiesel (1962).     

Differentiation and decrement in the Mueller-Lyer illusion

Two experiments were conducted to test the hypothesis that decrement of the Mueller-Lyer illusion with inspection is due to learning to differentiate the test element from the accessory lines. In one experiment, the test element is predifferentiated for the observer by means of configurational variations and in the other by restriction of attention. Although the initial magnitude of the illusion is found to be inversely proportional to the amount of predifferentiation, the slopes of the decrement curves are not affected.     

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.     

Three elemental illusions determine the Zöllner illusion

We have discovered an apparent contraction illusion of acute angles in a special form of the Z?llner figure at the intersecting angles between 36 degrees and 83 degrees (i.e., a reversal of the Z?llner illusion). The necessary condition for this illusion is that inducing lines are long enough and the induced line (test line) is single. When an illusory line is used as the induced line, the magnitude of contraction increases. Short inducing lines give no illusion or a slight expansion of acute angles at the intersecting angle of 45 degrees. We have ascertained that the source of this expansion is the narrow region in the vicinity of the induced line, whereas the source of the contraction is much broader regions. Furthermore, we have discovered another expansion mechanism, which is generated by the symmetrical configuration of the standard Z?llner figure.     

Selective attention and asymmetry in the Müller-Lyer illusion

Two experiments reexamined the effect of selective spatial attention on the magnitudes of the wings- in and wings-out forms of the Müller-Lyer (M-L) illusion and a version of the illusion in which the two forms are superimposed to produce a figure (XX) flanked at both ends by an X. For the XX figure, ignoring the outer wings produced significant underestimation of shaft length, whereas ignoring the inner wings had no significant effect. For the M-L figures, ignoring the wings was more effective in attenuating the magnitude of the wings-out than of the wings-in illusion. The results are discussed with reference to space-based approaches to visual attention and to claims that attentional modulation of illusion magnitudes implicates high-level or cognitive factors in the formation of the M-L illusion.     

Mueller-Lyer illusion and size estimation performance in schizophrenics compared to normal controls

A size estimation (SE) paradigm and the Mueller-Lyer (ML) illusion were used to examine perceptual disturbances in schizophrenics. 35 reliably diagnosed (DSM III-R) schizophrenics were compared to 20 subjects with no history of psychiatric illness. Perceptual distortions found in previous studies of schizophrenics were only to a certain extent confirmed in the present results. More overestimators were found among the schizophrenics than among the normals on the SE task. The schizophrenics, first of all the chronic patients, also proved to be more prone to the Mueller-Lyer illusion. A reason why the very clear differences between schizophrenics and normals found in previous examinations were not confirmed in the present study, might be that a reliable diagnostic instrument was for the first time used in this kind of study.     

Three elemental illusions determine theZöllner illusion

We have discovered an apparent contraction illusion of acute angles in a special form of the Zöllner figure at the intersecting angles between 36° and 83° (i.e., a reversal of the Zöllner illusion). The necessary condition for this illusion is that inducing lines are long enough and the induced Une (test line) is single. When an illusory line is usedas the induced line, the magnitude of contraction increases. Short inducing lines give no illusion or a slight expansion of acute angles at the intersecting angle of 45°. We have ascertained that the source of this expansion is the narrow region in the vicinity of the induced line, whereas the source of the contraction is much broader regions. Furthermore, we have discovered another expansion mechanism, which is generated by the symmetrical configuration of the standard Zöllner figure.     

An increase in strength of tilt aftereffect associated with tryptophan depletion

The effects of a tryptophan-free amino acid mixture on tilt aftereffect, movement aftereffect, and the Mueller-Lyer illusion were studied. 12 male subjects ingested either a balanced amino acid mixture or a tryptophan-free mixture which causes a marked depletion of brain tryptophan and serotonin. The tryptophan-free mixture significantly increased the strength of tilt aftereffect but had no effect on movement aftereffect or the Mueller-Lyer illusion. These results were discussed with reference to the pharmacological activity of serotonin and its influence on the strength of lateral inhibition in mammalian brains.