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.     

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     

The effects of varying fins in Müller-Lyer and Holding illusions

Summary Five experiments were conducted to determine how distortion of spatial position induced by unidirectional Müller-Lyer fins varied as a function of angle and length of fins. Research employing Cornsweet's staircase method yielded ambiguous results, but psychophysical methods of magnitude estimation, paired comparisons, and production showed conclusively that distortions of position are affected by angle and length of fins in a manner similar to that found in distortions of length. It was concluded that similar strategies are employed in processing attributes of length and position and that a theory based on averaging of attributes within an attentional field describes the performance of real observers.Experiments 1 and 2 were reported in a Master's thesis submitted by Nancy Smith to the University of Manitoba in 1987.     

The human Müller-Lyer illusion in goalkeeping

We examined whether a goalkeeper can influence a penalty-taker's actions by assuming postures that mimic Müller-Lyer configurations. The results of two studies indicate that (i) goalkeeper posture affects the perception of the goalkeeper's height in a manner consistent with the Müller-Lyer illusion; (ii) this influences penalty-taking accuracy; and (iii) a posture which resembles a wing-out Müller-Lyer configuration results in wider and lower throws.     

The haptic Müller-Lyer illusion in sighted and blind people

We examined the effect of visual experience on the haptic Müller-Lyer illusion. Subjects made size estimates of raised lines by using a sliding haptic ruler. Independent groups of blind-folded-sighted, late-blind, congenitally blind, and low-vision subjects judged the sizes of wings-in and wings-out stimuli, plain lines, and lines with short vertical ends. An illusion was found, since the wings-in stimuli were judged as shorter than the wings-out patterns and all of the other stimuli. Subjects generally underestimated the lengths of lines. In a second experiment we found a nonsignificant difference between length judgments of raised lines as opposed to smooth wooden dowels. The strength of the haptic illusion depends upon the angles of the wings, with a much stronger illusion for more acute angles. The effect of visual status was nonsignificant, suggesting that spatial distortion in the haptic Müller-Lyer illusion does not depend upon visual imagery or visual experience.     

The role of eye movements in the Müller-Lyer illusion

The size of the illusion was found to be unaffected by reducing the exposure of the figures tachistoscopically, or by reducing the size of the figures. The illusion therefore does not seem to be due to eye movements or a tendency to make eye movements.     

The relationship between perceived length and egocentric location in Müller-Lyer figures with one versus two chevrons

We examined the apparent dissociation of perceived length and perceived position with respect to the Müller-Lyer (M-L) illusion. With the traditional (two-chevron) figure, participants made accurate open-loop pointing responses at the endpoints of the shaft, despite the presence of a strong length illusion. This apparently non-Euclidean outcome replicated that of Mack, Heuer, Villardi, and Chambers (1985) and Gillam and Chambers (1985) and contradicts any theory of the M-L illusion in which mislocalization of shaft endpoints plays a role. However, when one of the chevrons was removed, a constant pointing error occurred in the predicted direction, as well as a strong length illusion. Thus, with one-chevron stimuli, perceived length and location were no longer completely dissociated. We speculated that the presence of two opposing chevrons suppresses the mislocalizing effects of a single chevron, especially for figures with relatively short shafts.     

Amplitude and phase in the Müller-Lyer illusion

It has previously been claimed that the Müller-Lyer illusion is the result of low-pass spatial filtering. One way to understand this would be that the distribution of amplitudes is what generates this illusion. This possibility was investigated by computing the 2-D Fourier transforms of the two Müller-Lyer stimuli and extracting their phase and amplitude spectra. These spectra were combined to create hybrid spectra having the phase of one Müller-Lyer figure and the amplitudes of the other. Images were then created by computing the inverse Fourier transform of the hybrid spectra. Except in cases where the analysis was performed patchwise on very small patches, the figures generated with the phase spectrum of the stimuli having outward-pointing fins appear the longer. This was also the case when stimuli were generated with flat amplitude spectra. Because they show that the Müller-Lyer illusion does not depend on any particular distribution of amplitudes, these demonstrations do not support the theory that the Müller-Lyer illusion is the result of low-frequency filtering.     

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.     

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.     

The reversed Müller-Lyer illusion and figure-ground organization theory.

When the shaft is shortened and reaches neither of the vertices of the two pairs of wings, a reversed Müller-Lyer illusion is observed: a shaft between inward-pointing wings appears to be longer than a shaft between the outward-pointing wings. In this paper it is examined whether this illusion can be explained in terms of figure-ground organization. A circle was used as the focal area, instead of a shaft or a pair of dots, so that the figure-ground character could be seen more definitely in this focal area. The apparent size of the focal circle was measured under different conditions with three variables (enclosure, wings direction, and depth). The focal circle appeared to be largest in the condition where the circle should appear most readily as a hole, ie in the single, wings-in, space condition. The circle appeared to be smallest in the condition where the circle should appear most readily as a disc, ie in the separate, wings-out, object condition. This is consistent with an explanation of the usual, as well as the reversed, Müller-Lyer illusion in terms of figure-ground organization theory.     

Discriminability in length of lines in the Müller-Lyer figure

Receiver-operating characteristics for the discriminability in the length of the lines of the Müller-Lyer figure were obtained by the rating method of detection theory. Six observers judged the shaft length of the lines of the figure with reference to the same standard line. Maximum-likelihood estimates of the index of (discriminability,d’, were a linear function of the difference in the length of the lines, but the functions did not pass through the origin because of a constant error of judgment. Because discriminability was determined by ROC analysis, the constant error could not be attributed solely to changes in criterion placement; instead, it showed that the Müller-Lyer figure induced a change in the discriminability of the lines.     

The Müller-Lyer illusion in touch and vision: implications for multisensory processes

In six experiments, we used the Müller-Lyer illusion to investigate factors in the integration of touch, movement, and spatial cues in haptic shape perception, and in the similarity with the visual illusion. Latencies provided evidence against the hypothesis that scanning times explain the haptic illusion. Distinctive fin effects supported the hypothesis that cue distinctiveness contributes to the illusion, but showed also that it depends on modality-specific conditions, and is not the main factor. Allocentric cues from scanning an external frame (EF) did not reduce the haptic illusion. Scanning elicited downward movements and more negative errors for horizontal convergent figures and more positive errors for vertical divergent figures, suggesting a modality-specific movement effect. But the Müller-Lyer illusion was highly significant for both vertical and horizontal figures. By contrast, instructions to use body-centered reference and to ignore the fins reduced the haptic illusion for vertical figures in touch from 12.60% to 1.7%. In vision, without explicit egocentric reference, instructions to ignore fins did not reduce the illusion to near floor level, though external cues were present. But the visual illusion was reduced to the same level as in touch with instructions that included the use of body-centered cues. The new evidence shows that the same instructions reduced the Müller-Lyer illusion almost to zero in both vision and touch. It suggests that the similarity of the illusions is not fortuitous. The results on touch supported the hypothesis that body-centered spatial reference is involved in integrating inputs from touch and movement for accurate haptic shape perception. The finding that explicit egocentric reference had the same effect on vision suggests that it may be a common factor in the integration of disparate inputs from multisensory sources.     

The Müller-Lyer illusion Mark II.

A new illusion of size is described. A passage of print occupying about half a standard A4 sheet appeared larger than the same passage when the sheet was cropped immediately above and below it. This illusion is demonstrated and explained in terms of perceptual compromise between the vertical extent of the printed passage and the sheet of which it is an intrinsic feature. In this sense it is held to be essentially the same as the Müller-Lyer illusion of extent in which the spaces between the apexes are intrinsic to the figure.     

The effect of the Müller-Lyer illusion on map reading

One important reason for studying visual illusions is that they can influence real-world perception as people interact with human-made displays. Three experiments examined how the Müller-Lyer illusion affects distance judgments and decision-making in the complex graphical context of a map by having subjects estimate the lengths of road segment lines framed by inward-going or outward-going wings in actual maps, in control displays that had the map context removed, and in simulated maps. The experiments showed that (1) outward-going wings led to higher distance estimates than did inward-going wings to the same extent both with and without the map context, (2) decisions based on distances determined from maps were affected by Müller-Lyer elements in the maps, and (3) map readers’ measurement behavior influenced the effect of the Müller-Lyer elements in maps. The discussion focuses on how certain display manipulations and task manipulations affect the Müller-Lyer illusion. In addition, the discussion addresses the instances in which using a map might be affected by misestimation due to Müller-Lyer elements.     

Distribution of practice and the Müller-Lyer illusion1

Two experiments were conducted to determine the influence of distribution of practice on the decrement of the Muller-Lyer illusion. In the first experiment, Ss judged the illusion figure 100 times per session in five sessions separated by intervals of seven days. In the second, Ss judged the figure 200 limes in a single session. The data were compared with those from an earlier experiment (Dewar, 1967) in which Ss judged the figure 100 times per session in five sessions separated by 24 h. In all three experiments two configurations of the illusion were used-one with a 60° angle between the obI ique lines and one with a 120° ang Ie. The distribution of practice did not influence the decrement of the illusion for the 120° figure. The only effect of this variable was to produce a more rapid practice decrement for the 60° figure when sessions of 100 trials were separated by a 24-h intewal.