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.     

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.     

Selective looking and the Müller-Lyer illusion: the effect of changes in the focus of attention on the Müller-Lyer illusion

According to a selective looking paradigm subjects were required to attend to the inward-going or outward-going components of a combined Müller-Lyer figure in which both components were present and distinguishable by colour. The amount of the illusion was found to vary according to which component the subject attended. Subsidiary findings relate the amount of the illusion to fin angle, fin length, and length of shaft.     

Framing effects and the reversed Müller-Lyer illusion

The enclosure hypothesis of the reversed Müller-Lyer illusion was examined in three experiments. In Experiment 1, the ingoing- and outgoing-wings forms of the illusion were measured separately, as a function of the size of the gap between the ends of the shaft and the apices of the wings. In Experiments 2 and 3, the effects of a square frame and of complete and amputated versions of a rectangle on the perceived length of an enclosed horizontal line were examined, For all non-Müller-Lyer illusion figures, an inverted U-shaped function describes the relationship between illusion magnitude and the length of the test line. The peak overestimation of the test line’s length was obtained when the ratio of total figure length to test line length was about 3:2. Taken together, the results of the three experiments suggest that the reversed Müller-Lyer illusion can be explained within current theoretical frameworks, such as assimilation theory, without recourse to a special factor of enclosure.     

Three-dimensional Müller-Lyer illusion

Three-dimensional (3-D) variants of the Müller-Lyer pattern were created to address the question of where along the path of information flow in the visual system the illusion might occur. These variants, which yielded a robust illusion, included dihedral angles in place of the arrowheads of the classical pattern. The enormous difference in the shape of the resulting retinal image, compared with that of the classical pattern, makes it difficult to explain the present illusion by resorting to image-processing theories such as selective filtering (Ginsburg, 1984, 1986) or depth processing (Gregory, 1963, 1966, 1968). It was also shown that this 3-D illusion is homologous with the classical illusion, and that the two may thus share a common causal mechanism. A new type of 3-D figure, which yielded the same retinal image as did the classical pattern, was then employed. However, since the figure was 3-D, its shape in spatial coordinates was very different compared to that of the classical pattern. The magnitude of the illusion obtained with this figure was half that of the classical pattern. This finding suggests that the illusion might be caused by processes that occur after the computation of depth. All three experiments indicated that the illusion may be produced later in the processing stream than has previously been suggested.     

Framing effects and the reversed Müller-Lyer illusion.

The enclosure hypothesis of the reversed Müller-Lyer illusion was examined in three experiments. In Experiment 1, the ingoing- and outgoing-wings forms of the illusion were measured separately, as a function of the size of the gap between the ends of the shaft and the apices of the wings. In Experiments 2 and 3, the effects of a square frame and of complete and amputated versions of a rectangle on the perceived length of an enclosed horizontal line were examined. For all non-Müller-Lyer illusion figures, an inverted U-shaped function describes the relationship between illusion magnitude and the length of the test line. The peak overestimation of the test line's length was obtained when the ratio of total figure length to test line length was about 3:2. Taken together, the results of the three experiments suggest that the reversed Müller-Lyer illusion can be explained within current theoretical frameworks, such as assimilation theory, without recourse to a special factor of enclosure.     

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.     

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 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 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.     

Comment on “Eye movements and decrement in the Müller-Lyer illusion”

Festinger et al conflrm the findings of previous investigators that the magnitude of the Müller-Lyer illusion diminishes with prolonged observation of the test figure, but only if gross eye movements are allowed. To explain this phenomenon, they advance the hypothesis that “the perception of length is determined by efferent readiness activated by the visual input.” We offer evidence that the hypothesis is incorrect.     

Influence of instructions and cognitive articulation on reducing the Müller-Lyer illusion with a repeated trial

The role of specific, suggestive instructions and of the subject's cognitive articulation in fostering modifications of Müller-Lyer illusory effect was studied. 60 female students were divided into four subgroups on the basis of (a) Witkin's GEFT scores and (b) instructions given to the subjects for the repeated trial. Analysis shows no statistically significant difference between the more and less articulated subjects on the first trial, for influence of both cognitive articulation and instructions or their interaction on the reduction of the illusion. Data are interpreted in terms of some theoretical explanations of geometrical illusions, such as 'centration theory' and 'assimilation theory'.