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.     

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.     

Virtual and drawing structures for the Müller-Lyer illusions

This research assessed the relative contribution of 3-D virtual structure that generated the stimulus drawings (scene-based and picture-based theories) and 2-D structure of the drawings (object-based theories). Virtual structures were right-angle convex and concave corners in front of and behind the picture plane, respectively. Virtual corner size was manipulated directly (Experiment 1) and indirectly by manipulating drawing station point distance (Experiments 2 and 3), corner depth (Experiment 4), and corner distance from the picture plane (Experiments 5 and 6). Experiments 2 and 4 held the size of the projected corner edge (interior target line) constant, causing virtual corner size to vary, whereas Experiments 3, 4, 5, and 6 held size of the virtual corners constant, causing size of the projected corner edge or interior target line to vary. Subjects reproduced the length of the projected corner edge (interior target line). The illusions (difference between reproduced size of the projected corner edge and T-junction control) were generally well fit by the weighted sum of virtual corner size and size of the projected corner edge, but the projected distance between boundary line terminations (intertip distance) appeared as an additional contributing factor in Experiments 5 and 6. The implications of this methodological approach are discussed for theories of the illusions.     

Arm-movement responses to Müller-Lyer stimuli

Similarities between eye- and arm-movement patterns during the Müller-Lyer illusion were investigated. The study was designed to find out if characteristics of a visual illusion would be reflected in tracings of an unseen ann. Six stimuli, three experimental and three control, were presented five times to each of seven Ss who were familiar with the illusion. Data were analyzed by measuring lengths of tracings and by making intraindividual comparisons using t tests for correlated means. Results for the arm were similar to those reported elsewhere for the eye. Arrows with outward-directed obliques were traced longer than arrows with inward-directed obliques, as well as longer than control stimuli. Agreement between eye- and arm-movement responses to the illusion lend support for using each technique to investigate stimuli that affect man’s distance metric.     

Age-related susceptibility to the Müller-Lyer and the horizontal-vertical illusions

Participants between the ages of 3 and 20 years adjusted the Müller-Lyer illusion and the inverted-T form of the Horizontal-Vertical illusion. Perceptual error was quantified using signal detection and nonparametric measures of sensitivity and responsivity. Significant changes in sensitivity and responsivity were found for each illusion across participants' ages. No effect of sex of participant was found. Sensitivity and responsivity were largely asymptotic between the ages of 13 to 15 years for the Müller-Lyer illusion and between the ages of 11 to 15 years for the Horizontal-Vertical illusion.     

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.     

Geometrical haptic illusions: The role of exploration in the Müller-Lyer,vertical-horizontal,and Delboeuf illusions

This article surveys studies of the occurrence, in the haptic modality, of three geometrical illusions well known in vision, and it discusses the nature of the processes underlying these haptic illusions.We argue that the apparently contradictory results found in the literature concerning them may be explained, at least partially, by the characteristics of manual exploratory movements. The Müller-Lyer illusion is present in vision and in haptics and seems to be the result of similar processes in the two modalities. The vertical-horizontal illusion also exists in vision and haptics but is due partly to similar processes (bisection) and partly to processes specific to each modality (anisotropy of the visual field and overestimation of radial vs. tangential manual exploratory movements). The Delboeuf illusion seems to occur only in vision, probably because exploration by the index finger may exclude the misleading context from tactile perception. The role of these haptic exploratory movements may explain why haptics is as sensitive as vision to certain illusions and less sensitive to others.     

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.     

Decrement of the Müller-Lyer and Poggendorff illusions: the effects of inspection and practice

Five experiments assessed the decline or decrement in illusion magnitude for the wings-out form and the combined or Brentano form of the Müller-Lyer illusion, and for the Poggendorff illusion. Judgments were obtained under conditions of either continuous or intermittent inspection of the illusion figure. In the continuous-inspection conditions observers scanned the illusion figure during the inter-trial intervals whereas in the intermittent-inspection conditions they did not. Substantial illusion decrement was found in all continuous-inspection conditions and in intermittent conditions with short inter-trial intervals (upto 20 s) but not with longer inter-trial intervals. However, intermittent-inspection with a long inter-trial interval (40 s) produced illusion decrement but only when observers were instructed during the decrement session to ignore the wings, and pay attention to the shaft, of the Müller-Lyer figure. Taken together, the pattern of results does not support the claim that illusion decrement is primarily a product of practice or repeated trials.     

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 dissociation of position and extent in Müller-Lyer figures

Three experiments were designed to determine whether Müller-Lyer figures cause a misperception of the positions of their fins and, if they do, whether it is commensurate with the distortion of extent. Observers marked the visible intersection of shaft and fins either with their unseen hands or with their visible hands after the figure had been removed from view. In the former case, no systematic distortions of position were evident. In the latter case, there were small, systematic distortions of position, which were significantly smaller when the observers fixated the target vertex than when they fixated the center of the figure. These differences are discussed in terms of the probable similarities between the control of eye movements and the control of pointing responses. Of particular importance is the finding that even the largest distortions of vertex position were much smaller than the distortions of shaft extent. The results appear to provide evidence of the independence of perceived position from perceived extent in Müller-Lyer figures and to contradict all existing theories of the illusion.     

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 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.     

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.     

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.     

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.