Category effects on estimates of stimuli: perception or reconstruction?

The present study examined a common category effect that has been reported in the literature: the tendency for estimates of individual stimuli to be biased toward the central value of the presented set of stimuli. Both encoding and reconstruction accounts of this central-tendency effect are considered. Plain vertical lines and vertical lines embedded in the Müller-Lyer illusion were estimated while still in view or from memory. Although bias due to the Müller-Lyer illusion remained constant across the two conditions, bias due to the context set (category) occurred only when stimuli were estimated from memory. The results suggest that the category bias occurs at a later stage of processing that the Müller-Lyer effect and offer support for a reconstruction account of category effects on stimulus estimation.     

Perception-action dissociations of a walkable Müller-Lyer configuration

These studies examined the role of spatial encoding in inducing perception-action dissociations in visual illusions. Participants were shown a large-scale Müller-Lyer configuration with hoops as its tails. In Experiment 1, participants either made verbal estimates of the extent of the Müller-Lyer shaft (verbal task) or walked the extent without vision, in an offset path (blind-walking task). For both tasks, participants stood a small distance away from the configuration, to elicit object-relative encoding of the shaft with respect to its hoops. A similar illusion bias was found in the verbal and motoric tasks. In Experiment 2, participants stood at one endpoint of the shaft in order to elicit egocentric encoding of extent. Verbal judgments continued to exhibit the illusion bias, whereas blind-walking judgments did not. These findings underscore the importance of egocentric encoding in motor tasks for producing perception-action dissociations.     

GEOMETRIC ILLUSIONS

The effects of instruction and training on the magnitude of illusion were investigated using as stimuli Müller-Lyer, Müller-Lyer-Ebbinghaus, and Oppel's figure, and a perspective illusion. The subjects estimated the difference between the standard and the variable. The results suggest that changes in judging attitudes, and perceptual learning, contribute to the decrement of illusion during repeated presentation; adaptation to a two-dimensional stimulus world seems to affect the size of illusions which can be explained on the basis of constancy theory. The interactions between the treatments were fairly high.     

ON THE RELATIONSHIP BETWEEN PHENOMENAL SPACE AND PHENOMENAL VELOCITY

The hypothesis that changing the phenomenal distance traversed by a moving spot, while keeping the physical distance constant, should affect the phenomenal velocity in a like direction was tested by having the stimulus motion path bounded by Müller-Lyer figures. It was found that while these affected motion path length judgements in the same direction as static length judgements, they did not have a corresponding effect on velocity judgements. The Müller-Lyer figure producing a decreased length judgement was actually found to increase velocity judgements. Two possible explanations of this result were tested and the conclusion drawn that this increase could be due to the enclosing nature of the Müller-Lyer figure in question.     

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.     

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.     

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.     

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.     

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.     

The creation and reversal of the Müller-Lyer illusion through attentional manipulation

A configuration is presented in which both the overestimated and the underestimated portions of the Müller-Lyer illusion are embedded. In free viewing no distortion of length occurs; however, overestimation or underestimation illusions can be produced by simple manipulation of the attentional set, thus demonstrating one cognitive component in the formation of the Müller-Lyer distortion.     

Müller-Lyer图形中长度加工与时距估计的关系

采用复制法,考察Müller-Lyer错觉条件下,长度加工与时距估计的关系。实验1和实验2分别采用实线段和空线段,结果发现,图形的客观长度越长,估计的时距越长;箭头朝向造成的主观长度错觉对时距估计无影响;时距对长度判断的影响较小。实验3进一步操作线段长度和箭杆方向,发现长度错觉不影响时距估计与错觉量的大小无关。研究表明刺激的客观长度与时间在心理表征上存在自动化的联结,也受到刺激、实验方法和时距等因素的影响。     

The assimilation theory applied to a modification of the Müller-Lyer illusion

The assimilation theory of illusions, which utilizes the principle that large magnitudes in a series are underestimated and small magnitudes are overestimated, was applied to a modification of the Müller-Lyer illusion. A close link was shown to exist between the Müller-Lyer illusion, a modification of the Müller-Lyer illusion, and the Sander parallelogram. In addition, a new illusory target was predicted.     

A comparison of length-matching and length-fractionation measures of Müller-lyer distortions

Two experiments were performed to evaluate the informational equivalence of length-matching (e.g., reproduction) and length-fractionation (e.g., bisection) procedures that are frequently used to quantify geometrical size distortions, such as the Müller-Lyer (M-L) illusion. In Experiment 1, the distortion in the apparent length of a horizontal test line was measured as a function of the angle between it and an abutting inducing line, and in Experiment 2 distortion was measured in the apparent length of the shaft of one-angle versions of the M-L illusion. Both procedures indexed the expansion of the obtuse-angle and the wings-out M-L illusion and the contraction of the acute-angle and the wings-in M-L illusion. However, whereas the reproduction measures indicated substantially greater expansion than contraction distortion, the bisection measures indicated greater contraction distortion. Some possible reasons for this difference, particularly the possibility that the reproduction and bisection procedures are unequally sensitive to the outputs of the mechanisms producing the M-L illusion, are discussed.     

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.     

Two-dimensional filtering,oriented line detectors,and figural aspects as determinants of visual illusions

Quantitative data of Müller-Lyer illusions from the literature were analyzed according to three different models. All three models predict the illusion effect, although with different magnitude and different parameter dependency. First, a filter model describing a certain amount of blurring of the retinal picture seems partly responsible for the observed illusion. With reasonable estimation of the filter constants, however, a sufficient magnitude of illusion cannot be obtained. A second model of oriented line or bar receptors is even less effective in explaining the observed length illusions. A third model, consisting of a size-constancy operator triggered by depth cues, may predict effects larger than actually observed. It is concluded that figural aspects such as depth-inducing cues are mainly responsible for the illusion effects observed in Müller-Lyer figures.     

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 influence of exploration mode, orientation, and configuration on the haptic Müller-Lyer illusion

We studied the impact of manner of exploration, orientation, spatial position, and configuration on the haptic Müller-Lyer illusion. Blindfolded sighted subjects felt raised-line Müller-Lyer and control stimuli. The stimuli were felt by tracing with the index finger, free exploration, grasping with the index finger and thumb, or by measuring with the use of any two or more fingers. For haptic judgments of extent a sliding tangible ruler was used. The illusion was present in all exploration conditions, with overestimation of the wings-out compared to wings-in stimuli. Tracing with the index finger reduced the magnitude of the illusion. However, tracing and grasping induced an overall underestimation of size. The illusion was greatly attenuated when stimuli were felt with the index fingers of both hands. Illusory misperception was not altered by the position in space of the Müller-Lyer stimuli. No effects of changes in the thickness of the line shaft were found, but there were effects of the length of the wing endings for the smaller, 5.1 cm stimuli. The theoretical and practical implications of the results are discussed.     

Diamond-winged variants of the Müller-Lyer figure: A test of Virsu’s (1971) centroid theory

Diamond-winged variants of the Müller-Lyer figure were used to test predictions of Virsu’s (1971) theory of the Müller-Lyer illusion based on efferent readiness for eye movements toward the figure’s center of gravity, A Müller-Lyer figure with diamond-shaped wings resulted in a greater center-of-gravity distance than the corresponding, conventional Müller-Lyer figure, but fin length and the rest of the figure remained constant; in Virsu’s study, fin length and center-of-gravity distance covaried. Results were consistent with Virsu’s data when we used the stimulus conditions that he reported. Results from a wider range of stimuli challenge Virsu’s theory, and thus are consistent with the conclusions of Brigell, Uhlarik, and Goldhorn (1977).     

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.     

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.