Geometrical illusions in solid objects under ordinary viewing conditions.

The Müller-Lyer and Ponzo illusions were obtained under free binocular viewing of three-dimensional objects, and the function relating magnitude of illusion to fin angle, characteristic of converging-line versions of the Müller-Lyer pattern, was closely paralleled by volumetric (three-cone), line-free objects (but not with an erect, planar "walk-through" construction and moving observers). Illusions cannot be dismissed as artifacts of static, impoverished viewing, therefore, but must be explained within any general theory of perception. Perspective explanations have difficulties with such three-dimensional manifestations, and seem completely inapplicable to our further finding that approximately the same amount of illusion occurred in objects and patterns with no oblique lines or edges. Confusion or averaging theories, not themselves tested here, remain unthreatened by these data.     

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.     

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.     

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.     

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.     

An intra-cultural investigation of susceptibility to 'perspective' and 'non-perspective' spatial illusions

Conventional Müller-Lyer and modified Müller-Lyer (without 'perspective' cues) illusions were presented to two samples of children aged between eight and 19, matched in education, but living in 'carpentered' and 'uncarpentered' environments in Zambia. Traditional differences in susceptibility have been obtained with both the variations of the Müller-Lyer illusion. In view of the lack of perspective cues in one of these, it is concluded that the perspective theory as presented within the 'carpentered world hypothesis' is inadequate. Since these differences are intra-cultural, they also do not support the hypothesis which suggests that cross-cultural variations in illusion susceptibility are due to genetic factors--such as macular (or retinal) pigmentation.     

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.     

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.     

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.     

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.     

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.     

Perception of the standard and the reversed Müller-Lyer figures in pigeons (Columba livia) and humans (Homo sapiens)

The authors compared perception of the standard and reversed Müller-Lyer figures between pigeons (Columbia livia) and humans (Homo sapiens). In Experiment 1, pigeons learned to classify 6 lengths of target lines into "long" and "short" categories by pecking 2 keys on the monitor, ignoring the 2 brackets so placed that they would not induce an illusion. In the test that followed, all 3 birds chose the "long" key more frequently for the standard Müller-Lyer figures with inward-pointing brackets (><) than for the figures with outward-pointing brackets (<>). The subjects' responses were accountable by neither overall lengths of the figures nor horizontal gaps between the 2 brackets. For the reversed figures, effects of the brackets were absent. These results suggested that the pigeons perceived the standard Müller-Lyer illusion but not the reversed one. Experiment 2 confirmed that humans perceived both types of the illusion. Pigeons and humans may perceive the same illusory figures in different ways.     

The Müller-Lyer contrast illusion: A computational approach

When a temporal delay is interposed between the contextual elements (wings) and the focal element (central axis) of the Müller-Lyer figures, the usual assimilation illusion changes to an illusion of contrast; that is, judged axis length is contrasted away from rather than assimilated toward the context provided by parallel extents between wings. Presentation time for the preceding contextual wings on the order of 1 sec or more was needed to produce contrast effects in judgments of the following focal axis (Experiment 3) and, given sufficient presentation time, these contrast effects were largely unaffected by the length of the temporal delay between contextual and focal elements, appearing equally strong for delays between 0 and 2 sec (Experiments 1 and 2). These results are consistent with a representational basis for these contrast effects that is high-level and long-lived. The Müller-Lyer contrast illusion may reflect the inadvertent error arising from basing judgments about particular objects on information about attribute differences among objects. Such judgmental errors may be the natural consequence of constrained computations that make explicit information required for certain common tasks, but at the expense of obscuring information required for less common tasks.     

Are size illusions in simple line drawings affected by shading?

In a number of simple line drawings, such as the Müller-Lyer or Judd figures, we can experience strong distortions of perceived space-geometric illusions. One way of explaining these effects is based on the perspective information that can be read from the line drawings. For instance, the 'inappropriate constancy scaling' theory advocates that the inferred three-dimensional structure of the pictured object is used by the perceptual system to adjust the size of line-drawing components. Such a theory would predict that additional depth cues, for instance shading added to line drawings, should affect these illusions because they influence the three-dimensional appearance. We present here systematic measurements of the magnitude of length misjudgments in horizontal Müller-Lyer and Judd figures for three configurations: (i) pure line drawings, and with shading attached to (ii) the top, and (iii) the bottom of the figures. The latter two configurations are unambiguously interpreted as 'folded' structures with a horizontal edge behind the image plane or protruding from it, respectively. While we could not find any effect of shading in our experimental data, we did observe a length misjudgment in Judd figures that corresponds precisely to the asymmetry that can be observed in the Müller-Lyer illusion for inward and outward fins. This pattern of results is not consistent with notions of inappropriate constancy scaling but is fully coherent with the view that neural filtering mechanisms, which are affecting the perceived position of line intersections, are responsible for this type of geometrical illusions.     

A test of the spatial-frequency explanation of the Müller-Lyer illusion

Previous investigations have shown that the response of spatial-frequency-specific channels in the human visual system is differentially affected by adaptation to gratings of distinct spatial frequencies and/or orientations. A study is reported of the effects of adaptation to vertical or horizontal gratings of a high or a low spatial frequency on the extent of the Brentano form of the Müller-Lyer illusion in human observers. It is shown that the illusion decreases after adaptation to vertical gratings of low spatial frequency, but seems unaffected otherwise. These results are consistent with the notion of visual channels that are spatial-frequency and orientation specific, and support the argument that the Müller-Lyer illusion may be due primarily to lower-spatial-frequency components in the Fourier spectra of the image.     

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.     

Single-band amplitude demodulation of Müller-Lyer illusion images

The perception of the Müller-Lyer illusion has previously been explained as a result of visual low band-pass spatial filtering, although, in fact, the illusion persists in band-pass and high-pass filtered images without visible low-spatial frequencies. A new theoretical framework suggests that our perceptual experience about the global spatial structure of an image corresponds to the amplitude modulation (AM) component (or its magnitude, also called envelope) of its AM-FM (alternatively, AM-PM) decomposition. Because demodulation is an ill-posed problem with a non-unique solution, two different AM-FM demodulation algorithms were applied here to estimate the envelope of images of Müller-Lyer illusion: the global and exact Daugman and Downing (1995) AMPM algorithm and the local and quasi-invertible Maragos and Bovik (1995) DESA. The images used in our analysis include the classic configuration of illusion in a variety of spatial and spatial frequency content conditions. In all cases, including those of images for which visual low-pass spatial filtering would be ineffective, the envelope estimated by single-band amplitude demodulation has physical distortions in the direction of perceived illusion. It is not plausible that either algorithm could be implemented by the human visual system. It is shown that the proposed second order visual model of pre-attentive segregation of textures (or "back-pocket" model) could recover the image envelope and, thus, explain the perception of this illusion even in Müller-Lyer images lacking low spatial frequencies.     

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 effect of insstructions on judgment of the Müller-Lyer illusion with normal and haptically mediated visual inspection

An experiment with the Müller-Lyer figure is reported in which variation in instructions resulted in a change in the magnitude of the visual illusion under normal viewing conditions. Variation in instructions did not, however, have a differential effect on the magnitude of the illusion when Ss inspected the figure by means of a point source of light attached to one fingertip. These results are equivalent to differences found between the effect of instructions on visual and haptic illusions using the same illusion figure and support the view that variation in inspection patterns rather than differences in higher processingof sensory input might account for differences between the two modalities.     

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.