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 lightness contrast on the colored Müller-Lyer illusion

Two subjects estimated the length of the central line in red-and blue Müller-Lyer figures that were viewed both foveally and parafoveally. The illusion figures were defined by either lightness and hue differences between figure and ground or by a hue difference alone. For both subjects, the figures defined solely by hue produced larger illusions. Since depth-cue scaling and other cognitive factors did not cause the enlargement, it was concluded that the robust, hue-produced illusions resulted from contour interactions generated within parvocellular channels that are specialized for coding color.     

The effect of the Müller-Lyer illusion on the planning and control of manual aiming movements

Two experiments used Müller-Lyer stimuli to test the predictions of the planning-control model (S. Glover, 2002) for aiming movements. In Experiment 1, participants aimed to stimuli that either remained the same or changed upon movement initiation. Experiment 2 was identical except that the duration of visual feedback for online control was manipulated. The authors found that the figures visible during movement planning and online control had additive effects on endpoint bias, even when participants had ample time to use visual feedback to modify their movements (Experiment 2). These findings are problematic not only for the planning-control model but also for A. D. Milner and M. A. Goodale's (1995) two visual system explanation of illusory bias. Although our results are consistent with the idea that a single representation is used for perception, movement planning, and online control (e.g., V. H. Franz, 2001), other work from our laboratory and elsewhere suggests that the manner in which space is coded depends on constraints associated with the specific task, such as the visual cues available to the performer.     

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.     

A microgenetic study of the Müller-Lyer illusion.

In two experiments a decomposed Müller-Lyer pattern was used to measure the time course of the illusion. A partial report procedure was used to prevent the subjects from focusing only on parts of the pattern and to maximize visual processing. The Müller-Lyer figure was decomposed into two parts, its angles and its line. A configuration of three pairs of angles, each corresponding to a row in the usual partial report arrangement, was used. A line that did or did not fit the gap was shown with a variable delay (interstimulus interval, ISI). By this procedure the relevant row (line gap) was cued. The subject had to decide whether the line fitted or was too short/long. Two exposure times for the angles were used, 50 or 200 ms in one experiment and 50 or 500 ms in the other. The result of the first experiment, with outward-pointing fins, was a stable illusion for all values of ISI (25-400 ms) and all exposure times, with one significant exception: exposure for 50 ms with an ISI of 50 ms yielded an illusion peak. It was shown that this was not caused by a reduction in length-discrimination performance. In the second experiment, with inward-pointing fins, no such peak occurred. There was only a tendency for the illusion to vanish with zero ISI. The results are discussed with respect to 'global to local' theories of visual processing.     

Effects of training in design on magnitude of the Müller-Lyer illusion.

The Müller-Lyer illusion was measured for 10 design and 10 optometry students. The illusion was smaller for design students and they improved significantly with practice. The results are discussed in relation to size-constancy, according to which part of the figure corresponding to a distant object is overestimated and to the aptitude of design students to draw according to their retinal image.     

The effect of angle between the oblique lines on the decrement of the Müller-Lyer illusion with extended practice

Early work on the Müller-Lyer illusion had indicated that it disappears with extended practice. The present experiment failed to confirm this finding. The magnitude of the illusion decreased for approximately 500 trials, but showed no further change over an additional 500 trials. The rate of the practice decrement was inversely related to the size of the angle formed by the oblique lines of the figure.     

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.     

Effect of size of angle on the ambiguous Müller-Lyer illusion

The ambiguous Müller-Lyer illusion was measured as a function of the angle formed by the oblique lines. The illusion was found to increase with an increase in the size of the angle. This result confirmed the validity of the attentive field postulate of the assimilation theory of geometric illusions.     

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.     

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.     

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 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.     

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 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.