Mueller-Lyer Figure Research Articles

Der Einfluss geometrisch-optischer Täuschungen auf sakkadische Augenbewegungen

The aim of this study was to investigate whether visually perceived length differences of Mueller-Lyer figures result in amplitude differences of saccadic eye movements along the figures. Video recordings of eye movements were obtained from 35 healthy volunteers (aged 18 - 30 years) when scanning the endpoints of Mueller-Lyer targets. Saccades between the ends of lines with inward-pointing arrowheads had significantly greater amplitudes than saccades between the ends of lines with outward-pointing arrowheads. This bias was observed for both horizontal and vertical target orientations, and was maintained with a smaller amplitude, after fixation periods were extended from 1 s to 4 s. Changes in length perception by visual illusions correspond with changes in the amplitude of saccadic eye movements. Therefore, recordings of saccadic eye movements offer the opportunity to assess changes in visual object perception based on changes of central image processing at the cortical level.

Decrement and the Illusions of the Mueller-Lyer Figure

Decrement, a time-related decrease in the magnitude of the Mueller-Lyer illusion, was measured separately for the wings-out and the wings-in variants of the Mueller-Lyer figure. There were significant reductions of wings-out illusion magnitude during the decrement period. Observers viewing the wings-in segment showed a non-significant decrement pattern. Analyses of individual decrement patterns showed that illusion magnitude did not decrease for a number of observers even when there were significant time-related trends at the group level. Data for 80 observers imply that the mechanisms of perceptual learning proposed by previous models of Mueller-Lyer illusion decrement are not sufficient explanations of the decrement process.

Selective Adaptation to Low Spatial Frequencies Does Not Decrease the Mueller-Lyer Illusion

The idea that low spatial-frequency information in the Mueller-Lyer figure accounts for a major part of the illusion was tested in a series of five studies. In Study 1, subjects were selectively adapted to high or low square-wave spatial-frequency gratings with no difference in the magnitude of illusion they experienced. Similarly, adaptation to sinusoidal grating patterns with either high or low spatial frequency had no effect on the magnitude of illusion experienced (Studies 2 to 5). The failure of adaptation to low spatial-frequency gratings to affect the magnitude of illusion experienced indicates either that the illusion cannot be accounted for by the low spatial-frequency information or that adaptation of the visual system by grating patterns cannot be used to explore any effects of the low spatial frequencies in the figure.

Comparison of the Wings-in, Wings-out, and Brentano Variants of the Mueller-Lyer Illusion

Illusion magnitude relationships between the Brentano Mueller-Lyer figure and its two component parts, the wings-in and the wings-out distortions, were explored in two experiments. Results indicated that the Brentano Mueller-Lyer form, a figural variant that combines both illusions, is related more closely to its underestimation rather than to its overestimation component. Data also supported the notion that a unique complement of perceptual mechanisms is involved in the formation of each Mueller-Lyer distortion

Wings in the intershaft space contribute to the Mueller-Lyer illusion.

The interference of the wings of the wings-in part of the Mueller-Lyer figure was examined for the version of the illusion in which one part of the figure is placed above the other. Wings were removed in pairs from either above or below the shaft of one of the two parts of the figure. Subjects indicated the apparent difference between the lengths of the shafts of the two parts of the figure. Removal of the wings between the shafts of the wings-in part of the figure reduced the amount of the illusion more than removal of the wings from outside the shafts. Removing wings from the wings-out part of the figure reduced the amount of illusion, but it made no difference whether the wing removal occurred between or outside the shafts.

The life-span trend in the magnitude of the Mueller-Lyer illusion as a function of hue and age.

Mueller-Lyer illustrations produced by hue contrast were used to investigate age differences with participants ranging in age from 20 to 79 years. As expected, there was no age difference in the magnitude of the illusion when the Mueller-Lyer figure was produced by hue contrast. A significant main effect of hue was found, with no interaction between hue and age. These findings support Pollack's nondevelopmental explanation for age effects on Type I illusions.

The role of structural components in the Mueller-Lyer illusion.

In order to assess the role of the structural components of the Mueller-Lyer illusion, subjects reproduced the central extent of standard Mueller-Lyer figures and configural variations. Illusory magnitude of the underestimated wings-in and overestimated wings-out figures was examined with selective amputations of the oblique wings and central line segment (shaft). Variations were presented at 0, 45, 90, and 135 deg from vertical. Orientation had no reliable effect on illusory magnitude. Elimination of the shaft effected a decrease in the apparent extent for all variations, presumably due to the addition of the filled-unfilled space illusory effect to the standard Mueller-Lyer effect. A second study corroborated this finding The decrease in apparent extent consequent to shaft removal occurred independently of any response factor. Selective wing removal differentially decreased the illusory magnitude of the standard Mueller-Lyer figures; this was discussed with regard to a dual-illusion hypothesis. Finally, variations that contained no intersecting lines produced a significant illusion in the direction of the standard Mueller-Lyer figures, suggesting the involvement of higher level, nonperipheral distortion mechanisms.

Does brightness contrast really affect the Mueller-Lyer illusion.

Several writers have hypothesized that the Mueller-Lyer illusion is influenced by brightness contrast between figure and background. According to them, lateral inhibition in the retina causes displacement in Mueller-Lyer figures at the intersections of lines. They argue that the strength of the displacement varies with brightness contrast between the background and the figure, and they cite research by Pollack and others for support. The experiments reported here show that the Mueller-Lyer illusion is no more affected by changes in contrast than are judgment of single straight lines. These results are not consistent with the view that lateral inhibition in the retina has an effect on the illusion.

Length Judgments in Modified Mueller-Lyer Figures

In two experiments, subjects made line length matches and relative line length comparisons of a transverse line perpendicularly intersecting the midpoints of the center shafts of the Mueller-Lyer figures. The results indicated that the illusion of transverse line length occurs in a direction opposite to the illusion of shaft length; findings suggesting an asymmetry in the distortion of the space across the Mueller-Lyer figures were thus confirmed. The possible contribution of framing effects induced by the fins of the Mueller-Lyer figures in determining the illusion of transverse line length is discussed.

Effects of Lightness Contrast and Fundus Pigmentation on Age-Related Decrement in Magnitude of the Mueller-Lyer Illusion

Components of the Mueller-Lyer figure, representing two levels of lightness contrast (1.5 black/ and 7.5 light grey/ each on 9.5 white/ ground) were viewed tachistoscopically for 500 msec. by 65 white elementary school children and 50 white college students. The contrast effect was significant, with black figures yielding a greater illusion than the light grey figures at all age levels. Further, a bimodal distribution of fundus density was evident in both age categories, with more densely pigmented Ss yielding smaller illusions.

Morinaga’s paradox and figure-ground organization

Morinaga’s paradox of displacement is constructed by setting several copies of the two Mueller-Lyer figures one above the other. The Mueller-Lyer illusion is that the wings pointing out seem farther apart than wings pointing in, and Morinaga’s paradox is that when one looks down a column of wings pointing alternately one way and the other, they appear misaligned but in the opposite direction from the Mueller-Lyer illusion. The hypothesis of this paper is that the subject, under instructions to align the vertical array of wings, sets up a vertical figure-ground organization different from that used in judging the horizontal distance between wings, and that the two illusions are contingent upon the two organizations. The experiment showed that Morinaga’s paradox occurs when only one column of wings is shown, in agreement with the figure-ground hypothesis, and also shows that Morinaga’s paradox disappears when short line segments are introduced which disrupt the vertical figure-ground organization.

Illusion magnitude as a function of visual field exposure

Forty-eight right-handed subjects divided into four groups, each consisting of six males and six females, were employed in an investigation of cerebral hemispheric influence on the perception of tachistoscopically presented simultaneous and successive versions of the Mueller-Lyer figure. The simultaneous version exposed in the left visual field resulted in a larger effect than did right visual field exposures. The successive version exposed in the right visual field resulted in a larger illusion magnitude than it did in the left visual field. The magnitude of visual field differences in response to the successive version was greater than visual field differences found in response to the simultaneous version

Constancy scaling theory and the Mueller-Lyer illusion: More disconfirming evidence

Length and width judgments were made for modified Mueller-Lyer figures (the center shaft of each of the two figures was replaced by a rectangle). The rectangle with outgoing fins was judged longer and wider than a control rectangle of equal size with no fins, but longer and narrower than the rectangle with ingoing fins. The rectangle with ingoing fins was judged shorter and wider than the control rectangle. These results did not support Gregory’s inappropriate constancy scaling explanation of the Mueller-Lyer illusion.

Reversal in stereo discrimination by contrast reversal.

Mueller-Lyer figures were presented tachistoscopically in illuminant C in four experiments which explored the effects of viewing time (500, 1500, 4500 and 9000 msec), contrast level (1.5 black/, 5 gray/, 7.5 light gray/ each on 9.5 white/ background) and fundus pigmentation on the magnitude of illusion. Significant interactions of contrast level and viewing time were evident. Results further indicate density of fundus pigmentation to be related significantly to illusion magnitude at the shortest viewing time, with more darkly pigmented Ss yielding a significantly smaller illusion than lightly pigmented Ss sampled from a white population. Illusion magnitude at a reduced viewing time would seem to be a function of absolute contrast.

Successive Presentations of Elements of the Mueller-Lyer Figure and CA, MA, and IQ: An Age Extension and Unsuccessful Replication

HARTMANN, DONALD P.; GELFAND, DONNA M.; COURTNEY, ROBERT J., JR.; and MALOUF, ROBERTA E. Successive Presentations of Elements of the Mueller-Lyer Figure and CA, MA, and IQ: An Age Extension and Unsuccessful Replication. CHILD DEVELOPMENT, 1972, 43, 1060-1066. The present study was a replication and extension to younger children of Pollack's (1964) developmental study of the Mueller-Lyer illusion. 50 Ss ranging in age from 6 to 9 years made comparative judgments of the altered Mueller-Lyer figure and were administered the California Short-Form Test of Mental Maturity. The results generally were inconsistent with Pollack's findings; although Ss underestimated the size of the illusion in the predicted direction, no significant correlations between size of illusion and either age or IQ were found.

A test of constancy scaling theory in a modified Mueller-Lyer illusion

The center line of each of the two Mueller-Lyer figures was replaced by a rectangle whose length and width were both judged. The rectangle, bounded by wings positioned outward, was judged both longer and narrower than a standard rectangle of equal size, while the rectangle bounded by wings oriented inward was judged to be both shorter and wider than the standard rectangle. These results were considered to provide evidence against a constancy scaling explanation of geometric illusions. Other theories to account for the results were considered and found inadequate.

Magnitude of the Mueller-Lyer illusion as a function of lightness contrast, viewing time, and fundus pigmentation

Mueller-Lyer figures of three levels of contrast (1.5 black/, 5 gray/, and 7.5 light gray/, each on 9.5 white/ground) were presented tachistoscopically for 1,500 msec and 500 msec in Illuminant C. Results indicate a significant interaction between contrast level and viewing time. In a second experiment, density of fundus pigmentation was found to be a significant factor in determining illusion magnitude across all contrast levels for a viewing time of 500 msec.

Illusion decrement in intersecting line figures

This study tests the generality of illusion decrement using four illusion figures involving intersecting lines: the Zoellner, Poggendorff, Wundt-Hering, and Mueller-Lyer figures. Five minutes of inspection with testing at 1-min intervals led to significant decrement in all figures. The rate of decrement was the same for all figures. These data are consistent with a judgmental theory of geometric illusions.

The Sander illusion as a function of relative space and component lines

Magnitude of the Sander illusion was measured as a function of two variables: (1) the orientation of the line normally separating the two smaller parallelograms and (2) the presence or absence of the horizontal lines and of the diagonal test lines. The results showed that, as the angle of the dividing line varied so as to shift the relative sizes of the two parts of the figure toward equality, the illusion effect decreased, approaching zero when the two areas were equal. The illusory effect was enhanced by the removal of the two test lines. Results were discussed in relation to the problem of assimilation vs contrast effects. Woodworth and Schlosberg (1954) describe the confusion theory of geometric illusions as stating that the S's judgment of part of the figure is influenced by the structure of the whole. Supporting this position, Benussi (1904), using the Mueller-Lyer figure, found conditions engendering a whole-perceiving attitude to produce a greater illusion than those favoring a part-isolating attitude. The confusion theory may also account for the Sander illusion where it is difficult for the viewer to separate his impression of the lengths of the test lines from the sizes of the areas surrounding them. The primary purpose of the present experiment was to investigate the effects of manipulating the relative size of the two major areas of the Sander figure on the magnitude of the illusion. It was hypothesized that, as the areas surrounding the diagonal lines to be compared approached equality, the illusion effects

Contrast and assimilation effects in judgments of line configurations containing the Mueller-Lyer figure

Two experiments are reported in which contrast and assimilation effects of anchor line lengths upon focal line lengths were observed. In Experiment 1 straight-line anchors shorter than, and parallel to, focal Mueller-Lyer figures made the figures appear shorter than the same Mueller-Lyers anchored by straight lines longer than the figures. In Experiment 2, focal stimuli were straight lines and parallel anchors were Mueller-Lyer figures. When focal length approximated anchor length, judged length of the focal stimulus was less if anchoring Mueller-Lyers had inward obliques than if the obliques pointed outward. However, as focal length deviated from anchor length, this effect of Mueller-Lyer obliques reversed; outward obliques made focal lines appear shorter than did inward obliques. Results are discussed in terms of adaptation-level theory (A-L theory).