Altering Mueller-Lyer illusion magnitude using figural additions at the wing-shaft intersections

The Mueller-Lyer (ML) illusion has been used to study the way in which perceived length is affected by processes of information extraction when a visual target of interest (the ML shaft) is surrounded by other nontarget figural elements (inward-or outward-turning wings). It is argued that the perception of length is computed in terms of the center of gravity or centroid of figural elements at the wing-shaft intersection. The outward-turning wings shift the computational centroid away from the shaft end, giving rise to an erroneous overestimation of shaft length, while the inward-turning wings have the opposite effect. In three experiments, we observed that figural changes, which theoretically shifted the center of gravity of figural elements at the wing-shaft intersection, also increased or decreased the magnitude of the ML illusion.     

Differentiation and decrement in the Mueller-Lyer illusion

Two experiments were conducted to test the hypothesis that decrement of the Mueller-Lyer illusion with inspection is due to learning to differentiate the test element from the accessory lines. In one experiment, the test element is predifferentiated for the observer by means of configurational variations and in the other by restriction of attention. Although the initial magnitude of the illusion is found to be inversely proportional to the amount of predifferentiation, the slopes of the decrement curves are not affected.     

A Mueller-Lyer illusion induced by selective attention

Subjects estimated the length of a horizontal line which was flanked by oblique angles pointing both inside and outside (this figure would be created by superimposing the wings-in and wings-out figures of the Mueller-Lyer illusion). Ignoring the outside wings resulted in an underestimation of the line length of comparable magnitude to that obtained for the wings-in Mueller-Lyer figure. Ignoring the inside wings caused an overestimation of the line length only when the inner and outer wings were of non-corresponding orientations. These results emphasize the role of cognitive factors in the Mueller-Lyer illusion.     

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.     

Factors affecting the magnitude of the Ponzo perspective illusion among the Baganda

The magnitude of the Ponzo perspective illusion, utilizing stimuli with varying amounts of context, was determined for a population of Ugandan villagers. The subjects were classified as two-dimensional, three-dimensional, or mixed perceivers based upon their verbal responses to photographs portraying symbolic depth cues. The illusion magnitude among those subjects classified as three-dimensional was similar to that of college observers who demonstrate an increase in illusion magnitude with increasing background context. The two-dimensional observers’ responses were similar to those of villagers tested previously, showing no significant increase for the same conditions. The role of two-dimensional flatness cues was eliminated on the basis of a control experiment. The data are interpreted as reflecting the operation of a. cognitive factor determining responsiveness to symbolic depth cues in two-dimensional reproductions.     

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.     

Peripheral and central components in variants of the Mueller-Lyer illusion

Illusion decrement with prolonged inspection was used as a technique to assess the relative amount of central component in seven variants of the Mueller-Lyer illusion. Results indicate that all of the variant forms share a common, central component, while the peripheral components, such as lateral inhibition, vary as a function of the presence of converging lines in the illusion configurations.     

Effects of contextual and local factors on Ponzo illusion magnitude

Ponzo illusion has been explained by considering either just the inducing elements present in a restricted area of the visual field, the same area in which the test elements are located, or the stimulus configuration as a whole in which even the most distal figural elements – i.e., the external converging lines, here called “Ponzo wedge”– play a crucial role. The two studies reported here aimed at showing that both global configurational characteristics and inducing elements locally interacting with the test stimuli can independently affect the illusory effect. This hypothesis was tested using stimuli in which graphic-inducing elements giving rise to a herringbone pattern (Coren & Girgus, 1978) were drawn in the same area of the test segments. Results of Exp. 1 confirmed the effect of the two factors. In particular, both factors proved to determine the illusion, since they induced illusory effects either in isolation or in the same/opposite direction. In Exp. 2 the relative weight of these two factors was evaluated in relation to the width of the angle of the inducing elements and to the distance of the test segments from the vertex. Results showed no linear relationships between the distance of the test segments from the external inducing elements and the weight of the Ponzo wedge factor. Received: 25 June 1996 / Accepted: 1 October 1997     

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.