The Müller-Lyer illusion is an optical illusion consisting of three stylized arrows. When viewers are asked to place a mark on the figure at the midpoint, they tend to place it more towards the "tail" end. The illusion was devised by Franz Carl Müller-Lyer (1857–1916), a German sociologist, in 1889. Research suggests all humans are susceptible to the illusion across cultures. A variation of the same effect (and the most common form in which it is seen today) consists of a set of arrow-like figures. Straight line segments of equal length comprise the "shafts" of the arrows, while shorter line segments (called the fins) protrude from the ends of the shaft. The fins can point inwards to form an arrow "head" or outwards to form an arrow "tail". The line segment forming the shaft of the arrow with two tails is perceived to be longer than that forming the shaft of the arrow with two heads.
Susceptibility
The illusion appears to be experienced by all human beings seeing it, even those who have been blind. This suggests susceptibility to the illusion is neurologically constant across humans, and undermines hypothesis promulgated in the twentieth century proposing that susceptibility was culturally determined. Such hypotheses were based on research that suffered from poor methodology and contamination by false cultural assumptions. Non-human animals are also susceptible to the illusion.
Perspective explanation
One possible explanation, given by Richard Gregory, is that the Müller-Lyer illusion occurs because the visual system learns that the "angles in" configuration corresponds to a rectilinear object, such as the convex corner of a room, which is closer, and the "angles out" configuration corresponds to an object which is far away, such as the concave corner of a room. In a report from 2005, the hypothesis is tested by analyzing templates corresponding to the illusion in natural images, finding that the sort of image caused by a Müller-Lyer stimulus was more likely to come from a physical source with the source of the outward pointing line being longer on average than the source of the inward pointing line. The visual system of human beings learn how to make a very efficient interpretation of 3D scenes. That is why when somebody goes away from a viewer, the viewer does not perceive them as getting shorter. Likewise, someone who stretches one arm and looks at both of their hands will perceive them to be the same size. Visual illusions are sometimes held to show that what is seen is an image created in the brain. The brain supposedly projects the image of the smaller hand to its correct distance in an internal 3D model. This is what is called the size constancy mechanism hypothesis. In the Müller-Lyer illusion, the visual system would in this explanation detect the depth cues, which are usually associated with 3D scenes, and incorrectly decide it is a 3D drawing. Then the size constancy mechanism would make us see an erroneous length of the object which, for a true perspective drawing, would be farther away. In the perspective drawing in the figure, we see that in usual scenes the heuristic works quite well. The width of the rug should obviously be considered shorter than the length of the wall in the back. Ross Day developed explanations in which position on these illusions opposes Richard Gregory's argument for acculturation of architectural space as influencing a false sense of perspective in such illusions. Ross countered that it is not the result of misapplied size constancy, but that such illusions rely on whole-part determination and space–time reciprocity, that the whole figure is the primary determinant of the illusion; "you don't change the perception of illusions very much with experience; it hardly changes them at all."
Catherine Howe and Dale Purves contradicted Gregory's explanation:Although Gregory's intuition about the empirical significance of the Müller-Lyer stimulus points in the right general direction (i.e., an explanation based on past experience with the sources of such stimuli), convex and concave corners contribute little if anything to the Müller-Lyer effect.
Centroid explanation
According to the so-called centroid hypothesis, judgments of distance between visual objects are strongly affected by the neural computation of the centroids of the luminance profiles of the objects, in that the position of the centroid of an image determines its perceived location. Morgan et al., suggest that the visual procedure of centroid extraction is causally related to a spatial pooling of the positional signals evoked by the neighboring object parts. Though the integration coarsens the positional acuity, such pooling seems to be quite biologically substantiated since it allows fast and reliable assessment of the location of the visual object as whole, irrespective of its size, the shape complexity, and illumination conditions. Concerning the Müller-Lyer and similar illusions, the pattern of neural excitation evoked by contextual flank (e.g., the Müller-Lyer wings themselves) overlaps with that caused by the stimulus terminator (e.g., the wings apex), thereby leading (due to the shift of the centroid of summed excitation) to its perceptual displacement. The crucial point in the centroid explanation regarding the positional shifts of the stimulus terminators in the direction of the centroids of contextual flanks was confirmed in psychophysical examination of illusory figures with rotating distractors. The relative displacement of all stimulus terminators leads to misjudgment of distances between them; that is, the illusion occurs as a side effect due to necessarily low spatial resolution of the neural mechanism of assessment of the relative location of the visual objects. Besides, it was shown that well-known asymmetry in manifestation of the wings-in and wings-out modifications of the Müller-Lyer illusion can be successfully explained by supplemental effects of the filled-space illusion.
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