Changes: Müller-Lyer illusion

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The Müller-Lyer illusion is an optical illusion consisting of nothing more than an arrow. When viewers are asked to place a mark on the figure at the mid-point, they invariably place it more towards the "tail" end. Another variation consists of two arrow-like figures, one with both ends pointing in, and the other with both ends pointing out. When asked to judge the lengths of the two lines, which are equal, viewers will typically claim that the inward pointing pair is longer. One possible explanation is that one sees the lines as three-dimensional, such as the outgoing and ingoing corners of a room. Another possible explanation is that the line with arrows pointing inwards may simply appear longer because the arrows themselves extend past the line.

The illusion is not cross-cultural. Non-Western subjects, and particularly subjects whose day-to-day surroundings are usually not rectangular (few buildings, doors, walls) are much less likely to be affected by it (Segall, et al., 1963).

The perspective explanation

One possible explanation states that the Müller-Lyer illusion occurs because the visual system processes that judge depth and distance assume in general that the “angles in” configuration corresponds to an object which is closer, and the “angles out” configuration corresponds to an object which is far away. Basically, there seems to be a simple heuristic that takes those configurations as 90º angles. This heuristic speeds up the interpretation process, but gives rise to many optical illusions in unusual scenes.

Neural nets in the visual system of (western) human beings learn how to make a very efficient interpretation of 3D scenes. That is why, when somebody goes away from us, we do not see him getting shorter. And when we stretch one arm and look at the two hands we do not see one hand smaller than the other. We should not forget that, as visual illusions show us quite clearly, what we see is an image created in our brain. Our brain projects the image of the smaller hand to its correct distance in our internal 3D model. This is what is called the size constancy mechanism.

In the Müller-Lyer illusion, the visual system detects the depth cues, which are usually associated with 3D scenes, and incorrectly decides it is a 3D drawing. Then the size constancy mechanism makes us see an erroneous length of the object which, for a true perspective drawing, would be more far away.

In the perspective drawing in the figure, we see that in usual scenes the heuristic works quite well. The length of the rug should obviously be considered shorter than the length of the wall in the back.