How the Statistical Structure of the Environment Affects Perception of the Müller-Lyer Illusions

How the Statistical Structure of the Environment Affects Perception of the Muller-Lyer Illusion Stephen Blessing (sblessing@ut.edu) Martina Svetlik (msvetlik@ut.edu) Department of Psychology, University of Tampa 401 W. Kennedy Blvd., Box Q Tampa, FL 33606 USA through variants of the original stimulus (see Figure 1) in which the corner explanation is not valid, and also through behavioral accounts as well (McGraw & Stanford, 2001). Other explanations include an eye movement account, stating that because the eye moves more in analyzing the figure where the adornments point out than with the other figure, the observer perceives that line as longer (Carr, 1935). However, research has shown that even in the absence of eye movements, the illusion still exists (Bolles, 1969). Another account is referred to as assimilation theory, as it states that the illusion exists because the observer finds it hard to separate the single horizontal line from the rest of the figure (Pressey, 1971). However, this account has also shown not to be upheld by behavioral data (Bross, Blair, Longtin, 1978). More recently, Bulatov, Bertulis, and MicKiene analyzed the Muller-Lyer according to its spatial properties, and developed a neurophysiogical model. They obtained similar patterns between their model and behavioral data. The research presented here takes the probabilistic explanation of the Muller-Lyer illusion by Howe and Purves (2005a) and attempts to match it to behavioral data. In contrast to the accounts mentioned above, this one bases itself on the statistical nature of the environment. In that regards, this account is consonant with theories that explain human behavior and cognition as adapting to the environment (e.g., Anderson, 1993; Gibson, 1966). Howe and Purves analyzed natural scenes for the standard version of the Muller-Lyer illusion and four of its variants. These natural scenes were gathered in a variety of settings using a laser device that converts 3-D space into numerical data representing the distance and direction of all points on visible surfaces that can then be related to retinal images (see Howe & Purves, 2005b, for a more detailed explanation). Using a selection of such scenes, they generated probability distributions of various line lengths and adornments. These distributions indicate that given a target adornment found in the scene, the probability of Abstract Past researchers have attempted to explain the Muller-Lyer illusion through such means as eye movements (Carr, 1935) and isolating parts from the whole (Pressey, 1971). A recent explanation is that observers are sensitive to statistical regularities within the environment (Howe & Purves, 2005a). Certain configurations of lines appear more often than others within the environment, and this accounts for the illusion. Experiment 1 investigated whether these observed environmental statistical regularities are matched by behavioral data. In Experiment 2 the probability of shorter or longer lines within the illusion was manipulated in order to influence people’s perception of the illusion. The evidence from both experiments provides data that are consistent with the hypothesis that perception of the Muller-Lyer Illusion is affected by the statistical nature of the environment. Keywords: perception; geometrical illusions; probability distributions Introduction The Muller-Lyer effect is a classic visual illusion. The standard presentation is shown in Figure 1a. The horizontal line contained within the figure on the bottom is generally perceived as longer than the horizontal line in the upper figure, though both are in fact the same length. Somehow the arrowhead adornments pointing out drive the observer to perceive that figure differently than when the arrowhead adornments are pointing in. Several hypotheses have been posited to explain this observation. Most concern themselves either with properties of the figure itself or properties of the visual system, though more recent attempts have examined the nature of the environment itself. An older explanation by Gregory (1963) suggested that the illusion exists because the observer interprets the figure where the arrowheads point out as a concave corner (that is, the corner is farther away than the walls), whereas the figure with the arrowheads pointing in is interpreted as a convex corner (that is, the corner is closer). However, this account is called into question not only by the illusion persisting (a) (b) (c) (d) Figure 1: Standard Muller-Lyer illusion (a), box variant (b), shaftless variant (c), and dot variant (d).