The Müller-Lyer illusion explained by the statistics of image–source relationships

Abstract

The Mü ller-Lyer effect, the apparent difference in the length of a line as the result of its adornment with arrowheads or arrow tails, is the best known and most controversial of the classical geometrical illusions. By sampling a range-image database of natural scenes, we show that the perceptual effects elicited by the Mü llerLyer stimulus and its major variants are correctly predicted by the probability distributions of the possible physical sources underlying the relevant retinal images. These results support the conclusion that the Mü ller-Lyer illusion is a manifestation of the probabilistic strategy of visual processing that has evolved to contend with the uncertain provenance of retinal stimuli.geometrical illusions ͉ natural scene statistics ͉ vision T he standard Müller-Lyer stimulus (Fig. 1A) has been the subject of hundreds of studies since its introduction in the late 19th century (1). The perceptual effect is that two identical straight lines appear different in length when they are terminated, respectively, with ''arrowheads'' that extend inward or ''arrow tails'' that extend outward with respect to the ''shaft.'' Although there is considerable variation in the reported magnitude of the effect (presumably due to the different experimental conditions in various studies), the line terminated by the arrowheads always appears shorter than same line terminated by arrow tails (2-8).Rationalizing this illusion has been made especially difficult by persistence of the effect when the identical lines are terminated with a variety of other adornments (9), a fact that undermines intuitive explanations based on what arrowheads and tails might signify. In Fig. 1B, for instance, the same perceptual discrepancy is generated when identical lines are terminated by outward and inward squares. A further obstacle for any simple explanation of the Müller-Lyer effect is that neither the shaft (Fig. 1C) nor continuous lines (Fig. 1D) is needed to elicit a misperception of the relevant spatial interval. Although the effects produced by these several variants have not been quantitatively compared, there is a general agreement that the shaft or the corresponding interval in the ''outward'' figure always appears longer than its counterpart in the ''inward'' figure. As a result, there has been much controversy about the genesis of the Müller-Lyer effect (6,(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20), which still has no generally accepted explanation (21,22).Here we test the hypothesis that the standard Müller-Lyer effect and its variants are a result of the fundamentally probabilistic strategy of visual processing that contends with inverse optics problem. Any geometrical stimulus (or indeed any visual stimulus) can have been generated by many different real-world sources (23-27), presenting a quandary to observers whose survival depends on appropriate visually guided behavior. A plausible solution would be to generate visual percepts predicated on the probability distributions of the physical sources of retinal images. In t...

A new illusion of height and width: taller people are perceived as thinner

“…Indeed, one of the more wellknown explanations of a number of size illusions, including the Müller-Lyer (arrowhead) illusion and the Ponzo illusion, was put forth by Richard Gregory (Gregory, 1963). He argued that many geometric illusions stem from an erroneous application of size constancy on the basis of depth cues (although see Howe & Purves, 2005, for an alternative explanation). Our height/width illusion may, like the Shepard (described above) and the Müller-Lyer (arrowhead) illusions, stem from the visual system's compensating for a perceived difference in depth.…”

Why do animals differ in their susceptibility to geometrical illusions?

“…Size-classification task Reversed susceptibility Sovrano, Albertazzi, and Rosa Salva (2015) 8 Xenotoca eiseni (redtail splitfin fish) Two-choice discrimination task Yes The arrows on the ends of the lines are similar to the corners on the inside and outside of a building or room, such that the two target lines are perceived as being at different distances, and thus different sizes Pressey (1972) Assimilation theory The '> <' arrows at the ends of one line make it appear longer than the line with arrows facing outward '< >' since the overall figure is longer Howe and Purves (2005) Probabilistic theory In natural scenes, '> <' arrows are more likely to indicate longer lines, suggesting that the Müller-Lyer illusion could be due to a probabilistic strategy of visual processing Ginsburg (1984) Selective filtering theory We judge visual information with lower spatial frequencies as being further away, causing the inner line of the '> <' arrow to be perceptually rescaled as longer inward pointing arrows '> <' were attached and shorter when outward pointing arrows '< >' were attached (Table 2). This potentially argues against Gregory's (1963) inappropriate constancy-scaling theory, since few of the species tested are likely to have been exposed to modern architecture.…”

Relative luminance and binocular disparity preferences are correlated in macaque primary visual cortex, matching natural scene statistics

“…Statistical trends in natural scenes often manifest as a perceptual bias in psychophysical studies (6)(7)(8)(9)(10)(11)(12). One perceptual bias that has been observed is that, all other things being equal, humans perceive lighter image regions as being closer.…”