A long-standing puzzle in vision is the assignment of illusory brightness values to visual territories based on the characteristics of their edges (the Craik-O'Brien-Cornsweet effect). Here we show that the perception of the equiluminant territories flanking the Cornsweet edge varies according to whether these regions are more likely to be similarly illuminated surfaces having the same material properties or unequally illuminated surfaces with different properties. Thus, if the likelihood is increased that these territories are surfaces with similar reflectance properties under the same illuminant, the Craik-O'BrienCornsweet effect is diminished; conversely, if the likelihood is increased that the adjoining territories are differently reflective surfaces receiving different amounts of illumination, the effect is enhanced. These findings indicate that the Craik-O'BrienCornsweet effect is determined by the relative probabilities of the possible sources of the luminance profiles in the stimulus.

Although it has long been apparent that observers tend to overestimate the magnitude of acute angles and underestimate obtuse ones, there is no consensus about why such distortions are seen. Geometrical modeling combined with psychophysical testing of human subjects indicates that these misperceptions are the result of an empirical strategy that resolves the inherent ambiguity of angular stimuli by generating percepts of the past significance of the stimulus rather than the geometry of its retinal projection.T he fact that the subtense of any acute angle is seen as being somewhat larger than the measured angle of the stimulus, whereas the subtense of any obtuse angle is seen as being somewhat smaller, was first reported by Wundt (1) and subsequently by both Hering (2) and Helmholtz (3), all of whom surmised that these distortions might underlie some of the classical geometrical illusions (4). These 19th century investigations were, however, descriptive rather than experimental, and the interpretations, speculative. Despite numerous modern studies (5-15), the phenomenon of angle misperception has never been explained.Here we provide evidence that the systematic misperception of angle subtense is the consequence of a radically empirical strategy of perception in which the angle seen is determined by the relative frequency of the possible sources of angle projections that observers have experienced. The biological rationale for this strategy is a solution to the problem posed by the inevitable ambiguity of angular stimuli. The inability of an angle projected onto a plane to specify uniquely the source is illustrated in Fig. 1. Indeed, because space is divisible without limit, the number of possible real-world sources underlying a given retinal projection is infinite.Because the well being of an observer depends on appropriate interactions with the sources of visual stimuli, the ambiguity of retinal images has long been regarded as a central problem in vision (16). Recent studies of simultaneous brightness contrast (17,18), Mach bands (19,20),, and the perception of color (22) have all suggested that this dilemma is solved by an empirical strategy in which retinal activation triggers associations (percepts) determined by the relative frequencies of the possible sources of the stimulus in past experience. A limitation in validating this concept of vision has been the practical difficulty of quantifying the frequency distribution of the real-world sources underlying the various categories of visual experience. (This problem has also been an obstacle to psychologists who have sought to model perception in terms of Bayes' decision theorem; see ref. 23 for a recent review.) Examining the perception of oriented lines circumvents this obstacle in that the frequency distribution of the possible sources of a given retinal projection-for example, the subtense of the typical source of a given angle projected on the retina-can be computed by geometrical principles, thus providing a more concrete basis for predicting perceptual...

Because the retinal activity generated by a moving object cannot specify which of an infinite number of possible physical displacements underlies the stimulus, its real-world cause is necessarily uncertain. How, then, do observers respond successfully to sequences of images whose provenance is ambiguous? Here we explore the hypothesis that the visual system solves this problem by a probabilistic strategy in which perceived motion is generated entirely according to the relative frequency of occurrence of the physical sources of the stimulus. The merits of this concept were tested by comparing the directions and speeds of moving lines reported by subjects to the values determined by the probability distribution of all the possible physical displacements underlying the stimulus. The velocities reported by observers in a variety of stimulus contexts can be accounted for in this way. P hysical motion is the continuous displacement of an object within a frame of reference; as such, motion is fully described by measurements of translocation. Perceived motion, however, is not so easily defined. Because the real-world displacement of an object is conveyed to an observer only indirectly by a changing pattern of light projected onto the retinal surface, the translocation that uniquely defines motion in physical terms is always ambiguous with respect to the possible causes of the changing retinal image (1-3). This ambiguity presents a fundamental problem in vision: how, in the face of such uncertainty, does the visual system generate definite percepts and visually guided behaviors that usually (but not always) accord with the realworld causes of retinal stimuli?In the present article, we examine the hypothesis that the visual system solves this dilemma by a strategy in which the retinal image generates the probability distributions of the possible sources of the stimulus. MethodsThe stimuli we used consisted of a line translating from left to right in the frontal parallel plane behind an aperture. The line was presented at orientations of 20-60°in 10°increments relative to the horizontal axis (except for the inverted V aperture, in which case the moving line was presented at 10-50°). All stimuli subtended Ϸ4 ϫ 4°and were shown on a 19-inch monitor at a frame rate of 25, 30, or 35 frames per second; the viewing distance was 150 cm. The luminance of stimulus line and aperture boundaries was 119 cd͞m 2 (white), and background 0.7 cd͞m 2 (black). The stimuli used in the control experiments mentioned at the end of Results were the same, except that the aperture boundaries were invisible, and the background was a uniform texture of intermediate luminance (46 cd͞m 2 ).Subjects (the authors and three naïve subjects, all of whom had normal or corrected-to-normal vision) identified the direction and speed of the line by adjusting a dot that was initially moving in a random direction and speed, presented within a separate but otherwise similar aperture (Fig. 1). The observers were instructed to regard the stimuli as they would any oth...

The motion of objects that are both translating and rotating can be decomposed into an infinite number of translational and rotational combinations. How, then, do such stimuli routinely elicit specific percepts and behavioral responses that are usually appropriate? A possible answer is that motion percepts are fully determined by the probability distributions of all the possible correspondences and differences in the stimulus sequence. To test the merits of this conceptual framework, we investigated the perceived motion elicited by a line that is both translating and rotating behind an aperture. When stimuli are presented such that a particular sequence of appearance and disappearance occurs at the aperture boundary, subjects report that the line is rotating only; furthermore, the perceived centers of rotation appear to describe a cycloidal trajectory, even when one aperture shape is replaced by another. These and other perceptual effects elicited by translating and rotating stimuli are all accurately predicted by the probability distribution of the possible sources of the physical movements, supporting the conclusion that motion perception is indeed generated by a wholly probabilistic strategy.