The relationship between luminance (i.e., the photometric intensity of light) and its perception (i.e., sensations of lightness or brightness) has long been a puzzle. In addition to the mystery of why these perceptual qualities do not scale with luminance in any simple way, "illusions" such as simultaneous brightness contrast, Mach bands, Craik-O'Brien-Cornsweet edge effects, and the Chubb-Sperling-Solomon illusion have all generated much interest but no generally accepted explanation. The authors review evidence that the full range of this perceptual phenomenology can be rationalized in terms of an empirical theory of vision. The implication of these observations is that perceptions of lightness and brightness are generated according to the probability distributions of the possible sources of luminance values in stimuli that are inevitably ambiguous.A fundamental problem in vision (and perception generally) was recognized at the beginning of the 18th century by George Berkeley (1709Berkeley ( /1975, who pointed out that the sources underlying visual stimuli are unknowable in any direct sense. The light that falls on the eye from any region of a scene conflates the contributions of reflectance, illumination, and transmittance (as well as a host of subsidiary factors that affect these parameters). As a result, the physical provenance of light reaching the eye-and therefore the significance of the stimulus for visually guided behavior-is profoundly uncertain. This fundamental fact presents a biological quandary. Successful behavior in a complex and potentially hostile environment clearly depends on responding appropriately to the physical sources of visual stimuli rather than to the stimuli as such. If, however, the retinal images generated by light cannot uniquely define the underlying reality the observer must deal with, how then does the visual system produce behavior that is generally successful?The purpose of this review is thus to consider evidence, much of it derived from our own experiments over the last few years, about the way the uncertain relationship between the physical world and the perceptual world is resolved by the nervous system (see Purves & Lotto, 2003). The gist of this body of work is that what one sees at any moment appears to be fully determined by the probability distributions of the possible sources of the stimulus rather than the physical qualities of the stimulus (which are ambiguous) or the properties of the objects and conditions that generated the stimulus (which cannot be known directly). Although this framework has several important precedents (see below), it differs from most mainstream neurobiological thinking in recent decades and suggests other ways of conceptualizing the purposes served by the known physiology of visual system circuitry. The context here for exploring the merits of this conception of vision is sensations of lightness and brightness, which are arguably the most fundamental qualities of human visual experience. Luminance, Brightness, and LightnessLuminance is ...

Many otherwise puzzling aspects of the way we see brightness, colour, orientation and motion can be understood in wholly empirical terms. The evidence reviewed here leads to the conclusion that visual percepts are based on patterns of re£ex neural activity shaped entirely by the past success (or failure) of visually guided behaviour in response to the same or a similar retinal stimulus. As a result, the images we see accord with what the sources of the stimuli have typically turned out to be, rather than with the physical properties of the relevant objects. If vision does indeed depend upon this operational strategy to generate optimally useful perceptions of inevitably ambiguous stimuli, then the underlying neurobiological processes will eventually need to be understood within this conceptual framework.

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...