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Mach bands is the name given to the light and dark zones seen at the onset and offset, respectively, of luminance gradients that lack any photometric basis (Figure 1). Although the physical brightness is constant over the distance from the ambient object, the observer perceives an "undershoot" and "overshoot" in brightness at what is physically a step edge. Thus, at a certain point, the observer perceives a slight decrease in brightness compared to the true physical value. Although Mach and many others have suggested this effect, it is caused by lateral inhibition of the receptors in the eye.
It is at first difficult to imagine what empirical (or historical) facts about human interactions with the sources of luminance gradients could explain this gratuitous addition of light and dark bands to the percepts elicited by these stimuli. A more recent interpretation of Mach bands is that the effect closely parallels the accounts of the simultaneous brightness contrast and Cornsweet effects (Lotto, RB, Williams SM, Purves D 1999 a,b) (see DEMONSTRATIONS #02-05 and #07) . By interacting with the objects that give rise to luminance gradients, observers will have experienced that the underlying source of such stimuli is sometimes differences in the reflectance properties of flat surfaces (as in the Mach stimulus), sometimes penumbras, and sometimes differences in the illumination of curved surfaces (among other less frequent possibilities not considered here).
An important aspect of experience derived from interacting with curved surfaces is that the luminance gradients associated with such surfaces are frequently adorned with photometric highlights and lowlights at the beginning and end of the gradient. Highlights are a consequence of the relatively greater amount of light returned to the observer from curved surfaces that are to some degree specular  (Figure 2); lowlights arise because objects on the surface of the earth are typically illuminated by indirect as well as direct light  (Figure 3) ( see Lotto, RB, Williams SM, Purves D 1999a abd b for a fuller explanation of these phenomena).
Since the source of the luminance gradient in the Mach stimulus in  (Figure 4) (and DEMONSTRATIONS #07)  could be either a curved surface or a penumbra on a flat surface (or the result of the surface reflectances, which are, in fact, the source of the printed stimulus), the percept elicited incorporates hightlights and lowlights in proportion to the frequency of their historical occurrence as accompaniments of luminance gradients. As predicted by this reasoning, proximal stimuli more consistent with a curved surface as the underlying source (which would normally be adorned with highlights and lowlights) elicit a stronger sensation of Mach bands than oppositely biased stimuli, which elicit such sensations weakly or not at all (see Lotto, RB, Williams SM, Purves D 1999b). This modulation is similar to the enhancement or diminishment of simultaneous brightness contrast or edge effects achieved by manipulating the relative probabilities of the possible sources of the stimulus in the examples given earlier.
The empirical explanation of Mach bands is the same, in principle, as the explanations of simultaneous brightness and Cornsweet effects. The common cause is the genesis of visual percepts according to a strategy in which percepts are elicited as reflexes whose network connectivity has been wholly determined by the history of human visual experience. Because the perceptual responses to the several stimulus categories considered here (i.e., the phenomena in DEMONSTRATIONS #01-07) manifest this strategy in superficially different ways, the common basis of these effects is less obvious than it might otherwise be.
Lotto RB, Williams SM, Purves D (1999a) Mach bands as empirically derived associations. Proc Natl Acad Sci USA 96:5245-5250
Lotto RB, Williams SM, Purves D (1999b) An empirical basis for Mach bands. Proc Natl Acad Sci USA 96:5239-5244
Purves D, Lotto RB (2003) Why We See What We Do: An Empirical Theory of Vision Sunderland, MA: Sinauer Associates.
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