An Empirical Explanation: Mach Bands
As with simultaneous brightness and Cornsweet effects, Mach bands can be rationalized in terms of 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.
A particularly challenging problem for this way of explaining the anomalous relationship between luminance and brightness is Mach bands - the name given to the light and dark zones seen at the onset and offset, respectively, of luminance gradients that lack any photometric basis for this effect (Figure 1
; also see Demonstration
). 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.
Figure 1 / Mach bands. A) Diagram of the painted disk used by Mach to elicit this effect. When the disk is spun, a luminance gradient is established between the uniformly lighter center of the disk and the uniformly darker region at its periphery. B) Blowup of a portion of the spinning stimulus in (A), indicating the nature and position of Mach bands (the curvature has been removed for simplicity of presentation). As can be seen in response to viewing this stimulus, a band of maximum lightness is apparent at position (2), and a band of maximum darkness at position (3), neither of which are present in the photometric measurements shown in (C). C) Because the portion of the black sector between points (2) and (3) in (A) is a segment of an Archimedean spiral, the luminance gradient generated between the corresponding points on the spinning disk is linear, as indicated by photometric measurement along the line in (B). D) A similar graph of the relative lightness/brightness seen by observers, indicating the illusory lightness maximum just before the initiation of the linear gradient (2), and the illusory minimum just after its termination (3). (After Lotto et al., 1999a)
Nevertheless, there is an entirely empirical explanation of Mach bands (Lotto et al., 1999a,b). By interacting with the objects that give rise to luminance gradients (e.g. curved surfaces, changing reflectance values of surfaces and the penumbral gradients generated by cast shadows), perceptual responses will eventually correspond to the frequency of occurrence of luminance patterns, as responding in this way accords the ability to distinguish the same object or surface in different illumination (e.g. cast shadows) and different objects or surfaces illuminated similarly (e.g. changing reflectance values of surfaces).
This empirical explanation of Mach bands is the same, in principle, as for other edge effects. For behavioral success, human perception and behavior will have to be molded by the frequencies of luminance gradients arising from the graded illumination of curves surfaces. 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 (for instance, see Demonstration
for another edge effect ) manifest this strategy in superficially different ways, the common basis of these effects is less obvious than it might otherwise be.
Purves D, Lotto B (2011) Why We See What We Do Redux: A Wholly Empirical Theory of Vision. Sunderland, MA: Sinauer Associates.
Lotto RB, Williams SM, Purves D (1999b) An empirical basis for Mach bands. Proc Natl Acad Sci USA 96:5239-5244.
Lotto RB, Williams SM, Purves D (1999a) Mach bands as empirically derived associations. Proc Natl Acad Sci USA 96:5245-5250.