Perceptual Coherence : Hearing and Seeing

256 Perceptual Coherence
multiplicative process is shown in figure 6.6C. The basic notion underlying
this process is that both the background and test flash illuminations are effectively
reduced by multiplying both illuminations by a fraction m(a) between
0 and 1, assumed to be determined by the overall illumination. The
background becomes m(a) × I b, the test flash becomes m(a) × I f, and the
(background + flash) becomes m(a)(I f + I b). This type of mechanism has
been called von Kries adaptation, cellular adaptation, pigment depletion, or
the dark glasses hypothesis, and is discussed further in chapter 7. Since the
multiplicative adaptation acts on both the background and test flash, it is as
if there was a neutral density filter in front of the stimulus, much like dark
glasses (or like closing down the pupil). The decrease in the background illumination
acts to reduce the threshold because the background intensity is
reduced, but at the same time the decrease in the test flash acts to increase
the threshold because the test flash intensity also is reduced. The multiplicative
adaptation recovers some of the response range, as shown by the leftward
shift of the response curve; for a fraction of 0.1 the shift is roughly 1
log unit. Moreover, the dynamic range of the response is increased: there is
roughly a 1 log unit increase in the range of firing rates.
The operation of the subtractive mechanism is illustrated in figure 6.6D.
The subtractive process is assumed to decrease the intensity of long-duration
lights by removing some of the signal. The subtractive process does not affect
lights presented for brief periods, so it will not affect the test flash. The
effective intensity of the background is I b − s(I b), where s is the subtractive
constant that is a function of the background intensity; the intensity of the
test flash remains I f. The function in figure 6.6D illustrates the outcomes if
the subtractive process removes 95% of the background light. There is a
great deal of recovery of the response function, and the difference between
the subtractive function and the original dark background function is relatively
constant across all the background illuminations.
If the multiplicative and subtractive processes are combined (as in figure
6.6E), the effective background becomes m(a)[I b − s(I b )] and the effective
test flash becomes m(a)I f. The combination of the two mechanisms removes
the effect of the background illumination at higher intensities where the
response reaches the asymptote at the no-background firing rate, but does
not completely compensate at the lowest intensities.
Kortum and Geisler (1995) suggested that the multiplicative constant
is inversely proportional to the background illumination, particularly at the
higher intensities. Thus the multiplicative processes create the constant
Weber ratio. In contrast, the subtractive constant is fixed (at higher illuminations)
so that the subtractive mechanism only reduces the Weber ratio.
These mechanisms are illustrated in a different way for a flashed stimulus
presented against a fixed background in figure 6.7. The two dashed lines
represent the response rate if there is no gain control. The bottom line