Perceptual Coherence : Hearing and Seeing

246 Perceptual Coherence
For the detection of spatial gratings in dynamic noise, the observer’s
equivalent input noise at most spatiotemporal frequencies mainly reflects
the inability to capture or make use of all the quanta coming from the
image, photon noise. Across a fourfold range of luminances (10,000), just a
small fraction of the corneal quanta (1–10%) are actually encoded and used
perceptually. Only at very low spatiotemporal frequencies, when the image
is essentially constant, does the neural noise become predominant. This
suggests that our simple model should incorporate a filter that reflects the
frequency selectivity of the pathway.
We can put all of this together in a basic model of the human observer
detecting a grating embedded in noise, shown in figure 6.2. Z-L. Lu and
Dosher (1999) termed these sorts of models noisy linear amplifiers (perfect
linear amplification with additive noise). If we track the figure from input
to output, an external noise and the signal (in terms of the contrast of the
image squared, c 2 ) controlled by the experimenter are summed together.
We use c 2 (contrast power or variance) because the variance of the sum of
independent components is simply the sum of the individual components,
and that makes the theoretical development easier. (We could use the variance
to model the contrast necessary for the perception of second-order
movement in chapter 5.) The signal + external noise first passes through a
template (e.g., a spatial frequency filter) that restricts the processing to just
part of the energy reaching the observer. The filtered signal + external noise
Figure 6.2. A model of noisy linear amplifiers (perfect linear amplification with
additive noise). The input signal is squared, multiplied by the input multiplicative
noise fraction (N M ) and then added back to the signal path. In similar fashion, the
additive noise (N A ) is added to the signal path. From “Characterizing Human Perceptual
Inefficiencies With Equivalent Internal Noise,” by Z.-L. Lu and B. A.
Dosher, 1999, Journal of the Optical Society of America, A, 16, 764–778. Copyright
1999 by the Optical Society of America. Reprinted with permission.