Perceptual Coherence : Hearing and Seeing

Transformation of Sensory Information Into Perceptual Information 47
to lines connecting the receptive field maximums. The receptive field generated
in figure 2.7 is separable, as are cells A and B in figure 2.8. In contrast,
cells C and D, in particular, are not separable because their on-off regions
shift across the receptive field.
We easily can see how different black-and-white gratings affect the firing
rate. Suppose the on-off regions are assumed to be oriented vertically,
as shown in figure 2.9. The on-region is shown in white and the off-region
is shown in black. The firing rate will be highest when the lighter and
darker bars of the grating line up with the on and off receptive fields as in
B1. The firing rate will not change from baseline if the grating is shifted
one-half bar right or left (B2), or if the grating is rotated so that both the
light and dark stripes overlap the on-off regions (B3 and B4), or if the frequency
of the bars (i.e., width) increases as in (A) or decreases as in (C), so
that again the light/dark stripes of the grating overlap the on-off regions.
These cells will respond identically if the grating moves in either direction.
This is the same analysis used for the circular on-off ganglion cells in the
retina. What is different is that the firing rate of cells in V1 is determined by
the orientation of the grating as well as by the frequency of the grating,
while the firing rate of the retinal cells is determined by frequency only. (A
second difference is that cortical cells have very low spontaneous rates so
that we can detect inhibition only indirectly.)
Hubel and Weisel (1962) presented the working hypothesis that simple
cells with a specific orientation in V1 could be created by summing the outputs
of on-off and off-on cells in the lateral geniculate that lie along that
same angular direction (i.e., linear-orientation receptive fields). This has
been termed a feed-forward model by Ferster and Miller (2000). As shown
in figure 2.10, it is possible to construct several different horizontal line or
edge detectors with different spatial orientation and frequency resolutions
by summing varying numbers of on-off cells and off-on cells (see Derrington
& Webb, 2004). The same cells also can be combined vertically to produce
simple cortical cells with a different orientation. What this means is
that every on-off and off-on cell contributes its output to several cortical
cells. Ferster and Miller (2000) argued that Hubel and Weisel’s model is to
a large degree correct; the outputs from the lateral geniculate do determine
the orientation specificity. Sharon and Grinvold (2002) suggested that in
addition to the input from the lateral geniculate, recurrent inhibition in V1
acts to accentuate the response to the preferred orientation by suppressing
responses to orthogonal orientations.
The feed-forward model cannot account for all of the properties of the
simple cortical cells. One issue, to which I return in chapter 6, is that the orientation
response is relatively independent of the contrast of the black-andwhite
grating. We need contrast invariance to identify boundaries between
objects at different light levels. But at high contrasts, the on-response would