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edge detector neurons.
As one might imagine, there are many different kinds
of edges in the visual world. Edges differ in their orien-
tation, size (i.e., spatial frequency, where low frequency
means large, and high frequency means small), position,
and
polarity
(i.e., going from light-to-dark or dark-to-
light, or dark-light-dark and light-dark-light). The V1
edge detectors exhibit sensitivity (
tuning
) for different
values of all of these different properties. Thus, a given
edge detector will respond maximally to an edge of a
particular orientation, size, position, and polarity, with
diminished responses as these properties diverge from
its optimal tuning. This is an example of the
coarse
coding
of these visual properties. A particularly use-
ful way of summarizing the tuning properties of sim-
ple cells is in terms of a
Gabor
wavelet function, which
is the product of an oriented sine wave (capturing the
orientation, polarity and size properties) and a Gaus-
sian (which restricts the spatial extent of the sine wave).
We will see what these look like in a subsequent explo-
ration.
The different types of edge detectors (together with
the surface coding neurons) are packed into the two-
dimensional sheet of the visual cortex according to a
topographic
organization. This topography is proba-
bly a result of both innate biases in initial connectiv-
ity patterns, and learning influenced by factors such as
the lateral connectivity among neurons within V1. At
the broadest level of organization, all the neurons are
roughly arranged according to the retinal position that
they encode (i.e., a retinotopic organization, like the
LGN). Thus, V1 can be thought of as a two-dimensional
map
organized according to retinal space. This map is
distorted, in that there is a disproportionate number of
neurons encoding positions within the fovea in the cen-
ter of the visual field, because this is the most sensitive,
high-resolution area.
Within the large-scale positional map, neurons are
generally organized topographically according to their
different tuning properties. One account of this orga-
nization (Livingstone & Hubel, 1988) is that the sur-
face coding neurons and the oriented edge detectors are
separated, with the surface neurons grouped together in
a structure called a
blob
, which is surrounded by the
interblob
region where the edge detectors are found.
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Figure 8.3:
A string of on-center receptive fields can repre-
sent an edge of a surface, where the illumination goes from
darker (on the left) to lighter (on the right). The on-center part
of the receptive field is excited more than the off-surround due
to the placement of the edge, resulting in net excitation.
Considering the on- and off-center coding scheme
provided by the retina (and LGN) in isolation, one
might expect that the world consisted of little points of
light surrounded by darkness (like the night sky), or the
opposite (points of darkness surrounded by light). How-
ever, one can combine these basic receptive field ele-
ments together to represent what are arguably the basic
building blocks of visual form,
edges
(figure 8.3). An
edge is simply a roughly linear separation between a
region of relative light and dark. Hubel and Wiesel
(1962) showed that some neurons in V1 called
simple
cells
encode
oriented
edges or bars of light. They pro-
posed something very much like figure 8.3 to explain
how these
edge detectors
could be constructed from
a set of LGN center-surround neurons. Although this
proposal is still controversial, it is consistent with some
recent evidence (Reid & Alonso, 1995).
Edge detectors make sense functionally, because
edges provide a relatively compact way of representing
the form of an object — with the assumption that the re-
gion between edges is relatively homogeneous, the vi-
sual system can capture most of the form information
with just the outline. However, this is not to suggest
that the visual system only encodes the outline — other
types of neurons encode things like the color and tex-
ture of surfaces. These surface coding neurons can also
be more efficient by summarizing the surface properties
over larger regions of space. Again, we will focus pri-
marily on the visual form information encoded by the
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