Perceptual Coherence : Hearing and Seeing

134 Perceptual Coherence
cell as portrayed in figure 3.10 and the corresponding basis function represents
the input that maximally stimulates that filter. Passing an image
through any filter yields the strength of the corresponding basis function.
Given that primary cells have spatial-temporal receptive fields (see figures
2.18 and 2.19), Hateren and Ruderman (1998) utilized sequences of
natural images to more closely simulate normal vision. They performed independent
component analyses on sequences of 12 images (roughly 0.5 s
total) taken from television shows. The basis functions resembled bars or
edges that moved as a unit perpendicular to their orientation. The majority
respond to edges moving in one direction only, exactly what would occur
with nonseparable spatial-temporal receptive fields (also found by Olshausen,
2002). Generally speaking, there is a negative correlation between
spatial and temporal tuning; filters centered at higher spatial frequencies
are more likely to be tuned to lower temporal frequencies and vice versa.
Hateren and Ruderman (1998) suggested that the space-time properties
of the filters explain the sparse response distribution. The visual world consists
of rigid homogeneous objects moving at different speeds that occlude
one another. A localized space-time filter would typically measure small
brightness differences within a single homogeneous object and therefore
would have a high probability of not responding at all (i.e., peaky at zero).
Such a space-time filter would respond strongly to the brightness contrasts
found at edges that move into or out of the receptive field, and those responses
make up the long, low probability but high firing rate tails of the
response distribution.
Up to this point, the analyses have not made use of any properties of the
nervous system. All of the outcomes have been based on an analysis of sets
of images (although physiological considerations act to impose constraints).
A second strategy begins with a hypothetical but naive nervous
system. It is hypothetical because, based on current knowledge, you build
in a plausible set of interconnections and cortical units, a model of how the
interconnections combine, a model of how the outputs of the cortical cells
are integrated, a model of learning, a measure of error to drive the learning
procedure, and so on. It is naive because at the beginning of the simulation
all of the interconnections and units have equal strength (although the procedural
“software” is in place). Then you present a series of images and
measure the difference between the original image and the reproduction of
the image by the hypothetical model. 13 On the basis of the learning and error
models, the strengths of the connections and units are changed across
the set of images to yield the closest matches. The resulting structure of the
interconnections and units is then thought to be a model for how the actual
13. The term reproduction is used in a least-squares error sense. The visual system obviously
does not create a replica of the image.