simple pictures, tough problems

[Alan B. Cobo-Lewis]

Peter J. B. Hancock <pjh at park.bu.edu> argues...
 
> evidence that some complex cells respond {\em before}
> simple cells.  I understand there is some debate about the
> simple/complex dichotomy anyway, but such a result does challenge the
> traditional story of simple cells feeding into complex ones.
 
Steve Lehar <slehar at park.bu.edu> responds...
 
> The fact that a complex cell fires BEFORE a simple cell does not
> preclude the possibility that the signal was provided originally by
> the simple cells.
 
The nice hierarchical classification of simple, complex, and hypercomplex
cells has been assaulted for two reasons: the hypercomplex category is
questionable, and the hierarchy is questionable.
 
Hubel and Wiesel (1965) added the hypercomplex classification to describe
cells that otherwise seemed like complex cells, but were also end-stopped.
Since then, end-stopping has been reported in both simple and complex cells
(Schiller et al., 1976; Gilbert, 1977; Kato et al., 1978).  The conclusion
that end-stopped cells represent a distinct population, rather than there
being a continuous distribution of amount of end-stopping has been
challenged (Schiller et al., 1976), though Kato et al. (1978) report
justification for the use of the discrete classifications "hypercomplex
(simple family)" and "hypercomplex (complex family)".  Whatever the outcome
of that argument, the singular discrete classification "hypercomplex" is
typically abandoned today.
 
Hubel and Wiesel (1962, 1965) proposed that one level's input consists of
purely excitatory connections from the immediately inferior level (simple
-(+)-> complex -(+)-> hypercomplex).  This arrangement cannot account for
certain features of the cells' receptive fields, but to what extent their
proposal for the wiring must be modified is unclear (Rose, 1979).
 
There is evidence that the processing by simple and complex cells take
place at least partially in parallel.  For one thing, input to the striate
cortex feeds into complex cells as well as simple cells.  Direct
monosynaptic input from the lateral geniculate nucleus to complex cells has
been reported (Hoffman & Stone, 1971; Stone, 1972; Bullier & Henry, 1979a,
b, c; Henry et al., 1979).  For another thing, output from the striate
cortex must include projections from simple as well as complex cells.
After all, we certainly have absolute phase specificity in our visual
perception, though complex cells lack such specificity.
 
Steve Lehar <slehar at park.bu.edu> continues...
 
> current implementations of the BCS and MRBCS are of necessity
> performed iteratively on sequential binary machines.  But the visual
> architecture that they presume to emulate is a parallel analog
> resonant system, like a violn string (but of course much more
> complex) so that it does not take any number of "cycles" as such for a
> resonance to set in.
 
Even a parallel system evolves through time.  We can treat the vibration of
a violin string as proceding in discrete time if our sampling rate is high
enough (for bandlimited behavior).  Each moment of this discrete time
constitutes an iteration.  To the extent that the time constant of a
biological neural network's behavior is finite, we _do_ have to worry about
how many iterations (how much time) it takes for the system to arrive at a
solution.
 
 
 
 
 
 
                                   References
 
Bullier, J., & Henry, G. H. (1979a). Ordinal position of neurons in cat
     striate cortex. JOURNAL OF NEUROPHYSIOLOGY, 42, 1251-1263.
 
Bullier, J., & Henry, G. H. (1979b). Neural path taken by afferent streams
     in striate cortex of the cat. JOURNAL OF NEUROPHYSIOLOGY, 42,
     1264-1270.
 
Bullier, J., & Henry, G. H. (1979c). Laminar distribution of first-order
     neurons and afferent terminals in cat striate cortex. JOURNAL OF
     NEUROPHYSIOLOGY, 42, 1271-1281.
 
Gilbert, C. D. (1977). Laminar differences in receptive field properties of
     cells in cat primary visual cortex. JOURNAL OF PHYSIOLOGY, 268,
     391-421.
 
Henry, G. H., Harvey, A. R., & Lund, J. S. (1979). The afferent connections
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Hoffman, K.-P., & Stone, J. (1971). Conduction velocity of afferents to cat
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Hubel, D. H., & Wiesel, T. N. (1962). Receptive fields, binocular
     interaction and functional architecture in the cat's visual cortex.
     JOURNAL OF PHYSIOLOGY, 160, 106-154.
 
Hubel, D. H., & Wiesel, T. N. (1965). Receptive fields and functional
     architecture in two nonstriate visual areas (18 and 19) of the cat.
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Kato, H., Bishop, P. O., & Orban, G. A. (1978). Hypercomplex and
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Rose, D. (1979). Mechanisms underlying the receptive field properties of
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Schiller, P. H., Finlay, B. L., & Volman, S. F. (1976). Quantitative
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Stone, J. (1972). Morphology and physiology of the geniculocortical synapse
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