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Simon B. Laughlin
of neural constraints on coding (e.g. the number of signal levels, neural noise),
information theory predicts the optimum encoder, defined as the set of operations
that transfers the greatest quantity of information from image to neuron. The
shapes of signals and the form of redundancy are measured in terms of the
statistical properties of natural images (probability distributions, correlation
functions, power spectra). Signal-to-noise ratios are derived from calibrations of
photon flux, and by direct recordings from photoreceptors and neurons. This
data on signal and noise is fed into the theory to derive the optimum encoder.
The relevant properties of the neurons are measured and compared with the
optimum.
The compound eye of the blowfly demonstrates the high degree of coding
efficiency achieved in eyes. Each facet of the compound eye defines a single
pixel in the retinal image. A precisely defined group of photoreceptors and
intemeurons is devoted to coding the relative light intensity, the contrast, at each
pixel. This neural module consists of six identical photoreceptors, Rl-6, and two
postsynaptic interneurons, the large monopolar cells (LMCs) Ll and L2 (Fig. 2).
Contrast is coded by the amplitudes of the analogue voltage signals in
photoreceptors and LMCs. The relationship between response amplitude and
contrast (Fig. 2) is matched to the statistical distribution of contrast in natural
scenes (Laughlin 1981) to ensure that all of the LMCs response levels are used
equally often. This matching maximizes the information transmitted.
Both the spatial and the temporal filtering of signals are optimized. Van Hateren
(1992a,b) defined the statistics of natural input signals encountered at one pixel of
a blowfly compound eye, using the power spectrum of natural images, the range
of velocities at which images move, the fly's optics and the rate at which
photoreceptors absorb photons. He then used information theory to predict the
response of the optimum encoder. This is a filter that manipulates the natural
inputs so as to maximize the information coded by an LMC, within the
limitations imposed by the two neural constraints, response range and neural
noise. The correspondence between the responses recorded from LMCs and the
response of the optimum filter is remarkable (Fig. 2). To remain optimal, the
LMC response waveform changes with the background light level. At low light
levels the response is slow and monophasic, to average out photon noise (random
fluctuations that result from the Poisson statistics of photon absorption). At the
highest light levels the optimum response is fast and biphasic, to pick out rapid
changes and reject redundancy in time, just as lateral inhibition removes
redundancy in space. Between these two extremes, the LMC response changes
gradually from one form to the other, maintaining the optimum over an intensity
range of I 0 5 . This virtuoso performance in optim urn tuning is a concerted effort,
brought about by an increase in the speed of photoreceptor response with light
adaptation, and adjustments to the transfer function of the photoreceptor - LMC
synapses (Laughlin 1998). The human visual system behaves in a similar manner,
to optimize information uptake within the constraints of natural image statistics
and neural information capacity (Atick 1992).
Simon B. Laughlin
of neural constraints on coding (e.g. the number of signal levels, neural noise),
information theory predicts the optimum encoder, defined as the set of operations
that transfers the greatest quantity of information from image to neuron. The
shapes of signals and the form of redundancy are measured in terms of the
statistical properties of natural images (probability distributions, correlation
functions, power spectra). Signal-to-noise ratios are derived from calibrations of
photon flux, and by direct recordings from photoreceptors and neurons. This
data on signal and noise is fed into the theory to derive the optimum encoder.
The relevant properties of the neurons are measured and compared with the
optimum.
The compound eye of the blowfly demonstrates the high degree of coding
efficiency achieved in eyes. Each facet of the compound eye defines a single
pixel in the retinal image. A precisely defined group of photoreceptors and
intemeurons is devoted to coding the relative light intensity, the contrast, at each
pixel. This neural module consists of six identical photoreceptors, Rl-6, and two
postsynaptic interneurons, the large monopolar cells (LMCs) Ll and L2 (Fig. 2).
Contrast is coded by the amplitudes of the analogue voltage signals in
photoreceptors and LMCs. The relationship between response amplitude and
contrast (Fig. 2) is matched to the statistical distribution of contrast in natural
scenes (Laughlin 1981) to ensure that all of the LMCs response levels are used
equally often. This matching maximizes the information transmitted.
Both the spatial and the temporal filtering of signals are optimized. Van Hateren
(1992a,b) defined the statistics of natural input signals encountered at one pixel of
a blowfly compound eye, using the power spectrum of natural images, the range
of velocities at which images move, the fly's optics and the rate at which
photoreceptors absorb photons. He then used information theory to predict the
response of the optimum encoder. This is a filter that manipulates the natural
inputs so as to maximize the information coded by an LMC, within the
limitations imposed by the two neural constraints, response range and neural
noise. The correspondence between the responses recorded from LMCs and the
response of the optimum filter is remarkable (Fig. 2). To remain optimal, the
LMC response waveform changes with the background light level. At low light
levels the response is slow and monophasic, to average out photon noise (random
fluctuations that result from the Poisson statistics of photon absorption). At the
highest light levels the optimum response is fast and biphasic, to pick out rapid
changes and reject redundancy in time, just as lateral inhibition removes
redundancy in space. Between these two extremes, the LMC response changes
gradually from one form to the other, maintaining the optimum over an intensity
range of I 0 5 . This virtuoso performance in optim urn tuning is a concerted effort,
brought about by an increase in the speed of photoreceptor response with light
adaptation, and adjustments to the transfer function of the photoreceptor - LMC
synapses (Laughlin 1998). The human visual system behaves in a similar manner,
to optimize information uptake within the constraints of natural image statistics
and neural information capacity (Atick 1992).