Humans can identify and discriminate between different contrasts of sinusoidal gratings over about a 300-fold range of contrast. Electrophysiological studies in macaque and cat show single V1 neurons to have more limited dynamic ranges, responding differentially to only about a 10-fold contrast range. However, different neurons have different contrast thresholds and cover different, overlapping parts of the full discriminable range.

It is not known how neuronal responses are pooled to identify contrast, but it has been suggested that observers make maximum likelihood estimates, either taking account of the different firing rate of each neuron (Geisler & Albrecht, 1997) or simply summing the neural activity indiscriminately (Heeger et al. 2000).

We implemented two computational models of neural pooling, evaluating the contrast identification performance of each. Both models simulated the responses of 18 neurons, taken at uniform intervals of threshold contrast from a set of 138 cat V1 neurons (D.J. Tolhurst, unpublished observation). The neurons’ contrast-response functions were modelled with steep sigmoidal curves (Albrecht & Hamilton, 1982), and the variability of their responses to a stimulus was modelled with a variance of about twice the mean firing rate (Tolhurst et al. 1983).

We simulated 10 000 trials of each of many contrasts. On each trial, firing rates of the 18 neurons were stochastically chosen, and used to decide on the contrast presented. The decision process was a maximum likelihood estimate of contrast, using Bayes’ Theorem, based on knowledge of the distribution of either the individual (model 1) or summed (model 2) neuronal responses (r) to contrast (c), and of the prior probabilities of the range of possible responses and presented contrasts, i.e.

P (c | r) = P (r | c) P (c)/P (r),

where P is probability. The contrast chosen was that for which P (c | r) was greatest on that trial.

The performance measure was the inverse of the mean squared difference between the logarithms of estimated and presented contrasts, averaged over the 10 000 trials. The contrast identified most accurately was about 0.07 for both models, close to the contrast most often found in natural scenes (Tolhurst, 1996); accuracy fell steeply on either side of the peak. Model 1 (which accounted for the different behaviour of each neuron) was about 1.5 times more accurate for contrast identification.This work was supported by MRC and DERA.

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