Binocular summation and efficient coding.

Two eyes are better than one at detecting a pattern, an advantage termed binocular summation. It is widely believed that binocular summation is mediated by neurons that sum the two eyes' inputs. Here we suggest an alternative model based on a model of binocular interactions proposed by Cohn, Leong & Lasley (Vision Research, 1981, 21, 1017-1023) and further motivated by the efficient coding framework proposed by Li & Atick (Network: Computation in Neural Systems, 1994, 5, 157-174). In the model, termed MAX(S+S-), binocular summation is mediated by channels that compute the sum, S+, and difference, S-, of the two eyes' monocular signals. The S+ and S- signals are assumed to be perturbed by independent noise, have independent gains and contribute independently to detection via the MAX rule. To test the model we measured binocular summation for horizontally-oriented Gabor patches at a range of spatial-frequencies and bandwidths, at both contrast detection threshold and for increment thresholds on binocular pedestals at contrasts set to 10x detection threshold. The model's performance was compared to that of two conventional models of binocular summation, one in which the two eyes' signals remain separate at the decision stage, termed MAX(LR), the other in which the two eye's signals are summed by a single channel, termed B+, with both models incorporating interocular inhibition. The MAX(S+S-) model gave as good a performance as the other two models. Together with the evidence for the involvement of separately gain controlled S+ and S- signals underpinning a wide range of binocular behaviors, we conclude that the MAX(S+S-) model can and should be considered as a viable model for binocular summation.