Depth perception in humans is obtained by comparing images generated by the two eyes to each other. Given the highly stochastic nature of neurons in the brain, this comparison requires maximizing the mutual information (MI) between the neuronal responses in the two eyes by distributing the coding information across a large number of neurons. Unfortunately, MI is not an extensive quantity, making it very difficult to predict how the accuracy of depth perception will vary with the number of neurons (N) in each eye. To address this question we present a two-arm, distributed decentralized sensors detection model. We demonstrate how the system can extract depth information from a pair of discrete valued stimuli represented here by a pair of random dot-matrix stereograms. Using the theory of large deviations we calculated the rate at which the global average error probability of our detector; and the MI between the two arms’ output, vary with N. We found that MI saturates exponentially with N at a rate which decays as 1/N. The rate function approached the Chernoff distance between the two probability distributions asymptotically. Our results may have implications in computer stereo vision that uses Hebbian-based algorithms for terrestrial navigation.
