Classification error analysis in stereo vision

• Depth perception model is presented in which mutual information in stereo vision can be analyzed using the theory of large deviations.
• For Gaussian neurons and a discrete input variable our model predicts that the mutual information saturates exponentially with NN.
• For large NN, the mutual information saturates exponentially with a rate determined by the Chernoff distance.

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 (NN) 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 NN. We found that MI saturates exponentially with NN at a rate which decays as 1/N1/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.