Mathematical models of depth perception in weakly electric fish
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Weakly electric fish use electrolocation - the detection of electric fields - to sense their environment. The task of electrolocation involves the decoding of the third dimension - depth - from a two-dimensional electric image. In this work we present three advances in the area of depth-perception. First, we develop a model for electrolocation based on a single parameter, namely the width of the electric image. In contrast to previous suggested algorithms, our algorithm would only require a single narrow tuned topographic map to accurately estimate distance. This model is used to study the effects of electromagnetic noise and the presence of stochastic resonance. Second, considering the problem of depth perception from the perspective of information constraints, we ask how much information is necessary for location disambiguation? That is, what is the minimum amount of information that fish would need to localize an object? This inverse problem approach gives us insight into biological electrolocation and provides a guide for future experimental work. Our final contribution is to provide a mathematical foundation for two of the most accepted depth perception models currently in use.