Mathematical model of the simple cells in the visual cortex

A mathematical model for the spatial computations performed by simple cells in the mammalian visual cortex is derived. The construction uses as organizing principles the experimentally observed simple cell linearity and rotational symmetry breaking, together with the constraint that simple cell inputs must effectively be ganglion cell outputs. This leads to a closed form expression for the simple cellkernel in terms of Jacobiϑ-functions. Using aϑ-function identity, it is also shown how Gabor sampling arises as an approximation to this exact kernel for most cells. In addition, the model provides a natural mechanism for introducing the type of nonlinearity observed in some simple cells. The cell's responses to a variety of visual stimuli are calculated using the exact kernel and compared to single cell recordings. In all cases, the model's predictions are in agreement with available experimental data.

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