The constitution of visual perceptual units in the functional architecture of V1

In this paper we show that the emergence of perceptual units in V1 can be explained in terms of a physical mechanism of simmetry breaking of the mean field neural equation. We consider a mean field neural model which takes into account the functional architecture of the visual cortex modeled as a group of rotations and translations equipped with a degenerate metric. The model generalizes well known results of Bressloff and Cowan which, in absence of input, accounts for hallucination patterns. The main result of our study consists in showing that in presence of a visual input, the stable eigenmodes of the linearized operator represent perceptual units of the visual stimulus. The result is strictly related to dimensionality reduction and clustering problems.