Mathematics

In collaboration with A. Sarti and J. Petitot, we propose a model of the functional architecture of the primary visual cortex V1 as a principal fiber bundle. The 2-dimensional retinal plane is the base manifold and the secondary variables (which can be orientation or scale) constitute the vertical fibers over each point. In the description of the odd simple cells we consider only the orientation, and the resulting structure is a contact structure. When we consider the even cells we add the scale variable, and the total space is equipped with a symplectic structure, which naturally extends the previous one. Both geometrical structure are implemented by the long range horizontal connections. The model shows what could be the deep structure for both boundary and figure completion and for morphological structures such as the medial axis of a shape.