Functional geometry of the horizontal connectivity in the primary visual cortex

We present a geometrical model of the functional architecture of the primary visual cortex. In particular we describe the geometric structure of connections found both in neurophysiological and psychophysical experiments, modeling both co-axial and trans-axial excitatory 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.