A Gauge Field Model of Modal Completion

Perceptual completion of figures is a basic process revealing the deep architecture of low level vision. In this paper a complete gauge field Lagrangian is proposed allowing to couple the retinex equation with neurogeometrical models and to solve the problem of modal completion, i.e. the pop up of the Kanizsa triangle. Euler-Lagrange equations are derived by variational calculus and numerically solved. Plausible neurophysiological implementations of the particle and field equations are discussed and a model of the interaction between LGN and visual cortex is proposed.