A Gauge Field Model of Modal Completion

TL;DR

This paper introduces a gauge field Lagrangian model that integrates retinex equations with neurogeometrical frameworks to explain and simulate the perceptual phenomenon of modal completion, such as the Kanizsa triangle.

Contribution

It presents a novel gauge field Lagrangian approach that couples retinex and neurogeometrical models, providing a new mathematical framework for understanding modal completion.

Findings

Derived Euler-Lagrange equations for the model

Numerically solved the coupled equations

Proposed neurophysiological implementation of the model

Abstract

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.