Symmetric Networks with Geometric Constraints as Models of Visual Illusions

Abstract

Multistable illusions occur when the visual system interprets the same image in two different ways. We model illusions using dynamic systems based on Wilson networks, which detect combinations of levels of attributes of the image. In most examples presented here, the network has symmetry, which is vital to the analysis of the dynamics. We assume that the visual system has previously learned that certain combinations are geometrically consistent or inconsistent, and model this knowledge by adding suitable excitatory and inhibitory connections between attribute levels. We first discuss 4-node networks for the Necker cube and the rabbit/duck illusion. The main results analyze a more elaborate model for the Necker cube, a 16-node Wilson network whose nodes represent alternative orientations of specific segments of the image. Symmetric Hopf bifurcation is used to show that a small list of natural local geometric consistency conditions leads to alternation between two global percepts: cubes in two different orientations. The model also predicts brief transitional states in which the percept involves impossible rectangles analogous to the Penrose triangle. A tristable illusion generalizing the Necker cube is modelled in a similar manner.