M. Golubitsky and I. Stewart
Symmetric networks with geometric constraints as models of visual illusions
Symmetry.
11(6) (2019) 799; http://dx.doi.org/10.3390/sym11060799
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.