  In this work we have aimed to reproduce supra-threshold perception phenomena,
specifically visual illusions, with Wilson-Cowan-type models of neuronal
dynamics. We have found that it is indeed possible to do so, but that the
ability to replicate visual illusions is related to how well the neural
activity equations comply with the efficient representation principle. Our
first contribution is to show that the Wilson-Cowan equations can reproduce a
number of brightness and orientation-dependent illusions, and that the latter
type of illusions require that the neuronal dynamics equations consider
explicitly the orientation, as expected. Then, we formally prove that there
can't be an energy functional that the Wilson-Cowan equations are minimizing,
but that a slight modification makes them variational and yields a model that
is consistent with the efficient representation principle. Finally, we show
that this new model provides a better reproduction of visual illusions than the
original Wilson-Cowan formulation.
