Visual information flow in Wilson-Cowan networks.

In this paper, we study the communication efficiency of a psychophysically tuned cascade of Wilson-Cowan and divisive normalization layers that simulate the retina-V1 pathway. This is the first analysis of Wilson-Cowan networks in terms of multivariate total correlation. The parameters of the cortical model have been derived through the relation between the steady state of the Wilson-Cowan model and the divisive normalization model. The communication efficiency has been analyzed in two ways: First, we provide an analytical expression for the reduction of the total correlation among the responses of a V1-like population after the application of the Wilson-Cowan interaction. Second, we empirically study the efficiency with visual stimuli and statistical tools that were not available before 1) we use a recent, radiometrically calibrated, set of natural scenes, and 2) we use a recent technique to estimate the multivariate total correlation in bits from sets of visual responses, which only involves univariate operations, thus giving better estimates of the redundancy. The theoretical and the empirical results show that, although this cascade of layers was not optimized for statistical independence in any way, the redundancy between the responses gets substantially reduced along the neural pathway. Specifically, we show that 1) the efficiency of a Wilson-Cowan network is similar to its equivalent divisive normalization model; 2) while initial layers (Von Kries adaptation and Weber-like brightness) contribute to univariate equalization, and the bigger contributions to the reduction in total correlation come from the computation of nonlinear local contrast and the application of local oriented filters; and 3) psychophysically tuned models are more efficient (reduce more total correlation) in the more populated regions of the luminance-contrast plane. These results are an alternative confirmation of the efficient coding hypothesis for the Wilson-Cowan systems, and, from an applied perspective, they suggest that neural field models could be an option in image coding to perform image compression.NEW & NOTEWORTHY The Wilson-Cowan interaction is analyzed in total correlation terms for the first time. Theoretical and empirical results show that this psychophysically tuned interaction achieves the biggest efficiency in the most frequent region of the image space. This is an original confirmation of the efficient coding hypothesis and suggests that neural field models can be an alternative to divisive normalization in image compression.

Visual illusions via neural dynamics: Wilson-Cowan-type models and the efficient representation principle.

We reproduce suprathreshold perception phenomena, specifically visual illusions, by Wilson-Cowan (WC)-type models of neuronal dynamics. Our findings show that the ability to replicate the illusions considered is related to how well the neural activity equations comply with the efficient representation principle. Our first contribution consists in showing that the WC equations can reproduce a number of brightness and orientation-dependent illusions. Then we formally prove that there cannot be an energy functional that the WC dynamics are minimizing. This leads us to consider an alternative, variational modeling, which has been previously employed for local histogram equalization (LHE) tasks. To adapt our model to the architecture of V1, we perform an extension that has an explicit dependence on local image orientation. Finally, we report several numerical experiments showing that LHE provides a better reproduction of visual illusions than the original WC formulation, and that its cortical extension is capable also to reproduce complex orientation-dependent illusions.NEW & NOTEWORTHY We show that the Wilson-Cowan equations can reproduce a number of brightness and orientation-dependent illusions. Then we formally prove that there cannot be an energy functional that the Wilson-Cowan equations are minimizing, making them suboptimal with respect to the efficient representation principle. We thus propose a slight modification that is consistent with such principle and show that this provides a better reproduction of visual illusions than the original Wilson-Cowan formulation. We also consider the cortical extension of both models to deal with more complex orientation-dependent illusions.