Figure 1.

Divisive normalization in the GSM model and attention. (a) Cartoon of image statistics in the GSM model. The center and surround are either statistically dependent and share a common mixer variable (green for homogenous regions of the scene, such as within the zebra) or are independent each with their own mixer variable (blue for nonhomogenous regions, such as across the zebra border). Filter activations are given by x_c (for center) and x_s (for surround). The cartoon shows two filters, but the model generalizes for more filters. (b) The canonical divisive normalization version of the GSM model assumes that center and surround filter activations are always dependent, and thus the center filter activation is always divided by the surround activation. The cartoon illustrates example experimental stimuli. Attention is assumed to modulate the observed filter activations in both center and surround locations multiplicatively (only surround attention shown by the red circle). Attention weights are given by a_c (for center) and a_s (for surround). The cortical model estimates the mean firing rate corresponding to the center location via divisive normalization (formally, this is done by estimating the Gaussian component in the GSM model; see main text). This model is similar to Reynolds and Heeger (2009) but includes a tuned surround. (c) The flexible pool divisive normalization model determines the degree to which center and surround activations are deemed dependent or independent. For the dependent case, the surround is in the normalization pool of the center; for the independent case, the surround is not in the normalization pool of the center.