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A Two-Stage Cascade Model of BOLD Responses in Human Visual Cortex

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Second-order contrast (SOC) model.

(A) Schematic of model. First, the stimulus is filtered with a set of Gabor filters at different positions, orientations, and phases; the outputs of quadrature-phase pairs are squared, summed, and square-rooted (V1 energy). Second, filter outputs are divided by local population activity (Divisive normalization). Third, filter outputs are summed across orientation, producing a map of local contrast-energy. Contrast-energy is then weighted and summed across space using a 2D Gaussian (Spatial summation). The summation is not linear; rather, the summation is performed using a variance-like nonlinearity in which average contrast-energy is subtracted before squaring and summing across space (Second-order contrast). Finally, the output of the summation is subjected to a compressive power-law function (Compressive nonlinearity), yielding the predicted response. (B) Computation of second-order contrast. Second-order contrast is computed as the variance of the contrast-energy distribution within the 2D Gaussian. In this example, there is high variation in contrast-energy and thus a high amount of second-order contrast. (C) Simplified versions of the model. To motivate the SOC model, we consider several simplified versions of the model. Each version incorporates a model component not present in the previous version.

Figure 2

doi: https://doi.org/10.1371/journal.pcbi.1003079.g002