Figure 3 Analytical solution for the spatial integration: the ROG model. To model the integration over a grating limited to a disk, we may consider that the density (or weight) of neurons pooling responses for the OFR is a centered Gaussian with a width of $\omega$ degrees of visual space. However this class of models can only generate monotonously increasing response functions which are incompatible with the suppression observed in the response after a specific contrast (the so-called \emph{super saturation}). One may therefore add another integration term which accounts for a surround inhibition, pooling information toward the null velocity on a similar Gaussian distribution but with a larger size $\omega_i$. This framework gives a rationale for the Ratio-Of-Gaussian (ROG) model (Sceniak, 99; Cavanaugh,02) and explicitly states the underlying choice for the fitting formula. We plot the amplitude of the oculomotor response in the macaque to a central disk grating (dots) with fits to this model (continuous lines) and the original ROG (dashed lines), showing an improvement of the order of 2.5 in the $\chi^2$ score.

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