Abstract
An influential account of neuronal responses in primary visual cortex is the normalized energy model. This model is often implemented as a two-stage computation. The first stage is the extraction of contrast energy, whereby a complex cell computes the squared and summed outputs of a pair of linear filters in quadrature phase. The second stage is normalization, in which a local population of complex cells mutually inhibit one another. Because the population includes cells tuned to a range of orientations and spatial frequencies, the result is that the responses are effectively normalized by the local stimulus contrast. Here, using evidence from human functional MRI, we show that the classical model fails to account for the relative responses to two classes of stimuli: straight, parallel, band-passed contours (gratings), and curved, band-passed contours (snakes). The snakes elicit fMRI responses that are about twice as large as the gratings, yet traditional energy models, including normalized energy models, predict responses that are about the same. Here, we propose a computational model, in which responses are normalized not by the sum of the contrast energy, but by the orientation anisotropy, computed as the variance in contrast energy across orientation channels. We first show that this model accounts for differential responses to these two classes of stimuli. We then show that the model successfully generalizes to other band-pass textures, both in V1 and in extrastriate cortex (V2 and V3). We speculate that high anisotropy in the orientation responses leads to larger outputs in downstream areas, which in turn normalizes responses in these later visual areas, as well as in V1 via feedback.
Competing Interest Statement
The authors have declared no competing interest.
Footnotes
Revise figure 8, add error bar