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Jonathan Winawer, Zeming Fang, Wei Ji Ma; Normalization by the variance across orientation channels in human V1–V3. Journal of Vision 2019;19(10):43b. doi: https://doi.org/10.1167/19.10.43b.
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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; as a result, 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 (which we call ‘sparse gratings’), and curved, band-passed contours (‘sparse patterns’). The second class of stimuli elicits fMRI responses that are about twice as large as the first class, yet traditional energy models, including normalized energy models, predict responses that are about the same. We propose a novel computational model, in which responses are normalized not by the sum of the contrast energy, but by the variance in contrast energy, computed across orientation channels. We first show that this model accounts for the responses to these two classes of stimuli. We then show that the model successfully generalizes to a large number of other band-pass textures, both in V1 and in extrastriate cortex (V2 and V3). We speculate that the variability in the output of orientation channels reflects the pooled activity of neurons that analyze the outputs of V1, and that this signal normalizes the V1 responses via feedback.
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