There is increasing evidence that the brain relies on a set of canonical neural computations, repeating them across brain regions and modalities to apply similar operations to different problems. A promising candidate for such a computation is normalization, in which the responses of neurons are divided by a common factor that typically includes the summed activity of a pool of neurons. Normalization was developed to explain responses in the primary visual cortex and is now thought to operate throughout the visual system, and in many other sensory modalities and brain regions. Normalization may underlie operations such as the representation of odours, the modulatory effects of visual attention, the encoding of value and the integration of multisensory information. Its presence in such a diversity of neural systems in multiple species, from invertebrates to mammals, suggests that it serves as a canonical neural computation.

The linear transform model of functional magnetic resonance imaging (fMRI) hypothesizes that fMRI responses are proportional to local average neural activity averaged over a period of time. This work reports results from three empirical tests that support this hypothesis. First, fMRI responses in human primary visual cortex (V1) depend separably on stimulus timing and stimulus contrast. Second, responses to long-duration stimuli can be predicted from responses to shorter duration stimuli. Third, the noise in the fMRI data is independent of stimulus contrast and temporal period. Although these tests can not prove the correctness of the linear transform model, they might have been used to reject the model. Because the linear transform model is consistent with our data, we proceeded to estimate the temporal fMRI impulse-response function and the underlying (presumably neural) contrast-response function of human V1. Functional magnetic resonance imaging (fMRI) measures changes in blood oxygenation and blood volume that result from neural activity (Ogawa et al., 1990;Belliveau et al., 1992) (for review, see Moseley and Glover, 1995). Deoxygenated hemoglobin acts as an endogenous paramagnetic agent, so a reduction in the concentration of deoxygenated hemoglobin increases the T2*-weighted magnetic resonance signal.A typical fMRI experiment measures the correlation between the fMRI response and a stimulus. From this, scientists hope to infer something about neural activity. Often it is assumed that there is a simple and direct relationship between neural activity and fMRI response, but the nature of this relationship remains unclear.The goal of the research reported in this article is to understand how the fMRI response relates to neural activity. The vascular source of the fMRI signal places important limits on the technique. Because the hemodynamic response is sluggish, perhaps the fMRI response is proportional to the local average neural activity, averaged over a small region of the brain and averaged over a period of time. We will refer to this as the "linear transform model" of fMRI response. The linear transform model, specialized for a visual area of the brain, is depicted in Figure 1. According to this model, neural activity is a nonlinear function of the contrast of a visual stimulus, but fMRI response is a linear transform (averaged over time) of the neural activity in V1. Noise might be introduced at each stage of the process, but the effects of these individual noises can be summarized by a single noise source that is added to the output.To date, this linear transform model of fMRI response has not been tested, despite the fact that some studies rely explicitly on the linear model for their data analysis (Friston et al., 1994;Lange and Zeger, 1996). The sequence of events from neural response to fMRI response is complicated and only partially understood. It is unlikely that the complex interactions among neurons, hemodynamics, and the MR scanner would result in a precisely linear transform. However, the line...

Simple cells in the striate cortex have been depicted as half-wave-rectified linear operators. Complex cells have been depicted as energy mechanisms, constructed from the squared sum of the outputs of quadrature pairs of linear operators. However, the linear/energy model falls short of a complete explanation of striate cell responses. In this paper, a modified version of the linear/energy model is presented in which striate cells mutually inhibit one another, effectively normalizing their responses with respect to stimulus contrast. This paper reviews experimental measurements of striate cell responses, and shows that the new model explains a significantly larger body of physiological data.

Attention has been found to have a wide variety of effects on the responses of neurons in visual cortex. We describe a model of attention that exhibits each of these different forms of attentional modulation, depending on the stimulus conditions and the spread (or selectivity) of the attention field in the model. The model helps reconcile proposals that have been taken to represent alternative theories of attention. We argue that the variety and complexity of the results reported in the literature emerge from the variety of empirical protocols that were used, such that the results observed in any one experiment depended on the stimulus conditions and the subject’s attentional strategy, a notion that we define precisely in terms of the attention field in the model, but that has not typically been completely under experimental control.

Simple cells in the primary visual cortex often appear to compute a weighted sum of the light intensity distribution of the visual stimuli that fall on their receptive fields. A linear model of these cells has the advantage of simplicity and captures a number of basic aspects of cell function. It, however, fails to account for important response nonlinearities, such as the decrease in response gain and latency observed at high contrasts and the effects of masking by stimuli that fail to elicit responses when presented alone. To account for these nonlinearities we have proposed a normalization model, which extends the linear model to include mutual shunting inhibition among a large number of cortical cells. Shunting inhibition is divisive, and its effect in the model is to normalize the linear responses by a measure of stimulus energy. To test this model we performed extracellular recordings of simple cells in the primary visual cortex of anesthetized macaques. We presented large stimulus sets consisting of (1) drifting gratings of various orientations and spatiotemporal frequencies; (2) plaids composed of two drifting gratings; and (3) gratings masked by full-screen spatiotemporal white noise. We derived expressions for the model predictions and fitted them to the physiological data. Our results support the normalization model, which accounts for both the linear and the nonlinear properties of the cells. An alternative model, in which the linear responses are subject to a compressive nonlinearity, did not perform nearly as well.Key words: visual cortex; contrast; nonlinearity; gain control; normalization; masking; noise A longstanding view of simple cells in the primary visual cortex is that they compute a weighted sum of the light intensities falling on their receptive field (Hubel and Wiesel, 1962;Movshon et al., 1978a; C arandini et al., 1997b). This linear model is depicted in Figure 1 A and is usually taken to include a rectification (thresholding) stage to account for the transformation of intracellular signals into firing rates.Although many aspects of simple cell responses are consistent with the linear model, there also are important violations of linearity. For example, scaling the contrast of a stimulus would identically scale the responses of a linear cell. At high contrasts, however, the responses of simple cells show clear saturation . Moreover, simple cells are subject to cross-orientation inhibition; the responses to an optimally oriented stimulus can be diminished by superimposing an orthogonal stimulus that is ineffective in driving the cell when presented alone (Morrone et al., 1982;Bonds, 1989;Bauman and Bonds, 1991).According to a view that has emerged in recent years, the nonlinearities of simple cells could be explained by extending the linear model to include a gain control stage (Albrecht and Geisler, 1991;Heeger, 1991Heeger, , 1992bHeeger, , 1993DeAngelis et al., 1992;Carandini and Heeger, 1994;Nestares and Heeger, 1997; Tolhurst and Heeger, 1997a,b). In particular, one of us (Heeger, 1...