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.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0952523800009640

Normalization of cell responses in cat striate cortex

The majority of synapses in the mammalian cortex originate from cortical neurons. Indeed, the largest input to cortical cells comes from neighboring excitatory cells. However, most models of cortical development and processing do not reflect the anatomy and physiology of feedback excitation and are restricted to serial feedforward excitation. This report describes how populations of neurons in cat visual cortex can use excitatory feedback, characterized as an effective "network conductance", to amplify their feedforward input signals and demonstrates how neuronal discharge can be kept proportional to stimulus strength despite strong, recurrent connections that threaten to cause runaway excitation. These principles are incorporated into models of cortical direction and orientation selectivity that emphasize the basic design principles of cortical architectures.

https://science.sciencemag.org/content/sci/269/5226/981.full.pdf

Recurrent excitation in neocortical circuits.

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.

/pdf/linearity-and-normalization-in-simple-cells-of-the-macaque-55rc1ohksj.pdf

Linearity and Normalization in Simple Cells of the Macaque Primary Visual Cortex

The small visual area known as MT or V5 has played a major role in our understanding of the primate cerebral cortex. This area has been historically important in the concept of cortical processing streams and the idea that different visual areas constitute highly specialized representations of visual information. MT has also proven to be a fertile culture dish--full of direction- and disparity-selective neurons--exploited by many labs to study the neural circuits underlying computations of motion and depth and to examine the relationship between neural activity and perception. Here we attempt a synthetic overview of the rich literature on MT with the goal of answering the question, What does MT do?

/pdf/structure-and-function-of-visual-area-mt-5cgljbd95o.pdf

Structure and Function of Visual Area MT

A white noise technique is presented for estimating the response properties of spiking visual system neurons. The technique is simple, robust, efficient and well suited to simultaneous recordings from multiple neurons. It provides a complete and easily interpretable model of light responses even for neurons that display a common form of response nonlinearity that precludes classical linear systems analysis. A theoretical justification of the technique is presented that relies only on elementary linear algebra and statistics. Implementation is described with examples. The technique and the underlying model of neural responses are validated using recordings from retinal ganglion cells, and in principle are applicable to other neurons. Advantages and disadvantages of the technique relative to classical approaches are discussed.

/pdf/a-simple-white-noise-analysis-of-neuronal-light-responses-a56aehnicm.pdf

A simple white noise analysis of neuronal light responses.

1. Simple cells in cat striate cortex were studied with a number of stimulation paradigms to explore the extent to which linear mechanisms determine direction selectivity. For each paradigm, our aim was to predict the selectivity for the direction of moving stimuli given only the responses to stationary stimuli. We have found that the prediction robustly determines the direction and magnitude of the preferred response but overestimates the nonpreferred response. 2. The main paradigm consisted of comparing the responses of simple cells to contrast reversal sinusoidal gratings with their responses to drifting gratings (of the same orientation, contrast, and spatial and temporal frequencies) in both directions of motion. Although it is known that simple cells display spatiotemporally inseparable responses to contrast reversal gratings, this spatiotemporal inseparability is demonstrated here to predict a certain amount of direction selectivity under the assumption that simple cells sum their inputs linearly. 3. The linear prediction of the directional index (DI), a quantitative measure of the degree of direction selectivity, was compared with the measured DI obtained from the responses to drifting gratings. The median value of the ratio of the two was 0.30, indicating that there is a significant nonlinear component to direction selectivity. 4. The absolute magnitudes of the responses to gratings moving in both directions of motion were compared with the linear predictions as well. Whereas the preferred direction response showed only a slight amount of facilitation compared with the linear prediction, there was a significant amount of nonlinear suppression in the nonpreferred direction. 5. Spatiotemporal inseparability was demonstrated also with stationary temporally modulated bars. The time course of response to these bars was different for different positions in the receptive field. The degree of spatiotemporal inseparability measured with sinusoidally modulated bars agreed quantitatively with that measured in experiments with stationary gratings. 6. A linear prediction of the responses to drifting luminance borders was compared with the actual responses. As with the grating experiments, the prediction was qualitatively accurate, giving the correct preferred direction but underestimating the magnitude of direction selectivity observed.(ABSTRACT TRUNCATED AT 400 WORDS)

Directional selectivity and spatiotemporal structure of receptive fields of simple cells in cat striate cortex

We have used Sutter's (1987) spatiotemporal m-sequence method to map the receptive fields of neurons in the visual system of the cat. The stimulus consisted of a grid of 16 x 16 square regions, each of which was modulated in time by a pseudorandom binary signal, known as an m-sequence. Several strategies for displaying the m-sequence stimulus are presented. The results of the method are illustrated with two examples. For both geniculate neurons and cortical simple cells, the measurement of first-order response properties with the m-sequence method provided a detailed characterization of classical receptive-field structures. First, we measured a spatiotemporal map of both the center and surround of a Y-cell in the lateral geniculate nucleus (LGN). The time courses of the center responses was biphasic: OFF at short latencies, ON at longer latencies. The surround was also biphasic--ON then OFF--but somewhat slower. Second, we mapped the response properties of an area 17 directional simple cell. The response dynamics of the ON and OFF subregions varied considerably; the time to peak ranged over more than a factor of two. This spatiotemporal inseparability is related to the cell's directional selectivity (Reid et al., 1987, 1991; McLean & Palmer, 1989; McLean et al., 1994). The detail with which the time course of response can be measured at many different positions is one of the strengths of the m-sequence method.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0952523800011743

The use of m-sequences in the analysis of visual neurons: linear receptive field properties.

The role of linear spatial summation in the directional selectivity of simple cells in cat striate cortex was investigated. The experimental paradigm consisted of comparing the response to drifting grating stimuli with linear predictions based on the response to stationary contrast-reversing gratings. The spatial phase dependence of the response to contrast-reversing gratings was consistent with a high degree of linearity of spatial summation within the receptive fields. Furthermore, the preferred direction predicted from the response to stationary gratings generally agreed with the measurements made with drifting gratings. The amount of directional selectivity predicted was, on average, about half the measured value, indicating that nonlinear mechanisms act in concert with linear mechanisms in determining the overall directional selectivity.

https://www.pnas.org/content/pnas/84/23/8740.full.pdf

Linear mechanisms of directional selectivity in simple cells of cat striate cortex.

The rapid estimation of the brightness of objects is one of the nervous system's major visual tasks. Exactly how the eye and brain perform this basic task is still not understood. Two mechanisms that contribute to human perception of the brightness of objects have been identified previously: (i) the visual response to physical contrast and (ii) assimilation. Use of a unique visual display device allowed us to measure the relative importance of these two mechanisms. The present results reveal that assimilation is about half as effective as physical contrast in determining the apparent brightness of objects. These results imply that previous theories of vision--for instance, the retinex theory--will have to be revised; the importance of physical contrast must be weighted more strongly.

https://www.pnas.org/content/pnas/82/17/5983.full.pdf

Contrast and assimilation in the perception of brightness

We have studied the responses of striate cortical neurons to stimuli whose contrast is modulated in time by either a single sinusoid or by the sum of eight sinusoids. The sum-of-sinusoids stimulus resembles white noise and has been used to study the linear and nonlinear dynamics of retinal ganglion cells (Victor et al., 1977). In cortical neurons, we have found different linear and second-order responses to single-sinusoid and sum-of-sinusoids inputs. Specifically, while the responsivity near the optimal temporal frequency is lower for the sum-of-sinusoids stimulus, the responsivity at higher temporal frequencies is relatively greater. Along with this change in the response amplitudes, there is a systematic change in the time course of responses. For complex cells, the integration time, the effective delay due to a combination of actual delays and low-pass filter stages, changes from a median of 85 ms with single sinusoids to 57 ms with a sum of sinusoids. For simple cells, the integration times for single sinusoids range from 44-100 ms, but cluster tightly around 40 ms for the sum-of-sinusoids stimulus. The change in time constant would argue that the increased sensitivity to high frequencies cannot be explained by a static threshold, but must be caused by a fundamental alteration in the response dynamics. These effects are not seen in the retina (Shapley & Victor, 1981) and are most likely cortical in origin.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0952523800006350

R.C. Reid

Papers

Directional selectivity and spatiotemporal structure of receptive fields of simple cells in cat striate cortex

The use of m-sequences in the analysis of visual neurons: linear receptive field properties.

Linear mechanisms of directional selectivity in simple cells of cat striate cortex.

Contrast and assimilation in the perception of brightness

Broadband temporal stimuli decrease the integration time of neurons in cat striate cortex.