Spatio-temporal organization of receptive fields of the cat striate cortex. The receptive fields as the grating filters

The divisive normalization model of V1 neurons: a comprehensive comparison of physiological data and model predictions

The physiological responses of simple and complex cells in the primary visual cortex (V1) have been studied extensively and modeled at different levels. At the functional level, the divisive normalization model (DNM; Heeger DJ. Vis Neurosci 9: 181-197, 1992) has accounted for a wide range of single-cell recordings in terms of a combination of linear filtering, nonlinear rectification, and divisive normalization. We propose standardizing the formulation of the DNM and implementing it in software that takes static grayscale images as inputs and produces firing rate responses as outputs. We also review a comprehensive suite of 30 empirical phenomena and report a series of simulation experiments that qualitatively replicate dozens of key experiments with a standard parameter set consistent with physiological measurements. This systematic approach identifies novel falsifiable predictions of the DNM. We show how the model simultaneously satisfies the conflicting desiderata of flexibility and falsifiability. Our key idea is that, while adjustable parameters are needed to accommodate the diversity across neurons, they must be fixed for a given individual neuron. This requirement introduces falsifiable constraints when this single neuron is probed with multiple stimuli. We also present mathematical analyses and simulation experiments that explicate some of these constraints.

Feature-based attention modulates surround suppression

Stimuli appearing in the surround of the classical receptive field (CRF) can reduce neuronal firing and perceived contrast of a preferred stimulus in the CRF, a phenomenon referred to as surround suppression. Suppression is greatest when the surrounding stimulus has the same orientation and spatial frequency (SF) as the central target. Although spatial attention has been shown to influence surround suppression, the effects of feature-based attention have yet to be characterized. Using behavioral contrast adaptation in humans, we examined center-surround interactions between SF and orientation, and asked whether attending to one feature dimension versus the other influenced suppression. A center-surround triplet comprised of a central target Gabor and two flanking Gabors were used for adaptation. The flankers could have the same SF and orientation as the target, or differ in one or both of the feature dimensions. Contrast thresholds were measured for the target before and after adapting to center-surround triplets, and postadaptation thresholds were taken as an indirect measure of surround suppression. Both feature dimensions contributed to surround suppression and did not summate. Moreover, when center and surround had the same feature value in one dimension (e.g., same orientation) but had different values in the other dimension (e.g., different SF), there was more suppression when attention was directed to the feature dimension that matched between center and surround than when attention was directed to the feature dimension that differed. These results demonstrate that feature-based attention can influence center-surround interactions by enhancing the effects of the attended dimension.

Hebbian plasticity and homeostasis in a model of hypercolumn of the visual cortex

Neurons in the nervous system display a wide variety of plasticity processes. Among them are covariance-based rules and homeostatic plasticity. By themselves, the first ones tend to generate instabilities because of the unbounded potentiation of synapses. The second ones tend to stabilize the system by setting a target for the postsynaptic firing rate. In this work, we analyze the combined effect of these two mechanisms in a simple model of hypercolumn of the visual cortex. We find that the presence of homeostatic plasticity together with nonplastic uniform inhibition stabilizes the effect of Hebbian plasticity. The system can reach nontrivial solutions, where the recurrent intracortical connections are strongly modulated. The modulation is strong enough to generate contrast invariance. Moreover, this state can be reached even beginning from a weakly modulated initial condition.

Spatial and temporal features of synaptic to discharge receptive field transformation in cat area 17

The aim of the present study was to characterize the spatial and temporal features of synaptic and discharge receptive fields (RFs), and to quantify their relationships, in cat area 17. For this purpose, neurons were recorded intracellularly while high-frequency flashing bars were used to generate RFs maps for synaptic and spiking responses. Comparison of the maps shows that some features of the discharge RFs depended strongly on those of the synaptic RFs, whereas others were less dependent. Spiking RF duration depended poorly and spiking RF amplitude depended moderately on those of the underlying synaptic RFs. At the other extreme, the optimal spatial frequency and phase of the discharge RFs in simple cells were almost entirely inherited from those of the synaptic RFs. Subfield width, in both simple and complex cells, was less for spiking responses compared with synaptic responses, but synaptic to discharge width ratio was relatively variable from cell to cell. When considering the whole RF of simple cells, additional variability in width ratio resulted from the presence of additional synaptic subfields that remained subthreshold. Due to these additional, subthreshold subfields, spatial frequency tuning predicted from synaptic RFs appears sharper than that predicted from spiking RFs. Excitatory subfield overlap in spiking RFs was well predicted by subfield overlap at the synaptic level. When examined in different regions of the RF, latencies appeared to be quite variable, but this variability showed negligible dependence on distance from the RF center. Nevertheless, spiking response latency faithfully reflected synaptic response latency.

Origins of cross-orientation suppression in the visual cortex

The response of a neuron in striate cortex to an optimally oriented stimulus is suppressed by a superimposed orthogonal stimulus. The neural mechanism underlying this cross-orientation suppression (COS) may arise from intracortical or subcortical processes or from both. Recent studies of the temporal frequency and adaptation properties of COS suggest that depression at thalamo-cortical synapses may be the principal mechanism. To examine the possible role of synaptic depression in relation to COS, we measured the recovery time course of COS. We find it too rapid to be explained by synaptic depression. We also studied potential subcortical processes by measuring single cell contrast response functions for a population of LGN neurons. In general, contrast saturation is a consistent property of LGN neurons. Combined with rectifying nonlinearities in the LGN and spike threshold nonlinearities in visual cortex, contrast saturation in the LGN can account for most of the COS that is observed in the visual cortex.

Do we know what the early visual system does?

We can claim that we know what the visual system does once we can predict neural responses to arbitrary stimuli, including those seen in nature. In the early visual system, models based on one or more linear receptive fields hold promise to achieve this goal as long as the models include nonlinear mechanisms that control responsiveness, based on stimulus context and history, and take into account the nonlinearity of spike generation. These linear and nonlinear mechanisms might be the only essential determinants of the response, or alternatively, there may be additional fundamental determinants yet to be identified. Research is progressing with the goals of defining a single "standard model" for each stage of the visual pathway and testing the predictive power of these models on the responses to movies of natural scenes. These predictive models represent, at a given stage of the visual pathway, a compact description of visual computation. They would be an invaluable guide for understanding the underlying biophysical and anatomical mechanisms and relating neural responses to visual perception.

The contribution of spike threshold to the dichotomy of cortical simple and complex cells

The existence of two classes of cells, simple and complex, discovered by Hubel and Wiesel in 1962, is one of the fundamental features of cat primary visual cortex. A quantitative measure used to distinguish simple and complex cells is the ratio between modulated and unmodulated components of spike responses to drifting gratings, an index that forms a bimodal distribution. We have found that the modulation ratio, when derived from the subthreshold membrane potential instead of from spike rate, is unimodally distributed, but highly skewed. The distribution of the modulation ratio as derived from spike rate can, in turn, be predicted quantitatively by the nonlinear properties of spike threshold applied to the skewed distribution of the subthreshold modulation ratio. Threshold also increases the spatial segregation of ON and OFF regions of the receptive field, a defining attribute of simple cells. The distinction between simple and complex cells is therefore enhanced by threshold, much like the selectivity for stimulus features such as orientation and direction. In this case, however, a continuous distribution in the spatial organization of synaptic inputs is transformed into two distinct classes of cells.

A synaptic explanation of suppression in visual cortex

The responses of neurons in the primary visual cortex (V1) are suppressed by mask stimuli that do not elicit responses if presented alone. This suppression is widely believed to be mediated by intracortical inhibition. As an alternative, we propose that it can be explained by thalamocortical synaptic depression. This explanation correctly predicts that suppression is monocular, immune to cortical adaptation, and occurs for mask stimuli that elicit responses in the thalamus but not in the cortex. Depression also explains other phenomena previously ascribed to intracortical inhibition. It explains why responses saturate at high stimulus contrast, whereas selectivity for orientation and spatial frequency is invariant with contrast. It explains why transient responses to flashed stimuli are nonlinear, whereas spatial summation is primarily linear. These results suggest that the very first synapses into the cortex, and not the cortical network, may account for important response properties of V1 neurons.

Spatial organization of receptive fields of V1 neurons of alert monkeys: comparison with responses to gratings

We studied the spatial organization of receptive fields and the responses to gratings of neurons in parafoveal V1 of alert monkeys. Activating regions (ARs) of 228 cells were mapped with increment and decrement bars while compensating for fixational eye movements. For cells with two or more ARs, the overlap between ARs responsive to increments (INC) and ARs responsive to decrements (DEC) was characterized by a quantitative overlap index (OI). The distribution of overlap indices was bimodal. The larger group (78% of cells) was composed of complex cells with strongly overlapping ARs (OI >/= 0.5). The smaller group (14%) was composed of simple cells with minimal spatial overlap of ARs (OI </= 0.3). Simple cells were preferentially located in layers dominated by the magnocellular pathway. A third group of neurons, the monocontrast cells (8%), responded only to one sign of contrast and had more sustained responses to flashed stimuli than other cells. One hundred fourteen neurons were also studied with drifting sinusoidal gratings of various spatial frequencies and window widths. For complex cells, the relative modulation (RM, the ratio of the 1st harmonic to the mean firing rate), ranged from 0.6 +/- 0.4 to 1.1 +/- 0.5 (mean +/- SD), depending on the stimulus conditions and the mode of correction for eye movements. RM was not correlated with the degree of overlap of ARs, indicating that the spatial organization of receptive fields cannot reliably be predicted from RM values. In fact, a subset of complex cells had RM > 1, the traditional criterion for identifying simple cells. However, unlike simple cells, even those complex cells with high RM could exhibit diverse nonlinear responses when the spatial frequency or window size was changed. Furthermore, the responses of complex cells to counterphase gratings were predominantly nonlinear even harmonics. These results show that RM is not a robust test of linearity. Our results indicate that complex cells are the most frequently encountered neurons in primate V1, and their behavior needs to receive more emphasis in models of visual function.

Suppression without inhibition in visual cortex

Neurons in primary visual cortex (V1) are thought to receive inhibition from other V1 neurons selective for a variety of orientations. Evidence for this inhibition is commonly found in cross-orientation suppression: responses of a V1 neuron to optimally oriented bars are suppressed by superimposed mask bars of different orientation. We show, however, that suppression is unlikely to result from intracortical inhibition. First, suppression can be obtained with masks drifting too rapidly to elicit much of a response in cortex. Second, suppression is immune to hyperpolarization (through visual adaptation) of cortical neurons responding to the mask. Signals mediating suppression might originate in thalamus, rather than in cortex. Thalamic neurons exhibit some suppression; additional suppression might arise from depression at thalamocortical synapses. The mechanisms of suppression are subcortical and possibly include the very first synapse into cortex.

Neural mechanisms for processing binocular information II. Complex cells

Complex cells in the striate cortex exhibit extensive spatiotemporal nonlinearities, presumably due to a convergence of various subunits. Because these subunits essentially determine many aspects of a complex cell receptive field (RF), such as tuning for orientation, spatial frequency, and binocular disparity, examination of the RF properties of subunits is important for understanding functional roles of complex cells. Although monocular aspects of these subunits have been studied, little is known about their binocular properties. Using a sophisticated RF mapping technique that employs binary m-sequences, we have examined binocular interactions exhibited by complex cells in the cat's striate cortex and the binocular RF properties of their underlying functional subunits. We find that binocular interaction RFs of complex cells exhibit subregions that are elongated along the frontoparallel axis at different binocular disparities. Therefore responses of complex cells are largely independent of monocular stimulus position or phase as long as the binocular disparity of the stimulus is kept constant. The binocular interaction RF is well described by a sum of binocular interaction RFs of underlying functional subunits, which exhibit simple cell-like RFs and a preference for different monocular phases but the same binocular disparity. For more than half of the complex cells examined, subunits of each cell are consistent with the characteristics specified by an energy model, with respect to the number of subunits as well as relationships between the subunit properties. Subunits exhibit RF binocular disparities that are largely consistent with a phase mechanism for encoding binocular disparity. These results indicate that binocular interactions of complex cells are derived from simple cell-like subunits, which exhibit multiplicative binocular interactions. Therefore binocular interactions of complex cells are also multiplicative. This suggests that complex cells compute something analogous to an interocular cross-correlation of images for a local region of visual space. The result of this computation can be used for solving the stereo correspondence problem.

Contrast-invariant orientation tuning in cat visual cortex: thalamocortical input tuning and correlation-based intracortical connectivity

The origin of orientation selectivity in visual cortical responses is a central problem for understanding cerebral cortical circuitry. In cats, many experiments suggest that orientation selectivity arises from the arrangement of lateral geniculate nucleus (LGN) afferents to layer 4 simple cells. However, this explanation is not sufficient to account for the contrast invariance of orientation tuning. To understand contrast invariance, we first characterize the input to cat simple cells generated by the oriented arrangement of LGN afferents. We demonstrate that it has two components: a spatial-phase-specific component (i.e., one that depends on receptive field spatial phase), which is tuned for orientation, and a phase-nonspecific component, which is untuned. Both components grow with contrast. Second, we show that a correlation-based intracortical circuit, in which connectivity between cell pairs is determined by the correlation of their LGN inputs, is sufficient to achieve well tuned, contrast-invariant orientation tuning. This circuit generates both spatially opponent, "antiphase" inhibition ("push-pull"), and spatially matched, "same-phase" excitation. The inhibition, if sufficiently strong, suppresses the untuned input component and sharpens responses to the tuned component at all contrasts. The excitation amplifies tuned responses. This circuit agrees with experimental evidence showing spatial opponency between, and similar orientation tuning of, the excitatory and inhibitory inputs received by a simple cell. Orientation tuning is primarily input driven, accounting for the observed invariance of tuning width after removal of intracortical synaptic input, as well as for the dependence of orientation tuning on stimulus spatial frequency. The model differs from previous push-pull models in requiring dominant rather than balanced inhibition and in predicting that a population of layer 4 inhibitory neurons should respond in a contrast-dependent manner to stimuli of all orientations, although their tuning width may be similar to that of excitatory neurons. The model demonstrates that fundamental response properties of cortical layer 4 can be explained by circuitry expected to develop under correlation-based rules of synaptic plasticity, and shows how such circuitry allows the cortex to distinguish stimulus intensity from stimulus form.

Mechanisms of direction selectivity in macaque V1

Mechanisms underlying direction selectivity were studied in V1 of alert fixating macaque monkeys. Some direction-selective cells showed delayed asymmetric inhibition, some showed a shifting excitatory time course across the receptive field, and some showed both. Both the direction of the spatial offset of the inhibition and the direction of the shift in excitatory response time course correlated with the cells' preferred directionality. The delayed asymmetric inhibition may contribute to the shifting response time course. The data suggest that asymmetric inhibition is the major determinant for directionality in these cells, though both mechanisms could contribute. Based on this physiology, a simple, single-cell model is proposed, consistent with the known anatomy of some direction-selective cells.

Comparison of contrast-normalization and threshold models of the responses of simple cells in cat striate cortex

In almost every study of the linearity of spatiotemporal summation in simple cells of the cat's visual cortex, there have been systematic mismatches between the experimental observations and the predictions of the linear theory. These mismatches have generally been explained by supposing that the initial spatiotemporal summation stage is strictly linear, but that the following output stage of the simple cell is subject to some contrast-dependent nonlinearity. Two main models of the output nonlinearity have been proposed: the threshold model (e.g. Tolhurst & Dean, 1987) and the contrast-normalization model (e.g. Heeger, 1992a,b). In this paper, the two models are fitted rigorously to a variety of previously published neurophysiological data, in order to determine whether one model is a better explanation of the data. We reexamine data on the interaction between two bar stimuli presented in different parts of the receptive field; on the relationship between the receptive-field map and the inverse Fourier transform of the spatial-frequency tuning curve; on the dependence of response amplitude and phase on the spatial phase of stationary gratings; on the relationships between the responses to moving and modulated gratings; and on the suppressive action of gratings moving in a neuron's nonpreferred direction. In many situations, the predictions of the two models are similar, but the contrast-normalization model usually fits the data slightly better than the threshold model, and it is easier to apply the equations of the normalization model. More importantly, the normalization model is naturally able to account very well for the details and subtlety of the results in experiments where the total contrast energy of the stimuli changes; some of these phenomena are completely beyond the scope of the threshold model. Rigorous application of the models' equations has revealed some situations where neither model fits quite well enough, and we must suppose, therefore, that there are some subtle nonlinearities still to be characterized.

Nonlinear responses of simple cells to Mach band stimuli: evidence from early monocularly deprived cats

We have previously shown that, cat simple cells respond linearly to edges of variable blur widths: cells with receptive fields (RFs) of even symmetry respond better to a luminance ramp (where Mach bands are observed); cells with RFs of odd symmetry respond better to a luminance step (where no Mach bands are perceived). Our evidence has also indicated the existence of inhibitory interaction between cells with RFs of even and odd symmetry as predicted by the Tolhurst-Ratliff Mach band model. Since monocular deprivation is known to impair cortical inhibitory mechanisms, we studied the responses of simple cells of adult cats monocularly deprived at the age of 8-10 weeks to Mach band stimuli in order to delineate specific changes in inhibitory interactions caused by monocular deprivation. In pattern-deprived cats, particularly for cells driven by the deprived eye, there were many cells that responded contrary to linear models: odd-symmetric cells responded maximally to blurred edges while even-symmetric cells responded maximally to sharp edges. Cells that responded maximally as predicted, responded, similarly to normal cat cells, less than expected at suboptimal widths. All cells in normal and light-deprived cats responded in a linear fashion to sinusoidal stimuli. We conclude, therefore, that intracortical inhibition shapes simple cells' responses to edges. Monocular deprivation impairs this mechanism, thus causing simple cells in monocularly deprived cats to respond nonlinearly to edges. All simple cells responded linearly to gratings since it is not the linear spatiotemporal RF of these simple cells that was impaired under monocular deprivation.

Space-time spectra of complex cell filters in the macaque monkey: a comparison of results obtained with pseudowhite noise and grating stimuli

White noise stimuli were used to estimate second-order kernels for complex cells in cortical area V1 of the macaque monkey, and drifting grating stimuli were presented to the sample of neurons to obtain orientation and spatial-frequency tuning curves. Using these data, we quantified how well second-order kernels predict the normalized tuning of the average response of complex cells to drifting gratings. The estimated second-order kernel of each complex cell was transformed into an interaction function defined over all spatial and temporal lags without regard to absolute position or delay. The Fourier transform of each interaction function was then computed to obtain an interaction spectrum. For a cell that is well modeled by a second-order system, the cell's interaction spectrum is proportional to the tuning of its average spike rate to drifting gratings. This result was used to obtain spatial-frequency and orientation tuning predictions for each cell based on its second-order kernel. From the spatial-frequency and orientation tuning curves, we computed peaks and bandwidths, and an index for directional selectivity. We found that the predictions derived from second-order kernels provide an accurate description of the change in the average spike rate of complex cells to single drifting sine-wave gratings. These findings are consistent with a model for complex cells that has a quadratic spectral energy operator at its core but are inconsistent with a spectral amplitude model.

Contribution of linear mechanisms to the specification of local motion by simple cells in areas 17 and 18 of the cat

A reverse correlation technique, which permits estimation of three-dimensional first-order properties of receptive fields (RFs), was applied to simple cells in areas 17 and 18 of cat. Two classes of simple cells were found. For one class, the spatial and temporal RF characteristics were separable, i.e. they could be synthesized as the product of spatial and temporal weighting functions. RFs in the other class were inseparable, i.e. bright and dark subregions comprising each field were obliquely oriented in space-time. Based on a linear superposition model, these observations led to testable hypotheses: (1) simple cells with separable space-time characteristics should be speed but not direction selective and (2) simple cells with inseparable space-time characteristics should be direction selective and the optimal velocity of moving stimuli should be predictable from the slope of the oriented subregions. These hypotheses were tested by comparing responses to moving bars with those predicted by application of the convolution integral. Linear predictions accounted for waveforms of responses to moving bars in detail. For cells with oriented space-time characteristics, the preferred direction was always predicted correctly and the optimal speed was predicted quite well. Most cells with separable space-time characteristics were not direction selective as predicted. The major discrepancies between measured and predicted behavior were twofold. First, 8/32 cells with separable space-time RFs were direction selective. Second, predicted directional indices were weakly correlated with actual measurements. These conclusions hold for simple cells in both areas 17 and 18. The major difference between simple RFs in these areas is the coarser spatial scale seen in area 18. These results demonstrate a significant linear contribution to the speed and direction selectivity of simple cells in areas 17 and 18. Where additional, nonlinear mechanisms are inferred, they appear to act synergistically with the linear mechanism.

Half-squaring in responses of cat striate cells

Simple cells in striate cortex have been depicted as rectified linear operators, and complex cells have been depicted as energy mechanisms (constructed from the squared sums of linear operator outputs). This paper discusses two essential hypotheses of the linear/energy model: (1) that a cell's selectivity is due to an underlying (spatiotemporal and binocular) linear stage; and (2) that a cell's firing rate depends on the squared output of the underlying linear stage. This paper reviews physiological measurements of cat striate cell responses, and concludes that both of these hypotheses are supported by the data.

Normalization of cell responses in cat striate cortex

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.

The processing of spatial frequency and orientation information

Three identification experiments were completed to disambiguate the associations between spatial frequency and orientation information at the sensory, decisional, and response levels. The stimuli were gratings generated by crossing four levels each of spatial frequency and orientation. In Experiment 1, the subjects made a single identification response to the stimuli. In Experiment 2, two identification responses were made, one for the spatial frequency component and the other for the orientation component. In Experiment 3, the subjects identified either the spatial frequency or the orientation component in any block of trials. The data were confusion matrices, and an information-transmission approach was used to investigate the interactions in the system. The results show that although there were sensory associations, there were no interactions at the decisional level. Performance parity was found: there was no significant difference between the single- and double-judgment paradigms in terms of information transmitted. Overall, the results suggest that although spatial frequency and orientation information is coded jointly at the sensory level, subsequent processing is independent, with each dimension drawing upon different attentional resources.

The effect of threshold on the relationship between the receptive-field profile and the spatial-frequency tuning curve in simple cells of the cat's striate cortex

It is believed that spatial summation in most simple cells is a linear process. If this were so, then the Fourier transform of a simple cell's line weighting function should predict the cell's spatial frequency tuning curve. We have compared such predictions with experimental measurements and have found a consistent discrepancy: the predicted tuning curve is much too broad. We show qualitatively that this kind of discrepancy is consistent with the well-known threshold nonlinearity shown by most cortical cells. We have tested quantitatively whether a response threshold could explain the observed disagreements between predictions and measurements: a least-squares minimization routine was used to fit the inverse Fourier Transform of the measured frequency tuning curve to the measured line weighting function. The fitting procedure permitted us to introduce a threshold to the reconstructed line weighting function. The results of the analysis show that, for all of the cells tested, the Fourier transforms produced better predictions when a response threshold was included in the model. For some cells, the actual magnitude of the response threshold was measured independently and found to be compatible with that suggested by the model. The effects of nonlinearities of spatial summation are considered.

Harmonic basis functions for spatial coding in the cat striate cortex

The number of subregions in the activity profiles of simple cells varies in different cells from 2-8; that is, the number of cycles in the weighting function varies from 1-4. The distribution of receptive-field (RF) sizes at eccentricities of 0-6 deg are clustered at half-octave intervals and form a discrete distribution with maxima at 0.62, 0.9, 1.24, 1.8, 2.48, and 3.4 deg. The spatial frequencies to which the cells are tuned are also clustered at half-octave intervals, forming a discrete distribution peaking at 0.45, 0.69, 0.9, 1.35, 1.88, 2.7, 3.8, and 5.6 cycles/deg. If we divide the RF sizes by the size of the period of the subregions, then the average indices of complexity (really existing) or the number of cycles in the weighting function form (after normalization) the sequences: 1, 1.41, 2.0, 2.9, 4.15. The relation between the bandwidth of the spatial-frequency characteristic and the optimal spatial frequency is in accordance with predictions of the Fourier hypothesis. The absolute bandwidth does not change with the number of cycles/module. This means that inside the module the absolute bandwidth does not change with the number of the harmonic. The results allow us to suggest the following. A module of the striate cortex, which is a group of cells with RFs of equal size projected onto the same area of central visual field, accounts for the Fourier description of the image. The basis functions of the module are composed of four harmonics only, irrespective of size and position of the module. Besides linear cells (sinusoidal and cosinusoidal elements), the module contains nonlinear cells, performing a nonlinear summation of the responses of sinusoidal and cosinusoidal elements. Such cells are characterized by an index of complexity which is more than the number of cycles in the weighting function and by marked overlap of ON and OFF zones. The analysis of organization suggests that the cells can measure the amplitude and phase of the stimulus.

Spatial organization of subfields in receptive fields of cells in cat striate cortex

Spatial organization of receptive fields (RF) of cells in cat striate cortex was investigated with moving and flashing light and dark bars and with grating-patterns of a varying number of cycles. It was shown that the maximum number of subfields in a simple cell is equal to eight or the number of periods in weighting function is equal to four. Quantitative comparison of the data with the results of seven other studies allows us to suggest that the number of periods in linear component of some complex cells is close to this value. The discrepancies between the results of different authors in estimation of the number of subfields are explained by the experimental data.

Lateral interactions at direction-selective striate neurones in the cat demonstrated by local cortical inactivation

1. Single neurones were recorded with glass-coated tungsten electrodes from area 17 of the cat's visual cortex. The cats were anaesthetized and artificially respirated with a mixture of halothane, nitrous oxide and oxygen. 2. For local cortical inactivation a multibarrel pipette was placed 0.5-2.5 mm posterior (or anterior) to the recording site, at a depth of 400-600 micron. Four separate barrels of the pipette were filled with gamma-aminobutyric acid (GABA); the fifth was filled with Pontamine Sky Blue for labelling of the centre of the inactivation site. 3. Direction-selective cells, of differing optimal orientations and preferred directions of motion, were classified as simple or complex and tested with computer-controlled stimuli presented on an oscilloscope. 4. During continuous recording GABA was microionophoretically applied for different durations and with different ejection currents. The effectiveness of GABA microionophoresis was evident from the direct GABAergic effects (strong overall inhibition of the recorded cells) observed with high ejection currents and prolonged application. 5. Two discrete effects could be observed during local inactivation distant from the cortical cell under study: an increase of the response in either the non-preferred or the preferred direction; or a decrease of the response in the preferred direction. All GABA-induced changes were reversible. 6. The depressant action of GABA was independent of the relative topography between recording and inactivation site and affected mainly the response to the preferred direction of stimulus motion. 7. Disinhibition was only observed when the stimulus-evoked response moved on the cortical map in a direction from the GABA pipette towards the recording electrode. It is concluded that GABA reversibly silences inhibitory interneurones that are situated in the vicinity of the micropipette tip and are involved in generation of direction selectivity. 8. No fundamental differences between cells from different cortical layers were observed. The disinhibitory effects of GABA inactivation were more pronounced and more frequently seen in simple cells (61%) than in complex cells (38%), while the opposite was true for reduced excitation during lateral GABA inactivation (observed in 62% of the complex vs. 39% of the simple cells). Accordingly, lateral inhibition statistically prevails in simple cells and lateral excitation in complex cells. 9. Among the inhibitory and excitatory mechanisms affected by lateral GABA inactivation, inhibition is organized with a higher topographic specificity.(ABSTRACT TRUNCATED AT 400 WORDS)

Is direction selectivity of cat area 17 cells always independent of contrast and dependent on short-distance interactions?

In a study of area 17 of the paralysed and anesthetized cat it was found that for a small subgroup of cells with peripherally located receptive fields (11/123), the direction selectivity was critically dependent on the use of high contrast stimulation. By covering parts of the receptive field with a mask, it was found that in some cells the suppression of responses to movement in the non-preferred direction was due to the presence of a suppressive area located just outside the discharge region. Direction selective suppression was present only when a high contrast bar (light or dark) crossed this area before entering the discharge region.

Spatial summation by simple cells in the striate cortex of the cat

Spatial summation has been studied in simple cells of the cat's visual cortex by examining the responses of pairs of lines. One line was placed in an ON region of the receptive field; the other was placed in an OFF region. When the luminances of the lines were modulated in anti-phase, the excitatory responses to the individual lines were almost synchronous. A simple cell's overt response to the composite stimulus was usually greater than the sum of the overt responses to the two components. The result could be explained by supposing that the underlying response was the linear sum of the excitatory signals but that an overt response occurred only when the underlying response exceeded a fixed threshold value. This was true even of simple cells which exhibited non-linearities of spatial summation, as judged from the waveforms of their responses to moving sinusoidal gratings. When the two lines were modulated in phase, the excitatory responses occurred in different halves of the temporal cycle. Some cells summed antagonistic signals linearly. The waveforms of their responses to moving sinusoidal gratings also implied linear spatial summation. However, other cells whose responses to moving gratings implied linearity of summation did not, in fact, sum antagonistic signals linearly. The excitatory responses evoked in a receptive field region were weaker than the inhibitory responses that could be evoked in the same region. The remaining cells did not sum antagonistic signals linearly. There was imperfect cancellation, resulting in the generation of ON-OFF response components. The excitatory responses evoked in a receptive field region were stronger than the inhibitory responses that could be evoked in the same region. These cells gave responses to sinusoidal gratings that did imply nonlinear spatial summation.

The structure and symmetry of simple-cell receptive-field profiles in the cat's visual cortex

Receptive fields of simple cells in the cat visual cortex have recently been discussed in relation to the 'theory of communication' proposed by Gabor (1946). A number of investigators have suggested that the line-weighting functions, as measured orthogonal to the preferred orientation, may be best described as the product of a Gaussian envelope and a sinusoid (i.e. a Gabor function). Following Gabor's theory of 'basis' functions, it has also been suggested that simple cells can be categorized into even- and odd-symmetric categories. Based on the receptive field profiles of 46 simple cells recorded from cat visual cortex, our analysis provides a quantitative description of both the receptive-field envelope and the receptive-field 'symmetry' of each of the 46 cells. The results support the notion that, to a first approximation, Gabor functions with three free parameters (envelope width, carrier frequency and carrier phase) provide a good description of the receptive-field profiles. However, our analysis does not support the notion that simple cells generally fit into even- and odd-symmetric categories.

Relationship between spatial and spatial-frequency characteristics of receptive fields of cat visual cortex

The spatial (magnitude and eccentricity) and spatial-frequency (optimum frequency and width of pass band) characteristics of the receptive fields of the cat visual cortex were investigated. It was shown that in accordance with the predictions of the theory of piecewise Fourier analysis, linear and quasilinear receptive fields of a single size comprise a modulus in each of the fields of which the index of complexity (ratio of size of field to number of periods of its optimum frequency) equals the optimum frequency multiplied by a coefficient that is constant for the given modulus. Five moduli were found with field sizes of 2.6, 3.8, 5.2, 6.2, and 7.0 degrees, shifting with increase in the size of the modulus towards the periphery of the field of view. In accordance with predictions, when the index of complexity is fixed the width of the pass band declines inversely proportionately to the size of the fields. The obtained data directly support the hypothesis according to which the receptive fields effect a piecewise quasi-Fourier expansion of the image.

Colour-spatial vision

A critical survey is made of neurophysiological and psychophysiological investigations of colour vision. A neuronal model of colour-spatial vision is suggested. The model allows a unified explanation of the whole range of psychophysiological phenomena: the mixing of colours of high-frequency image components, the McCollough type colour after-effects, the simultaneous and successive colour contrast, the hue constancy perception, the appearance of non-spectral colours by mixing of monochromatic lights. A suggestion is made as to the existence of two main mechanisms of colour vision. The first of these, by means of Fourier transforms, gives a set of coefficients which describes the spatial distribution of light (quantity of energy) and hue (quality of energy) in the visual field. The second mechanism establishes colour names in each chromatically homogenous area of the field described by the first mechanism. Both mechanisms cooperate on the basis of their common spatial organization.

Spatial visual channels in the Fourier plane

Properties of human spatial visual channels were studied in two-dimensional form by a signal detection masking paradigm. Tuning surfaces of contrast threshold elevation induced by a sinusoidal mask were generated for four Subjects, interpolated from an 11 X 11 Cartesian grid over the Fourier plane, and numerically Fourier transformed in two dimensions to infer putative filter profiles in the 2D space domain. Among the main findings in the 2D frequency domain were: (1) Threshold elevation surfaces are highly polar nonseparable--they cannot be described as the product of a spatial frequency tuning curve times an orientation tuning curve. (2) Iso-half-amplitude contours of the spectral tuning surfaces have a length/width elongation ratio of about 2:1. (3) Necessarily, resolution for spatial frequency and for orientation are in fundamental competition with 2D spatial resolution. By calculating the occupied area of the inferred filters both in the 2D space domain and in the 2D frequency domain, it was estimated that these mechanisms approach within a factor of 2.5 of the theoretical limit of joint resolution in the two 2D domains that can be derived by 2D generalization of Gabor's famous Theory of Communication (1946). Other classes of 2D filters, such as an ideal 2D bandpass filter, have joint 2D entropies which are suboptimal by a factor of 13 or more. Subject to the inherent constraints on inference from these 2D masking experiments, the evidence suggests that 2D spatial frequency channels can be described as elongated 2D spatial wave-packets which crudely resemble optimal forms for joint information resolution in the 2D spatial and 2D frequency domains.

Non-fusable stimuli and the role of binocular inhibition in normal and pathologic vision, especially strabismus

Stimuli on corresponding points of both retinae that cannot be fused may cause binocular rivalry: the stimuli suppress each other alternately. This effect was used to study the influence of image sharpness upon binocular inhibition. Blurring an image means decreasing its contrast and attenuating its high spatial frequencies. Both factors diminish the time that a stimulus is perceived during rivalry. This fact has implications both for normal vision--as objects off the horopter are normally blurred--and for disturbed vision when the image of one or both eyes is (locally) deteriorated. In both cases, the binocular field of view can be combined from the 'good' parts of both eyes. Hence, the field of view may consist, in a piece-meal fashion, of parts stemming from the right or the left eye exclusively and others where both images are superimposed. We present evidence for the hypothesis that there is a common neural mechanism causing both binocular rivalry and functional amblyopia in anisometropia and strabismus. Consequences of the results on rivalry suppression for the pathophysiology and therapy of strabismic amblyopia are discussed.