Search

Some neurons in early visual cortex are highly selective for the position of oriented edges in their receptive fields (simple cells), whereas others are largely position insensitive (complex cells). These characteristics are reflected in their sensitivity to the spatial phase of moving sine-wave gratings: simple cell responses oscillate at the fundamental frequency of the stimulus, whereas this is less so for complex cells. In primates, when assessed at high stimulus contrast, simple cells and complex cells are roughly equally represented in the first visual cortical area, V1, whereas in the second visual area, V2, the majority of cells are complex. Recent evidence has shown that phase sensitivity of complex cells is contrast dependent. This has led to speculation that reduced contrast may lead to changes in the spatial structure of receptive fields, perhaps due to changes in how feedforward and recurrent signals interact. Given the substantial interconnections between V1 and V2 and recent evidence for the emergence of unique functional capacity in V2, we assess the relationship between contrast and phase sensitivity in the two brain regions. We show that a substantial proportion of complex cells in macaque V1 exhibit significant increases in phase sensitivity at low contrast, whereas this is rarely observed in V2. Our results support a degree of hierarchical processing from V1 to V2 with the differences possibly relating to the fact that V1 combines both subcortical and cortical input, whereas V2 receives input purely from cortical circuits.

Orientation selectivity and its development are basic features of visual cortex. The original model of orientation selectivity proposes that elongated simple cell receptive fields are constructed from convergent input of an array of lateral geniculate nucleus neurons. However, orientation selectivity of simple cells in the visual cortex is generally greater than the linear contributions based on projections from spatial receptive field profiles. This implies that additional selectivity may arise from intracortical mechanisms. The hierarchical processing idea implies mainly linear connections, whereas cortical contributions are generally considered to be nonlinear. We have explored development of orientation selectivity in visual cortex with a focus on linear and nonlinear factors in a population of anesthetized 4-wk postnatal kittens and adult cats. Linear contributions are estimated from receptive field maps by which orientation tuning curves are generated and bandwidth is quantified. Nonlinear components are estimated as the magnitude of the power function relationship between responses measured from drifting sinusoidal gratings and those predicted from the spatial receptive field. Measured bandwidths for kittens are slightly larger than those in adults, whereas predicted bandwidths are substantially broader. These results suggest that relatively strong nonlinearities in early postnatal stages are substantially involved in the development of orientation tuning in visual cortex.

We develop a new analysis of the lateral geniculate nucleus (LGN) input to a cortical simple cell, demonstrating that this input is the sum of two terms, a linear term and a nonlinear term. In response to a drifting grating, the linear term represents the temporal modulation of input, and the nonlinear term represents the mean input. The nonlinear term, which grows with stimulus contrast, has been neglected in many previous models of simple cell response. We then analyze two scenarios by which contrast-invariance of orientation tuning may arise. In the first scenario, at larger contrasts, the nonlinear part of the LGN input, in combination with strong push-pull inhibition, counteracts the nonlinear effects of cortical spike threshold, giving the result that orientation tuning scales with contrast. In the second scenario, at low contrasts, the nonlinear component of LGN input is negligible, and noise smooths the nonlinearity of spike threshold so that the input-output function approximates a power-law function. These scenarios can be combined to yield contrast-invariant tuning over the full range of stimulus contrast. The model clarifies the contribution of LGN nonlinearities to the orientation tuning of simple cells and demonstrates how these nonlinearities may impact different models of contrast-invariant tuning.

1. To investigate the functional significance of temporally correlated discharge between nearby cells in the visual cortex, we obtained receptive-field maps of correlated discharge for 68 cell pairs in kittens and cats. Discharge from cell pairs was measured by a single extracellular electrode. A reverse correlation procedure was used to relate neural discharge to particular stimuli within a random sequence of briefly flashed bright and dark bars. Bicellular receptive fields (BRFs) were mapped by applying reverse correlation to approximately synchronous discharge from two cells. Unicellular receptive fields (URFs) were simultaneously mapped by separately applying reverse correlation to the discharge of each cell. 2. The receptive fields of the two neurons within each pair were initially studied by varying the orientation and spatial frequency of drifting sinusoidal gratings. After these tests a random sequence of appropriately oriented bars was used to evoke discharge suitable for reverse correlation analysis. For most cell pairs, the temporal pattern or strength of correlated discharge produced by such stimulation is different from that observed with stimulation by sinusoidal gratings. This indicates that visually evoked correlated discharge between nearby cells is stimulus dependent. 3. BRFs were classified according to their pattern of spatial sensitivity into three groups that roughly correspond to the single-cell receptive-field types of the lateral geniculate nucleus (LGN; center-surround) and visual cortex (simple and complex). These classifications were compared with the receptive-field types of the single cells within each pair. LGN-type and simple-type BRFs were only seen for pairs in which at least one of the cells was simple. Conversely, complex-type BRFs were only seen for pairs in which at least one of the cells was complex. 4. Because the reverse correlation procedure can be used to characterize the spatiotemporal receptive-field structure of simple cells, we were able to compare both the spatial and temporal properties associated with the URFs and BRFs of simple cell pairs. The spatiotemporal structure of the BRF of a simple-cell pair can largely be predicted on the basis of the two URFs. Although this prediction suggests the possibility that BRFs are stimulus artifacts, a shuffle procedure, in which multiple repetitions of random sequences were presented, verifies the neural origin of BRFs. BRFs emerge from specific neural pathways and are not simply a consequence of unicellular response preferences. 5. Five measures were derived from the reverse correlation analysis of simple-cell receptive fields: width, duration, optimal spatial and temporal frequency, and optimal velocity.(ABSTRACT TRUNCATED AT 400 WORDS)

A highly effective kernel-based strategy used in machine learning is to transform the input space into a new “feature” space where nonlinear problems become linear and more readily solvable with efficient linear techniques. We propose that a similar “problem-linearization” strategy is used by the neocortical input layer 4 to reduce the difficulty of learning nonlinear relations between the afferent inputs to a cortical column and its to-be-learned upper layer outputs. The key to this strategy is the presence of broadly tuned feed-forward inhibition in layer 4: it turns local layer 4 domains into functional analogs of radial basis function networks, which are known for their universal function approximation capabilities. With the use of a computational model of layer 4 with feed-forward inhibition and Hebbian afferent connections, self-organized on natural images to closely match structural and functional properties of layer 4 of the cat primary visual cortex, we show that such layer-4-like networks have a strong intrinsic tendency to perform input transforms that automatically linearize a broad repertoire of potential nonlinear functions over the afferent inputs. This capacity for pluripotent function linearization, which is highly robust to variations in network parameters, suggests that layer 4 might contribute importantly to sensory information processing as a pluripotent function linearizer, performing such a transform of afferent inputs to a cortical column that makes it possible for neurons in the upper layers of the column to learn and perform their complex functions using primarily linear operations.

1. A longstanding view of simple cells is that they sum their inputs linearly. However, the linear model falls short of a complete account of simple-cell direction selectivity. We have developed a nonlinear model of simple-cell responses (hereafter referred to as the normalization model) to explain a larger body of physiological data. 2. The normalization model consists of an underlying linear stage along with two additional nonlinear stages. The first is a half-squaring nonlinearity; half-squaring is half-wave rectification followed by squaring. The second is a divisive normalization non-linearity in which each model cell is suppressed by the pooled activity of a large number of cells. 3. By comparing responses with counterphase (flickering) gratings and drifting gratings, researchers have demonstrated that there is a nonlinear contribution to simple-cell responses. Specifically they found 1) that the linear prediction from counterphase grating responses underestimates a direction index computed from drifting grating responses, 2) that the linear prediction correctly estimates responses to gratings drifting in the preferred direction, and 3) that the linear prediction overestimates responses to gratings drifting in the nonpreferred direction. 4. We have simulated model cell responses and derived mathematical expressions to demonstrate that the normalization model accounts for this empirical data. Specifically the model behaves as follows. 1) The linear prediction from counterphase data underestimates the direction index computed from drifting grating responses. 2) The linear prediction from counterphase data overestimates the response to gratings drifting in the nonpreferred direction. The discrepancy between the linear prediction and the actual response is greater when using higher contrast stimuli. 3) For an appropriate choice of contrast, the linear prediction from counterphase data correctly estimates the response to gratings drifting in the preferred direction. For higher contrasts the linear prediction overestimates the actual response, and for lower contrasts the linear prediction underestimates the actual response. 5. In addition, the normalization model is qualitatively consistent with data on the dynamics of simple-cell responses. Tolhurst et al. found that simple cells respond with an initial transient burst of activity when a stimulus first appears. The normalization model behaves similarly; it takes some time after a stimulus first appears before the model cells are fully normalized. We derived the dynamics of the model and found that the transient burst of activity in model cells depends in a particular way on stimulus contrast. The burst is short for high-contrast stimuli and longer for low-contrast stimuli.(ABSTRACT TRUNCATED AT 400 WORDS)

1. We have tested the hypothesis that simple cells in the cat's visual cortex perform a linear spatiotemporal filtering of the visual image. To conduct this study we note that a visual neuron behaves linearly if the responses to small, brief flashes of light are mathematically related, via the Fourier transform, to the responses elicited by sinusoidal grating stimuli. 2. We have evaluated the linearity of temporal and spatial summation for 118 simple cells recorded from the striate cortex (area 17) of adult cats and kittens at ages 4 and 8 wk postnatal. These neurons represent a subset of the population of cells for which we have described the postnatal development of spatiotemporal receptive-field structure in the preceding paper. Spatiotemporal receptive-field profiles are constructed, with the use of a reverse correlation technique, from the responses to random sequences of small bar stimuli that are brighter or darker than the background. Fourier analysis of spatiotemporal receptive-field profiles yields linear predictions of the cells' spatial and temporal frequency tuning. These predicted responses are compared with spatial and temporal frequency tuning curves measured by the use of drifting, sinusoidal-luminance grating stimuli. 3. For most simple cells, there is good agreement between spatial and temporal frequency tuning curves predicted from the receptive-field profile and those measured by the use of sinusoidal gratings. These results suggest that both spatial and temporal summation within simple cells are approximately linear. There is a tendency for predicted tuning curves to be slightly broader than measured tuning curves, a finding that is consistent with the effects of a threshold nonlinearity at the output of these neurons. In some cases, however, predicted tuning curves deviate from measured responses only at low spatial and temporal frequencies. This cannot be explained by a simple threshold nonlinearity. 4. If linearity is assumed, it should be possible to predict the direction selectivity of simple cells from the structure of their spatiotemporal receptive-field profiles. For virtually all cells, linear predictions correctly determine the preferred direction of motion of a visual stimulus. However, the strength of the directional bias is typically underestimated by a factor of about two on the basis of linear predictions. Consideration of the expansive exponential nonlinearity revealed in the contrast-response function permits a reconciliation of the discrepancy between measured and predicted direction selectivity indexes. 5. Overall, these findings show that spatiotemporal receptive-field profiles obtained with the use of reverse correlation may be used to predict a variety of response properties for simple cells.(ABSTRACT TRUNCATED AT 400 WORDS)

1. Most studies of cortical neurons have focused on the spatial structure of receptive fields. For a more complete functional description of these neurons, it is necessary to consider receptive-field structure in the joint domain of space and time. We have studied the spatiotemporal receptive-field structure of 233 simple cells recorded from the striate cortex of adult cats and kittens at 4 and 8 wk postnatal. The dual goal of this study is to provide a detailed quantitative description of spatiotemporal receptive-field structure and to compare the developmental time courses of spatial and temporal response properties. 2. Spatiotemporal receptive-field profiles have been measured with the use of a reverse correlation method, in which we compute the cross-correlation between a neuron's response and a random sequence of small, briefly presented bright and dark stimuli. The receptive-field profiles of some simple cells are space-time separable, meaning that spatial and temporal response characteristics can be dissociated. Other cells have receptive-field profiles that are space-time inseparable. In these cases, a particular spatial location cannot be designated, unambiguously, as belonging to either an on or off subregion. However, separate on and off subregions may be clearly distinguished in the joint space-time domain. These subregions are generally tilted along an oblique axis. 3. Our observations show that spatial and temporal aspects of receptive-field structure mature with clearly different time courses. By 4 wk postnatal, the spatial symmetry and periodicity of simple-cell receptive fields have reached maturity. The spatial extent (or size) of these receptive fields is adult-like by 8 wk postnatal. In contrast, the response latency and time duration of spatiotemporal receptive fields do not mature until well beyond 8 wk postnatal. 4. By applying Fourier analysis to spatiotemporal receptive-field profiles, we have examined the postnatal development of spatial and temporal selectivity in the frequency domain. By 8 wk postnatal, spatial frequency tuning has clearly reached maturity. On the contrary, temporal frequency selectivity remains markedly immature at 8 wk. We have also examined the joint distribution of optimal spatial and temporal frequencies. From 4 wk postnatal until 8 wk postnatal, the range of optimal spatial frequencies increases substantially, whereas the range of optimal temporal frequencies remains largely unchanged. From 8 wk postnatal until adulthood, there is a large increase in optimal temporal frequencies for cells tuned to low spatial frequencies. For cells tuned to high spatial frequencies, the distribution of optimal temporal frequencies does not change much beyond 8 wk postnatal.(ABSTRACT TRUNCATED AT 400 WORDS)

1. Simple cells in the visual cortex have been subdivided into nondirection-selective (NDS), direction asymmetric (DA), and direction-selective (DS) cells. DA cells reverse their preferred direction with reversal of the stimulus contrast; DS2 cells respond with the same preferred direction for light and dark stimuli, whereas DS1 cells respond only to one (light or dark) contrast. Also, four velocity response groups have been distinguished: velocity broadband, low-pass, high-pass, and -tuned cells. This study describes an analytic model of feed-forward spatiotemporal interactions within a receptive field that reproduces these basic features of cortical simple cell behavior in the cat. 2. The spatial structure of the receptive fields is simulated with Gabor functions. Two neurobiologically plausible mechanisms, temporal low-pass filtering and intracortical spatial distribution of activity, are modeled. The central feature of the study is the implementation of both mechanisms in a spatially continuous way. The model is analytic, but an equivalent neural network diagram was drawn and is used to explain the features of the model. 3. First-order temporal low-pass filtering is performed both after convolving the stimulus light-intensity function with the Gabor type receptive field and also at the final output step of the model. In the circuit diagram this would correspond to low-pass filtering in lateral geniculate nucleus (LGN) and cortical cells. Filtering was adjusted to have a -3-dB drop-off frequency of 2-3 Hz, corresponding to the drop-off frequencies observed in response to temporal modulation of sine-wave gratings. 4. The mechanism that we call intracortical distribution of activity is implemented along the axis of stimulus motion. A response elicited from the part of the receptive field that is stimulated at a given time will spread out in the receptive field, influencing regions that have not been stimulated. It is equivalent to spreading of activity on the cortical surface. This mechanism extends the existing ideas of discrete interactions between subfields to a continuous scheme throughout the whole receptive field. It is based on findings that intracortical interactions exist even within single subfields. The impact of distributing the activity is assumed to decrease exponentially with the Euclidian distance between the stimulated region and the region under consideration. 5. Thresholds are implemented only at the level of the cortex. Both the activity distributing mechanism and the output of the cell being studied are thresholded.(ABSTRACT TRUNCATED AT 400 WORDS)

The receptive fields of complex cells in the early visual cortex are economically modeled by combining outputs of a quadrature pair of linear filters. For actual complex cells, such a minimal model may be insufficient because many more simple cells are thought to make up a complex cell receptive field. To examine the minimalist model physiologically, we analyzed spatial relationships between the internal structure (subunits) and the overall receptive fields of individual complex cells by a two-stimulus interaction technique. The receptive fields of complex cells are more circular and only slightly larger than their subunits in size. In addition, complex cell subunits occupy spatial extents similar to those of simple cell receptive fields. Therefore in these respects, the minimalist schema is a fair approximation to actual complex cells. However, there are violations against the minimal model. Simple cell receptive fields have significantly fewer subregions than complex cell subunits and, in general, simple cell receptive fields are elongated more horizontally than vertically. This bias is absent in complex cell subunits and receptive fields. Thus simple cells cannot be equated to individual complex cell subunits and spatial pooling of simple cells may occur anisotropically to constitute a complex cell subunit. Moreover, when linear filters for complex cell subunits are examined separately for bright and dark responses, there are significant imbalances and position displacements between them. This suggests that actual complex cell receptive fields are constructed by a richer combination of linear filters than proposed by the minimalist model.

I present measurements of the spatial structure of simple-cell receptive fields in macaque primary visual cortex (area V1). Similar to previous findings in cat area 17, the spatial profile of simple-cell receptive fields in the macaque is well described by two-dimensional Gabor functions. A population analysis reveals that the distribution of spatial profiles in primary visual cortex lies approximately on a one-parameter family of filter shapes. Surprisingly, the receptive fields cluster into even- and odd-symmetry classes with a tendency for neurons that are well tuned in orientation and spatial frequency to have odd-symmetric receptive fields. The filter shapes predicted by two recent theories of simple-cell receptive field function, independent component analysis and sparse coding, are compared with the data. Both theories predict receptive fields with a larger number of subfields than observed in the experimental data. In addition, these theories do not generate receptive fields that are broadly tuned in orientation and low-pass in spatial frequency, which are commonly seen in monkey V1. The implications of these results for our understanding of image coding and representation in primary visual cortex are discussed.

Responses of cat striate cortical cells to a drifting sinusoidal grating were modified by the superimposition of a second, perturbing grating (PG) that did not excite the cell when presented alone. One consequence of the presence of a PG was a shift in the tuning curves. The orientation tuning of all 41 cells exposed to a PG and the spatial frequency tuning of 83% of the 23 cells exposed to a PG showed statistically significant dislocations of both the response function peak and center of mass from their single grating values. As found in earlier reports, the presence of PGs suppressed responsiveness. However, reductions measured at the single grating optimum orientation or spatial frequency were on average 1.3 times greater than the suppression found at the peak of the response function modified by the presence of the PG. Much of the loss in response seen at the single grating optimum is thus a result of a shift in the tuning function rather than outright suppression. On average orientation shifts were repulsive and proportional (∼0.10 deg/deg) to the angle between the perturbing stimulus and the optimum single grating orientation. Shifts in the spatial frequency response function were both attractive and repulsive, resulting in an overall average of zero. For both simple and complex cells, PGs generally broadened orientation response function bandwidths. Similarly, complex cell spatial frequency response function bandwidths broadened. Simple cell spatial frequency response functions usually did not change, and those that did broadened only 4% on average. These data support the hypothesis that additional sinusoidal components in compound stimuli retune cells' response functions for orientation and spatial frequency.

We estimate the rates at which neurons in the primary visual cortex (V1) of anesthetized macaque monkeys transmit stimulus-related information in response to three types of visual stimulus. The stimuli—randomly modulated checkerboard patterns, stationary sinusoidal gratings, and drifting sinusoidal gratings—have very different spatiotemporal structures. We obtain the overall rate of information transmission, which we call formal information, by a direct method. We find the highest information rates in the responses of simple cells to drifting gratings (median: 10.3 bits/s, 0.92 bits/spike); responses to randomly modulated stimuli and stationary gratings transmit information at significantly lower rates. In general, simple cells transmit information at higher rates, and over a larger range, than do complex cells. Thus in the responses of V1 neurons, stimuli that are rapidly modulated do not necessarily evoke higher information rates, as might be the case with motion-sensitive neurons in area MT. By an extension of the direct method, we parse the formal information into attribute-specific components, which provide estimates of the information transmitted about contrast and spatiotemporal pattern. We find that contrast-specific information rates vary across neurons—about 0.3 to 2.1 bits/s or 0.05 to 0.22 bits/spike—but depend little on stimulus type. Spatiotemporal pattern-specific information rates, however, depend strongly on the type of stimulus and neuron (simple or complex). The remaining information rate, typically between 10 and 32% of the formal information rate for each neuron, cannot be unambiguously assigned to either contrast or spatiotemporal pattern. This indicates that some information concerning these two stimulus attributes is confounded in the responses of single neurons in V1. A model that considers a simple cell to consist of a linear spatiotemporal filter followed by a static rectifier predicts higher information rates than are found in real neurons and completely fails to replicate the performance of real cells in generating the confounded information.

1. We have studied the nature, development, and plasticity of local intracortical interactions by examining the visual responses from pairs of cells in the visual cortex of anesthetized and paralyzed adult cats and kittens at postnatal age 4 wk. Simultaneous discharge from nearby cells was analyzed by the cross-correlation method to infer three types of neuronal interactions: monosynaptic excitation, monosynaptic inhibition, and polysynaptic excitation. 2. Among cell pairs that exhibit correlated discharge, the nature of these interactions is similar in kittens and adults. For example, the mean monosynaptic delay is the same for cell pairs in the adult cat and the kitten: 0.8 ms. The primary difference in the distribution of neural interactions is the increased prevalence of inhibitory interactions among adult cat cell pairs compared with kitten cell pairs. However, in both age groups and in nearly all laminae, polysynaptic interactions are the most commonly observed type of interaction. 3. Neural interactions revealed by cross-correlation analysis also were studied with respect to the receptive field properties of the cells. The hierarchical theory proposed by Hubel and Wiesel suggests that monosynaptic excitation should be seen from simple to complex cells. It further suggests that complex cells do not provide monosynaptic excitation either to simple or to other complex cells. However, we find no cases of monosynaptic excitation from simple to complex cells in the adult cat. Moreover, we find explicitly antihierarchical connections, i.e., excitatory connections from complex to simple cells, in both kittens and adults. The excitatory influence of complex cells on simple cell receptive field properties is not incorporated into current models of receptive field structure formation. Our results suggest that complex cells might have an important modulatory role in simple cell discharge. 4. Plasticity of intracortical synaptic connections was studied by examining the dynamics of monosynaptic peaks with cross-correlograms. We examined Hebb's seminal hypothesis regarding synaptic plasticity that the excitatory connections between two neurons should strengthen with simultaneous activity. To test directly whether Hebbian plasticity can be rapidly induced by stimulus-evoked activity, the strength of monosynaptic excitation between pairs of neurons was monitored during periods of visual stimulation lasting < or = 2 h. Synaptic strength was computed by summing the cross-correlogram bins containing the monosynaptic peak. Transient increases in monosynaptic peak area are found among cell pairs linked by monosynaptic excitation after 8-15 min of visual stimulation. The duration and amplitude of these changes are similar in adult cats and kittens.(ABSTRACT TRUNCATED AT 400 WORDS)

1. Responses of simple cells in cat striate cortex were studied with flashed light-slit stimuli. The responses to bars flashed in different positions in the receptive field were assessed quantitatively before and after periods of prolonged stimulation of one small region. This type of prolonged stimulation resulted in reduced responsivity over a limited zone within the simple cell receptive field. 2. The adaptation-induced responsivity decrement was generally confined to the receptive-field subregion that was adapted (either ON or OFF). Prolonged stimulation within an ON region did not usually result in adaptation effects that spread into neighboring OFF regions. Furthermore, the adaptation-induced response decrement did not necessarily spread throughout the subregion in which the adapting stimulus was presented. The adaptation effects from prolonged stimulation at a single receptive-field position spread throughout the subregion in nearly one-half of the 25 cells examined for position-specific adaptation. Another subpopulation of neurons (n = 12) displayed adaptation effects that spread through only one-half of the subregion, whereas in two neurons the spread of the adaptation effect was even more restricted and encompassed only one-fourth of the subregion. 3. The spread of adaptation was not systematically related to the size of the stimulus presented, the size of the receptive field, or the magnitude of the adaptation-induced response decrements but was significantly correlated with the spatial wavelength of the cell (the reciprocal of the cell's preferred spatial frequency) and with the size of the subregion in which the adapting stimulus was presented. Cells with large receptive-field subregions and long wave-lengths showed adaptation effects that spread further than those of cells with small subregions. 4. The adaptation effects from repeated stimulation at a single receptive-field position did not spread symmetrically across the receptive field, and the preferred direction of motion for a given cell indicated the direction of the asymmetric spread of the adaptation. Receptive-field positions that would be stimulated by a light slit originating at the point of adaptation and moving in the preferred direction (preferred side) showed greater adaptation-induced response decrements than did receptive-field positions that would be stimulated by a light slit moving in the opposite direction from the point of adaptation (nonpreferred side). There was significant enhancement of responses at some receptive-field positions on the nonpreferred side of the point of adaptation.(ABSTRACT TRUNCATED AT 400 WORDS)

1. Using the two-dimensional (2D) spatial and spectral response profiles described in the previous two reports, we test Daugman's generalization of Marcelja's hypothesis that simple receptive fields belong to a class of linear spatial filters analogous to those described by Gabor and referred to here as 2D Gabor filters. 2. In the space domain, we found 2D Gabor filters that fit the 2D spatial response profile of each simple cell in the least-squared error sense (with a simplex algorithm), and we show that the residual error is devoid of spatial structure and statistically indistinguishable from random error. 3. Although a rigorous statistical approach was not possible with our spectral data, we also found a Gabor function that fit the 2D spectral response profile of each simple cell and observed that the residual errors are everywhere small and unstructured. 4. As an assay of spatial linearity in two dimensions, on which the applicability of Gabor theory is dependent, we compare the filter parameters estimated from the independent 2D spatial and spectral measurements described above. Estimates of most parameters from the two domains are highly correlated, indicating that assumptions about spatial linearity are valid. 5. Finally, we show that the functional form of the 2D Gabor filter provides a concise mathematical expression, which incorporates the important spatial characteristics of simple receptive fields demonstrated in the previous two reports. Prominent here are 1) Cartesian separable spatial response profiles, 2) spatial receptive fields with staggered subregion placement, 3) Cartesian separable spectral response profiles, 4) spectral response profiles with axes of symmetry not including the origin, and 5) the uniform distribution of spatial phase angles. 6. We conclude that the Gabor function provides a useful and reasonably accurate description of most spatial aspects of simple receptive fields. Thus it seems that an optimal strategy has evolved for sampling images simultaneously in the 2D spatial and spatial frequency domains.

1. A reverse correlation (6, 8, 25, 35) method is developed that allows quantitative determination of visual receptive-field structure in two spatial dimensions. This method is applied to simple cells in the cat striate cortex. 2. It is demonstrated that the reverse correlation method yields results with several desirable properties, including convergence and reproducibility independent of modest changes in stimulus parameters. 3. In contrast to results obtained with moving stimuli, we find that the bright and dark excitatory subregions in simple receptive fields do not overlap to any great extent. This difference in results may be attributed to confounding the independent variables space and time when using moving stimuli. 4. All simple receptive fields have subregions that vary smoothly in all directions in space. There are no sharp transitions either between excitatory subregions or between subregions and the area surrounding the receptive field. 5. Simple receptive fields vary both in the number of subregions observed, in the elongation of each subregion, and in the overall elongation of the field. In contrast with results obtained using moving stimuli, we find that subregions within a given receptive field need not be the same length. 6. The hypothesis that simple receptive fields can be modeled as either even symmetric or odd symmetric about a central axis is evaluated. This hypothesis is found to be false in general. Most simple receptive fields are neither even symmetric nor odd symmetric. 7. The hypothesis that simple receptive fields can be modeled as the product of a width response profile and an orthogonal length response profile (Cartesian separability) is evaluated. This hypothesis is found to be true for only approximately 50% of the cells in our sample.

The organization of geniculate inputs to a cat's visual cortical cell was studied by a cross-correlation technique. Simultaneous extracellular recordings were made in the lateral geniculate nucleus and in the striate cortex, and neuronal connectivity between a geniculate cell and a striate cell was examined by cross-correlograms of their impulse discharges under photic stimuli. Of 243 pairs of geniculate and striate cells with overlapping receptive fields, 82 showed positive correlations with short (0.9-2.7 ms) delay times. The delays in 65 of the 82 pairs were short enough to infer that the geniculate cell exerted monosynaptic excitatory action on the striate cell. Monosynaptic excitations were found in all types of striate cells. Those in cells with exclusively an on area or an off area (E-on/off cells) or in simple cells originated mostly from X geniculate cells; those in special-complex cells originated exclusively from Y geniculate cells; and those in standard-complex cells arose from both X and Y geniculate cells. The convergence number from geniculate cells to an E-on/off or simple striate cell was estimated as more than 10, since about 1/10 of the discharges from an E-on/off or simple cell in response to a moving stimulus was correlated with discharges from a geniculate cell. A larger convergence number (more than 30) was obtained for complex cells. Convergence from 2 to 5 geniculate cells was actually demonstrated in 17 of the 32 striate cells, each of which was tested in pair with 3-14 geniculate cells. The converging inputs thus observed included both X and Y geniculate cells in one E-on, one simple, and three standard-complex cells. They included both on-center and off-center geniculate cells in one simple, one special-complex, and five standard-complex cells. Under stimulation with a stationary light slit, the center fields but not the surround fields of geniculate cells were found to contribute to the receptive fields of the simple striate cells. However, the surround fields of geniculate cells contributed to the subliminal response areas flanking the central areas of E-on/off cells. The center fields of the geniculate cells also contributed to the central areas of the E-on/off cells. These observations suggest different models for simple cells and E-on/off cells as regards the organization of their geniculate inputs; simple cells may receive inputs from both on-center and off-center geniculate cells, but E-on/off cells receive inputs only from one or the other of them.

Following our earlier study on direction selectivity in simple cells (5), the present findings on complex cells made it possible to compare the direction selectivity in the two types of striate cell. Common properties were found in the dimension of the smallest stimulus displacement giving a direction-selective response and in the role of inhibition in suppressing the response as the stimulus moved in the nonpreferred direction. However, the effectiveness of this inhibition varied in the two cell types since it suppressed both driven and spontaneous activity in the simple cell, but only driven firing in the complex cell. It is argued that direction selectivity must enter the response before the complex cell if the inhibition responsible for it's generation fails to influence the spontaneous activity of the cell. The consequences of this finding are considered in the terms of parallel or sequential processing of visual information in striate cortex.