Space-Time RF of Simple Cells: II. Linearity

Citation Info

Gregory C. DeAngelis, Izumi Ohzawa, and Ralph D. Freeman (1993b)
Spatiotemporal organization of simple-cell receptive fields in the cat's striate cortex. II. Linearity of temporal and spatial summation.
J. Neurophysiol. 69: 1118-1135.
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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. These results are generally consistent with recent theoretical work in which simple cells are modelled as the combination of a linear spatiotemporal filter, an exponent nonlinearity, and a contrast normalization mechanism.