Simple cell

Abstract: 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.

Abstract: 1. We have examined the responses of simple cells in the cat's atriate cortex to visual patterns that were designed to reveal the extent to which these cells may be considered to sum light-evoked influences linearly across their receptive fields. We used one-dimensional luminance-modulated bars and grating as stimuli; their orientation was always the same as the preferred orientation of the neurone under study. The stimuli were presented on an oscilloscope screen by a digital computer, which also accumulated neuronal responses and controlled a randomized sequence of stimulus presentations. 2. The majority of simple cells respond to sinusoidal gratings that are moving or whose contrast is modulated in time in a manner consistent with the hypothesis that they have linear spatial summation. Their responses to moving gratings of all spatial frequencies are modulated in synchrony with the passage of the gratings' bars across their receptive fields, and they do not produce unmodulated responses even at the highest spatial frequencies. Many of these cells respond to temporally modulated stationary gratings simply by changing their response amplitude sinusoidally as the spatial phase of the grating the grating is varied. Nonetheless, their behavior appears to indicate linear spatial summation, since we show in an Appendix that the absence of a 'null' phase in a visual neurone need not indicate non-linear spatial summation, and further that a linear neurone lacking a 'null' phase should give responses of the form that we have observed in this type of simple cell. 3. A minority of simple cells appears to have significant non-linearities of spatial summation. These neurones respond to moving gratings of high spatial frequency with a partially or totally unmodulated elevation of firing rate. They have no 'null' phases when tested with stationary gratings, and reveal their non-linearity by giving responses to gratings of some spatial phases that are composed partly or wholly of even harmonics of the stimulus frequency ('on-off' responses). 4. We compared simple receptive fields with their sensitivity to sinusoidal gratings of different spatial frequencies. Qualitatively, the most sensitive subregions of simple cells' receptive fields are roughly the same width as the individual bars of the gratings to which they are most sensitive. Quantitatively, their receptive field profiles measured with thin stationary lines, agree well with predicted profiles derived by Fourier synthesis of their spatial frequency tuning curves.

Abstract: 1 The iontophoretic application of the GABA antagonist bicuculline to simple and complex cells in the striate cortex of the cat produced extensive modifications of receptive field properties These modifications appear to relate to a block or reduction of GABA-mediated intracortical inhibitory influences acting on the cells examined 2 For simple cells the effects of bicuculline on receptive field properties involved a loss of the subdivision of the receptive field into antagonistic "on" and "off" regions, a reduction in orientation specificity and a reduction or elimination of directional specificity 3 The effect on the "on" and "off" subdivisions of the simple cell receptive field was such that all stationary flashing stimuli, whether covering the whole receptive field, or located within the receptive field over a previously determined "on" or "off" region, resulted in an "on and off" response 4 The orientation specificity of complex cells was reduced during the application of bicuculline such that in many cases the original specificity of the cell was virtually lost with the response to the orientation at 90 degrees to the optimal being of similar magnitude to the optimal The directional specificity of complex cells was generally less affected than that of simple cells Often when large changes in orientation specificity were observed the directional specificity was relatively unaffected 5 For some cells apparently showing to all visual stimuli only inhibitory responses, the application of bicuculline resulted in the appearance of excitatory responses 6 In all cases receptive field properties reverted to the original state after termination of the bicuculline application It was not generally possible to duplicate the effects of bicuculline by raising neuronal excitability with iontophoretically applied glutamate 7 On the basis of these results it is suggested that the normal subdivision of the simple cell receptive field into separate "on" and "off" regions and its directional specificity are dependent on intracortical inhibitory processes that are blocked by bicuculline The orientational tuning of simple cells conversely appears to be largely determined by the excitatory input but normally enhanced by lateral type inhibitory processes acting in the orientation domain 8 It also appears that the excitatory input to some complex cells is not orientation specific This suggests that for these cells it is extremely unlikely that they receive an orientation specific excitatory input from simple cells

Abstract: Recordings from monkey primary visual cortex (V1) were used to test a model for the visually driven responses of simple cells. According to the model, simple cells compute a linear sum of the responses of lateral geniculate nucleus (LGN) neurons. In addition, each simple cell's linear response is divided by the pooled activity of a large number of other simple cells. The cell membrane performs both operations; synaptic currents are summed and then divided by the total membrane conductance. Current and conductance are decoupled (by a complementary arrangement of excitation and inhibition) so that current depends only on the LGN inputs and conductance depends only on the cortical inputs. Closed form expressions were derived for fitting and interpreting physiological data. The model accurately predicted responses to drifting grating stimuli of various contrasts, orientations, and spatiotemporal frequencies.