Simple cells in the striate cortex have been depicted as half-wave-rectified linear operators. Complex cells have been depicted as energy mechanisms, constructed from the squared sum of the outputs of quadrature pairs of linear operators. However, the linear/energy model falls short of a complete explanation of striate cell responses. In this paper, a modified version of the linear/energy model is presented in which striate cells mutually inhibit one another, effectively normalizing their responses with respect to stimulus contrast. This paper reviews experimental measurements of striate cell responses, and shows that the new model explains a significantly larger body of physiological data.

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

Normalization of cell responses in cat striate cortex

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.

Spatial summation in the receptive fields of simple cells in the cat's striate cortex.

Primate visual cortical area 18 (visual area 2), when stained for the enzyme cytochrome oxidase, shows a pattern of alternating dark and light stripes; in squirrel monkeys, the dark stripes are clearly of 2 alternating types, thick and thin. We have recorded from these 3 subdivisions in macaques and squirrel monkeys, and find that each has distinctive physiological properties: (1) Cells in one set of dark stripes, in squirrel monkeys the thin stripes, are not orientation- selective; a high proportion show color-opponency. (2) Cells in the other set of dark stripes (thick stripes) are orientation-selective; most of them are also selective for binocular disparity, suggesting that they are concerned with stereoscopic depth. (3) Cells in the pale stripes are also orientation-selective and more than half of them are end-stopped. Each of the 3 subdivisions receives a different input from area 17: the thin stripes from the blobs, the pale stripes from the interblobs, the thick stripes from layer 4B. The pale stripes are thus part of the parvocellular system, and the thick stripes part of the magnocellular system. The physiological properties of the cells in the thin and pale stripes reflect the properties of their antecedent cells in 17, but nevertheless exhibit differences that suggest the kinds of processing that might occur at this stage.

https://www.jneurosci.org/content/jneuro/7/11/3378.full.pdf

Segregation of form, color, and stereopsis in primate area 18.

Organization of visual pathways in normal and visually deprived cats.

1. All complex cells in the cat's striate cortex exhibit gross non-linearities of spatial summation when tested with sinusoidal grating stimuli. Their responses to moving gratings of all but the lowest spatial frequencies are usually dominated by a component that is not modulated by the passage of the bars of the grating across the receptive field. They give responses to temporally modulated stationary gratings that consist mostly of even harmonics of the stimulus frequency and that vary little in amplitude or wave form as the spatial phase of the grating is varied. 2. We compared complex cells' receptive fields with their sensitivity to sinusoidal gratings of different spatial frequencies. Qualitatively, the receptive fields are usually two to five times wider than the bars of the gratings that stimulate them most effectively. Quantitatively, the receptive field profiles of complex cells are invariably broader than those predicted by Fourier synthesis of their spatial frequency tuning curves, and in particular lack predicted spatially antagonistic regions. 3. We further examined the receptive field organization of these cells, using pairs of stationary lines flashed synchronously on their receptive fields. If both lines are of the same polarity (bright or dark), complex cells respond to the paired stimulus much less well than they do to either of its component bars, unless the bars are separated by less than about one quarter of the width of the receptive field. If the lines are of opposite polarity, one bright and one dark, the opposite situation obtains: closely spaced bars elicit small responses, while paired bars of larger separation are much more effective. In either case, the results are independent in general character of the absolute positions of the stimuli within the receptive field; rather, they depend in a manner characteristic of each cell on the relative positions of the two bars. 4. The two-line interaction profile that plots the change in a complex cell's response to one bar as a function of the position of a second added bar corresponds closely to the receptive field profile predicted from Fourier synthesis of the cell's spatial frequency tuning curve. These profiles may thus reveal the spatial characteristics of subunits within complex cell-receptive fields. We examined the nature of the interaction between these subunits by performing several two-line interaction experiments in which the onset of the second bar was delayed some time after the onset of the first. The results suggest that neighbouring subunits interact in a facilitatory fashion: for an interval after the presentation of one bar, responses to neighbouring bars are enhanced. 5. The subunits of a complex receptive field may, by their spatial properties, determine the spatial selectivities of complex cells, while the nature of the interaction among the subunits may determine these cells' sensitivity and selectivity for moving visual stimuli...

Receptive field organization of complex cells in the cat's striate cortex.

1. The responses of single units in the cat's primary visual cortex to moving bars have been examined quantitatively as a function of bar length.2. For about half the cells studied, very long bars evoked weaker responses than short bars, implying that there were inhibitory regions flanking the receptive field centre. In another quarter of the cell sample, there was evidence of flanking regions which were facilitatory in effect.3. The strength of the flanking regions was found to vary from cell to cell and there was no sudden transition between cells which were ;hyper-complex' and those which were not.4. Within the central region of the receptive field, the responses of most (but not all) cells increased with bar length. About half the cells responded to very short bars or spots of light, but about one in six would not respond at all to short bars.5. Correlations were sought between the properties of cells as simple or complex, their responsiveness to moving spots of light, the size of their receptive field centre and the polarity, strength and size of their receptive field flanks. Simple and complex cells with small receptive fields were more likely to respond well to spots, and to have strong inhibitory flanks.6. Correlations were also sought between the above properties and several other parameters of cell behaviour. Cells with strong inhibitory flanks were found to be more broadly tuned for orientation. Individual cells were also more broadly tuned for the orientation of short bars than of long bars.7. Evidence was obtained that spatial summation can be linear or non-linear for different cells.

https://physoc.onlinelibrary.wiley.com/doi/pdf/10.1113/jphysiol.1977.sp011987

David Rose

Papers

Responses of single units in cat visual cortex to moving bars of light as a function of bar length.