The nonlinear pathway of Y ganglion cells in the cat retina.

Retinal ganglion cells of the Y type in the cat retina produce two different types of response: linear and nonlinear. The nonlinear responses are generated by a separate and independent nonlinear pathway. The functional connectivity in this pathway is analyzed here by comparing the observed second-order frequency responses of Y cells with predictions of a "sandwich model" in which a static nonlinear stage is sandwiched between two linear filters. The model agrees well with the qualitative and quantitative features of the second-order responses. The prefilter in the model may well be the bipolar cells and the nonlinearity and postfilter in the model are probably associated with amacrine cells.

Receptive field mechanisms of cat X and Y retinal ganglion cells.

We investigated receptive field properties of cat retinal ganglion cells with visual stimuli which were sinusoidal spatial gratings amplitude modulated in time by a sum of sinusoids. Neural responses were analyzed into the Fourier components at the input frequencies and the components at sum and difference frequencies. The first-order frequency response of X cells had a marked spatial phase and spatial frequency dependence which could be explained in terms of linear interactions between center and surround mechanisms in the receptive field. The second-order frequency response of X cells was much smaller than the first-order frequency response at all spatial frequencies. The spatial phase and spatial frequency dependence of the first-order frequency response in Y cells in some ways resembled that of X cells. However, the Y first-order response declined to zero at a much lower spatial frequency than in X cells. Furthermore, the second-order frequency response was larger in Y cells; the second-order frequency components became the dominant part of the response for patterns of high spatial frequency. This implies that the receptive field center and surround mechanisms are physiologically quite different in Y cells from those in X cells, and that the Y cells also receive excitatory drive from an additional nonlinear receptive field mechanism.

The eel retina. Ganglion cell classes and spatial mechanisms.

We have been able to separate optic fibers in the eye of the eel Anguilla rostrata into two distinct classes on the basis of spatial summation properties. X fibers, the first class, are like X ganglion cells in the cat: they have null positions for contrast reversal sine gratings; they respond at the modulation frequency; and many have a strong surround mechanism. X fibers, the second class, respond with an "on-off" response to local stimulation, to diffuse light modulation, to coarse drifting gratings, and to contrast reversal gratings. We have put forward a model for the receptive field of X fibers which involves two subunits, with rectification before the subunits add their signals. This model accounts for many of the quirks of X fibers.

The eel retina. Receptor classes and spectral mechanisms.

Light and electron microscopy revealed that there are both rods and cones in the retina of the eel Anguilla rostrata. The rods predominate with a rod to cone ratio of 150:1. The spectral sensitivity of the dark-adapted eyecup ERG had a peak at about 520 nm and was well fit by a vitamin A2 nomogram pigment with a lambdamax = 520 nm. This agrees with the eel photopigment measurements of other investigators. This result implies that a single spectral mechanism--the rods--provides the input for the dark-adapted ERG. The spectral sensitivity of the ERG to flicker in the light-adapted eyecup preparation was shifted to longer wavelengths; it peaked at around 550 nm. However, there was evidence that this technique might not have completely eliminated rod intrusion. Rod responses were abolished in a bleached isolated retina preparation, in which it was shown that there were two classes of cone-like mechanisms, one with lambdamax of 550 nm and the other with lambdamax of less than 450 nm. Ganglion cell recording provided preliminary evidence for opponent-color processing. Horizontal cells were only of the L type with both rod and cone inputs.

The relatively small decline in orientation acuity as stimulus size decreases.

Orientation acuity was measured with circular patches of sinusoidal gratings of various sizes. Threshold estimates were lowest (acuity highest) for the largest size patch, and increased as the stimulus size was reduced, consistent with the results of many researchers using line stimuli. These results are compared with the predictions of a simple and widely accepted model of spatial vision whereby the output of independent feed-forward filters are combined to produce threshold estimates. Specifically, the rectified output of a number of independent filters (i.e. Gabors) spanning the stimulus space (i.e. orientation) are combined via Bayesian decision theory. This model cannot account quantitatively for the relatively low thresholds estimated for the small sized stimuli when compared to the thresholds measured with larger patches. Application of a comparable analysis, with preliminary measurements of neuronal responses from primary visual cortex replacing the response rectified Gabor filter's responses, provides a more reasonable account of behavioral acuity. This indicates a fundamental inadequacy of the feed-forward filter model in accounting for V1 neurons' role in perception.

Contextual influences on orientation discrimination: binding local and global cues.

We sought to determine how local and global features within an image interact by examining whether orientation discrimination thresholds could be modified by contextual information. In particular, we investigated how local orientation signals within an image are pooled together, and whether this pooling process is dependent on the global orientation content present in the image. We find that observers' orientation judgments depend on surround contextual information, with performance being optimal when the center and surround stimuli are clearly distinct. In cases where the center and surround were not clearly segregated, we report two sets of results. If there was an ambiguity regarding the perception of a global structure (i.e. a small mismatch between local cues), observers' performance was impaired. If there was no mismatch and local and global cues were consistent with the perception of a single surface, observers performed as well as in the distinct surfaces case. Although some of our results can be largely accounted for by interactions between differently oriented filters, other aspects are more difficult to reconcile with this explanation. We suggest that low level filtering constrains observers' performance, and that influences arising from image segmentation modify how local orientation signals are pooled together.

Linearity and non-linearity in cortical receptive fields.

Visual neurons in striate (V1) cortex have been studied as feature detectors or as spatiotemporal filters. A useful way to distinguish between these two conceptual approaches is by studying the way in which visual signals are pooled across space and time. Many neurons in layer IV of striate cortex exhibit linear spatial summation and their response time course is consistent with linear temporal summation. Neurons in supragranular and infragranular layers sum signals in a non-linear manner. A particularly important non-linearity seen in many cortical complex cells is non-linear summation along an axis parallel to their preferred orientation. This leads to responsiveness to 'illusory contours', borders defined by texture differences only. These and other results on non-linear summation of chromatic and achromatic signals imply that V1 cortex performs sophisticated and complex image processing and is not simply an array of spatiotemporal filters.

The effect of contrast on the transfer properties of cat retinal ganglion cells.

1. Variation in stimulus contrast produces a marked effect on the dynamics of the cat retina. This contrast effect was investigated by measurement of the responses of X and Y ganglion cells. The stimuli were sine gratings or rectangular spots modulated by a temporal signal which was a sum of sinusoids. Fourier analysis of the neural response to such a stimulus allowed us to calculate first order and second order frequency kernels. 2. The first order frequency kernel of both X and Y ganglion cells became more sharply tuned at higher contrasts. The peak amplitude also shifted to higher temporal frequency at higher contrasts. Responses to low frequencies of modulation (less than 1 Hz) grew less than proportionally with contrast. However, response amplitudes at higher modulation frequencies (greater than 4 Hz) scaled approximately proportionally with contrast. Also, there was a marked phase advance in these latter components as contrast increased. 3. The contrast effect was significantly larger for Y cells than for X cells. 4. The first order frequency kernel was measured with single sine waves as well as with the sum of sinusoids as a modulation signal. The transfer function measured in this way was much less affected by increases in contrast. This implied that stimulus energy at one temporal frequency could affect the response amplitude and phase shift at another temporal frequency. 5. Direct proof was found that modulation at one frequency modifies the response at other frequencies. This was demonstrated by perturbation experiments in which the modulation stimulus was the sum of one strong perturbing sinusoid and seven weak test sinusoids. 6. The shape of the graph of the amplitude of the first order frequency kernel vs. temporal frequency did not depend on the amplitudes of the first order components, but rather on local retinal contrast. This was shown in an experiment with a sine grating placed at different positions in the visual field. The shape of the first order kernel did not vary with spatial phase, while the magnitudes of the first order responses varied greatly with spatial phase. 7. Models for the contrast gain control mechanism are considered in the Discussion.

The effect of contrast on the non-linear response of the Y cell.

1. Second-order frequency responses were obtained from cat retinal ganglion cells of the Y type. The cells were stimulated by a spatial sine grating whose contrast was modulated in time by a sum of eight sinusoids. 2. Second-order frequency responses obtained at higher contrasts have a peak amplitude at higher input temporal frequency, and phase shifts, compared to their low-contrast counterparts. 3. This change in shape of the second-order frequency response is a departure from the prediction of the linear/static non-linear/linear sandwich model of the non-linear pathway in the cat retina. The departure is analysed by means of the hypothesis that the two filters of the sandwich model are parametric in contrast. 4. Most of the change in shape of the second-order frequency response with contrast is accounted for in terms of the sandwich model by changes in the transfer characteristics of the filter preceding the static non-linearity. 5. The effect of contrast on the second-order responses of Y cells is qualitatively similar in several ways to the effect of contrast on first-order responses. This suggests that the contrast gain control mechanism acts early in the retina, before linear and non-linear pathways have diverged.

How the contrast gain control modifies the frequency responses of cat retinal ganglion cells.

1. A model is proposed for the effect of contrast on the first-order frequency responses of cat retinal ganglion cells. The model consists of several cascaded low pass filters ('leaky integrators') followed by a single stage of negative feed-back. 2. Values of time constants and gain of the components in this model were chosen to approximate (with least-squared deviation) experimentally measured first-order frequency responses. In the experiments used for the analysis, the visual stimulus was a sine grating modulated by a sum of sinusoids. 3. For both X cells and Y cells, the over-all gain and the time constants of the cascade of low pass filters were insensitive to contrast. 4. In all cells, the gain-bandwidth product of the negative feed-back loop was markedly increased with increasing contrast. 5. The effect of stimulation in the periphery of the receptive fields on the first-order frequency response to a centrally placed spot was identical to the effect of increasing contrast in the grating experiments. In all cases, the gain-bandwidth product of the negative feed-back loop was the only model parameter affected by peripheral stimulation. 6. A similar effect of non-linear summation was investigated for two bars located in the receptive field periphery. 7. This analysis of the contrast gain control mechanism is compared with other models of retinal function.

Nonlinear spatial summation and the contrast gain control of cat retinal ganglion cells.

1. We studied how responses to visual stimuli at spatially separated locations were combined by cat retinal ganglion cells. 2. The temporal signal which modulated the stimuli was a sum of sinusoids. Fourier analysis of the ganglion cell impulse train yielded first order responses at the modulation frequencies, and second order responses at sums and differences of the input frequencies. 3. Spatial stimuli were spots in the centre and periphery of the cell's receptive field. Four conditions of stimulation were used: centre alone, periphery alone, centre and periphery in phase, centre and periphery out of phase. 4. The effective first order response of the centre was defined as the response due to centre stimulation in the presence of periphery stimulation, but independent of the relative phases of the two regions. Likewise, the effective first order response of the periphery was defined as the response due to periphery in the presence of centre stimulation, but independent of the relative phases of the two regions. These effective responses may be calculated by addition and subtraction of the measured responses to the combined stimuli. 5. There was a consistent difference between the first order frequency kernal of the effective centre and the first order kernel of the centre alone. The amplitudes of the effective centre responses were diminished at low frequencies of modulation compared to the isolated centre responses. Also, the phase of the effective centre's response to high frequencies was advanced. Such non-linear interaction occurred in all ganglion cells, X or Y, but the effects were larger in Y cells. 6. In addition to spatially uniform stimuli in the periphery, spatial grating patterns were also used. These peripheral gratings affected the first order kernal of the centre even though the peripheral gratings produced no first order responses by themselves. 7. The temporal properties of the non-linear interaction of centre and periphery were probed by modulation in the periphery with single sinusoids. The most effective temporal frequencies for producing non-linear summation were: (a) 4-15 Hz when all the visual stimuli were spatially uniform, (b) 2-8 Hz when spatial grating patterns were used in the periphery. 8. The characteristics of non-linear spatial summation observed in these experiments are explained by the properties of the contrast gain control mechanism which we have previously postulated.

The primate retina contains two types of ganglion cells, with high and low contrast sensitivity.

Previously, we discovered that the broadband cells in the two magnocellular (large cell) layers of the monkey lateral geniculate nucleus (LGN) are much more sensitive to luminance contrast than are the color-sensitive cells in the four parvocellular (small cell) layers. We now report that this large difference in contrast sensitivity is due not to LGN circuitry but to differences in sensitivity of the retinal ganglion cells that provide excitatory synaptic input to the LGN neurons. This means that the parallel analysis of color and luminance in the visual scene begins in the retina, probably at a retinal site distal to the ganglion cells.

Adaptation and dynamics of cat retinal ganglion cells.

1. The impulse/quantum (I/Q) ratio was measured as a function of background illumination for rod-dominated, pure central, linear square-wave responses of retinal ganglion cells in the cat.2. The I/Q ratio was constant at low backgrounds (dark adapted state) and inversely proportional to the 0.9 power of the background at high backgrounds (the light adapted state). There was an abrupt transition from the dark-adapted state to the light-adapted state.3. It was possible to define the adaptation level at a particular background as the ratio (I/Q ratio at that background)/(dark adapted I/Q ratio).4. The time course of the square-wave response was correlated with the adaptation level. The response was sustained in the dark-adapted state, partially transient at the transition level, and progressively more transient the lower the impulse/quantum ratio of the ganglion cell became. This was true both for on-centre and off-centre cells.5. The frequency response of the central response mechanism at different adaptation levels was measured. It was a low-pass characteristic in the dark-adapted state and became progressively more of a bandpass characteristic as the cell became more light-adapted.6. The rapidity of onset of adaptation was measured with a time-varying adapting light. The impulse/quantum ratio is reset within 100 msec of the onset of the conditioning light, and is kept at the new value throughout the time the conditioning light is on.7. These results can be explained by a nonlinear feedback model. In the model, it is postulated that the exponential function of the horizontal cell potential controls transmission from rods to bipolars. This model has an abrupt transition from dark- to light-adapted states, and its response dynamics are correlated with adaptation level.

Flux, not retinal illumination, is what cat retinal ganglion cells really care about.

1. Evidence was obtained that the impulse/quantum (I/Q) ratio of the central response mechanism of retinal ganglion cells in the cat is controlled by the steady effective retinal flux of the background.2. One experiment revealed that the I/Q ratio was decreased as the area of an adapting spot, of constant illumination, was increased. The curve relating the I/Q ratio to background flux was the same regardless of the size of the adapting spot.3. The effective central summing area of many retinal ganglion cells was determined. For the same cells, the transition level (Enroth-Cugell & Shapley, 1973) of the impulse/quantum curve was also measured. Diffuse illumination at the transition level was inversely proportional to the effective summing area, when variation in dark-adapted sensitivity between cells was taken into account.4. Therefore, retinal ganglion cells with large central summing areas are more light-adapted by any given diffuse background than cells with small centres.

X and Y cells in the lateral geniculate nucleus of macaque monkeys.

1. Cells of the lateral geniculate nucleus (l.g.n.) in macaque monkeys were sorted into two functional groups on the basis of spatial summation of visually evoked neural signals. 2. Cells were called X cells if their responses to contrast reversal of fine sine gratings were at the fundamental temporal modulation frequency with null positions one quarter of a cycle away from positions for peak response. Cells were called Y cells if their responses to such stimuli were at twice the modulation frequency and were approximately independent of spatial phase. 3. Ninety-nine percent of the cells in the four dorsal parvocellular layers of the l.g.n. were X cells; about seventy-five percent of the cells in the two ventral magnocellular layers were also X cells. The remainder were Y cells. 4. We confirmed previous findings that magnocellular cells had a shorter latency of response to electrical stimulation of the optic chiasm. 5. Magnocellular cells had much higher contrast sensitivities than did parvocellular cells. 6. Therefore, two distinct classes of X cells exist in the macaque l.g.n.: parvocellular X cells and magnocellular X cells. The great difference in their properties suggests that they have different functions in vision. The Y cells in the magnocellular layers form a third functional group with spatial properties distinctly different from the X cells. 7. We propose that the magnocellular layers of the macaque monkey's l.g.n. may be homologous to the A and A1 layers of the cat's l.g.n.

Quantitative analysis of retinal ganglion cell classifications.

The classification of cat retinal ganglion cells as X or Y on the basis of linearity or nonlinearity of spatial summation has been confirmed and extended. Recordings were taken from optic tract fibres of anaesthetized, paralysed cats. 2. When an alternating phase sine wave grating was used as a stimulus, X cells had null positions and Y cells responded at all positions of the grating. 3. These results did not depend on the temporal wave form or the temporal frequency of pattern alternation over a wide range. 4. At high spatial frequencies for the particular cell, a Y cell gave abig 'on-off' response, or frequency doubling, at all positions of the grating, while an X cell did not. 5. The use of contrast sensitivity versus spatial phase also served to differentiate the two cell types. With an alternating sine grating stimulus X cells had a sinusoidal dependence on spatial phase, while each Y cell's sensitivity depended in a complicated manner on spatial phase. 6. Sensitivity versus spatial phase for different Fourier components of the neural response also separated the two classes of cells. Significant second harmonic distortion was present in Y cells. The second harmonic component was spatial phase insensitive, and became dominant at high spatial frequencies. 7. The maximum of the 2nd/1st harmonic ratio was taken as an index of nonlinearity. X cells always had a nonlinearity index less than 1 while in Y cells this index always exceeded 1. 8. Response to spots, diffuse light and drifting gratings were compared to the nonlinearity index as a basis for classifying cells. The nonlinearity index was most reliable because it was least dependent on retinal eccentricity.

Linear and nonlinear spatial subunits in Y cat retinal ganglion cells.

1. The mechanism which makes Y cells different from X cells was investigated. 2. Spatial frequency contrast sensitivity functions for the fundamental and second harmonic responses of Y cells to alternating phase gratings were determined. 3. The fundamental spatial frequency response was predicted by the Fourier transform of the sensitivity profile of the Y cell. The high spatial frequency cut-off of a Y cell's fundamental response was in this way related to the centre of the cell's receptive field. 4. The second harmonic response of a Y cell did not cut off at such a low spatial frequency as the fundamental response. This result indicated that the source of the second harmonic was a spatial subunit of the receptive field smaller in spatial extent than the centre. 5. Contrast sensitivity vs. spatial phase for a Y cell was measured under three conditions: a full grating, a grating seen through a centrally located window, a grating partially obscured by a visual shutter. The 2nd/1st harmonic sensitivity ratio went down with the window and up with the shutter. These results implied that the centre of Y cells was linear and also that the nonlinear subunits extended into the receptive field surround. 6. Spatial localization of the nonlinear subunits was determined by means of a spatial dipole stimulus. The nonlinear subunits overlapped the centre and surround of the receptive field and extended beyond both. 7. The nature of the Y cell nonlinearity was found to be rectification, as determined from measurements of the second harmonic response as a function of contrast. 8. Spatial models for the Y cell receptive field are proposed.

Edge detectors in human vision.

1. The spatial properties of edge detectors were measured psychophysically with the technique of subthreshold addition. Subthreshold patterns used to add to an edge were lines, sine gratings, Gaussian edges, and ramps.2. The sensitivity profile, determined from experiments on subthreshold addition of lines to an edge was an antisymmetric function, with peak sensitivity approximately +/- 1.5' from its midpoint. Its total extent was about +/- 6'.3. The spatial frequency response of edge detectors was measured in experiments on subthreshold addition of sine gratings to an edge. The spatial frequency response was peaked at about 3 c/deg, and was broadly tuned in frequency. It was approximately equal to the Fourier transform of the sensitivity profile, implying linearity of edge detectors.4. The visibility of Gaussian edges and ramps could be explained largely in terms of the activation of edge detector neurones.5. The role of edge detectors in perception, in creating apparent brightness, and as an explanation of contour illusions, is discussed.