Suppression and Contrast Normalization in Motion Processing

Superimposed static mask: dependence on SF and contrast

We started our investigation on the impact of a mask on the processing of motion information by measuring the vertical OFRs induced by a drifting (18.75 Hz) horizontal sinusoidal grating (stimulus) alone or in the presence of a superimposed static horizontal grating (mask). Both gratings had the same Michelson contrast (32%). The two gratings appeared together suddenly on a mid-luminance background and the stimulus started drifting immediately (phase change of 45° in each successive frame). The entire presentation lasted 24 frames (160 ms).

In Figure 1, we show the time course of two sample OFRs for three subjects. One trace (black) shows the OFR generated when the drifting stimulus (0.25 cpd, 32% contrast) was presented in isolation and the other (gray) shows the effect of adding to this drifting stimulus a static mask (0.5 cpd) having the same contrast. Space–time plots of both stimuli are shown in the leftmost panel. In all subjects, the mask strongly suppressed the response. To quantify this suppressive effect, we computed the average eye speed in a time window (slightly different for the three subjects and indicated with a horizontal bar above the time axis in Fig. 1), which is contained within the so-called open-loop period (the period during which the motion of the eyes cannot affect the processing of the visual stimulus). From here on, we focus on this measure, which we simply call the OFR.

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Figure 1.

Masking of sample OFRs. The sudden onset of a drifting horizontal sinusoidal grating (0.25 cpd SF, 18.75 Hz TF, 32% contrast) induces a short-latency (∼70 ms in humans) vertical OFR (black). When a static horizontal sinusoidal grating (0.5 cpd SF, 32% contrast) is added to the stimulus, the ensuing OFR is much smaller (gray), although its latency is unchanged. Most tuning properties of the OFR are highly similar across subjects, although the absolute magnitude of a response to a given stimulus can vary widely across subjects (vertical scale corresponds to 0.25 deg/s). We quantify the strength of the response by computing the average eye speed in a time window that goes from the onset of the response to twice the latency (open-loop period), indicated here with a gray bar above the abscissa. Space–time diagrams show the temporal evolution of unmasked and masked stimuli. Data are shown from three subjects (S1, S2, and S3).

To estimate the SF tuning of the suppressive mechanism(s), we varied independently the SF of stimulus and mask while keeping the contrast fixed at 32% for both stimulus and mask. In Figure 2A we show how the normalized response N (defined as the ratio between the OFR measured when the mask is present and that induced by the drifting grating alone) varies as a function of the SF of the two gratings. The drifting grating had one of three SFs: 0.125 cpd (red), 0.25 cpd (blue), or 0.5 cpd (green); the mask had one of six SFs (from 0.0625 to 2 cpd in one-octave steps). We fit the normalized response as a function of the SF of the mask separately for each SF of the drifting grating, using a log-Gaussian function (see Materials and Methods, Eq. 1). The SF associated with the strongest suppression (μ in Eq. 1, indicated with color-matched dots and SEM bars at the top of each panel) shifts significantly as the SF of the stimulus is varied. Parameter values for the fits are listed in Table 1.

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Figure 2.

SF tuning of masking suppression. A, When the SF of stimulus and mask are varied while keeping their contrast fixed (32% each), the extent of suppression varies widely. Here, three different SFs are used for the stimulus: 0.125 cpd (red), 0.25 cpd (blue), and 0.5 cpd (green). Each of these is paired with six SFs of the mask, from 0.0625 to 2.0 cpd in one-octave steps. For each SF of the stimulus, a SF of the mask can be found that exerts almost complete suppression. In all three subjects, the SF tuning of suppression varies considerably as a function of the SF of the stimulus (log-Gaussian fits are shown; Eq. 1). Small colored dots and bars indicate mean and SEM of the location of the trough in each fit. Parameters of the fitting functions (mean and SEM) as a function of the SF of the stimulus are shown in B–E. B, SF corresponding to the strongest attenuation (μ). C, FWHH bandwidth (γ). D, Low SF cutoff (SF_fL). E, High SF cutoff (SF_fH). Values for the parameters are also listed in Table 1.

In Figure 2 we also show, for each subject, mean and SEM of μ (Fig. 2B), bandwidth γ (Fig. 2C), low (Fig. 2D), and high (Fig. 2E) SF cutoff (SF at which the normalized response equals 0.8, Eq. 2) of the fitting functions, as a function of the SF of the moving grating. The low SF cutoff (Fig. 2D) shifts approximately in step with the SF of the moving grating and is approximately two octaves lower (1.78 octaves, average across all subjects and conditions), indicating that masks at a larger scale than the stimulus are not very effective. The high SF cutoff (Fig. 2E) is instead fairly constant at ∼5 cpd (4.76 cpd, average across all subjects and conditions). It follows that the bandwidth (Fig. 2C) decreases as the SF of the moving grating increases. Obviously, neither the absolute SF of the mask nor the relative SF of the two gratings fully determine the extent of suppression (Fig. 2B). Because the strongest effects are not seen when stimulus and mask have the same SF, they cannot simply be imputed to the impact that the mask has on the response of the linear filter that detects the stimulus. This is especially true for static masks, which are poor stimuli for direction-selective cells. This linear interaction, which is the subject of many psychophysical studies of masking, might play some role, but the bulk of the effects observed here reflect nonlinear interactions either in the feed-forward pathway or through lateral or feedback inhibition.

To gain further insights into the mechanism(s) underlying suppression, we then fixed the SF of both gratings and varied their contrasts independently (between 2.5% and 40%, in one-octave steps); in addition, the mask could also be absent (0% contrast). We selected a pair of SFs (0.25 cpd for the drifting grating and 0.5 cpd for the mask) for which a strong suppression was induced by the mask in all three subjects in the first experiment. In Figure 3, we plot the OFRs as a function of the contrast of the drifting grating. In the no-mask condition (Fig. 3, black), the response saturates at high contrast, indicating that a strong contrast normalization mechanism is at work, as expected from previous reports (Miles et al., 1986; Sheliga et al., 2005; Miura et al., 2006). As the contrast of the mask is increased progressively (see color key), the response is increasingly suppressed. We fit two Naka–Rushton functions to the data (see Materials and Methods), one accounting for a divisive effect of the mask (Eq. 3) and the other allowing for both divisive and scaling effects (Eq. 5). The fits shown in Figure 3 were obtained using the divisive model: all curves have a common value for A and n, but c₅₀ is a function of mask contrast (Eq. 4). The high quality of the fits indicates that the effect of the mask is simply to shift the contrast response curve for the drifting stimulus to the right by an extent that is a function of the contrast of the mask. Adding a scaling component to the model did not improve the fits significantly. The overall effect of the mask is thus compatible with any of the various divisive normalization schemes proposed in the past to account for contrast gain control and suppressive effects in cortical and subcortical neurons (Heeger, 1992; Carandini et al., 1997). Fit parameters are reported in Table 2.

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Figure 3.

Contrast tuning of masking suppression. When the contrast of stimulus and mask are varied while keeping their SF fixed (0.25 cpd for the stimulus, 0.5 cpd for the mask), the extent of suppression varies as a function of both. We used five contrast levels for the stimulus, from 2.5% to 40% in one-octave increments and five for the mask (see color key), which could also be absent (0% contrast). A Naka–Rushton function in which the mask acts in a divisive manner (Eq. 3) fits the data remarkably well in all three subjects. Parameter values for the fitting function are reported in Table 2.

Based on neurophysiological studies (Wiesel and Hubel, 1966; Dreher et al., 1976; Krüger, 1977) and psychophysical studies (Breitmeyer and Williams, 1990; Breitmeyer and Breier, 1994; Edwards et al., 1996; Pammer and Lovegrove, 2001; Bedwell et al., 2003, 2006; Chapman et al., 2004), it has been proposed that red illumination might interfere with the proper functioning of the magnocellular pathway. Because of the strong evidence that OFRs are mediated by magnocellular neurons (Takemura and Kawano, 2002; Miles and Sheliga, 2010; Masson and Perrinet, 2012), this raises the possibility that our use of red stimuli might have biased our results. To examine this hypothesis, we tested one subject using a subset of the conditions used in the previous experiment (unmasked and 10% mask, corresponding to the black and green curves in Fig. 3, respectively), but using achromatic (i.e., gray) stimuli and background. All responses at all contrast levels in both masked and unmasked conditions were not significantly different from those found with red illumination (data not shown).

If the strength of suppression were a separable function of mask SF and contrast, then the two relationships just described could be used to predict the attenuation induced by the mask under a wide range of conditions. To test this hypothesis, we replicated the last experiment using a different pair of SFs for the two gratings (0.125 cpd for the drifting grating and 1.0 cpd for the mask), chosen to be much farther apart (three octaves) than those used before. The pattern of mask-induced response attenuation that we found (Fig. 4) was very different from that reported above, now clearly showing a scaling of the contrast response. Consequently, a purely divisive model like the one used above provided poor fits (data not shown). The suppressive effects were, however, well captured by the function that included both a divisive and a scaling component, each a function of the contrast of the mask (according to Eqs. 4 and 6). In Figure 4, we show the fits obtained with the divisive plus scaling model (parameter fits are listed in Table 2).

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Figure 4.

Contrast tuning of masking suppression. Same as Figure 3, but the SFs of stimulus and mask are now farther apart (0.125 cpd for the stimulus, 1.0 cpd for the mask). In this case, a purely divisive model does not provide a good fit to the data; a model that incorporates both divisive and scaling effects (Eq. 5), the fits of which are shown, is necessary. Parameter values can be found in Table 2.

The data in Figures 3 and 4 differ in both the SF of the mask (0.5 vs 1.0 cpd) and the SF of the drifting grating (0.25 vs 0.125 cpd). It is thus unclear whether the scaling component arises because, in the second experiment, the SF of the mask is higher, the SF of the drifting grating is lower, or the SF separation between mask and stimulus is increased (three octaves instead of one). To address this question, we measured responses to two additional combinations of stimulus and mask SF. First, in two subjects (S1 and S3), we paired a 1.0 cpd mask (as in Fig. 3) with a 0.5 cpd stimulus, thus reducing the SF separation to one octave (as in Fig. 3). Second, in one subject (S1), we paired a 0.125 cpd stimulus (same as in Fig. 4) with a 0.25 cpd mask (again, one octave separation). In all cases ΔAICc was positive (ranging between 6.09 and 6.29), so the purely divisive model was sufficient to account for the mask-induced suppression (data not shown). We conclude that the SF separation between mask and stimulus is the determining factor: When the SF of the mask and stimulus are similar, a purely divisive model is sufficient to account for the masking effect; when they are far apart, a scaling component emerges.

Increasing the separation between the SFs of stimulus and mask revealed a significant scaling component of the suppressive mechanism not observed with nearby SFs. This implies that the effect of the mask is not separable in SF and contrast. Reaching this conclusion based exclusively on a model selection procedure is hazardous because it depends on the particular models used, the model selection criterion, the quality of the data, and the effectiveness of the masks used (if the mask is ineffectual or completely suppresses the responses, then both models fit equally well and the divisive one is thus selected only by virtue of having fewer parameters). As a direct experimental test of non-separability, we fixed SF (0.25 cpd) and contrast (20%) of the drifting grating and varied the contrast and SF of the mask (Fig. 5A). If separability held, then the SF of the mask yielding the strongest attenuation (fit parameter μ, indicated with small color-matched dots and SEM bars at the top of each panel in Fig. 5) should always be the same. We instead found that μ increases as the contrast of the mask is reduced (parameters of the fitting functions are listed in Table 1). Even ignoring the fits, it is apparent from looking at the data that, when the contrast of the mask is 20% (cyan), a 0.5 cpd mask is more suppressive than a 1.0 cpd mask, but when the mask contrast is decreased to 5% (gray), the opposite is true. This is compatible with our previous finding that increasing the separation between the SFs of mask and stimulus engages a scaling mechanism, which is generally more effective than a divisive mechanism when the contrast of the mask is low compared with that of the stimulus. This experiment further revealed that the bandwidth of the mechanism increases (for a constant contrast of the stimulus) with the contrast of the mask. Neither the shift in peak nor the broadening of the tuning curve are predicted by a classic normalization model (see Fig. 7D in Heeger, 1992), but cells with such behavior have been observed in cat primary visual cortex (see Fig. 9C in Bonds, 1989). Note that, if the contrast of both stimulus and mask are equal, then neither the most effective mask SF nor the bandwidth of the suppressive effect vary with contrast (Fig. 5B). The SF bandwidth of the mechanisms can thus be specified only for the relative contrast at which it has been measured. The same mechanism can appear highly tuned if the contrast of the mask, relative to that of the stimulus, is low (with an FWHH bandwidth of ∼2 octaves), but much less so if it is high (with an FWHH bandwidth of 4 octaves).

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Figure 5.

Nonseparable interactions between contrast and SF. A, When the SF and contrast of the stimulus are kept constant (0.25 cpd, 20%) and those of the mask are varied (SF on the abscissa, see color key for contrast), the mask SF resulting in the strongest suppression varies as a function of mask contrast and so does the bandwidth of the effect. B, When contrast of mask and stimulus are the same (see color key), the SF tuning of suppression is essentially invariant, with only a slight broadening and deepening of the curves with increasing contrast. Fit parameters can be found in Table 3.

These results are puzzling if considered in terms of a single masking mechanism and strongly suggest that two (or possibly more) nonlinear mechanisms may be at work. To better characterize these putative mechanisms, we explored the impact of manipulating other properties of the mask and stimulus, starting with their spatial overlap.

Nonoverlapping static mask: dependence on SF and contrast

In the study of vision, suppressive influences are divided into those that originate from the same area of the visual field as the stimulus and those that originate from the surrounding region of the visual field. When studied in single neurons, suppression is then said to arise from the classical RF (CRF) or from the surround. The stimuli that we used above were very large, much larger than the size of RFs in visual areas up to and including area MT, and thus probably engage both center and surround mechanisms in most visual areas. Although analysis of OFRs cannot be used to distinguish these mechanisms in a rigorous manner, reducing the size of stimulus and mask and separating them in space can provide some indication of the relative strength of center and surround mechanisms (Barthélemy et al., 2006).

We thus presented stimulus (0.25 cpd, 32% contrast) and mask (0.5 cpd, 32% contrast) within narrow vertical apertures. The mask and the stimulus could be superimposed (overlap condition) or separated in space (surround condition). We first ran an experiment in which, as is typically done, the drifting stimulus was presented within a centrally placed aperture (4° wide and 28° high) and the mask was either superimposed on the stimulus (indicated as −2° gap in Fig. 6) or composed of two apertures, 8° wide and 28° high, one on each side of the stimulus, with a variable gap between the two. The eccentricity of the inner edge of the apertures ranged from 2° (no gap) to 7.3° (5.3° gap). We found that the attenuation was maximal when stimulus and mask were superimposed and decreased rapidly as the gap increased (Fig. 6A). This finding could be interpreted as indicating that masking suppression arises mostly from the CRF and not from the surround. However, this result might also arise if the mask is less effective when presented in the periphery of the visual field. Both of these interpretations are compatible with reports that, in a center-surround configuration with the moving stimulus presented in a 20° central disk and the static mask presented in an annular surround, a static mask has no effect (Barthélemy et al., 2006). To clarify the contribution of relative and absolute mask location, in another experiment, we placed the mask aperture (4° wide, 28° high) centrally and varied the location of the stimulus, which was shown through two apertures (each 2° wide and 28° high). We also measured the OFRs induced by the stimulus alone at all locations (thus explicitly accounting for the effect of absolute stimulus location) and computed the ratio between the response to the stimulus without and with the static mask. The results are plotted in Figure 6B as a function of the gap between stimulus and mask. Once again, suppression is strongest when stimulus and mask are superimposed (−2° gap); however, the suppression does not fade away gradually with separation, it quickly asymptotes to an intermediate level. A surrounding stimulus can thus exert a considerable suppression on a behavioral response even when it is far from the classical RFs of subcortical and early cortical neurons.

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Figure 6.

Suppression in center-surround configurations. A, When the stimulus (0.25 cpd, 32% contrast) is presented in a central aperture and the mask (0.5 cpd, 32% contrast) flanks it with a variable gap (abscissa; negative values indicates overlap), the strength of suppression decreases as the gap increases. The spatial configuration of stimulus and mask apertures is represented graphically: gray/dot represent the static mask, black/arrow represent the drifting grating; both are presented in rectangular apertures, arranged as shown. B, When the mask is presented in a central aperture and the stimulus flanks it with a variable gap, the strength of suppression varies only slightly with gap size, although it is still considerably weaker than in the overlap condition.

Two different mechanisms might mediate this suppression phenomena. First, it might be the result of long-range surround suppression in area V1 (Cavanaugh et al., 2002a), so its tuning properties might very well be different from those seen with overlay suppression. Alternatively, it might result from interactions that occur in later areas, where the RFs are large enough that their CRF encompasses both stimulus and mask in our configuration. In this case, even though mask and stimulus do not overlap physically, it would qualify as overlay suppression and the tuning properties of masking would be expected to be largely the same whether stimulus and mask overlap or are (moderately) separated. To test these alternatives, we measured the tuning properties of suppression when stimulus and mask are separated in space by a 1° gap, with the mask in the center and the stimulus in the surround. Given the low SF of our stimuli, this is by all measures a small separation.

First, we varied the SF of the mask (from 0.0625 to 2 cpd in one-octave steps) for two values of the SF of the stimulus (0.25 and 0.5 cpd). Both stimulus and mask had 32% contrast. We found (Fig. 7, Table 1) that the SF of the mask producing the strongest suppression was the same for both SFs of the stimulus. This is obviously quite different from what we found with overlapping stimuli (Fig. 2). Next, we varied the contrast of stimulus and mask independently while keeping their SF constant (0.25 and 0.5 cpd, respectively). Whereas a divisive model accounted remarkably well for the suppression observed in the overlapping condition with these same SFs (Fig. 3), it failed with nonoverlapping stimuli. A model including both a divisive and a scaling component was necessary to obtain acceptable fits to the data (Fig. 8, Table 2), similar to what we found for the overlapping conditions in which the SF of grating and mask were widely separated (Fig. 4). Therefore, a mask that exerts a strong and purely divisive suppression when it overlaps the stimulus produces a milder suppression, but one that includes a scaling component, when presented at a different location.

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Figure 7.

SF tuning of masking for nonoverlapping masks. Same format as in Figure 2. Two different SFs, 0.25 cpd (blue) and 0.5 cpd (green), are used for the stimulus, whereas the mask can have one of six SFs. Both have 32% contrast and are arranged in a center-surround configuration with a small (1°) gap. Log-Gaussian fits to the data are shown (parameter values in Table 1). When stimulus and mask overlap, the two SF tuning curves are shifted relative to each other with the one associated with the lower stimulus SF having its trough at a lower mask SF (Fig. 2). Now the two curves are very similar and the location of their trough is not significantly different. The curves are also considerably shallower because the strength of suppression is weaker in the center-surround configuration (Fig. 6).

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Figure 8.

Contrast tuning of masking for nonoverlapping masks. Same format and SF for stimulus (0.25 cpd) and mask (0.5 cpd) as in Figure 3. Because stimulus and mask do not overlap, a wider range of contrasts could be explored. In the overlap condition, a purely divisive model was sufficient to account for the effect of the mask (i.e., the mask mostly shifted the contrast response function to the right without changing its slope). In the center-surround condition shown here, a significant scaling component of suppression is also present (note how the slope of the curves decreases as mask contrast increases). Fit parameters are listed in Table 2.

These results strongly argue in favor of suppression by nonoverlapping stimuli being mediated by surround interactions in area V1, not by overlay mechanisms in late cortical areas (MT or MST). There is, however, a potential confound: in our overlap experiments, both stimulus and mask were much larger than those used in the nonoverlapping condition. We therefore measured again, in one subject (S1), the SF-tuning functions in the overlapping condition, but using the smaller stimulus sizes used in the surround experiment. When SF was varied, we found a shift in the attenuation curves as a function of the SF of the stimulus similar to that seen with large stimuli. When stimulus and mask were shown in a central aperture (4° wide, 28° high), μ was 0.50 cpd [68% confidence interval (CI): 0.48–0.52 cpd] when SF_d = 0.25 cpd and 0.68 cpd (68% CI: 0.66–0.70 cpd) when SF_d = 0.5 cpd; when they were shown in two peripheral apertures (each 2° wide, 28° high, separated by a 4° gap), μ was instead 0.46 cpd (68% CI: 0.44–0.48 cpd) when SF_d = 0.25 cpd and 0.62 cpd (68% CI: 0.59–0.65 cpd) when SF_sd = 0.5 cpd. Similarly, when contrast was varied, a purely divisive model was sufficient to account for the suppressive effects when mask and stimulus were both shown in the two peripheral apertures (ΔAICc = 6.59). Therefore, overlap (or lack of it) is the determining factor, not size.

Binocular properties

The effects reported above could arise at any of a number of neural processing stages or might more likely reflect a cascade of effects across stages. Teasing out the contribution of individual processing stages is quite difficult. However, it is possible to at least determine whether the suppressive effects are confined either to neurons that receive inputs from only one eye (retina, LGN, and the input layer of area V1) or to neurons that receive inputs from both eyes (the rest of cortex). If suppression is stronger when stimulus and mask are seen by the same eye (monocular condition) than when they are presented to different eyes (dichoptic condition), then it can then be argued that suppression has a subcortical component, which is then inherited by later stages.

We presented, within a 28° circular aperture, stimulus (0.25 cpd SF, 32% contrast) and mask (0.5 cpd SF, 32% contrast) either to the same eye (monocular conditions) or one to each eye (dichoptic conditions). During monocular presentation, the other eye saw a mid-luminance blank screen. We found (Fig. 9) that OFR suppression induced by the mask was significantly stronger in the monocular (orange) than in the dichoptic (blue) condition, indicating that, for these choices of mask and stimulus, a substantial fraction of the suppression originates at the subcortical level. Note that the significant suppression observed when a dichoptic mask is presented (normalized OFR significantly smaller than 1) cannot be unequivocally imputed to a cortical mechanism of masking suppression: other, less specific cortical mechanisms such as binocular rivalry might also be responsible (Quaia et al., 2016).

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Figure 9.

Suppression from overlapping monocular and dichoptic masks. With stimulus (0.25 cpd SF, 32% contrast) and mask (0.5 cpd SF, 32% contrast) spatially overlapping, the mask is significantly more effective at suppressing the OFR induced by the stimulus (i.e., lower normalized OFR) when it is presented to the same eye (orange) than when it is presented to the other eye (blue). Black bars indicate SEM. Unpaired bootstrap-based (i.e., nonparametric) test was used to compute significance levels.

The large stimulus used here activates a large number of subcortical and cortical neurons and, for many of them, it probably engages both center and surround mechanisms. In an attempt to isolate the contribution of surround mechanisms, we presented the static mask (0.5 cpd) in a central aperture (4° wide, 28° high) and the stimulus in two peripheral apertures (each 2° wide, 28° high). To ensure that poor vergence control did not lead to a spatial overlap of stimulus and mask for dichoptic presentations, we separated them by 4°. Because this is larger than Panum's fusional area, this guarantees that, as long as the subjects perceive the fixation cross as fused, stimulus and mask will be projected on distinct retinotopic areas in the two retinae. Because suppressive effects are much weaker in the surround configuration (Fig. 8), we only used a high-contrast mask (80%). We found (Fig. 10) that a good fit to the data required using a model that included both divisive and scaling effects, just as in Figure 8. Because only one mask contrast was used, we did not use the full models described above, but simply compared Naka–Rushton functions in which either only c₅₀ or both c₅₀ and A could change across the two masked (same or other eye) and the unmasked conditions (fit parameters in Table 3). Importantly, the mask was, at all contrasts of the stimulus, equally effective whether it was presented to the same or to the other eye. Because rivalry is minimal with spatially separated stimuli (Blake et al., 1992) and is thus unlikely to act as a confounding factor, these results suggest that a cortical mechanism is mostly responsible for masking suppression originating from the surround.

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Figure 10.

Suppression from nonoverlapping monocular and dichoptic masks. When stimulus (0.25 cpd SF) and mask (0.5 cpd SF, 80% contrast) are presented in a center-surround configuration (4° gap), the mask is equally effective whether is presented to the same (orange) or to the other eye (blue). In both cases, a divisive and a scaling suppressive effect of the mask are observed. Fit parameters are listed in Table 3.

To summarize, it appears that, when stimulus and mask have similar SFs, masks that overlap with the stimulus (or are in its immediate surround) engage a monocular mechanism of suppression and the overall pattern of suppression appears divisive. Based on our dichoptic presentations, additional suppression at a binocular stage for overlapping stimuli can be neither proven nor excluded. In contrast, dichoptic masks and masks that are in the surround induce suppression predominantly (and possibly even exclusively) at a cortical level and their effect appears to include both divisive and scaling components.

Flickering masks: a separate mechanism?

Recently, we (Sheliga et al., 2016) reported that a flickering 1D noise stimulus superimposed on a drifting 1D pattern having the same orientation can suppress the OFRs induced by the latter; we noted that broadband noise stimuli presented on digital displays, which are affected by temporal aliasing, would engage such suppression mechanism. Here, we have shown that static masks covering a broad range of SFs can also strongly suppress OFRs. It is thus natural to ask whether there is something special about the suppression induced by flicker, as we suggested in our previous study, or if it can be seen as a special case of the suppression phenomenon that we have described here.

To explore this question, we masked a drifting sinusoidal grating (0.25 cpd, 15 Hz, 8% contrast) with a 1D noise pattern (see Materials and Methods, “Temporal filter analysis” section). The mask always had motion energy balanced in both directions (and thus induced no OFR on its own), but it could either be scattered across the entire TF spectrum (flickering mask) or concentrated within a (relatively) narrow TF bandwidth, with a center TF ranging between 0 and 45 Hz (focused mask). Importantly, focused masks are flicker free. We found (Fig. 11) that focused masks with center TF below 15 Hz provided the strongest suppression. We then identified the monophasic (i.e., low-pass) and biphasic (i.e., band-pass) temporal filters that best reproduce the strength of the suppression induced by the focused masks (Fig. 11, blue and orange lines). Finally, we used these two models to predict the strength of suppression of the flickering mask. The two filters generated almost identical predictions, which matched the measured flicker-induced suppression (right side of plots in Fig. 11). This indicates that, at least under the conditions tested, the suppression strength of a flickering stimulus is captured by the masking mechanism discussed here without having to postulate the presence of an additional nonlinearity or flicker detector.

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Figure 11.

Suppression from nonstatic masks. Stimulus (drifting sinusoidal grating, SF = 0.25 cpd, TF = 15 Hz, contrast = 8%) and mask (high-pass-filtered 1D noise pattern) have both motion energy, but for the mask it is balanced in both directions. The TF around which the motion energy of the mask is concentrated is indicated on the abscissa. Low-TF masks are more effective at suppressing the OFR to the stimulus. Both a low-pass temporal filter (blue) and a band-pass temporal filter (orange) fit the data reasonably well. Importantly, both filters predict the amount of suppression exerted by a flickering mask (FL on the abscissa).

Cascade model of contrast normalization and masking

We described above two types of suppressive effects: one that is well captured by a purely divisive model of suppression based on the Naka–Rushton function and the other that requires a Naka–Rushton function that incorporates both divisive and scaling components. The former were observed only when the stimulus and the mask overlapped and had similar SFs. The latter were observed when stimulus and mask overlapped but their SFs differed considerably, when stimulus and mask did not overlap even if they had similar SF, and when stimulus and mask were presented to different eyes. These effects closely mirror those observed in cat area 17 (Sengpiel et al., 1998). Dichoptic presentations revealed that some effects are mediated mostly by monocular mechanisms, but others, especially those that result in scaling, involve binocular and thus cortical mechanisms. We now describe a simple model that is capable of capturing these various effects.

The model is structured as a cascade of two stages, loosely associated with monocular (and thus subcortical plus possibly the input layer of area V1) and binocular (and thus cortical) stages of neural processing. Each stage is modeled as a nonlinear input–output relationship described by a Naka–Rushton function with three parameters (gain, exponent, and semisaturation constant). Because the gain parameters in the two stages are redundant, in the first stage, we simply imposed a unity gain. The basic model thus has five parameters. To account for the impact of the mask, in each stage, the semisaturation constant is a function of the contrast of the mask. Indicating with y the output of the first stage and with z the output of the second, the cascade model is thus described by the following pair of equations: Initially, we parametrized c₅₀(c_m) and y₅₀(c_m) with the same quadratic functions used for the descriptive functions used above (Eq. 4), but inspection of the resulting fits led us to adopt simpler formulations. We found that the effect of the mask was well captured under all conditions tested using the following formulations: The overall model thus has eight parameters: n₁ and c₅₀ determine the strength of contrast normalization at the first stage, α determines the strength of masking at the first stage, n₂ and y₅₀ determine the strength of contrast normalization at the second stage, β and δ control masking at the second stage, and A₂ scales the overall responses. Because there are more parameters than in the descriptive functions previously fit to the data (which had five or seven parameters), this model is less well constrained and fitting it to the data requires some additional care.

Similar models have been used in the past, but because of the presence of two nonlinear contrast normalization mechanisms and two nonlinear masking mechanisms, it is far from intuitive how each parameter affects the overall behavior of the model. While exploring its properties over the entire range of parameter values is beyond the scope of this study, highlighting the behavior for a few choices of parameters can be quite useful. Accordingly, in Figure 12 we show the output of the first (Fig. 12A) and second (Fig. 12B) stage for four sets of parameter values. In all cases, we set n₁ = 1, c₅₀ = 10, A₂ = 1, n₂ = 3.5, y₅₀ = 0.32, and δ = 38.15 (the reason for these choices will become clear later on). We then assigned to α and β values [0, 0] (black), [1, 0] (gray), [0, 1] (dashed yellow), and [1, 1] (dashed pink), and varied c_d between 0 and 40%, with c_m = 10%. In the first instantiation of the model (black), the mask has no effect on either stage and thus only contrast normalization effects are seen, with the second stage adding to the first and thus making the relationship more saturated. These curves also show the responses of each stage for all model instantiations to the unmasked stimulus. When divisive masking is present only at the first stage (gray), a rightward shift of the curve is seen at the first stage. Because masking does not act at the second stage, a simple lateral shift is also apparent at the output of the second stage. When masking normalization occurs only at the second stage (yellow), the output of the first stage is unchanged. At the second stage, the effect is not simply to shift the relationship to the right, as expected from a divisive normalization effect; rather, a scaling effect is also present. Finally, when there is divisive masking at both stages (pink), the curve is shifted laterally at the first stage and even further at the second. A scaling effect is also present at the output of the second stage, but it is quite small, so it might be difficult to detect with noisy measurements. This simple and physiologically realistic cascade model can thus reproduce both divisive and scaling effects despite using only divisive mechanisms. The model can thus easily account for the variety of divisive and scaling effects observed in area V1 in monkeys (Cavanaugh et al., 2002b) and cats (Sengpiel et al., 1998): cells in which strong masking effects are inherited from earlier processing would show divisive masking, whereas cells in which masking acts mostly at the cortical level would exhibit scaling effects. This of course would hold under the assumption that masking at the early levels can be modeled as a divisive interaction and that the contrast input–output function of the first stage is compressive. As noted in the introduction, abundant experimental evidence supports these assumptions within the magnocellular pathway of primates. However, describing the effect of the mask as divisive should not be taken to imply that, at the neuronal level, a divisive mechanism (e.g., shunting inhibition) is at play because many alternatives are possible (Murphy and Miller, 2003; Priebe and Ferster, 2012).

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Figure 12.

Cascading effects of masking suppression. The behavior of the cascade model as a function of the relative contributions to masking suppression of the first and second stage is illustrated. Four different model instantiations are considered, differing only in the stage(s) at which the mask exerts divisive suppression: at neither stage (black), only at the first stage (gray), only at the second stage (dashed yellow), or at both stages (dashed pink). A, Output of the first stage. B, Output of the second stage.

Armed with an understanding of the types of behaviors that can be expected from the model, we can now use it to fit the data from our experiments. We started by fitting the effects of masking observed with overlapping stimulus and mask, shown in Figures 3 and 4. Because the model is not strongly constrained, we first computed best fits for a wide range of imposed values of n₁ and c₅₀. We found that similarly good fits could be obtained over a range of these parameters. By intersecting these regions across subjects and experiments, we found that imposing c₅₀ = 10 worked well in all cases; furthermore, using n₁ = 1 worked well when SF_d = 0.25 cpd, whereas n₁ = 0.75 was appropriate when SF_d = 0.125 cpd. With these two parameters so selected, the model fits were well constrained and excellent in all cases, usually indistinguishable from those obtained with the descriptive functions (so we chose not to show them in a separate figure). Parameter values and quality of fit measures are reported in Table 4.

To fully explore the range of effects that can be accounted for by the model, in one subject, we measured the effect of the overlapping mask across the full range of stimulus and mask contrasts for one SF of the stimulus (0.25 cpd) and six SFs of the mask (0.0625, 0.125, 0.25, 0.5, 1.0, and 2.0 cpd). Because, within each session, only a single mask SF was used, we collected six times as much data for each unmasked condition as for each masked condition. In fitting the model to the data, we thus first imposed n₁ = 1 and c₅₀ = 10 and fitted A₂, n₂, and y₅₀ to the unmasked data; with these parameters so selected, we then found, for each SF of the mask, the best fitting values for α, β, and δ. To further reduce the degrees of freedom, we then selected the value of δ from the dataset in which the mask exerts the strongest influence on the second stage (c_m = 1.0 cpd) and fit all datasets once again with this value for δ (which resulted in only marginally inferior fits). Data and model fits are shown in Figure 13A, with parameter values and quality of fit measures reported in Table 4. In Figure 13B, we show how the only two parameters that differed across datasets (α and β) vary as a function of the SF of the mask, together with log-Gaussian fits to this relationship (R² = 0.934 for first stage, R² = 0.994 for second stage). Note that the second stage is subject to stronger masking effects at higher SFs (β_peak = 0.81 cpd) relative to the first stage (α_peak = 0.34 cpd). At the lowest and highest SF, the mask had no effect on the first stage, whereas some masking was evident at all SFs in the second stage (β_min = 0.33). The SF spectrum over which the the parameters were modulated significantly was also different for the two stages, being broader for the first stage (α_BW = 1.86 and β_BW = 1.25, both expressed in octaves). Because this result might be contingent on the particular values selected for n₁, c₅₀, and δ, we repeated the entire optimization process sampling a wide range of values for n₁, c₅₀. We found that, whenever the final overall fits were acceptable [i.e., the mean AICc across the six mask SFs did not increase by >10 points, a lenient criterion, meaning that significantly worse fits than those obtained with our initial choice for (n₁, c₅₀) were included], α and β were always well fit by log-Gaussian functions (R² = 0.93 ± 0.03 for the first and R² = 0.99 ± 0.01 for the second stage), closely resembling those shown in Figure 13B (α_min = 0.04 ± 0.06, α_peak = 0.36 ± 0.02, α_BW = 1.77 ± 0.25, β_min = 0.26 ± 0.08, β_peak = 0.84 ± 0.04, β_BW = 1.35 ± 0.07). This result is thus robust relative to the particular choice of parameters and is a feature of the model (and possibly of the data to which it is applied). It must be stressed that the function β(SF) shown in Figure 13B illustrates the SF tuning of masking of the second stage in isolation without taking into account the effects that the mask has on the output of the first stage, so it is quite different from the SF tuning of masking of the visual input measured at the output of the second stage, which is shown in Figure 2. Importantly, it is the latter that would be measured if one were to “record” from the output of the second stage, as is done in neurophysiological experiments.

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Figure 13.

Modeling contrast tuning of masking suppression over a wide range of mask SFs. A, Same as Figures 3 and 4, but here for a single SF of the stimulus (0.25 cpd) the contrast tuning of suppression is measured for a wide range of mask SFs (indicated in each subpanel). The data are fit using a two-stage cascade model. The model has eight parameters, but only two are different in each of the six panels, one in the first stage (α) and one in the second stage (β). Therefore, all of the fits shown here require a combined total of 18 parameters. Parameters for the fits are listed in Table 4. B, α (top) and β (bottom) vary in a lawful manner as a function of the SF of the mask. Log-Gaussian fits are shown.

Figure 12 provided a general idea about the conditions under which scaling effects emerge. To better understand when scaling is significant enough to be detected reliably, we simulated the behavior of the cascade model over a wide range of values for α and β, with all the other parameters as in Figure 13 (which were also used in Fig. 12). From each simulation, we generated synthetic data at the same signal and mask contrast levels used in the experiment, with the average noise level observed in the experiments and fit to it the divisive and divisive plus scaling functions used earlier (Eqs. 3 and 5). In Figure 14, we plot the difference between the χ² measures for the two functions, a measure of the extent by which the fit was improved by the addition of the scaling component. The region over which the improvement is significant based on the AICc measure is outlined in orange. Blue lower-case letters indicate the parameter values associated with each of the six subpanels in Figure 13A. When SF of stimulus and mask are separated by two or more octaves, a significant scaling component of suppression can be detected; for smaller SF separations, the presence of such an effect cannot be demonstrated statistically and a purely divisive model suffices. As a first-order approximation, a significant scaling effect is detected whenever β is larger than ∼0.3 and α is smaller than 0.5.

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Figure 14.

Divisive and scaling components of suppression. The values of parameters α (abscissa) and β (ordinate) in the cascade model (Eq. 8) predict whether the effect of suppression can be described by a purely divisive model or if a scaling component of suppression must also be included. Here, a wide range of values for both parameters is explored using simulated data and the increase in the χ² measure associated with the purely divisive model is shown as a grayscale heatmap. The region over which the improvement is significant according to the AICc is outlined (orange). Lowercase letters are placed in correspondence to the parameter values for the fits in the subpanels in Figure 13A. a, 0.0625 cpd; b, 0.125 cpd; c, 0.25 cpd; d, 0.5 cpd; e, 1.0 cpd; f, 2.0 cpd. Mask SFs two or more octaves away from the stimulus SF required a scaling component, whereas closer ones did not.

We can also use the model to fit the data from nonoverlapping stimulus and mask, shown in Figure 8. Once again, the fits were excellent and slightly better than those obtained with the descriptive functions. Parameter values and quality of fit measures are reported in Table 4. Note that, whereas for overlapping stimuli (with the same SFs for stimulus and mask), α was quite large, now it is zero, indicating that the mask does not act at the first stage of the model when mask and stimulus do not overlap (at least for the combination of stimulus and mask SF tested here). Unfortunately, we do not have enough data to characterize fully the tuning properties of the second stage with surround masking (i.e., how β varies with mask SF). Nevertheless, if the mask were to act only at the second stage for all SFs, then the SF tuning of β at the second stage would simply mirror the SF tuning of the overall masking effect, as shown in Figure 7. It would thus be quite different from the SF tuning for overlapping masks (Fig. 13B): it would be tuned to a lower SF, much closer to the SF of the stimulus, and would have a much broader bandwidth (tuning parameters can be found in Table 1).

Another potentially interesting feature of the model relates to the signals used to normalize the response divisively at the two stages (Eq. 8). At the first stage, this signal is directly proportional to the mask contrast; at the second stage, it is proportional to a compressive function of the mask contrast. This tentatively suggests that, in subcortical magnocellular neurons, suppression might originate from photoreceptors and/or from parvocellular signals (the responses of which are linearly related to stimulus contrast); in cortical binocular neurons, magnocellular signals (which nonlinearly encode contrast) might instead contribute to the masking effect.

Our simple model is not meant to simulate the behavior of individual neurons in visual cortex and thus it embeds no RF concept. However, it would be straightforward to extend it in such a way, with stimulus contrast and mask contrast at the two stages being measured over defined regions of retinal space (i.e., RFs) and the second stage pooling across a subpopulation of first-stage outputs. The differences that we reported above between overlapping and center-surround masks would then readily emerge in a model in which at the first-stage mask and stimulus are measured over the same area, whereas at the second stage, the RF for the mask is larger than that for the stimulus.

Of course, other models could also account for our data. For example, mask and stimulus could be processed separately and their contrast and speed (zero for the mask) could be used to decide whether to move the eyes (i.e., follow the stimulus) or to keep fixating (i.e., follow the mask). This scheme would be especially applicable to the condition in which stimulus and mask are spatially separate and, as our binocular experiments revealed, the stimulus–mask interactions are mostly cortically mediated. This alternative interpretation, although conceptually different, might rely on an implementation that is similar to the simpler account that we propose and does not make distinct predictions for the experiments presented here.