The representation of complex images in spatial frequency domains of primary visual cortex

Abstract

The organization of cat primary visual cortex has been well mapped using simple stimuli such as sinusoidal gratings, revealing superimposed maps of orientation and spatial frequency preferences. However, it is not yet understood how complex images are represented across these maps. In this study, we ask whether a linear filter model can explain how cortical spatial frequency domains are activated by complex images. The model assumes that the response to a stimulus at any point on the cortical surface can be predicted by its individual orientation, spatial frequency, and temporal frequency tuning curves. To test this model, we imaged the pattern of activity within cat area 17 in response to stimuli composed of multiple spatial frequencies. Consistent with the predictions of the model, the stimuli activated low and high spatial frequency domains differently: at low stimulus drift speeds, both domains were strongly activated, but activity fell off in high spatial frequency domains as drift speed increased. To determine whether the filter model quantitatively predicted the activity patterns, we measured the spatiotemporal tuning properties of the functional domains in vivo and calculated expected response amplitudes from the model. The model accurately predicted cortical response patterns for two types of complex stimuli drifting at a variety of speeds. These results suggest that the distributed activity of primary visual cortex can be predicted from cortical maps like those of orientation and SF preference generated using simple, sinusoidal stimuli, and that dynamic visual acuity is degraded at or before the level of area 17.

Figure 1.

Functional maps in cat area 17. A, Orientation preference map. B, Orientation preference map from the same imaged field with the template overlaid. C, Vascular pattern of imaged area. D, SF preference map constructed from the responses to two spatial frequencies, with template overlaid.

Figure 2.

Parameters required in the linear filter model were measured optically in low and high SF domains separately. A, SF tuning in low and high SF domains (n = 3). B, TF tuning curves in two SF domains (n = 2). There was a slight difference in TF peak between low and high SF domains. C, Contrast tuning curves were similar in two SF domains (n = 3). Parameter values are reported in Table 1.

Figure 3.

Activity in SF domains changes with drift speed. A, Responses to slowly drifting paired sine gratings (speed of 0.6°/s). At slow drift speeds, stimuli activated both low (top) and high (bottom) SF domains. B, Responses to quickly drifting paired sine gratings (speed of 6.8°/s). As stimulus drift speed increased, responses decreased primarily in high SF domains. Pixel brightness is proportional to the amplitude of response (images have been clipped between 10 and 90% of the full range for display). The scale bars show the response amplitude scaled by 10⁴.

Figure 4.

Measured and predicted responses to paired sine stimuli. A, Response amplitudes to paired sine stimuli are plotted for low SF domains (gray) and high SF domains (black) as a function of stimulus drift speed (n = 4). B, Predicted responses to paired sine stimuli as a function of drift speed. C, Comparison of measured and predicted responses (data from A and B are displayed as a scatter plot). The response amplitude predicted for each stimulus is plotted against the measured amplitude (Pearson's correlation coefficient between measured and predicted values, r = 0.72 for low SF domains, r = 0.70 for high SF domains). The dashed line is the identity line.

Figure 5.

Measured and predicted responses to a 0.3 c/° sine wave grating. A, Response amplitudes to sine wave gratings are plotted for low SF domains (gray) and high SF domains (black) as a function of stimulus drift speed (n = 2). B, Predicted responses to a sine wave grating as a function of drift speed. C, Comparison of measured and predicted responses (r = 0.77 for low SF domains, r = 0.71 for high SF domains).

Figure 6.

Measured and predicted responses to square wave grating stimuli (fundamental SF is 0.3 c/°). A, Response amplitudes to square wave gratings are plotted for low SF domains (gray) and high SF domains (black) as a function of stimulus drift speed (n = 3). B, Predicted responses to square wave gratings as a function of drift speed. C, Comparison of measured and predicted responses (r = 0.88 for low SF domains, r = 0.87 for high SF domains).

Figure 7.

The predictions of a model that assumes that there is no TF tuning in SF domains (No-TF model). In this model, responses in low and high SF domains do not depend on stimulus TF. A, The predictions of the No-TF model (dashed lines) in response to a 0.3 c/° sine wave grating are plotted as a function of stimulus drift speed. Activity measured in response to the same stimuli is plotted for comparison (solid lines). Gray lines refer to activity in low SF domains; black lines refer to activity in high SF domains. B, Predictions (dashed lines) and measured activity (solid lines) in response to paired sine stimuli. C, Predictions (dashed lines) and measured activity (solid lines) in response to square wave gratings.

Figure 8.

The predictions of a model that assumes that SF preference does not vary across the cortical surface (No-SF model). In this model, low and high SF domains share the same SF tuning curve but have slightly different TF tuning curves. SF peak and bandwidth values were set to the average values of low and high SF domains (0.48 c/° and 1.12 octaves). A, The predictions of the No-SF model (dashed lines) in response to a 0.3 c/° sine wave grating are plotted as a function of stimulus drift speed. Activity measured in response to the same stimuli is plotted for comparison (solid lines). Gray lines refer to activity in low SF domains; black lines refer to activity in high SF domains. B, Predictions (dashed lines) and measured activity (solid lines) in response to paired sine stimuli. C, Predictions (dashed lines) and measured activity (solid lines) in response to square wave gratings.

Figure 9.

Comparison of model fits to data. The error in the fit of a model to data were calculated as the sum of χ² error values for each cortical domain. The error in the fit of the No-SF model (gray line) was smallest when the SF peak parameter was set to 0.7 c/°. Even when optimized, the error of the No-SF model was larger than that obtained using the full model (black line; note that “SF peak” is not a free parameter for the full model). The diamond marks the average SF preference measured in area 17 (0.47 c/°).