Standing waves and traveling waves distinguish two circuits in visual cortex.

The visual cortex represents stimuli through the activity of neuronal populations. We measured the evolution of this activity in space and time by imaging voltage-sensitive dyes in cat area V1. Contrast-reversing stimuli elicit responses that oscillate at twice the stimulus frequency, indicating that signals originate mostly in complex cells. These responses stand clear of the noise, whose amplitude decreases as 1/frequency, and yield high-resolution maps of orientation preference and retinotopy. We first show how these maps are combined to yield the responses to focal, oriented stimuli. We then study the evolution of the oscillating activity in space and time. In the orientation domain, it is a standing wave. In the spatial domain, it is a traveling wave propagating at 0.2-0.5 m/s. These different dynamics indicate a fundamental distinction in the circuits underlying selectivity for position and orientation, two key stimulus attributes.

Local luminance and contrast in natural images.

Within natural images there is substantial spatial variation in both local contrast and local luminance. Understanding the statistics of these variations is important for understanding the dynamics of receptive field stimulation that occur under natural viewing conditions and for understanding the requirements for effective luminance and contrast gain control. Local luminance and contrast were measured in a large set of calibrated 12-bit gray-scale natural images, for a number of analysis patch sizes. For each image and patch size we measured the range of contrast, the range of luminance, the correlation in contrast and luminance as a function of the distance between patches, and the correlation between contrast and luminance within patches. The same analyses were also performed on hand segmented regions containing only "sky", "ground", "foliage", or "backlit foliage". Within the typical image, the 95% range (2.5-97.5 percentile) for both local luminance and local contrast is somewhat greater than a factor of 10. The correlation in contrast and the correlation in luminance diminish rapidly with distance, and the typical correlation between luminance and contrast within patches is small (e.g., -0.2 compared to -0.8 for 1/f noise). We show that eye movements are frequently large enough that there will be little correlation in the contrast or luminance on a receptive field from one fixation to the next, and thus rapid contrast and luminance gain control are essential. The low correlation between local luminance and contrast implies that efficient contrast gain control mechanisms can operate largely independently of luminance gain control mechanisms.

Contrast statistics for foveated visual systems: fixation selection by minimizing contrast entropy.

The human visual system combines a wide field of view with a high-resolution fovea and uses eye, head, and body movements to direct the fovea to potentially relevant locations in the visual scene. This strategy is sensible for a visual system with limited neural resources. However, for this strategy to be effective, the visual system needs sophisticated central mechanisms that efficiently exploit the varying spatial resolution of the retina. To gain insight into some of the design requirements of these central mechanisms, we have analyzed the effects of variable spatial resolution on local contrast in 300 calibrated natural images. Specifically, for each retinal eccentricity (which produces a certain effective level of blur), and for each value of local contrast observed at that eccentricity, we measured the probability distribution of the local contrast in the unblurred image. These conditional probability distributions can be regarded as posterior probability distributions for the "true" unblurred contrast, given an observed contrast at a given eccentricity. We find that these conditional probability distributions are adequately described by a few simple formulas. To explore how these statistics might be exploited by central perceptual mechanisms, we consider the task of selecting successive fixation points, where the goal on each fixation is to maximize total contrast information gained about the image (i.e., minimize total contrast uncertainty). We derive an entropy minimization algorithm and find that it performs optimally at reducing total contrast uncertainty and that it also works well at reducing the mean squared error between the original image and the image reconstructed from the multiple fixations. Our results show that measurements of local contrast alone could efficiently drive the scan paths of the eye when the goal is to gain as much information about the spatial structure of a scene as possible.

Independence of luminance and contrast in natural scenes and in the early visual system.

The early visual system is endowed with adaptive mechanisms that rapidly adjust gain and integration time based on the local luminance (mean intensity) and contrast (standard deviation of intensity relative to the mean). Here we show that these mechanisms are matched to the statistics of the environment. First, we measured the joint distribution of luminance and contrast in patches selected from natural images and found that luminance and contrast were statistically independent of each other. This independence did not hold for artificial images with matched spectral characteristics. Second, we characterized the effects of the adaptive mechanisms in lateral geniculate nucleus (LGN), the direct recipient of retinal outputs. We found that luminance gain control had the same effect at all contrasts and that contrast gain control had the same effect at all mean luminances. Thus, the adaptive mechanisms for luminance and contrast operate independently, reflecting the very independence encountered in natural images.

Visual cortex neurons of monkeys and cats: temporal dynamics of the spatial frequency response function.

We measured the responses of striate cortex neurons as a function of spatial frequency on a fine time scale, over the course of an interval that is comparable to the duration of a single fixation (200 ms). Stationary gratings were flashed on for 200 ms and then off for 300 ms; the responses were analyzed at sequential 1-ms intervals. We found that 1) the preferred spatial frequency shifts through time from low frequencies to high frequencies, 2) the latency of the response increases as a function of spatial frequency, and 3) the poststimulus time histograms (PSTHs) are relatively shape-invariant across spatial frequency. The dynamic shifts in preferred spatial frequency appear to be a simple consequence of the latency shifts and the transient nature of the PSTH. The effects of these dynamic shifts on the coding of spatial frequency information are examined within the context of several different temporal integration strategies, and pattern-detection performance is determined as a function of the interval of integration, following response onset. The findings are considered within the context of related investigations as well as a number of functional issues: motion selectivity in depth, "coarse-to-fine" processing, direction selectivity, latency as a code for stimulus attributes, and behavioral response latency. Finally, we demonstrate that the results are qualitatively consistent with a simple feedforward model, similar to the one originally proposed in 1962 by Hubel and Wiesel, that incorporates measured differences in the response latencies and the receptive field sizes of different lateral geniculate nucleus inputs.

Visual cortex neurons of monkeys and cats: temporal dynamics of the contrast response function.

Cortical neurons display two fundamental nonlinear response characteristics: contrast-set gain control (also termed contrast normalization) and response expansion (also termed half-squaring). These nonlinearities could play an important role in forming and maintaining stimulus selectivity during natural viewing, but only if they operate well within the time frame of a single fixation. To analyze the temporal dynamics of these nonlinearities, we measured the responses of individual neurons, recorded from the primary visual cortex of monkeys and cats, as a function of the contrast of transient stationary gratings that were presented for a brief interval (200 ms). We then examined 1) the temporal response profile (i.e., the post stimulus time histogram) as a function of contrast and 2) the contrast response function throughout the course of the temporal response. We found that the shape and complexity of the temporal response profile varies considerably from cell to cell. However, within a given cell, the shape remains relatively invariant as a function of contrast and appears to be simply scaled and shifted. Stated quantitatively, approximately 95% of the variation in the temporal responses as a function of contrast could be accounted for by scaling and shifting the average poststimulus time histogram. Equivalently, we found that the overall shape of the contrast response function (measured every 2 ms) remains relatively invariant from the onset through the entire temporal response. Further, the contrast-set gain control and the response expansion are fully expressed within the first 10 ms after the onset of the response. Stated quantitatively, the same, scaled Naka-Rushton equation (with the same half-saturation contrast and expansive response exponent) provides a good fit to the contrast response function from the first 10 ms through the last 10 ms of the temporal response. Based upon these measurements, it appears as though the two nonlinear properties, contrast-set gain control and response expansion, are present in full strength, virtually instantaneously, at the onset of the response. This observation suggests that response expansion and contrast-set gain control can influence the performance of visual cortex neurons very early in a single fixation, based on the contrast within that fixation. In the DISCUSSION, we consider the implications of the results within the context of 1) slower types of contrast gain control, 2) discrimination performance, 3) drifting steady-state measurements, 4) functional models that incorporate response expansion and contrast normalization, and 5) structural models of the biochemical and biophysical neural mechanisms.