David J. Tolhurst

The statistical reliability of signals in single neurons in cat and monkey visual cortex

The variability of the discharge of visual cortical neurons in cats and macaque monkeys limits the reliability with which such neurons can relay signals about weak visual stimuli. In general, the variance of a neurons firing rate is directly proportional to its mean firing rate. The probability that a neuron will fire a criterion number of impulses on a stimulus trial grows monotonically with the contrast of a sinusoidal grating stimulus. Neural probability functions prepared either by computing the probability of criterion response or by integrating receiver operating characteristics to yield the probability of correct choice in a two-alternative forced-choice situation resemble psychometric functions obtained in psychophysical and behavioral experiments on humans and animals, but are shallower in slope. The slopes of neuronal probability functions are slightly higher when they are estimated over short time periods, but even so do not equal the slopes measured psychophysically in human and monkey observers. This discrepancy in slope could be explained if the whole observer responded only when about four neurons were active together.

Psychophysical evidence for sustained and transient detectors in human vision

1. The sensitivity to temporally modulated sinusoidal gratings was determined. Two thresholds could be distinguished for the modulated gratings: the contrast at which flicker could be perceived and the contrast at which the spatial structure became distinct.

Spatial and temporal contrast sensitivity of neurones in areas 17 and 18 of the cat's visual cortex.

1. We have examined the spatial and temporal tuning properties of 238 cortical neurones, recorded using conventional techniques from acutely prepared anaesthetized cats. We determined spatial and temporal frequency tuning curves using sinusoidal grating stimuli presented to each neurones receptive field by a digital computer on a cathode ray tube. 2. We measured tuning curves either by determining response amplitude as a function of spatial or temporal frequency, or by measuring contrast sensitivity (the inverse of the contrast of the grating that just elicited a detectable response). The two measures give very similar tuning curves in all cases. 3. We recorded from 184 neurones in area 17; of these 156 had receptive fields within 5 degrees of the area centralis. The range of preferred spatial frequency for these neurones was 0.3‐‐3 c/deg, and their spatial frequency tuning band widths varied from 0.7 to 3.2 octaves at half‐amplitude. The most common band width was roughly 1.3 octaves. Simple and complex cells in area 17 did not differ in their distributions of preferred spatial frequency, although complex cells were, on average, slightly less selective for spatial frequency than simple cells. 4. We recorded from fifty‐four neurones from area 18, and performed several experiments in which we recorded from corresponding portions of both area 17 and area 18 in the same electrode penetration. Neurones in area 18 preferred spatial frequencies that were, on average, one third as high as those preferred by area 17 neurones at the same retinal eccentricity. Thus the range of preferred spatial frequency in area eighteen cells having receptive fields within 5 deg of the area centralis was between less than 0.1 and 0.5 c/deg. The distributions of optimum spatial frequency in the two areas were practically non‐overlapping at eccentricities as high as 15 deg, the greatest eccentricity we examined. Neurones in area 18 were about as selective for spatial frequency as were neurones in area 17. 5. We determined temporal frequency tuning characteristics for some neurones from each area, using gratings that moved steadily across the screen. Neurones from area 17 all responded well to low temporal frequencies, and less well to higher frequencies (in excess of, usually, 2 or 4 Hz). In contrast, neurones recorded from area 18 sometimes had similar tuning properties, but more commonly showed a pronounced reduction in response as the temporal frequency was moved either above or below some optimum value (usually 2‐‐8 Hz). 6. We conclude from these results that areas 17 and 18 act in parallel to process different aspects of the visual information relayed from the retina via the lateral geniculate complex. Some or all of the differences between the areas may be attributable to the predominance of Y cell input to area 18 and the predominance of X cell input to area 17...

Do We Know What the Early Visual System Does

We can claim that we know what the visual system does once we can predict neural responses to arbitrary stimuli, including those seen in nature. In the early visual system, models based on one or more linear receptive fields hold promise to achieve this goal as long as the models include nonlinear mechanisms that control responsiveness, based on stimulus context and history, and take into account the nonlinearity of spike generation. These linear and nonlinear mechanisms might be the only essential determinants of the response, or alternatively, there may be additional fundamental determinants yet to be identified. Research is progressing with the goals of defining a single “standard model” for each stage of the visual pathway and testing the predictive power of these models on the responses to movies of natural scenes. These predictive models represent, at a given stage of the visual pathway, a compact description of visual computation. They would be an invaluable guide for understanding the underlying biophysical and anatomical mechanisms and relating neural responses to visual perception.

Amplitude spectra of natural images

Several studies have suggested that the amplitude spectra of photographs of natural scenes are remarkably similar and have the form: This is, of course, a straight line with slope of −1.0 when plotted on double logarithmic coordinates. We have examined the amplitude spectra of 135 digitized photographs of natural scenes and have Found that relatively few images conform exactly to the suggestion. About 25% of the images in our sample have spectra which show significant curvature when plotted on log log coordinates. The best‐fitting regression lines have slopes that range from −0.8 to −1.5: the average slope is −1.2, rather sleeper than previously suggested.

The Dependence of Response Amplitude and Variance of Cat Visual Cortical Neurones on Stimulus Contrast

SummaryFor neurones in the cats striate cortex, we examined the dependence of response on the contrast of moving sinusoidal gratings. Most neurones showed a clear threshold contrast below which no response was elicited. Such thresholds presumably contribute to the animals behavioural threshold, which should not be accounted for solely in terms of the detection of a signal in the presence of spontaneous “noise”. Above threshold, the response amplitude usually increased linearly with contrast until it began to saturate at the highest contrasts. The variance of the response increased with its amplitude; this finding perhaps underlies the Weber-Fechner relation for psychophysical contrast discrimination.

Reaction times in the detection of gratings by human observers: A probabilistic mechanism

Abstract Reaction times were measured for sinusoidal gratings which were flashed on with various temporal waveforms. The contrast was close to threshold. At low spatial-frequencies, the reaction times were grouped just after any sudden transient in the stimulus, even when this was at the end of the stimulus. At higher spatial-frequencies, the reaction times were not related to the time of sudden changes in contrast but were distributed throughout the body of the stimulus; the longer the stimulus duration, the greater was the chance that the stimulus would be detected. These results can be explained if a stimulus can be detected at any time when the visual systems response to it is moderately high and not simply at the time when the response is greatest. At low spatial-frequencies, the channels have transient step-responses; at higher frequencies, the responses are sustained.

Sustained and transient channels in human vision

Abstract The sensitivity for 4-msec flashes of sinusoidal grating was determined at various times during and after a subthreshold 800 msec flash of grating of the same spatial-frequency. At frequencies of 2 c/deg and below, the sensitivity to the short flash was transiently changed for about 100 msec after the onset and the offset of the long flash. If the gratings in the long and short flashes were spatially in phase, the sensitivity to the short flash was increased at the onset of the long flash but was decreased at the offset. A phase-shift of 180° caused an inversion of these effects. At higher spatial-frequencies, the sensitivity to the short flash was increased to a new steady level for the duration of the long flash, when the gratings were in phase. A phase-shift of 180° did not cause an inversion: the sensitivity was changed transiently at the onset and offset of the long flash. This might suggest a non-linearity of response, but it is argued that the results can be explained by supposing the existence of two types of channel at these spatial-frequencies.

Adaptation to square‐wave gratings: inhibition between spatial frequency channels in the human visual system

1. The observation that the detection threshold for a square‐wave grating depends only on that of its fundamental was confirmed by showing that adapting to the fundamental spatial frequency caused elevation of the square‐wave threshold, to the same extent as the fundamental threshold was elevated by the same adapting pattern. Adapting to the third harmonic frequency had no effect on the square‐wave threshold.

Interactions between spatial frequency channels.

Abstract The sensitivities for sinusoidal gratings of various spatial frequencies were determined by a two-alternative forced-choice technique. The effects of the simultaneous presence of a grating of 4.25 c/deg on sensitivity were examined. The effects of prolonged adaptation to the same grating were also examined. When the testing frequency was close to the masking or adapting frequency, threshold was elevated, but when the frequencies differed by 1–2 octaves, the threshold was lowered (sensitivity was increased).