Jacob Nachmias

Spatial-Frequency Channels in Human Vision*

Psychometric functions were determined concurrently for detection of simple gratings (luminance sinusoidally modulated with spatial frequency f) and complex gratings (luminance modulated by the sum of two sinusoids, with frequencies f and f′). Results were used to test the hypothesis that the two components of a complex grating may be detected independently. In an extensive experiment with f = 14 cycles/deg, the independence hypothesis was consistently rejected only when f/f′=54 or 45, but rarely rejected when the value of f/f′ lay outside this range. In other experiments, f was between 1.9 and 22.4 cycles/deg. All results are compatible with the assumption that the human visual system contains sensory channels, each selectively sensitive to different narrow ranges of spatial frequencies, whose outputs are detected independently.

Detection of grating patterns containing two spatial frequencies: A comparison of single-channel and multiple-channels models

Abstract Contrast thresholds were measured for gratings containing two superimposed sinusoidal components. The frequency of one component was always three times that of the other, but the phase between components and the ratio of their contrasts took on several values. Two models of pattern vision were tested (1) a single-channel model in which pattern vision is a function of a single neural network and (2) a multiple-channels model in which the stimulus information is processed by many channels, each sensitive to a narrow range of spatial frequencies. Results support the multiple-channels and reject the single-channel model.

Grating summation in fovea and periphery

Abstract Results from previous studies measuring the detectability of sinusoidal gratings have been interpreted by models postulating several sizes of receptive fields. It has not been clear, however, whether or not these several sizes coexist at a single position in the visual field. Perhaps there is only one size centered at each position, but the size varies as a function of eccentricity. In this study, the detectability of compound gratings containing two sinusoidal components was compared to that of each component alone. Measurements were made in the fovea and 7.5° into the periphery. Stimuli were localized in a small region of the visual field and sharp spatial and temporal transients eliminated by weighting grating contrast with Gaussian functions of space and time. To reduce possible effects of expectation, bias and frequency uncertainty, a temporal, forced-choice, interlaced staircase procedure was used. The results are consistent with models postulating several sizes of receptive fields at each position in the visual field but not with models postulating only one size at each position, even when the size varies as a function of eccentricity to account for the differences in spatial interaction characteristic of different parts of the visual field.

On the psychometric function for contrast detection.

Abstract The frequent current use in probability summation calculations of equations of the form. P = 1 − (1−γ)exp[−(I/α)β] to represent the psychometric function for contrast detection is based on two assumptions: (1) γ can be changed without affecting α and β (the high-threshold assumption) and (2) β is the same for all pattern-detecting mechnisms (the homogeneity assumption). Results of yes-no, rating-scale, and forced-choice experiments contradict the high-threshold assumption: estimates of α and β covary with γ. Contrary to the homogeneity assumption, bipartite fields yield lower values of β than do 12 c/deg gratings. Some consequences of these findings for probability summation calculations are discussed.

Patterns of temporal interaction in the detection of gratings

Abstract Threshold contrasts were determined for pairs of brief, temporally separated gratings of the same frequency, same or opposite phase, and various contrast ratios. For low spatial frequencies, a range of separations is found that results in facilitation between opposite-phased pairs and inhibition between same-phased pairs. For higher spatial frequencies, this range is absent or nearly absent. The relation between the contrasts of the two gratings in a threshold pair of fixed separation suggests either a detector operating on the squared, integrated output of a linear temporal filter, or probability summation over time of the noise-perturbed output of such a filter.

Summation and discrimination of gratings moving in opposite directions

Abstract We have measured the amount of summation occurring at threshold between gratings which move in opposite directions. The small amount of summation observed at low spatial and high temporal frequencies is approximately consistent with the action of direction-selective mechanisms, as proposed by Levinson and Sekuler (1975) , provided that probability summation between such mechanisms is taken into account. However, at high spatial and low temporal frequencies much more summation is found, an amount approximately consistent with detection by directionally non-selective mechanisms. We have also measured thresholds for identifying the direction of a moving grating. For those gratings which show little summation, direction of motion is judged correctly at the detection threshold, while for those gratings which show the most summation, the identification threshold is considerably above the detection threshold.

Spatial-Frequency Discrimination in Human Vision

Subjects were presented with two gratings with different spatial frequencies and they were asked to discriminate one from the other. Their ability to discriminate between the gratings was found to depend primarily on the ratio of their spatial frequencies over a wide range of absolute frequency. At high spatial frequencies, discrimination deteriorates when differences of subjective contrast are eliminated.

Visual Detection and Discrimination of Luminance Increments

A rating-scale psychophysical method was employed to obtain receiver operating characteristics for detection and for discrimination of luminance increments. These curves were used to estimate the parameters of a normal probability-density function which was assumed to describe the relevant internal effects of the test flash. The over-all results strongly indicate that the mean of this distribution is a positively accelerated function of luminance of the test flash, and suggest that the standard deviation is a non-monotonic function of luminance. It is argued that quantum fluctuations and criterion fluctuations cannot account for these findings, whereas channel uncertainty may be at the root of some of them.

Effect of Exposure Duration on Visual Contrast Sensitivity with Square-Wave Gratings*†

Contrast sensitivity for square-wave gratings of spatial frequencies between 0.44 and 33.2 cycles/deg was determined for exposure durations between 11 and 500 msec. The space-average luminance of the targets was kept constant at 10 mL, regardless of contrast, and equal to that of the pre- and post-exposure fields, which contained a cross-hair reticle to help maintain accommodation and fixation. At the longest exposure duration (500 msec) the contrast sensitivity function exhibited both the high- and the low-frequency declines described by previous investigators. At the briefest exposure duration tested (11 msec), the low-frequency decline of contrast sensitivity was virtually absent. Log contrast sensitivity improves with increasing exposure duration, but more for high-frequency than for low-frequency gratings. These results are compatible with the assumption that there is a time delay in the occurrence of inhibitory interactions in the retina.

Discrimination of simple and complex gratings

Abstract We investigated the discriminability of simple and complex gratings containing one or two barely detectable sinusoidal luminance modulations at 3 and 9 c/deg, which will be referred to as ƒ and 3ƒ. Our major findings were the following: (1) frequency discrimination of the simple gratings seems to be limited only by their detectability; (2) relative phase differences between components in a complex grating are essentially indiscriminable even when each component is nearly perfectly detectable in the presence of the other; (3) when the contrast of the ƒ-component is at least 4 times its threshold value, it is only the detectability of the 3ƒ-component which limits the discriminability of complex gratings differing in relative phase by π radians; (4) a high contrast 3ƒ-component hinders the detection of ƒ while a high contrast ƒ component facilitates the detection of 3ƒ It is possible to offer a plausible explanation of some of these phenomena by invoking the existence in the human visual system of broad-band, phase-sensitive channels, as well as of narrow-band channels.