Spatial Frequency Discrimination Research Articles

Locus of spatial-frequency discrimination.

In standard frequency-discrimination experiments either the retinal spatial frequencies (cycles per degree) or the object spatial frequencies (real world) could be compared, because the retinal and object frequency differences are the same. Current models of spatial-frequency discrimination assume that observers compare the retinal frequencies. I test this assumption by presenting gratings at different viewing distances (with strong depth cues). The object frequencies of the gratings bear the same relationship that they do in a standard frequency-discrimination experiment, but the retinal frequency of the more distant grating is always markedly higher than that of the near grating. The observer's task is to compare the object spatial frequencies. This change from one depth to two (with no change in the stimulus object) has a negligible effect on the observer's performance, suggesting that observers compare object frequencies even in standard spatial-frequency-discrimination experiments. This conclusion is supported by the findings that (1) observers appear unable to learn to compare retinal frequencies and (2) the interstimulus interval has no effect (over the range 0-1020 msec), implying long-term storage of the visual information. Suggests are made about why these results are consistent with good system design.

Spatial frequency discrimination in anisometropic and strabismic amblyopia

Spatial-frequency difference thresholds were measured in amblyopes over a wide range of spatial frequencies using a two-alternative forced-choice technique. Four amblyopes, three of whom were anisometropic, exhibited a higher threshold for discrimination at most frequencies in their amblyopic eye. In contrast, three other amblyopes, all of whom were strabismic, exhibited regions of normal discrimination alternating with regions of higher thresholds than found in their dominant eye. These results are discussed in terms of a multiple-spatial-frequency channel model. They suggest that there are different underlying mechanisms for the deficits in the two types of amblyopia: the anisometropic pattern may reflect a failure of normal development of spatial-frequency channels; the strabismic pattern is similar to that shown in the periphery of the retina by normal subjects and may reflect nonfoveal-type function.

The effects of contrast on visual orientation and spatial frequency discrimination: a comparison of single cells and behavior.

We have compared the effects of contrast on human psychophysical orientation and spatial frequency discrimination thresholds and on the responses of individual neurons in the cat's striate cortex. Contrast has similar effects on orientation and spatial frequency discrimination: as contrast is increased above detection threshold, orientation and spatial frequency discrimination performance improves but reaches maximum levels at quite low contrasts. Further increases in contrast produce no further improvements in discrimination. We measured the effects of contrast on response amplitude, orientation and spatial frequency selectivity, and response variance of neurons in the cat's striate cortex. Orientation and spatial frequency selectivity vary little with contrast. Also, the ratio of response variance to response mean is unaffected by contrast. Although, in many cells, response amplitude increases approximately linearly with log contrast over most of the visible range, some cells show complete or partial saturation of response amplitude at medium contrasts. Therefore, some cells show a clear increase in slope of the orientation and spatial frequency tuning functions with increasing contrast, whereas in others the slopes reach maximum values at medium contrasts. Using receiver operating characteristic analysis, we estimated the minimum orientation and spatial frequency differences that can be signaled reliably as a response change by an individual cell. This analysis shows that, on average, the discrimination of orientation or spatial frequency improves with contrast at low contrasts more than at higher contrasts. Using the optimal stimulus for each cell, we estimated the contrast threshold of 48 neurons. Most cells had contrast thresholds below 5%. Thresholds were only slightly higher for nonoptimal stimuli. Therefore, increasing the contrast of sinusoidal gratings above approximately 10% will not produce large increases in the number of responding cells. The observed effects of contrast on the response characteristics of nonsaturating cortical cells do not appear consistent with the psychophysical results. Cells that reach their maximum response at low-to-medium contrasts may account for the contrast independence of psychophysical orientation and spatial frequency discrimination thresholds at medium and high contrasts.

Visual orientation and spatial frequency discrimination: a comparison of single neurons and behavior.

Neurons in the visual cortex respond selectively to stimulus orientation and spatial frequency. Changes in response amplitudes of these neurons could be the neurophysiological basis of orientation and spatial frequency discrimination. We have estimated the minimum differences in stimulus orientation and spatial frequency that can produce reliable changes in the responses of individual neurons in cat visual cortex. We compare these values with orientation and spatial frequency discrimination thresholds determined behaviorally. Slopes of the tuning functions and response variability determine the minimum orientation and spatial frequency differences that can elicit a reliable response change. These minimum values were obtained from single cells using receiver operating characteristic (ROC) analysis. The average minimum orientation and spatial frequency differences that could be signaled reliably by cells from our sample were 6.4 degrees (n = 22) and 21.3% (n = 18), respectively. These values are approximately 0.20 of the average full tuning width at one-half height of the cells. Although these average values are well above the behaviorally determined thresholds, the most selective cells signaled orientation and frequency differences of 1.84 degrees and 5.25%, respectively. These values are of the same order of magnitude as the behavioral thresholds. We show that, because of slow fluctuations in a cell's responsivity, ROC analysis overestimates response variability. We estimate that these slow response fluctuations elevated our estimates of single cell "thresholds" by, on average, 30%. Our data point to an approximate correspondence between orientation and spatial frequency discrimination "thresholds" determined behaviorally and those estimated from the most selective single cortical cells. Interpretation of this quantitative correspondence is considered in the discussion.

Spatial frequency discrimination for sinewave gratings with random, bandpass frequency modulation: evidence for averaging in spatial acuity.

Spatial frequency difference thresholds for vertical, high contrast sinewave gratings were estimated at 1.25, 2.5, 5.0 and 10.0 cyc deg-1. Within an experiment two independent manipulations of the stimulus were employed: (1) the number of cycles of the sinewave grating was varied over a range of 2.0 to 15.0 cycles; and (2) a stationary, random frequency modulation was imposed on the sinewave. The probability density function of the frequency modulation was a Gaussian whose dispersion coefficient was varied, in different experiments, in the range of 0 to 10% of the frequency of the parent sinewave. Both of these experimental variables were found to affect the precision with which spatial frequency discrimination could be performed. The Weber fraction increased both as the number of cycles present was decreased and as the dispersion coefficient of the modulating function was increased. These two effects were independent. The data support previous psychophysical findings that spatial frequency discrimination involves averaging over the total area of the stimulus and are compatible with spatial primitive models of spatial contrast vision. The data are not compatible with those of Hirsch and Hylton (J. opt. Soc. Am. 72, 1367-1374) which suggest that spatial interval discrimination occurs solely by operation of foveal mechanisms.

Smooth frequency discrimination functions for foveal, high-contrast, mid spatial frequencies.

Intensive testing of spatial-frequency discrimination thresholds for 21% contrast gratings between 2.9 and 7.8 cycles/degree (c/deg) reveals, on average, smooth functions conforming to Weber's law. Discrimination overall is very sensitive, indicating highly skilled performance, but there are no consistent peaks or troughs. Individual, single-run functions do vary, resulting in candidate peaks and troughs that might be proposed to reflect true variations in an observer's sensory discrimination capacities. However, these features do not replicate from session to session nor from observer to observer. We do find consistent differences in overall sensitivity level between testing methods, with randomized presentation of reference frequencies giving significantly higher thresholds than blocked reference frequencies.

Neurophysiological evaluation of the differential response model for orientation and spatial-frequency discrimination.

Recent models have attempted to reconcile low psychophysical orientation and spatial-frequency discrimination thresholds with relatively broad orientation and spatial-frequency tuning of cortical neurons. These models have relied on the ability of the neurons to convert small stimulus changes into reliable response changes. We have examined this ability in a sample of neurons from the cat's striate cortex. We present here data from two cells that reliably signaled the smallest orientation and spatial-frequency differences. Using receiver operating characteristic analysis, we find that these cells could reliably signal orientation differences of 1.84 deg and spatial-frequency differences of 0.073 octave. We compare these single-cell results to cat and human behavioral discrimination thresholds.

Masking of spatial-frequency discrimination.

Spatial-frequency discrimination thresholds were measured using the temporal two-alternative forced-choice procedure. A superimposed masker grating reduced discrimination threshold more than 20-fold when the spatial frequency of the masker was close to the test spatial frequency because moiré fringes provided a sensitive cue to the test grating's spatial frequency. When the effectiveness of this cue was reduced by randomly changing the frequency of the masker grating on successive presentations, masked thresholds were found to be elevated when the masker frequency was within roughly 1 octave of the test frequency. On the other hand, postadaptation thresholds were not elevated when the test frequency was close to the adapting frequency but were elevated at about twice the adapting frequency. Thus masking and adaptation have quite different effects on spatial-frequency discrimination, though their effects on contrast sensitivity are qualitatively similar. It is proposed that discrimination is determined by opponent-size processing. Adaptation elevates discrimination threshold by reducing the sensitivity of opponent elements. The masker grating elevates threshold by increasing the noise level of opponent elements, thus reducing the precision with which the visual pathway encodes spatial frequency.

Discrimination of contour curvature: data and theory.

Visual discrimination of contour curvature was investigated using stimuli having a single point of maximum curvature and a continuous derivative. Curvature discrimination as a function of mean curvature could be described by a power law with an exponent averaging 1.57. Data were also gathered as a function of line width, stimulus orientation, and retinal eccentricity. Finally, masking experiments provided evidence that the mechanisms responsible for curvature discrimination were both orientation and spatial-frequency selective. The data are well fitted by theoretical results derived from a line-element model that has recently been applied to spatial-frequency discrimination.

Storage of spatial-frequency information and spatial-frequency discrimination

The spatial frequencies of two gratings can be discriminated when they differ by about 5%. This discrimination threshold was found to be remarkably independent of interstimulus interval in a temporal two-alternative forced-choice procedure. Discrimination threshold between parallel gratings did not change over a 50:1 range of interstimulus intervals between 0.4 and 20 sec; spatial-frequency information is stored with at least 5% precision without appreciable decay up to 20 sec at least. Spatial-frequency discrimination between orthogonal gratings was the same as spatial-frequency discrimination between parallel gratings and did not change over the 25:1 range of interstimulus intervals investigated (0.4 to 10 sec). It is suggested that, after being encoded to a high degree of precision by a size-opponent mechanism that is tuned to orientation, spatial-frequency information is stored in a form that is independent of orientation.

Contrast discrimination between stimuli of orthogonal orientations.

Previous investigations have shown that spatial frequency discrimination performance does not suffer when observers are made to compare the frequency of orthogonal gratings. It remains to be determined if contrast discrimination is similarly independent of the relative orientations of the two gratings to be compared. Using a 2AFC method of constant stimuli, contrast discrimination was studied under conditions in which observers compared the contrast of two orthogonal gratings. Contrast discrimination thresholds determined in this way were compared with thresholds obtained with parallel stimuli. Discrimination thresholds obtained under the two conditions were similar.

Spatial-frequency discrimination at low frequencies: evidence for position quantization by receptive fields.

In a recent study of spatial-frequency discrimination [J. Opt. Soc. Am. 72, 1367 (1982)], we reported evidence for the quantization of position in the human visual system with the fundamental unit of quantization being the photoreceptor spacing for spatial frequencies greater than 2 cycles per degree (c/deg). In this paper we extend our measurements to lower spatial frequencies, between 0.3 and 2, which we call the mid-spatial-frequency band, and find that this band of spatial frequencies shows similar evidence for spatial quantization. However, the spacing of the fundamental unit is about 0.056 deg or approximately seven or eight times the spacing of the foveal photoreceptor instead of about 0.008 deg or approximately equal to the spacing of foveal cones. We interpret this as evidence for a class of retinal receptive fields that we call spatial-sampling fields that perform a dual function of neural blurring and spatial sampling. We propose a scaled lattice model of spatial vision that allows apparently scale-free spatial processing while retaining the advantages of linear maps. The model generalizes the notion of hyperacuity to low-resolution tasks for which neural interpolation occurs not only on the photoreceptor sampling lattice to achieve hyperacuity but also on receptive-field sampling lattices to achieve lower resolutions.

The spatial frequency discrimination function at low contrasts.

Spatial frequency difference thresholds for sinewave gratings near contrast threshold were measured using a two-alternative forced-choice technique, and the threshold frequency differences were plotted as a proportion of standard frequency for standards from 2 to 7 cycles/degree. This function shows reliable local maxima and minima, and these features are more pronounced than they are when stimuli of 30% contrast are used. This result is consistent with the notion that at low contrasts, fewer spatial frequency channels are above threshold in the area of the visual field covered by the stimulus than when the stimulus is at high contrast.

Right-hemisphere superiority in the discrimination of spatial phase.

Visual field differences have been investigated in various detection and discrimination tasks for simple sinusoidal gratings or for complex gratings composed of two sinusoids of spatial frequencies f and 3f. Sinusoidal gratings were employed to evaluate contrast sensitivity, subthreshold summation effects, aftereffects of adaptation to a high-contrast grating, and spatial-frequency discrimination. The tasks with complex gratings were detection of the 3f component in the presence of a high-contrast f component and spatial-phase discrimination. The stimuli were presented either in the left or in the right visual hemifield. The results indicate a lack of lateralization for detection and spatial-frequency discrimination of sinusoidal gratings, and for the bandwidth of subthreshold summation effects and adaptation aftereffects, whereas the detection of the 3f component in the presence of a high-contrast f component, as well as spatial-phase discrimination of f +3f gratings, show a left-field advantage. This suggests a right-hemisphere superiority in the processing of spatial phase.

Spatial-frequency adaptation and grating discrimination: predictions of a line-element model.

Recent data have shown that spatial-frequency adaptation has little effect on spatial-frequency discrimination at the adapting frequency, but there is a substantial elevation of discrimination thresholds at frequencies about one octave higher than the adapting frequency. It has also been shown that adaptation produces elevations in grating-orientation discrimination at orientations displaced by +/- 12.0-15.0 deg from the adapting orientation. In this paper, we show that these results agree quantitatively with the predictions (some of which were made without knowledge of the experimental results) of a line-element model for spatial-frequency discrimination. Spatial-frequency bandwidths of the visual mechanisms were previously obtained from masking data. For the orientation-discrimination predictions, the line-element model was generalized to incorporate orientation bandwidths for the spatial mechanisms, again estimated from masking data.

Near-field acuity after visual system lesions in pigeons. I. Thalamus

Visual acuity determinations were made for 14 pigeons trained to discriminate high-contrast, square-wave gratings of successively higher spatial frequencies from blank stimuli of equal average luminances. The stimuli were presented according to the method of constant stimuli. Video-taped motion pictures of the key-pecking response provided a measure of the cornea-to-stimulus distance. The preoperative results indicated that the mean minimal-separable visual angle was 2.3 min (range 1.6–3.6) under conditions of photopic adaptation with the stimulus luminance at 70 cd/m 2. When performance was stable, bilateral electrolytic lesions were placed in: (1) nucleus rotundus (RT), (2) nucleus opticus principalis thalami (the OPT complex); and (3) RT plus the OPT complex. Lesions confined to the OPT complex did not impair resolution threshold while lesions confined to the nucleus rotundus produced permanent threshold elevations. When the destruction of OPT and RT was combined, the deficit was more severe. The results indicated that the integrity of the tectofugal pathway of the pigeon is required for normal performance of spatial frequency discrimination near threshold. These observations suggest that nuclei containing neurons with wide receptive fields are capable of processing visual information with fine spatial detail.

The effects of large orientation and spatial frequency differences on spatial discriminations

We have examined two questions: (1) can the finest orientation discrimination be achieved only between stimuli with similar spatial frequency content? and likewise, (2) can the lowest spatial frequency discrimination thresholds be achieved only with parallel gratings? In 2 AFC tests we found that neither type of discrimination was affected by stimulus differences along the other dimension. However, some small decreases in method of adjustment matching accuracy were associated with large differences along the secondary dimensions. Considering the neurophysiological implications, these data suggest that fine orientation and spatial frequency discrimination can occur even though separate populations of neurones in the primary visual cortex may be activated by the two stimuli to be discriminated.

Modified line-element theory for spatial-frequency and width discrimination.

Recent data from several laboratories have shown that spatial-frequency discrimination is not a smooth function of frequency but rather exhibits alternate peaks and troughs. A model for spatial-frequency discrimination analogous to line-element models for color discrimination is presented here and shown to provide a reasonable fit to the available data. This model is based on the predicted responses of six spatial-frequency-tuned mechanisms, whose sensitivity curves have been estimated in previously published masking experiments. In order to fit the data it is necessary to pool responses from units centered under the stimulus as well as from spatially neighboring units. Thus it appears that the visual system utilizes both spatial and spatial-frequency information in discrimination tasks.

Spatial-frequency discrimination and detection: comparison of postadaptation thresholds.

We found that inspecting a sine-wave grating elevated threshold for spatial-frequency discrimination as it does for contrast detection, but discrimination threshold was maximally elevated at about twice the adapting frequency, where detection threshold was little affected; and detection threshold was maximally elevated at the adapting frequency, where discrimination threshold was not elevated at all. Orientation tuning was roughly similar for contrast and for discrimination threshold elevations; elevations fell by half at between 7 and 17 deg from the adapting orientation. We compared our findings with the predictions of three models of discrimination: (1) The data are inconsistent with the idea that the most strongly stimulated channels are the most important channels for discrimination. (2) With an additional assumption, the Hirsch-Hylton scaled-lattice model could account for our finding that discrimination threshold elevations are asymmetric. (3) With no additional assumptions, the idea that discrimination is determined by the relative activities of multiple overlapping spatial-frequency channels or size-tuned neurons can account for our finding that discrimination thresholds are asymmetric. We propose a physiologically based discrimination model: Asymmetrically tuned cortical cells feed a ratio-tuned neural mechanism whose properties are formally analogous to those of ratio-tuned neurons that have recently been found in cat visual cortex. The linear relation between firing frequency and contrast can explain why discrimination threshold is substantially independent of contrast.

Independence of orientation and size in spatial discriminations.

This study of form vision explores the relationships between orientation and spatial frequency in suprathreshold discrimination tasks. Orientation discrimination thresholds for sine-wave gratings were 0.3-0.5 deg, much less than the roughly 10-24-deg orientational bandwidth of channels; spatial-frequency discrimination thresholds were 3-7%, much less than the roughly 1.2-octave spatial-frequency bandwidth of channels. We find that spatial-frequency discrimination between two gratings was as acute when the two gratings were orthogonal as when they were parallel. Orientation discrimination between two gratings was as acute when the two gratings had the same spatial frequencies as when they had different spatial frequencies. Thus orientation and spatial frequency are independent dimensions at the discrimination stage of spatial information processing.