Spatial Frequency Difference Research Articles

Spatial frequency difference thresholds depend on stimulus area

Spatial frequency difference thresholds were estimated for vertical, high contrast 5.0 cpd sinewave gratings that had been multiplied by a two dimensional Gaussian window function of contrast. A range of different elliptical window configurations were tested that varied in their relative height and width. Spatial frequency acuity improved as the area of the target was increased. The data are compatible with a model of spatial frequency discrimination that is based on statistical averaging of spatial intervals interpolated between local retinal signs.

Comparison of Two Clinical Methods for Measuring Tonic Accommodation in Children

Two methods have been described for measuring tonic accommodation (TA) under clinical conditions. One is the near retinoscopy (NEAR) method; the other uses Nott retinoscopy as the patient views a low spatial frequency difference of Gaussian (DOG) target. The purpose of this study was to compare the TA measures made by these two procedures on a group of 6- to 14-year-old children. The data indicate that the procedures yield significantly different information.

Visual search: spatial frequency and orientation.

Observers searched for a Gaussian-windowed patch of sinewave grating (Gabor pattern) through displays containing varying numbers of other such patterns (distractors). When the spatial frequencies of target and distractors differed by +/- 2 octaves and their orientations by +/- 60 degrees, the search proceeded spatially in parallel irrespective of whether the target could be discriminated in terms of spatial frequency differences alone, orientation differences alone, or their combination. However, when target and distractors differed by only +/- .5 octave in spatial frequency and by +/- 15 degrees in orientation, the search was serial and self-terminating, again irrespective of the nature of the target-distractor differences. These findings show that, contrary to some suggestions, the preattentive detection of targets defined by conjunctions of spatial frequency and orientation may occur, but only when the spectral distance between target and distractors allows their encoding by independent mechanisms.

Interocular differences in contrast and spatial frequency: Effects on stereopsis and fusion

Anisometropia produces interocular differences in contrast and spatial frequency. The influence of these two parameters on Panum's fusional limit (PFL) and stereoscopic depth thresholds was investigated with sinusoidal gratings and one-dimensional band-pass-limited targets. Vertical fusion limits were unaffected by large interocular differences in contrast (40-10%) at two spatial frequencies (0.8 and 1.6 cpd). However, when tested with a low spatial frequency (0.8 cpd), stereothresholds increased 150% with an interocular difference in contrast as small as 50-25%. Stereoacuity was reduced less by differential contrast when tested with higher spatial frequencies (3.2 cpd). When tested with low spatial frequencies the stereothreshold was elevated more by reducing the contrast of one image than by equal contrast reductions of both ocular images. Stereothresholds appear to be elevated by binocular suppression evoked by interocular differences in contrast. Vertical as well as horizontal fusion limits decreased with increasing interocular size difference. Horizontal fusion limits fell off more gradually with increasing size difference than did vertical fusion limits, particularly at higher spatial frequencies (2.4 cpd). Similarly, stereothresholds increased with increasing interocular size differences. Changes in the fusion limit and stereothreshold that occur with interocular size differences are predicted from positional disparities between edge features rather than from differences in spatial frequency.

A choice reaction time analysis of spatial frequency discrimination

Simple reaction time to the onset of sinewave gratings was measured as a function of spatial frequency in two observers. These results are compared to the choice reaction time required for the observer to correctly discriminate the spatial frequency of two gratings flashed sequentially. Grating contrast was either 0.75 or 1.5 logarithmic units above the detection threshold for each spatial frequency tested. The spatial phase and contrast of the reference and test gratings were varied from trial to trial by small random amounts to eliminate fixed cues other than the difference frequency. The spatial frequency difference between the reference and test grating was either 0.125, 0.25 or 0.5 octave. As has been earlier reported, simple reaction time increases with increasing spatial frequency. Contrary to this, choice reaction time first increases (up to 4c/deg) and then decreases. We derived the time required by the observer to make a spatial frequency judgement by subtracting the simple reaction time from the choice reaction time for a given spatial frequency and contrast. The maximum decision time occurs in the medium spatial frequency range (between 1 and 4 c/deg), at which frequencies we are most sensitive. The time required to make a correct spatial-frequency discrimination decreases with increasing spatial-frequency difference. The decision time is, however, fairly invariant over a large range of suprathreshold contrast levels. The findings suggest that the decision time for spatial frequency discrimination increases with the number of mechanisms involved.

The effect of feature uncertainty on spatial discriminations.

Just noticeable differences (JNDs) in orientation and spatial frequency were measured under two conditions. In one condition the subject was cued before stimulus presentation as to the feature to be discriminated on that trial, while in the other condition the subject was cued only after stimulus offset. JNDs were larger in the latter, feature uncertainty, condition. This feature uncertainty effect increased with decreasing stimulus processing time. The results suggest that this feature uncertainty effect is of sensorial origin. They also demonstrate that it is possible for humans to address selectively those mechanisms that are most relevant for a given discrimination task.

Interactions among spatial frequency and orientation channels adapted concurrently

Interactions between size and orientation-specific mechanisms in the human visual system were investigated using a sequential adaptation technique. Subjects adapted to a vertical, 4c/deg high-contrast (0.7) sinewave grating that was interleaved at a rate of 0.5 Hz with another adapting grating differing either in (1) spatial frequency or (2) orientation. Before and after adaptation contrast thresholds were measured for a vertical 4c/deg sinewave test grating. The resultant elevation in contrast threshold was plotted as a function of the (1) spatial frequency or (2) orientation differences between the first and second adapting gratings. Maximum threshold elevation was found when both adapting gratings shared the same spatial frequency and orientation. Minimum elevations were found when the second grating's spatial frequency or orientation differed by approx. 1.5 octaves or 45 deg, respectively. Beyond these values threshold elevations reapproached the baseline value measured in a control condition, where the 4.0 c/deg adapting grating was interleaved with a blank. The minimum threshold elevations were 0.2–0.3 log units below the baseline level. The results suggest the existence of inhibitory interactions between neural mechanisms tuned to the size and orientation of retinal images.

Perceptually unequal spatial frequencies do not yield stereoscopic tilt.

Stereoscopic tilt can be obtained by presenting vertical grating patterns differing in their spatial frequencies to the two eyes (Blakemore, 1970). Following monocular adaptation, theperceived spatial frequency of a test grating is different in the adapted and unadapted eyes by an amount that would yield stereoscopic tilt if corresponding physical spatial frequencies were presented (Experiment 1). Perceptually unequal (but physically identical) gratings presented to the two eyes do not yield stereoscopic tilt, but tilt is obtained if differences in physical spatial frequency exist (Experiment 2). Changes in perceived spatial frequency for a binocular test grating following monocular adaptation are smaller than those measured in the adapted eye but larger than those in the unadapted eye (Experiment 3). These results suggest that (1) stereopsis is immune to perceptual distortions of the monocular stimuli, and (2) perceived spatial frequency reflects the pooled activity of monocular and binocular neurons.

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.

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.

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.

Spatial frequency channels and perceptual grouping in texture segregation

The literature suggests that both spatial frequency components and grouping processes affect texture segregation. The experiments we report investigated texture segregation in a three-part (tripartite) pattern in which each part contains equal numbers of two different squares that are arranged in vertical stripes in the top and bottom parts and in a checkerboard in the center part. We found: (1) A difference in sign of contrast yields strong texture segregation. (2) Texture segregation is a negatively accelerated function of the ratio of the Rayleigh contrasts of the low-luminance and high-luminance squares. (3) Size and contrast are not independent attributes but can cancel each other. High spatial frequency differences are not sufficient to cause segregation in the presence of contradictory information from the low spatial frequency channels. (4) Hue is a weak feature relative to contrast. Hue differences are not sufficient to cause texture segregation in the presence of contradictory contrast information. The results of the experiments support the argument that the higher order processes in texture segregation have access to information corresponding to the outputs of the spatial frequency channels. They are qualitatively consistent with the hypothesis that tripartite segregation is primarily a function of spatial frequency components and not of grouping processes.

What causes stereoscopic tilt from spatial frequency disparity.

A controversy still exists concerning whether the tilt created with interocular spatial frequency disparity arises from a computation of spatial frequency differences or from cumulative positional disparity. In a first experiment, we examined the influence of positional disparity on tilt created with frequency disparity, reasoning that if tilt were computed from spatial frequency differences, the perceived angle should remain unaltered since adding a positional disparity does not change the harmonic content of the stimulus. The results indicated that positional disparity weakened perceived tilt. In a second experiment, we tested the idea that tilt results from the calculation of increasing positional disparity across the display, arguing if local matches of features in the two eyes are made in computing tilt, then the solution to binocular correspondence may be less ambiguous if the same number of cycles was displayed for both spatial frequencies. Perceived tilt increased when the number of cycles was equal, although the angle of tilt still decreased with positional disparity. In Experiment 3, we further reduced potential sources of ambiguity for the binocular matching process by employing D10s (the tenth derivative of a Gaussian) instead of grating patterns. Positional disparity exerted essentially no influence on the perceived angle of tilt of the D10s. Taken together, the results of these experiments suggest that tilt from frequency disparity can be explained solely on the basis of positional disparity.

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.

Spatial frequency differences can determine figure-ground organization.

In three experiments we examined the influence of spatial frequency on perceptual organization. In each experiment a pattern was tested that was ambiguous in terms of figure and ground. In each experiment, the stimuli were 20 variations of the pattern, which were generated by filling the two regions of the pattern with horizontal sine wave gratings differing in spatial frequency. Five spatial frequencies were tested: 0.5, 1, 2, 4, and 8 cycles per degree. The response measure was the percentage of response time one of the regions was seen as the figure. This region was seen as the figure a higher percentage of the time in those stimuli where it contained the relatively higher spatial frequency sine wave grating compared with those stimuli where it contained the relatively lower spatial frequency sine wave grating.

Spatial frequency differences can determine figure-ground organization.

In three experiments we examined the influence of spatial frequency on perceptual organization. In each experiment a pattern was tested that was ambiguous in terms of figure and ground. In each experiment, the stimuli were 20 variations of the pattern, which were generated by filling the two regions of the pattern with horizontal sine wave gratings differing in spatial frequency. Five spatial frequencies were tested: 0.5, 1, 2, 4, and 8 cycles per degree. The response measure was the percentage of response time one of the regions was seen as the figure. This region was seen as the figure a higher percentage of the time in those stimuli where it contained the relatively higher spatial frequency sine wave grating compared with those stimuli where it contained the relatively lower spatial frequency sine wave grating.

Temporal integration characteristics in spatial frequency identification

Spatial frequency detection and identification performances were measured simultaneously as a function of exposure duration. Detection and identification sensitivity/duration functions appeared to be parallel over durations ranging from 10 to 1000 msec, independent of both spatial frequency and spatial frequency difference between the stimuli to be discriminated. The results are compatible with both a simultaneous or a serial processing of the two types of tasks. In the former case, detection and identification would take place at the same neural level and they would, therefore, be indistinguishable. The second alternative implies that the identification stage must have a time-constant substantially shorter than the detection stage. Both possibilities are compatible with the concept of spatial frequency labelled detectors.

On the detection of Gabor signals and discrimination of Gabor textures.

We have explored the detection and discrimination of Gabor signals in two different paradigms in order to determine the signals' relative importance for spatial vision. In the first experiment we determined the "detection efficiency" of five such signals presented in isolation, and our results support the conclusion that, for optimal detection, the Gaussian profile should only span (to 1/e decay values) approximately two cycles. In three subsequent experiments we have observed the discriminability of textures composed of such signals over a range of spatial frequencies, Gaussian windows and orientation differences. Our results are consistent with the detection data only insofar as the discrimination thresholds vary in a predictable way with the Gaussian window parameters. Finally, we have determined the degree to which texture discrimination, in terms of differences in both orientation and spatial frequency, can be predicted from the independent manipulations of both codes within a given Gaussian window size.

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.

What is perceived when two images are combined?

When two images are combined three perceptual outcomes are possible. One, they can be perceived as they are--separate and independent images. Two, they can become perceptually fused into a new image. Three, one image may dominate, or mask, the other. These possibilities are demonstrated with a variety of images and it is proposed that it is their spatial correlation rather than their spatial frequency similarities or differences which is critical in determining the particular outcome.