Spatial frequency discrimination and detection characteristics for gratings defined by orientation texture

We describe evidence consistent with the proposal that the visual system contains a parallel array of size-tuned mechanisms sensitive to orientation texture-defined (OTD) form, and propose that the relative activity of these mechanisms determines spatial frequency discrimination threshold for OTD gratings. Using a pattern of short lines we measured spatial frequency discrimination thresholds for OTD gratings and luminance-defined (LD) gratings. For OTD gratings, the orientation of texture lines varied sinusoidally across the bars of the gratings, but line luminance was constant. For LD gratings, line orientation was constant, but line luminance varied sinusoidally across the bars of the grating. When the number of texture lines (i.e. spatial samples) per grating cycle was below about six, spatial sampling strongly affected both the spatial frequency discrimination and grating detection thresholds for OTD and LD gratings. However, when the number of spatial samples per grating cycle exceeded about six, plots of both discrimination threshold and detection threshold were different for OTD and LD gratings. For an OTD grating of any given spatial frequency, spatial frequency discrimination threshold fell as the number of samples per grating cycle was increased while holding texture line length constant: the lower limit was reached at six to ten samples per cycle. When we progressively increased the viewing distance (keeping the cycles per degree (cpd) constant), spatial frequency discrimination threshold reached a lower limit and increased thereafter. We propose that this minimum threshold represents a balance between opposing effects of the number of samples per grating cycle and the length of texture lines, and approaches the absolute physiological lower limit for OTD gratings. Spatial frequency discrimination was possible up to at least 7 cpd. Grating acuity for an OTD grating was considerably lower than the physiological limit for LD gratings, presumably because detectors of OTD form include a spatial integration stage following the processing of individual lines. For an LD grating, discrimination threshold fell as the number of samples per grating cycle was increased and asymptoted at six to ten samples per cycle. Spatial frequency discrimination thresholds for OTD and LD gratings were similar at low spatial frequencies (up to 3-4 cpd), but increased more steeply for OTD gratings at high spatial frequencies. For both OTD and LD gratings, discrimination threshold fell steeply as the number of grating cycles was increased from 0.5 to ca. 2.5 cycles, and thereafter decreased more slowly or not at all suggesting that, for both OTD and LD gratings, spatial frequency discrimination can be regarded as a special case of line interval or bar width discrimination. As orientation contrast was progressively increased, discrimination threshold for an OTD grating fell steeply up to about four to five times grating detection threshold, then saturated. This parallels the effect of luminance contrast on discrimination threshold for an LD grating.     

Spatial frequency discrimination of band-limited periodic targets: effects of stimulus contrast, bandwidth and retinal eccentricity.

Two experiments were conducted to explore the ability of human observers to discriminate the spatial frequency of briefly-presented, Gaussian-truncated sinewave gratings. In the first experiment, the influence of stimulus contrast and stimulus bandwidth on discrimination thresholds was measured after removing any position cues by randomizing the spatial phase of the gratings for each presentation. In a second experiment, the influence of retinal eccentricity on discrimination thresholds was explored for Gaussian-truncated gratings of constant spatial frequency bandwidth (0.5 octave) and suprathreshold contrast value (5 x detection threshold). The spatial frequency of the reference gratings varied from 1 to 8 c/deg. The gratings were positioned centered at the fixation point or 1-20 deg eccentric of the point of fixation along the horizontal meridian. Two observers responded in a two-interval forced-choice paradigm, which of two gratings had a higher spatial frequency. A difference frequency was randomly added to or subtracted from the spatial frequency of either the first or second grating. Using a maximum-likelihood algorithm, the spatial-frequency discrimination threshold delta f was computed from 40 trials, at which the observer responded with 75% accuracy. The results indicate that discrimination thresholds increase with (1) decreasing stimulus contrast, (2) increasing stimulus bandwidth, and (3) increasing retinal eccentricity. It is shown that spatial-frequency discrimination thresholds are only independent of contrast for narrow bandwidth stimuli having a contrast greater than 0.02. The eccentricity-dependent increase in discrimination thresholds varies with reference spatial frequency: with increasing retinal eccentricity delta f/f increases gradually for low spatial frequencies but rapidly for high spatial frequencies.     

Temporal contrast sensitivity and cortical magnification

We measured temporal and spatial contrast sensitivity functions of foveal and peripheral photopic vision at various locations in the nasal visual field. Sensitivity decreased monotonically with increasing eccentricity when it was measured by using the same test gratings at different eccentricities. When the gratings were normalized in area, spatial frequency, and translation velocity by means of the cortical magnification factor M so that the calculated cortical representations of the gratings became equivalent at different eccentricities, the temporal contrast sensitivity functions became similar at all eccentricities. The normalization was effective under all experimental conditions that included various kinds of temporal modulation from 0 to 25 Hz (movement, counterphase flicker and on-off flicker) and different threshold tasks (detection, orientation discrimination, and discrimination of movement direction), independently of the subjective appearances of the gratings at threshold. We conclude that central and peripheral vision are qualitatively similar in spatiotemporal visual performance. The quantitative differences observed without normalization seem to be caused by the spatial sampling properties of retinal ganglion cells that are directly related to the values of M used in the normalization.     

A comparison of contrast detection and discrimination

In order to complement previous studies of contrast detection, we have examined the effects of three stimulus variables (spatial frequency, retinal illuminance, retinal locus) and one visual disorder (amblyopia) on contrast discrimination. Although each factor has a profound effect on the detection of gratings on otherwise unpatterned displays, we find a similar dipper-shaped contrast discrimination function and similar supra-threshold Weber fractions for contrast under all these conditions.     

Second-order spatial frequency and orientation channels in human vision

We compared the number of spatial frequency and orientation mechanisms underlying first- versus second-order processing by measuring discrimination at detection threshold for first- and second-order Gabors to determine the smallest difference in spatial frequency and orientation that permits accurate discrimination at threshold. For second-order gratings, the number of channels is the same as for first-order gratings for spatial frequencies up to about 2 cpd; however, there are fewer second-order channels at higher spatial frequencies. In contrast, the number of labeled channels for orientation is the same for first- and second-order gratings. In conclusion, our findings provide evidence for distinct spatial frequency and orientation labeled detectors in second-order visual processing. We also show that, relative to first-order, there are fewer second-order channels processing higher spatial frequencies. This is consistent with a filter-rectify-filter scheme for second-order in which the second stage of filtering is at lower spatial frequencies.     

Orientation discrimination depends on spatial frequency

Thresholds were measured for discriminating the orientation of sinusoidal gratings of varying spatial frequency, and found to decrease monotonically with increasing spatial frequency. For discrimination of high-contrast (10 times threshold) near-vertical gratings, thresholds ranged from about 1 deg at 0.04 c/deg to 0.5 deg at 0.2 c/deg, after which there was little improvement. At lower contrasts and for discriminations around a mean of 45 deg, thresholds varied more so, and continued to improve until 1 c/deg. The variation of orientation discrimination thresholds with spatial frequency follows a similar trend to the variation in orientation bandwidth of visual units over the same range of spatial frequencies. Thus the present results are consistent with recent "opponent-process" models of orientation discrimination, that predict that thresholds to be limited (at least in part) by the maximum slope of orientation selectivity of visual detectors. That thresholds for high contrast vertical gratings did not improve for frequencies higher than 0.2 c/deg implies that orientation bandwidth and noisiness of oriented detectors may not be the sole factor limiting orientation discrimination, and suggests the existence of more central noise sources.     

Meridional anisotropies of orientation discrimination for sine wave gratings

The difference limen for perceived stimulus orientation was measured for thin lines, and for sine wave gratings between 2.5 and 20.0 c/deg. All observers exhibited a marked meridional anisotropy on this task with both the thin line and grating test targets. For the sine wave gratings orientation discrimination was not found to depend on their spatial frequency. Contrast threshold measurements with the same set of stimuli confirmed earlier reports that the meridional anisotropy for contrast detection increases with test spatial frequency. The data are consistent with published hypotheses (Regan and Beverley, 1985) that detection and discrimination of spatial patterns may be processed differently by orientation selective elements of the visual system and that there are fewer of these mechanisms subserving oblique orientations than either vertical or horizontal orientations.     

Discrimination of moving gratings at and above detection threshold

Two experiments examined the discriminability of moving gratings. Experiment 1 measured the difference between detection and discrimination thresholds for gratings of equal spatial frequency drifting in the same direction at different rates. It was found that, as Watson and Robson [Vision Res.21, 1115–1122 (1981)] had found with counterphase modulated gratings, only very coarse discriminations could be made. The results suggest that just two labelled channels can account for the velocity discrimination of gratings at detection threshold. The second experiment investigated the discriminability of suprathreshold moving gratings. These results also support the idea that rate of movement is mediated by two broadly tuned channels.     

Detection and discrimination of simple and complex patterns at low spatial frequencies

These experiments examined the extent to which low spatial frequencies are processed independently. The assessment was carried out with respect to both detection and discrimination performance. For simple sinusoidal gratings, pairs of stimuli could be discriminated when their contrasts reached threshold, if the ratio of their spatial frequencies was 3:1 or larger, suggesting idependent processing in separate channels. For smaller frequency ratios, slightly more contrast was required for discrimination than for detection, suggesting that stimuli were not processed by entirely separate channels. The detection and discrimination thresholds of complex grating stimuli fell within the ranges which would be expected if probability summation effects and summation of different closely spaced harmonic frequencies within single channels are considered, supporting the hypothesis of independent processing of low-spatial frequency information. The single exception to this involved discrimination of a square wave and a square wave with its fundamental component removed. In this case, discrimination required considerably more contrast than detection, even when factors of probability summation and within-channel summation of harmonics are considered.     

Velocity perception and discrimination: relation to temporal mechanisms

Measurements of three aspects of velocity detection are presented: the upper threshold of motion (UTM), perceived velocity and velocity discrimination. UTM (the highest velocity at which a drifting periodic pattern has the appearance of coherent motion) is reduced by adaptation to a similar drifting pattern of low but not medium or high velocity. The range of adaptation velocities over which the perceived velocity of a test pattern is reduced is quite different, the reduction being greatest at medium adaptation velocities. True velocity discrimination for gratings is possible only at low velocities; at higher velocities other cues (such as temporal frequency) are used. These findings are discussed in relation to current models of motion perception.     

Orientation and spatial frequency selectivity of adaptation to color and luminance gratings

Prolonged viewing of sinusoidal luminance gratings produces elevated contrast detection thresholds for test gratings that are similar in spatial frequency and orientation to the adaptation stimulus. We have used this technique to investigate orientation and spatial frequency selectivity in the processing of color contrast information. Adaptation to isoluminant red-green gratings produces elevated color contrast thresholds that are selective for grating orientation and spatial frequency. Only small elevations in color contrast thresholds occur after adaptation to luminance gratings, and vice versa. Although the color adaptation effects appear slightly less selective than those for luminance, our results suggest similar spatial processing of color and luminance contrast patterns by early stages of the human visual system.     

Elevated visual motion detection thresholds in adults with acquired ophthalmoplegia

AIMS: To test the hypothesis that in patients with acquired chronic bilateral ophthalmoplegia, abnormal retinal image slippage during head movements would result in abnormal thresholds for visual perception of motion. METHODS: Five patients (two males and three females) with ophthalmoplegia were included in the study. The average age was 44 years (range 30-69 years). The aetiology of ophthalmoplegia was myasthenia gravis (MG; n=2), chronic progressive external ophthalmoplegia (CPEO; n=2), and chronic idiopathic orbital inflammation. Visual motion detection thresholds were assessed using horizontal and vertical gratings (spatial frequency) set at thresholds for visibility. The grating was then accelerated at 0.09 deg/s(2). The subject's task was to detect the drift direction of the stimulus. RESULTS: Visual motion detection thresholds were raised to a mean of 0.434 deg/s (SD 0.09) (mean normal value 0.287 deg/s (SD 0.08)) for horizontal motion; and to a mean of 0.425 deg/s (SD 0.1) (mean normal value 0.252 deg/s (SD 0.08)) for vertical motion. The difference in values for both horizontal and vertical motion detection were statistically significant when compared with age matched controls; p <0.023 for horizontal motion and p<0.07 for vertical motion (two tailed t test). CONCLUSION: Abnormally raised visual motion thresholds were found in patients with ophthalmoplegia. This may represent a centrally mediated adaptive mechanism to ignore excessive retinal slip and thus avoid oscillopsia during head movements.     

Lower thresholds of motion for gratings as a function of eccentricity and contrast

We investigated the lower threshold for motion (LTM) of gratings as a function of position in the visual field, spatial frequency and contrast and we compared motion thresholds for sine wave and square wave luminance profiles. For contrasts below 0.05 the lower threshold for motion was raised; the increase in threshold being dependent upon spatial frequency. At contrast levels above 0.05, LTM was found to be a constant velocity at any given spatial location but increased with eccentricity of view. Raised thresholds for motion at eccentric locations could be compensated by increasing the size of eccentric gratings in proportion to M-1, where M is the cortical magnification factor, a procedure which standardises the cortical representation at differing eccentricities. Thus LTM could be expressed as a constant cortical velocity for grating contrasts above 0.05 at all stimulus locations investigated. We interpret our data as support for a ratio model of velocity coding.     

Spatial and velocity tuning of processes underlying induced motion

A nulling procedure was used to quantify the velocity and spatial frequency tuning of induced motion for sinusoidal gratings. For each spatial frequency of test and inducing gratings, there was a range of low velocities which resulted in strong induction, with a gain of close to 1. For low spatial frequencies induction occurred at higher velocities than was the case for high spatial frequencies. Induced motion shows bandpass spatial frequency tuning, with a bandwidth of about two octaves at half-height. Induced motion appears to be mediated by spatial channels with a low pass temporal characteristic. To a first approximation, induced motion appears to be a product of velocity and spatial frequency.     

A motion-energy model predicts the direction discrimination and MAE duration of two-stroke apparent motion at high and low retinal illuminance

Two-stroke apparent motion offers a challenge to current theoretical models of motion processing and is thus a useful tool for investigating motion sensor input. The stimulus involves repeated presentation of two pattern frames containing a spatial displacement, with a blank inter-stimulus interval (ISI) at one of the two-frame transitions. The resulting impression of continuous motion was measured here using both direction discrimination and motion after-effect duration in order to assess the extent to which data using the two measures can be explained by a computational model without reference to attentive tracking mechanisms. The motion-energy model was found to offer a very good account of the psychophysical data using similar parameters for both tasks. The experiment was run under both photopic and scotopic retinal illumination. Data revealed that the optimum ISI for perceiving two-stroke apparent motion shifts to longer ISIs under scotopic conditions, providing evidence for a biphasic impulse response at low luminance. Best-fitting model parameters indicate that motion sensors receive inputs from temporal filters whose central temporal frequency shifts from 2.5 to 3.0 Hz at high retinal illuminance to 1.0-1.5 Hz at low retinal illuminance.     

Spatial frequency and duration effects on the tilt illusion and orientation acuity

The simultaneous tilt illusion and the decline in variance of orientation judgements (Andrews effect) were measured as a function of exposure duration and spatial frequency. The illusions increased in size (to more than 10 deg) with exposure times up to 30-100 msec, then declined. The Andrews effect was largest at the shortest exposure and asymptoted (for a particular spatial frequency) at about the same exposure duration at which the illusion peaked. The exposure duration at which the illusion peaked was longer if the subject was more dark adapted. When the subjects' rating of the perceptual clarity of the gratings was plotted against the size of the Andrews effect (for the same duration and spatial frequency), the data fell on a single function, whether the spatial frequency was 2, 5, or 10 c/deg. The functional significance of these effects is discussed.     

The influence of spatial frequency on perceived temporal frequency and perceived speed

Speed matching experiments were conducted using drifting gratings of different spatial frequencies in order to assess the influence of spatial frequency on perceived speed. It was found that gratings of high spatial frequency appear to drift more slowly than low spatial frequency gratings of the same actual velocity. The perceived temporal frequency of a counterphase grating similarly declines as spatial frequency increases. The previously reported effect of temporal frequency on perceived spatial frequency probably does not contribute to these phenomena. Our results suggest that the motion sensors thought to operate within different spatial frequency ranges have different velocity transfer functions, a fact not incorporated in existing computational models of motion perception.     

Velocity discrimination in scotopic vision

To characterize scotopic motion mechanisms, we examined how variation in average luminance affects the ability to discriminate velocity. Stimuli were drifting horizontal sine-wave gratings (0.25, 1.0 and 2.0 c/deg) viewed through a 2 mm artificial pupil and neutral density filters to produce mean adapting levels from 2.5 to -1.5 log photopic trolands. Drift temporal frequency varied from 0.5 to 36.0 Hz. Grating contrasts were either three or five times direction discrimination threshold contrasts at each adaptation level. Following 30 min adaptation, two drifting gratings were presented sequentially at the fovea. Subjects were asked to indicate which interval contained the faster moving stimulus. The Weber fraction for each base temporal frequency was determined using a staircase method. As previously reported, velocity discrimination performance was most acute at temporal frequencies of about 8.0 Hz and greater than 20.0 Hz (though there are individual differences), and fell off at both higher and lower temporal frequencies under photopic conditions. As adaptation level decreased, discrimination of high temporal frequencies in the central retina became increasingly worse, while discrimination of low temporal frequencies remained largely unaltered. The overall scotopic discrimination performance was best at about 3.0 Hz. These results can be explained by a motion mechanism comprising both low-pass and band-pass temporal filters whose peak and temporal cut-off shifts to lower temporal frequencies under scotopic conditions.     

Precise velocity discrimination despite random variations in temporal frequency and contrast

Velocity discrimination is not affected by random changes in contrast or temporal frequency. Observers judged the relative velocity of a moving sinusoidal grating when target contrast was varied randomly from trial-to-trial over the range from 5 to 82%. The Weber fraction for the random mixture of interspersed contrast levels was about 0.06, comparable to velocity discrimination for targets presented at a fixed contrast. In a parallel experiment, the spatial frequency of the target was changed randomly from trial-to-trial, a procedure which produced concomitant random changes in the nominal temporal frequency. These variations had little effect on the velocity increment threshold; random changes in temporal frequency ranging from 2.25 to 8.25 Hz increased the Weber fraction from 0.05 to 0.07. Under identical experimental conditions, velocity discrimination was generally more precise than the discrimination of differences in temporal frequency, particularly when temporal frequency thresholds were measured with counterphase gratings. Our results indicate that velocity discrimination depends on velocity.