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.     

Consequences of spatial sampling for human motion perception

This paper describes evidence for spatial aliasing in human motion perception. For a certain range of spatial frequencies, interference fringes drifting across the extrafoveal retina resemble two-dimensional spatial noise drifting in the opposite direction. For retinal locations within 10 deg of the fovea, the perceived direction of motion is veridical up to spatial frequencies near the cone Nyquist frequency, reverses between one and two times the cone Nyquist frequency, and sometimes reverses back to the correct direction at still higher frequencies. Thus two "motion nulls", or spatial frequencies at which the direction of motion is ambiguous, are typically observed at each retinal eccentricity. A computational model is described in which sinusoidal gratings are sampled by a cone mosaic and the direction of motion of the filtered output is computed. The model predicts that the second motion null, but not the first, should be relatively immune to postreceptoral processing and should roughly equal twice the cone Nyquist frequency. This prediction is confirmed by psychophysical experiments, providing a new technique to estimate cone spacing in the living human eye.     

The contrast sensitivity function for detection and resolution of blue-on-yellow gratings in foveal and peripheral vision

Previous studies using polychromatic gratings have shown that the peripheral grating contrast sensitivity function is significantly different when the task is resolution rather than detection. Specifically, in the middle frequency range, while resolution acuity drops suddenly to zero, detection performance continues up to much higher frequencies, accompanied by observations of aliasing. We wanted to determine if the same holds true for blue-cone isolating gratings in either foveal or peripheral vision. Contrast sensitivity function (CSFs) were measured at the fovea and 20 degrees eccentricity in the temporal retina under conditions of short-wavelength-sensitive (SWS)-cone pathway isolation using a two-alternative forced choice paradigm. The detection and resolution CSF were identical at the low frequency end but at higher frequencies resolution sensitivity falls abruptly while contrast detection remained possible till higher frequencies [cut-off frequencies: fovea detection 6.0 cycles (degree)(-1), resolution 4.6 cycles (degree)(-1); periphery detection 1.6 cycles (degree)(-1), resolution 1.05 cycles (degree)(-1)]. Aliasing was observable when spatial frequency exceeded the resolution limit. Medium/high contrast blue-cone-mediated resolution acuity is sampling limited in both the fovea and periphery. Previous studies of blue-cone contrast sensitivity which employed a detection task do not reflect the true resolution limit.     

Separation of edge detection and brightness perception

When a low spatial frequency noise mask is superimposed onto a luminance staircase, the perceived brightness pattern is dramatically altered although the edges remain visible. We measured contrast thresholds for the edges and for the illusory scalloping (Chevreul-illusion), as a function of noise center spatial frequency. The masking tuning functions overlapped, but peaked at different spatial frequencies and contrast levels. The results suggest that perceived brightness is triggered only by the low spatial frequency components of the edges--the high spatial frequency components are not able to produce a brightness pattern.     

Aliasing in peripheral vision for flickering gratings under different levels of illumination

PURPOSE: To assess how far retinal illumination can be reduced for sine-wave gratings phase reversing at different temporal frequencies in peripheral vision, while maintaining sampling limited resolution acuity performance, as evidenced by an aliasing zone between detection and resolution. METHODS: Computer generated sine wave gratings were presented with flicker rates from 0 to 40 Hz under retinal illumination levels of 3.5 to -0.5 log trolands. Resolution and detection thresholds were measured at 30 degrees in the horizontal temporal field using a spatial and temporal 2AFC paradigm respectively. RESULTS: At high illumination levels, detection acuity is higher than resolution acuity between 0 and 40 Hz indicating that resolution is sampling limited. As illumination level decreases the aliasing zone becomes narrower, especially at high temporal frequency until it disappears completely at 0.5 log trolands. CONCLUSIONS: Peripheral resolution acuity ceases to be sampling limited below 1.5 log trolands for low temporal frequency gratings and at higher levels for high temporal frequency gratings. Sampling limited acuity was recorded for high frequency gratings under higher illumination levels which could be mediated by the M cells alone, but this is not the case for the lower levels of illumination.     

Discrimination of spatial phase shows a qualitative difference between foveal and peripheral processing

Detection and discrimination of compound grating stimuli were examined in foveal and peripheral vision. At the fovea, stimuli containing two components (spatial frequencies F and 3F) can be discriminated on the basis of their relative spatial phase when the 3F component is at a contrast below its independent detection threshold. This is no longer the case at increasing retinal eccentricity, where phase discrimination thresholds fall off much more steeply than simple detection thresholds. This relative fall-off in discrimination performance is still present for stimuli scaled for the cortical magnification factor, and is not attributable to fading of peripheral images due to the Troxler effect. The results therefore must imply a qualitative change in the processing of phase information between foveal and peripheral vision.     

Threshold visibility of frequency gradient patterns

The role of spatial inhomogeneity in threshold grating perception is studied using grating patterns containing a gradient of spatial frequencies. Based on both psychophysical and neurophysiological evidence, it was decided that an appropriate class of patterns would be those with a linearly varying spatial wavelength. Thresholds were measured both for patterns in which the spatial wavelength increased linearly with eccentricity and for patterns in which it decreased linearly with eccentricity. The results demonstrate that spatial inhomogeneity is indeed an important factor in the threshold visibility of gratings. The data support medium bandwidth estimates for the mechanisms underlying spatial frequency selectivity, and they are inconsistent with the notion that the visual system performs a Fourier analysis of visual images. The data can be fit quantitatively by a semi-empirical model which postulates that the sensitivity to all spatial frequencies is highest in the fovea, but that the sensitivity to high frequencies declines more rapidly than that to low frequencies with increasing eccentricity. A comparison of the model with measured line spread functions permits some estimates to be made of the range of receptive field sizes present at each eccentricity.     

The range of spatial frequency contingent color aftereffects

Checkerboard stimuli contain two-dimensional Fourier components oriented 45 degrees from edges of the individual checks. Adaptation to such stimuli and testing with rectilinear gratings showed that contingent color aftereffects are associated with the Fourier components rather than the edges of such patterned stimuli at high spatial frequencies. With low spatial frequency (0.8 c/d) contingent color aftereffects were aligned with the edges rather than the Fourier components. These data, obtained with a color cancellation procedure, are in agreement with previous reports of spatial frequency-contingent color aftereffects and indicate the range over which such effects can be obtained.     

The contrast dependence of spatial frequency channel interactions

Interactions between spatial frequency channels were tested in two ways: we measured the discriminability by the visual system between two compound spatial-frequency gratings, of components with spatial frequencies in the ratio 1:3, when the difference between the two gratings was an increase (or decrease) in contrast of both components of the compound grating (contrast discrimination), or when the difference between the two gratings was an increase in contrast of one component and a decrease in contrast of the other component (pattern discrimination). We found that the contrast: pattern discriminability ratio differs significantly from unity in most conditions. Furthermore, this ratio is generally greater when the components of the grating are in peaks-add relative phase than when in peaks-subtract phase. On the other hand, the ratio was close to unity for grating components of spatial frequencies 1 and 9 cycles/deg. These results suggest that the human visual system contains spatial frequency channels with bandwidths of between 1.6 and 3.2 octaves and that these relatively broad channels have peaks-add spatial profiles. The channels appear linear at intermediate contrasts and spatial frequencies, but super-linear at high spatial frequencies and contrasts. Contrast and spatial frequency may be interchangeable for the determination of the linearity of the visual system.     

Separate detectors for simple and complex grating patterns?

Grating having two sinusoidal components show a periodic variation in contrast which is visible as a "beat" pattern. The spatial frequency of the beat is the difference between the frequencies of the two components. Thresholds for a number of detection and discrimination tasks were measured using beat patterns of 1 c/deg (with components of 9 and 10 c/deg), and gratings of 1 and 10 c/deg. Temporal modulation at 6 Hz lowered detection thresholds for 1 c/deg gratings, but not for beats or 10 c/deg gratings. The effect of contrast on the range of temporal frequencies over which direction of movement can be discriminated differs for the three types of pattern: beats resemble neither low nor high spatial frequency gratings. Low and (for 2 of 3 observers) high spatial frequency gratings, but not beat patterns, are susceptible to a movement after effect induced by a low spatial-frequency grating. Beat patterns induce little or no movement after effect. We conclude that beat patterns are not detected by the same mechanisms that detect simple gratings.     

Vision beyond the resolution limit: aliasing in the periphery

Pattern resolution is generally considered a prerequisite for spatial vision because details too fine to be resolved cannot be distinguished from a uniform field. However, our experiments using peripheral vision demonstrate that reliable pattern detection is possible for images far beyond the resolution limit. The visual percept which arises in this case is an illusion called aliasing in which the apparent spatial structure of the stimulus is quite different from that actually present. Aliasing begins at spatial frequencies just above the classical resolution limit, which is taken as evidence that peripheral resolution is limited by the coarse spacing of visual neurons rather than by increased size of their receptive fields. At a given eccentricity, the very finest pattern which produces aliasing has a spatial period which approaches the smallest anatomical dimension: the diameter of a single cone photoreceptor.     

Functional organization of the peripheral retina: Sensitivity to periodic stimuli

Modulation sensitivity of the peripheral human retina was measured for photopic vision with an interference-fringe method that bypasses the optics of the eye. For all spatial frequencies, sensitivity decreases with eccentricity, but the manner in which sensitivity varies with eccentricity depends on the spatial frequency of the test object. At 20 c/deg and higher, sensitivity decreases linearly as eccentricity is increased, but when measured with low frequency test objects, sensitivity remains rather constant until a certain eccentricity (which depends on the spatial frequency) is reached, after which it decreases at the same rate as for high frequency test objects.     

Invariant tuning of motion aftereffect

Motion aftereffects (MAE) to drifting gratings were measured with a cancellation technique. For a constant adapting grating, MAE cancellation velocity increased linearly with visual field eccentricity. The slope of the function was dependent upon adapting temporal frequency. MAE velocity was independent of spatial frequency (2-16 c/deg) and approximately constant when expressed as an M-scaled velocity. The MAE was broadly tuned to temporal frequency and temporal tuning was independent of spatial frequency and eccentricity. Reducing contrast over the range 1.0-0.1 reduced the magnitude of the MAE at high temporal frequencies but had no influence at low and moderate temporal frequencies. The results support a ratio model of velocity coding whose spatial reference varies with eccentricity in approximate accordance with the human cortical magnification factor.     

Orientation discrimination in amblyopia

Using extended sinusoidal gratings to avoid potential problems of eccentric fixation, the authors have studied orientation discrimination in amblyopia. For all subjects, elevated orientation discrimination thresholds at high spatial frequencies were found. However, raised thresholds decrease with decreasing spatial frequency, and can be normal at low frequencies. Orientation discrimination thresholds for both amblyopic and non-amblyopic eyes are independent of contrast over most of the visible range. Therefore, amblyopic orientation discrimination thresholds cannot be mimicked in non-amblyopic eyes by reducing contrast. Control experiments show that the orientation discrimination deficits are not restricted to vertical stimuli and that they are not a result of exaggerated cyclotorsional eye movements.     

Characterization of spatial aliasing and contrast sensitivity in peripheral vision

Psychometric performance was measured for contrast detection and spatial resolution tasks in foveal and peripheral vision. Objective evidence was obtained for a quantitative difference between resolution acuity and detection acuity in the peripheral field. These two types of spatial acuity differed by up to an order of magnitude (3 vs 30 c/deg at 30 deg eccentricity) and they varied with stimulus contrast in distinctly different ways. Contrast sensitivity at the resolution limit was an order of magnitude above the absolute threshold of unity and the shape of the contrast sensitivity function was significantly different from that measured for foveal vision. The results suggest that current models of eccentricity scaling of contrast sensitivity be re-evaluated to take account of the extensive aliasing zone of spatial frequencies which becomes functional in peripheral vision when the retinal image is well focused.     

Perceived blur in amblyopia

Purpose:  It is well documented that visual acuity and contrast sensitivity in amblyopia are attenuated at high spatial frequencies: this would predict that amblyopes should perceive objects as blurred because they lack high spatial frequency information necessary to adequately represent sharp edges. In a series of experiments, we explored the representation of blur in amblyopia with blur discrimination and blur matching tasks.
Methods:  Monocular blur discrimination thresholds were measured in a spatial 2-Alternative Force Choice procedure. The luminance profiles of the blurred edge were cumulative Gaussians with the standard deviation of the reference blurred edge being fixed at 1.88, 3.75, 7.5, 15, 30, or 60 min arc. Observers were required to discriminate which edge (right or left) appeared to be the less blurred. Observers also interocularly matched edges which were identical to those employed in the blur discrimination tasks, with the exception that they were viewed dichoptically at all times.
Results:  Blur discriminination thresholds were elevated in both the amblyopic and fellow fixing eye but were within the normal range for interocular matching thresholds. Our results suggest that blur is veridically represented in the amblyopic visual system.
Conclusions:  The surprising result here is that all amblyopes, even those with the most severe visual loss, veridically matched all blurred edges, including the sharpest ones. This implies that amblyopes are able to represent levels of blur that are defined by spatial structure beyond their resolution limit. These results also raise interesting questions about the mechanism by which blur is represented in the visual system.     

Temporal frequency discrimination in human vision: evidence for an additional mechanism in the low spatial and high temporal frequency region

Temporal frequency discrimination at and above the detection threshold has been studied using gratings of low (0.2 c/deg) and medium (2 c/deg) spatial frequencies. At 2 c/deg the results of previous investigators are confirmed: The results being consistent with the existence of two broadly tuned and directionally selective temporal mechanisms (up to 32 Hz). For the lower spatial frequency an additional temporal frequency discrimination at threshold can be made between 4 and 32 Hz and enhanced temporal frequency discrimination at suprathreshold levels occurs above 24 Hz. One interpretation of this result is the existence of one or more additional temporal mechanisms with restricted spatial acuity responding to higher temporal frequencies.     

Threshold vision in amblyopia: orientation and phase

PURPOSE: The visual deficit in amblyopia involves both elevated contrast thresholds and distorted suprathreshold percepts at high spatial frequencies. It is currently unclear whether these two anomalies are part of the same neural disturbance or whether they reflect different neural dysfunction. METHODS: The quality of the spatial percepts in amblyopia was assessed at detection threshold. The ability of amblyopes to discriminate the orientation and local spatial phase of well-localized spatial stimuli was measured at the detection threshold. Measurements were made as a function of spatial frequency. RESULTS: Performance seemed normal for orientation discrimination, even at high spatial frequencies, but, in some cases, it was disturbed in phase discrimination. CONCLUSIONS: A different explanation and neural basis is needed to encompass both threshold and suprathreshold spatial deficits in amblyopia.     

Non-monotonic changes in performance with eccentricity modeled by multiple eccentricity-dependent limitations

Eccentricity-dependent resolution losses are sometimes compensated for in psychophysical experiments by magnifying (scaling) stimuli at each eccentricity. The use of either pre-selected scaling factors or unscaled stimuli sometimes leads to non-monotonic changes in performance as a function of eccentricity. We argue that such non-monotonic changes arise when performance is limited by more than one type of constraint at each eccentricity. Building on current methods developed to investigate peripheral perception [e.g., Watson, A. B. (1987). Estimation of local spatial scale. Journal of the Optical Society of America A, 4 (8), 1579-1582; Poirier, F. J. A. M., & Gurnsey, R. (2002). Two eccentricity dependent limitations on subjective contour discrimination. Vision Research, 42, 227-238; Strasburger, H., Rentschler, I., & Harvey Jr., L. O. (1994). Cortical magnification theory fails to predict visual recognition. European Journal of Neuroscience, 6, 1583-1588], we show how measured scaling can deviate from a linear function of eccentricity in a grating acuity task [Thibos, L. N., Still, D. L., & Bradley, A. (1996). Characterization of spatial aliasing and contrast sensitivity in peripheral vision. Vision Research, 36(2), 249-258]. This framework can also explain the central performance drop [Kehrer, L. (1989). Central performance drop on perceptual segregation tasks. Spatial Vision, 4, 45-62] and a case of "reverse scaling" of the integration window in symmetry [Tyler, C. W. (1999). Human symmetry detection exhibits reverse eccentricity scaling. Visual Neuroscience, 16, 919-922]. These cases of non-monotonic performance are shown to be consistent with multiple sources of resolution loss, each of which increases linearly with eccentricity. We conclude that most eccentricity research, including "oddities", can be explained by multiple-scaling theory as extended here, where the receptive field properties of all underlying mechanisms in a task increase in size with eccentricity, but not necessarily at the same rate.     

Optimal displacement in apparent motion

Measurements are made of the optimal displacement for an abruptly displaced sinewave grating to elicit a motion aftereffect. At a fixed nominal eccentricity of 4 deg, spatial frequencies ranging from 0.2 to 1.2 c/deg are effective in producing an aftereffect. At any given spatial frequency, the optimal displacement is slightly less than one quarter spatial cycle. The range of effective spatial frequencies does not correspond to the range of optimal spatial frequencies reported for neurons in primate Area V1, but does correspond to that for Area V2.