Variations in apparent spatial frequency with stimulus orientation: IL Matching data collected under normal and interferometric viewing conditions

Using an adjustment procedure, human observers matched the apparent spatial frequencies of sinusoidal gratings presented in different orientations (0, 45, 90, and 135 deg). Matches were made between all possible pairwise orientation combinations. Significant match deviations indicated that the apparent frequency of a grating depends on its orientation. The most consistent deviations were found between horizontal and vertical gratings, with horizontal gratings appearing to be of a lower spatial frequency than vertical gratings. These effects were relatively independent of stimulus contrast and persisted when the optics of the eye were bypassed with laser interferometry. A neurophysiological explanation of these effects is proposed.     

Variations in apparent spatial frequency with stimulus orientation: L Incidence of the effect in the general population

The human visual system is anisotropic not only for stimulus detection and discrimination but also for stimulus appearance. The apparent length of a stationary stimulus and the apparent velocity of a moving stimulus vary with orientation. These variations are predictable from a model assuming a compression of the horizontal spatial meridian relative to the vertical meridian. In this paper, the apparent spatial frequency of a suprathreshold grating is shown to depend on the grating orientation. Specifically, horizontal gratings appear coarser than vertical gratings of equivalent spatial frequency. Additional data collected from the same group of observers show that horizontal lines appear shorter than vertical lines of the same extent. The presence of the spatial frequency and length illusions, although both predictable from the compression model, were not found to be correlated within observers. Implications of these results for other data in the literature are discussed.     

Hemispheric differences are found in the identification,but not the detection,of low versus high spatial frequencies

The processing of sine-wave gratings presented to the left and right visual fields was examined in four experiments. Subjects were required either to detect the presence of a grating (Experiments 1 and 2) or to identify the spatial frequency of a grating (Experiments 3 and 4). Orthogonally to this, the stimuli were presented either at threshold levels of contrast (Experiments 1 and 3) or at suprathreshold levels (Experiments 2 and 4). Visual field and spatial frequency interacted when the task required identification of spatial frequency, but not when it required only stimulus detection. Regardless of contrast level (threshold, suprathreshold), high-frequency gratings were identified more readily in the right visual field (left hemisphere), whereas low-frequency gratings showed no visual field difference (Experiment 3) or were identified more readily in the left visual field (right hemisphere) (Experiment 4). Thus, hemispheric asymmetries in the processing of spatial frequencies depend on the task. These results support Sergent’s (1982) spatial frequency hypothesis, but only when the computational demands of the task exceed those required for the simple detection of the stimuli.     

Contrast constancy revisited: The perceived contrast of sinusoidal gratings above threshold

The contrast sensitivity function of the human visual system, measured with sinusoidal luminance gratings, has an inverted U shape with a peak around 2–4?c/deg. Above threshold, it is thought that luminance gratings of equal physical contrasts but of distinguishably different spatial frequencies are all perceived as having similar contrasts, a phenomenon that has been termed contrast constancy. However, when suprathreshold contrast matches were measured for pairs of luminance gratings whose spatial frequencies were indistinguishable, the matching curves were not flat and followed a similar inverted U shape form as the contrast sensitivity function at threshold. It was therefore suggested that contrast constancy may only be revealed when matching the contrasts of clearly distinguishable spatial frequencies. Here, observers matched the perceived contrasts of suprathreshold luminance gratings of similar but visibly different spatial frequencies between 0.25 and 16?c/deg. The results show that, much like the contrast sensitivity function at threshold, observers are more sensitive to intermediate spatial frequencies (1–6?c/deg) than they are to either higher or to lower spatial frequencies. This tuning is evident when matching reference contrasts of 30–80%, implying a significant role in everyday vision. To demonstrate that these results were not due to local adaptation, the experiment was repeated with shorter stimulus duration, producing the same results. The extent of departure from contrast constancy found in the present study is compared to previously reported suprathreshold measurements. The results are also discussed with consideration to limitations with display apparatus such as monitor blur.     

Transient and sustained masking

The detection threshold of a brief test stimulus was measured as a function of the onset asynchrony between it and a long-lasting suprathreshold masking stimulus. Both stimuli were sine-wave gratings of the same vertical orientation and in the peak-subtract phase but differed in spatial frequency by a factor of 3. The temporal masking functions obtained with 2- and 6-cycles/deg maskers of high contrast exhibited transient on- and off-peaks of masking and a sustained effect during the masker exposure. An 18-cycles/deg masker caused sustained masking only. Experiments with maskers of variable spatial frequency and contrast showed that, in the low-spatial-frequency range, the mechanism responsible for the transient effect was more sensitive than that generating the sustained effect, while the sustained effect required less contrast in the high-spatial-frequency range. The results are considered as evidence, in addition to previous findings, for the sustained/transient dichotomy in the temporal domain.     

Suprathreshold stereo-depth matches as a function of contrast and spatial frequency

Thresholds for stereoscopic-depth perception increase with decreasing spatial frequency below 2.5 cycles deg-1. Despite this variation of stereo threshold, suprathreshold stereoscopic-depth perception is independent of spatial frequency down to 0.5 cycle deg-1. Below this frequency the perceived depth of crossed disparities is less than that stimulated by higher spatial frequencies which subtend the same disparities. We have investigated the effects of contrast fading upon this breakdown of stereo-depth invariance at low spatial frequencies. Suprathreshold stereopsis was investigated with spatially filtered vertical bars (difference of Gaussian luminance distribution, or DOG functions) tuned narrowly over a broad range of spatial frequencies (0.15-9.6 cycles deg-1). Disparity subtended by variable width DOGs whose physical contrast ranged from 10-100% was adjusted to match the perceived depth of a standard suprathreshold disparity (5 min visual angle) subtended by a thin black line. Greater amounts of crossed disparity were required to match broad than narrow DOGs to the apparent depth of the standard black line. The matched disparity was greater at low than at high contrast levels. When perceived contrast of all the DOGs was matched to standard contrasts ranging from 5-72%, disparity for depth matches became similar for narrow and broad DOGs. 200 ms pulsed presentations of DOGs with equal perceived contrast further reduced the disparity of low-contrast broad DOGs needed to match the standard depth. A perceived-depth bias in the uncrossed direction at low spatial frequencies was noted in these experiments. This was most pronounced for low-contrast low-spatial-frequency targets, which actually needed crossed disparities to make a depth match to an uncrossed standard. This bias was investigated further by making depth matches to a zero-disparity standard (ie the apparent fronto-parallel plane). Broad DOGs, which are composed of low spatial frequencies, were perceived behind the fixation plane when they actually subtended zero disparity. The magnitude of this low-frequency depth bias increased as contrast was reduced. The distal depth bias was also perceived monocularly, however, it was always greater when viewed binocularly. This investigation indicates that contrast fading of low-spatial-frequency stimuli changes their perceived depth and enhances a depth bias in the uncrossed direction. The depth bias has both a monocular and a binocular component.     

Temporal integration and contrast sensitivity in foveal and peripheral vision

Spatial contrast sensitivity functions and temporal integration functions for gratings with dark surrounds were measured at various eccentricities in photopic vision. Contrast sensitivity decreased with increasing eccentricity at all exposure durations and spatial frequencies tested. The decrease was faster at high than at low spatial frequencies, but similar at different exposure durations. When cortically similar stimulus conditions were produced at different eccentricities by M-scaling, contrast sensitivity became independent of visual field location at all exposure durations tested. The results support the view that in photopic vision spatiotemporal information processing is qualitatively similar across the visual field, and that quantitative differences result from retino-topical differences in ganglion cell sampling. For gratings of constant retinal area temporal integration (improvement of contrast sensitivity with increasing exposure duration) was more extensive at high than at low retinal spatial frequencies but independent of cortical spatial frequency and eccentricity. For M-scaled gratings temporal integration was more extensive at high than at low cortical spatial frequencies but independent of retinal spatial frequency and eccentricity. The results suggest that the primary determinant of temporal integration is not spatial frequency but grating value that is calculated as AF2 square cycles (cycle2), where A is grating area and F spatial frequency.     

Simple reaction times to the onset,onset, and contrast reversal of sinusoidal grating stimuli

Response latencies to the onset, offset, and contrast reversal of sinusoidal gratings over a range of spatial frequencies were measured. For gratings of constant physical contrast, RT was monotonically related to spatial frequency regardless of presentation mode. Comparison of RTs to 1.0- and 9.0-cycle/deg gratings adjusted to equal apparent contrast showed that the RT shifts cannot be directly attributed to contrast sensitivity differences. It is concluded that spatial-frequency-dependent processing delays occur regardless of which temporal property of the stimulus the subject must respond to.     

Contrast and spatial frequency components in visual preferences of newborns

A preferential-looking procedure was used to investigate newborns' responses to square-wave gratings varying in spatial frequency and contrast. A preliminary study confirmed that the gratings used in the experiment were suprathreshold. In the experiment newborns' preference for a grating of 0.1 cycle deg-1 within the peak contrast sensitivity range was examined. Reduction in the contrast of this grating led to a transfer of the preference to a high-contrast grating of the same space-averaged luminance with a spatial frequency outside this range (0.42 cycle deg-1). The findings are discussed with reference to the role of the contrast sensitivity function in pattern preferences of newborns: it is suggested that contrast and spatial frequency interact in determining pattern preferences.     

眼跳的双相调节理论的行为证据

为了研究眼跳的双相调节理论是否适用于人类的视觉系统,本研究测量了人类被试对分别呈现在三种眼跳时间段（基线、眼跳抑制和眼跳增强）内的光栅的朝向辨别准确率。研究发现：相对于光栅呈现在基线时间段内,被试对呈现在抑制（或增强）时间段内的光栅的朝向辨别准确率显著地更低（或更高）（实验1）;另外,只有使用低或中等空间频率光栅作为测试刺激时,才有这种双相调节作用（实验2）。这些结果表明：人类的视觉系统在眼跳过程中存在双相调节机制,并且这种双相调节机制具有刺激选择性。     

Flicker adaptation in the periphery at constant perceived modulation depth

At constant physical flicker modulation depth, the time taken to adapt to flicker in the periphery varies inversely with temporal frequency. It has recently been suggested that this effect may indicate differential susceptibility to adaptation of the underlying temporal mechanisms. Using suprathreshold gratings, temporally modulated in contrast at constant perceived, rather than physical, modulation depth, we found the opposite result: the time required to adapt increased with temporal frequency. Given some uncertainty concerning the appropriateness of employing apparent or physically constant modulation depths, we conclude that rate of adaptation does not, at present, provide clear evidence as to the nature of the underlying temporal mechanisms.     

Comparing contrast-modulated and luminance-modulated masking: effects of spatial frequency and phase

The masking of a sinusoidal test grating by contrast-modulated (CM) gratings could, in principle, be attributable to the presence of a distortion product, injected into the stimulus during some nonlinear transformation at an early level of visual processing (e.g. Nachmias, 1989 Vision Research 29 137-142). If so, CM gratings and luminance-modulated (LM) gratings of similar effective contrast and spatial frequency should mask the detection of sinusoids in a similar fashion. We compared the effects of masking by 1 cycle deg-1 CM gratings [both simple beats (8 + 9 cycles deg-1) and amplitude-modulated gratings (8 + 9 + 10 cycles deg-1)], with those of masking by 1 cycle deg-1 LM gratings of low contrast. We found that: (i) CM and low-contrast LM grating masks yielded similar spatial-frequency tuning functions around the modulation frequency of 1 cycle deg-1; (ii) low-contrast LM gratings masked the detection of test sinusoids in a highly phase-dependent fashion, while masking by CM gratings did not vary systematically with relative spatial phase. The results suggest that masking produced by CM gratings cannot simply be explained by the presence of a distortion product at the beat or modulation frequency.     

The development of contrast constancy

The mature visual system possesses mechanisms that enable invariant perception of the contrast of an object and its features as the object undergoes changes in distance. This phenomenon, which has been called contrast constancy, obtains at suprathreshold contrasts only. Some models of contrast constancy assume the presence of narrowband spatial-frequency channels. An implication of M.S. Banks, B.R. Stephens, and E.E. Hartmann (1985, Journal of Experimental Child Psychology, 40, 501-527) is that contrast constancy should not be observed at 6 weeks but may be observed at 12 weeks. We examined this implication by investigating the development of contrast constancy in 6- and 12-week-old infants. Two sine wave gratings, differing in spatial frequency by a factor of 3, were presented side-by-side. The contrast of one grating was varied in order to estimate the contrast at which preference for the two gratings was equal. The equal preference points for 6-week-olds were predictable from their contrast thresholds. The 12-week-olds' equal preference points for low-contrast stimuli were predictable from their contrast thresholds, but those for intermediate and high-contrast stimuli were not. Thus, if one accepts the assumption that equal preference in infants is analogous to apparent contrast matches in adults, these data imply that contrast constancy is observed at 12 weeks but not 6 weeks. The perceptual consequences of this developmental transition are discussed.     

Binocular interactions in suprathreshold contrast perception

Suprathreshold binocular contrast interactions were studied psychophysically. A split-screen CRT display was used to present separate sine-wave gratings to the observer’s left and right eyes. The method of constant stimuli and a modified method of adjustment were used to find sets of binoculartest patterns that matched a given binocularstandard. Test patterns consisted of the simultaneous presentation of sine-wave gratings that differed in contrast to the left and right eyes. Standard patterns consisted of identical sine-wave gratings presented to the two eyes, and had the same spatial frequency as the test patterns. Binocular contrast matching functions were obtained for several standard contrasts at 1 and 8 c/deg. Binocular matching functions were obtained for luminance increments as well. The binocular contrast matching functions departed from a simple binocular averaging rule, and behaved as if the eye receiving the higher contrast disproportionately dominated the binocular contrast percept. Departures from the binocular averaging rule were slightly greater for higher standard contrasts. Spatial frequency had little effect, and the luminance increment matching functions also departed from the binocular averaging rule. There was evidence for a contrast version of Fechner’s paradox and for substantial individual differences in a form of ocular dominance. In a further experiment, additivity of suprathreshold binocular contrast summation was examined by testing the double-cancellation condition. We found no systematic violations of additivity at 1 and 8 c/deg. Models of suprathreshold binocular contrast summation were examined.     

The influence of spatial pattern on visual short-term memory for contrast

Several psychophysical studies of visual short-term memory (VSTM) have shown high-fidelity storage capacity for many properties of visual stimuli. On judgments of the spatial frequency of gratings, for example, discrimination performance does not decrease significantly, even for memory intervals of up to 30 s. For other properties, such as stimulus orientation and contrast, however, such “perfect storage” behavior is not found, although the reasons for this difference remain unresolved. Here, we report two experiments in which we investigated the nature of the representation of stimulus contrast in VSTM using spatially complex, two-dimensional random-noise stimuli. We addressed whether information about contrast per se is retained during the memory interval by using a test stimulus with the same spatial structure but either the same or the opposite local contrast polarity, with respect to the comparison (i.e., remembered) stimulus. We found that discrimination thresholds got steadily worse with increasing duration of the memory interval. Furthermore, performance was better when the test and comparison stimuli had the same local contrast polarity than when they were contrast-reversed. Finally, when a noise mask was introduced during the memory interval, its disruptive effect was maximal when the spatial configuration of its constituent elements was uncorrelated with those of the comparison and test stimuli. These results suggest that VSTM for contrast is closely tied to the spatial configuration of stimuli and is not transformed into a more abstract representation.     

Orientation discrimination across the visual field: size estimates near contrast threshold

Performance in detection and discrimination tasks can often be made equal across the visual field through appropriate stimulus scaling. The parameter E2 is used to characterize the rate at which stimulus dimensions (e.g., size or contrast) must increase in order to achieve foveal levels of performance. We calculated both size and contrast E2 values for orientation discrimination using a spatial scaling procedure that involves measuring combination size and contrast thresholds for stimuli with constant size-to-contrast ratios. E2 values for size scaling were 5.77 degrees and 5.92 degrees. These values are three to four times larger than those recovered previously using similar stimuli at contrasts well above detection threshold (Sally & Gurnsey, 2003). E2 values for contrast scaling were 324.2 degrees and 44.3 degrees, indicating that for large stimuli little contrast scaling (.3% to 2.3% increase) was required in order to equate performance in the fovea and the largest eccentricity (10 degrees). A similar pattern of results was found using a spatial scaling method that involves measuring contrast thresholds for target identification as a function of size across eccentricities. We conclude that the size scaling for orientation discrimination at near-threshold stimulus contrasts is much larger than that required at suprathreshold contrasts. This may arise, at least in part, from contrast-dependent changes in mechanisms that subserve task performance.     

On utrocular discrimination

Observers with good stereoacuity judged which eye received sine-wave grating patterns in a two-category forced-choice procedure. Large individual differences were found, but for most observers reliable discrimination was achieved at low spatial frequencies. No observer could perform the task above chance levels at high spatial frequencies. Discrimination was unaffected by retinal location, grating orientation, grating contrast, stimulus duration, or practice with feedback. Among observers who could perform the task, the following results were obtained: (1) Introduction of high spatial frequency components did not interfere with performance so long as a low spatial frequency component was present. (2) When gratings of low equal spatial frequency were presented to both eyes simultaneously at different contrast levels, observers could identify which eye received the higher contrast. (3) At low spatial frequencies, observers could distinguish monocular from binocular presentation. (4) Temporal frequency variations (counterphase flicker) influenced performance for some observers. Binocular summation and interocular transfer were unaffected by the spatial frequency variations which modulate utrocular discrimination. A new procedure for measuring stereopsis was developed which made possible comparison of utrocular discrimination with stereopsis at specific spatial frequencies. Stereopsis appeared mildly affected by spatial frequency.     

The effect of spatial frequency and contrast on visual persistence

The visual persistence of sinusoidal gratings of varying spatial frequency and contrast was measured. It was found that the persistence of low-contrast gratings was longer than that of high-contrast stimuli for all spatial frequencies investigated. At higher contrast levels of 1 and 4 cycles deg-1 gratings, a tendency for persistence to be independent of contrast was observed. For 12 cycles deg-1 gratings, however, persistence continued to decrease with increasing contrast. These results are compared with recently published data on other temporal responses, and are discussed in terms of the different properties of sustained and transient channels.     

The processing of spatial frequency and orientation information

Three identification experiments were completed to disambiguate the associations between spatial frequency and orientation information at the sensory, decisional, and response levels. The stimuli were gratings generated by crossing four levels each of spatial frequency and orientation. In Experiment 1, the subjects made a single identification response to the stimuli. In Experiment 2, two identification responses were made, one for the spatial frequency component and the other for the orientation component. In Experiment 3, the subjects identified either the spatial frequency or the orientation component in any block of trials. The data were confusion matrices, and an information-transmission approach was used to investigate the interactions in the system. The results show that although there were sensory associations, there were no interactions at the decisional level. Performance parity was found: there was no significant difference between the single- and double-judgment paradigms in terms of information transmitted. Overall, the results suggest that although spatial frequency and orientation information is coded jointly at the sensory level, subsequent processing is independent, with each dimension drawing upon different attentional resources.