Spatial frequency channels in human vision as asymmetric (edge) mechanisms

External noise distinguishes attention mechanisms

We developed and tested a powerful method for identifying and characterizing the effect of attention on performance in visual tasks as due to signal enhancement, distractor exclusion, or internal noise suppression. Based on a noisy Perceptual Template Model (PTM) of a human observer, the method adds increasing amounts of external noise (white gaussian random noise) to the visual stimulus and observes the effect on performance of a perceptual task for attended and unattended stimuli. The three mechanisms of attention yield three "signature" patterns of performance. The general framework for characterizing the mechanisms of attention is used here to investigate the attentional mechanisms in a concurrent location-cued orientation discrimination task. Test stimuli--Gabor patches tilted slightly to the right or left--always appeared on both the left and the right of fixation, and varied independently. Observers were cued on each trial to attend to the left, the right, or evenly to both stimuli, and decide the direction of tilt of both test stimuli. For eight levels of added external noise and three attention conditions (attended, unattended, and equal), subjects' contrast threshold levels were determined. At low levels of external noise, attention affected threshold contrast: threshold contrasts for non-attended stimuli were systematically higher than for equal attention stimuli, which were, in turn, higher than for attended stimuli. Specifically, when the rms contrast of the external noise is below 10%, there is a consistent 17% elevation of contrast threshold from attended to unattended condition across all three subjects. For higher levels of external noise, attention conditions did not affect threshold contrast values at all. These strong results are characteristic of a signal enhancement, or equivalently, an internal additive noise reduction mechanism of attention.

Why do anatomic backgrounds reduce lesion detectability?

RATIONALE AND OBJECTIVES

Developing metrics of medical image quality requires an understanding of how anatomic backgrounds reduce human visual detection performance. Visual psychophysics has shown that there are two distinct ways in which a complex background can degrade performance: (1) the presence of a deterministic high-contrast background, (2) variability in the background from location to location. The authors investigated how these two sources of performance degradation reduce human visual performance locating a lesion in anatomic backgrounds.

METHODS

Human performance localizing a disk-shaped lesion in one of four locations (four alternative forced choice) was measured for three background conditions. In the first condition the background was a uniform gray. In the second condition (the repeated background condition) an anatomic background was sampled on each trial and used as a background for the four possible lesion locations. In the third condition (the different background condition) four different anatomic backgrounds were sampled on each trial and used for the four possible lesion locations. Test images consisted of computer simulated lesions mathematically projected on digital x-ray coronary angiograms.

RESULTS

For five levels of lesion contrast, visual detection performance for two observers decreased significantly from the uniform background condition to the repeated background condition, and decreased even further for the different background condition.

CONCLUSIONS

Study results show that both the presence of a deterministic high-contrast background and the background variations contribute to performance degradation of human visual detection of signals in anatomic backgrounds.

The effect of white and filtered noise on contrast detection thresholds

Models of the dipper effect seen in contrast discrimination experiments predict that small amounts of noise should facilitate detection of a subthreshold sinusoidal grating. Although facilitation of chromatic sine waves has been measured with chromatic or luminance noise, a facilitory effect of luminance sinusoidal gratings has not been measured, most likely because the stimulus characteristics were not tuned for revealing facilitation. The present study measures contrast detection thresholds (CDTs) of sinusoidal gratings in two-dimensional, static, band-limited white noise and low-pass and high-pass filtered noise using a two-interval forced-choice paradigm. The results show facilitation in near threshold white noise of middle frequency sinusoidal gratings, and facilitation in filtered noise of sinusoidal gratings whose frequency is far outside the pass band of the noise. Based on these results, a model of contrast detection thresholds is modified such that the facilitation is attributed to reduced observer uncertainty caused by small amounts of noise.

Contrast discrimination function: spatial cuing effects

The effects of spatial cuing were measured for discrimination between an increment and a decrement on a target's pedestal contrast. Discrimination thresholds measured in the absence of a spatial cue were always higher than corresponding thresholds measured in the presence of a spatial cue, except when pedestal contrast was near zero. Uncued discrimination thresholds rose monotonically with pedestal contrast; cued discrimination thresholds formed a dipper function of pedestal contrast. A spatial-uncertainty model incorporating a nonlinear transducer produced similar results.

Motion thresholds can be predicted from contrast discrimination

The detection thresholds for oscillatory motion and flicker were compared across a wide range of pedestal contrasts, spatial frequencies, and temporal frequencies in both foveal and peripheral vision. Motion and flicker stimuli were both generated by summation of a counterphase test grating with a static pedestal grating. For the oscillatory motion task the test and the pedestal were presented 90 deg out of phase to each other, whereas for flicker the two gratings were presented in phase. Since detection of both stimuli would depend on the same test stimulus, detection thresholds could be similar even though the tasks differ. Although there was a slight elevation in flicker detection thresholds compared with motion thresholds, our main finding is that oscillatory motion and flicker thresholds for suprathreshold sinusoidal gratings are similar. This finding supports the idea that motion and flicker have a common underlying detection mechanism. Our finding that flicker thresholds are slightly higher than jitter thresholds indicates that the contrast gain control (or saturating energy transducer) has a weak phase dependence. The ability to discriminate motion from flicker was elevated relative to their detection thresholds, particularly at high temporal frequencies. We offer two models to account for this behavior. The discrimination of motion from flicker may require a temporal comparison of the outputs of directionally selective filters tuned to opposite directions or to the population statistics of a bank of separable mechanisms.

Resolution acuity is better than vernier acuity

Our impressive sensitivity to vernier offsets as compared to resolution acuity has long inspired vision researchers to study the phenomena in great detail. In this study we use the test-pedestal framework to compare resolution and vernier acuity. In these experiments the test stimulus is the same for both tasks, only the pedestals differ. When thresholds are expressed in common units of test strength, vernier acuity thresholds are higher (worse) than for resolution and contrast discrimination tasks over the range of pedestal strengths tested. This apparent reversal of sensitivity is actually consistent with expectations based on the presumed underlying visual mechanisms involved in the tasks.

Second-order illusions: Mach bands, Chevreul, and Craik--O'Brien--Cornsweet

Mach bands, which normally occur at the edges of ramp modulations of luminance, are demonstrated to occur in fullwave stimuli that have ramp modulations of contrast while maintaining constant expected luminance. [The fullwave stimuli are random textures that (1) have a ramp contrast modulation that is exposed by fullwave rectification (e.g. absolute value or square) or by halfwave rectification but (2) have a uniform expected luminance throughout, so the modulation remains hidden without rectification.] Two different textures were used: random pixels and 'Mexican hats'. Stimuli were presented dynamically, with a new instantiation of the texture every 67 msec (this enhances the magnitude of the illusion). Both fullwave Mach-band stimuli exhibit perceptual Mach bands that are decreases or increases in apparent texture contrast with no concomitant change in apparent brightness. The perceived contrast bands in fullwave Mach stimuli and the brightness bands in a conventional luminance Mach-band stimulus have approximately the same magnitude. Chevreul (staircase) illusions in luminance and in fullwave patterns also are found to have approximately similar magnitudes, as do luminance and fullwave Craik--O'Brien--Cornsweet illusions. None of these illusions can be perceived with halfwave textures. These results indicate that second-order (texture) illusions result from fullwave, not halfwave, rectification and involve spatial interactions that are remarkably similar to those in first-order (luminance) processing.

Color and luminance spatial tuning estimated by noise masking in the absence of off-frequency looking

We assessed the contribution of off-frequency looking for pattern detection and obtained bandwidths for chromatic and luminance mechanisms in conditions free from this effect. We used a simultaneous spatial masking technique with Gaussian enveloped sinusoidal test stimuli (0.5 cycle/deg) and filtered one-dimensional static-noise masks whose spectral power was uniformly distributed per octave. Stimuli were modulated in the chromatic (isoluminant red-green) or the luminance (yellow-black) domain. Color and luminance detection thresholds were compared for low-pass, high-pass, and notch- (band-stopped) filtered noise. We obtained the following results: (1) at high-noise spectral densities, masking by notched noise is greater than the summed masking of the high- and low-pass noise, indicating the presence of off-frequency looking for both color and luminance detection. There is no evidence for off-frequency looking at lower power densities. (2) Using notch-filtered noise, which avoids the problem of off-frequency looking, we found that color processing is subserved by bandpass channels with bandwidths similar to those revealed for luminance processing. (3) Both color and luminance mechanisms appear to have bandwidths proportional to their center frequency (constant in octaves). (4) The lower and upper sides of the color and luminance tuning functions were estimated individually by use of high-pass and low-pass noise of a low power density and are revealed to be asymmetric, with the lower side declining more steeply than the upper side.

Evidence for separate pathways for color and luminance detection mechanisms

We measure threshold versus contrast (TvC) functions for chromatic (red-green) and luminance sine-wave-grating stimuli for (1) the detection of luminance in the presence of color contrast and (2) the detection of color in the presence of luminance contrast. We find that, although these crossed TvC functions both display a dipperlike shape, their facilitation differs from that found for standard uncrossed dipper functions (luminance on luminance or color on color contrast). Their facilitation disappears (cross condition 1) or is reduced (cross condition 2) by randomized presentation of the phase of the test and the mask, and the remaining facilitation (cross condition 2) displays no spatial tuning. We argue that these crossed facilitatory interactions cannot be explained by detection mechanisms with common inputs from color and luminance contrast (a nonindependence of transduction), and we present evidence that instead they reflect the use of local cues in the stimuli. We also measure the luminance-luminance TvC function in the presence of a fixed suprathreshold color contrast. The results demonstrate that, even when the color contrast produces a masking of the luminance thresholds, luminance-luminance facilitation still occurs. Thus the opposing effects of masking and facilitation can occur simultaneously. Furthermore, while luminance-luminance facilitation occurs independently of color contrast, masking can be produced by either contrast. This suggests that masking and facilitation have different underlying origins. Similar results are found for the color detection thresholds in the presence of a luminance pedestal. We conclude that there are separate pathways for the detection of color and luminance contrast, each with no input from the other contrast. We suggest that the cross masking reflects divisive interactions between these pathways that is restricted to high contrasts.

Discrimination of position and contrast in amblyopic and peripheral vision

Many computational models of normal vernier acuity make predictions based on the just-noticeable contrast difference. Recently, Hu, Klein and Carney [(1993) Vision Research, 33, 1241-1258] compared vernier acuity and contrast discrimination (jnd) in normal foveal viewing using cosine gratings. In the jnd stimulus the test grating was added in-phase to the (sinusoidal) pedestal, whereas in the vernier stimulus the same test grating was added with an approx. 90 deg phase shift to the pedestal. In the present experiments, we measured thresholds for discriminating changes in relative position and changes in relative contrast for abutting, horizontal cosine gratings in a group of amblyopes using the Hu et al., test-pedestal approach. The approach here is to ask whether the reduced vernier acuity of amblyopes can be understood on the basis of reduced contrast sensitivity or contrast discrimination. Our results show that (i) abutting cosine vernier acuity is strongly dependent on stimulus contrast. (ii) In both anisometropic and strabismic amblyopes, abutting cosine vernier discrimination thresholds are elevated at all contrast levels, even after accounting for reduced target visibility, or contrast discrimination. (iii) For both strabismic and anisometropic amblyopes, the vernier Weber fraction is markedly degraded, while the contrast Weber fraction is normal or nearly so. (iv) In anisometropic amblyopes the elevated vernier thresholds are consistent with the observers' reduced cutoff spatial frequency, i.e. the loss can be accounted for on the basis of a shift in spatial scale. (v) In strabismic amblyopes and in the normal periphery, there appears to be an extra loss, which can not be accounted for by either reduced contrast sensitivity and contrast discrimination or by a shift in spatial scale. (vi) This extra loss cannot be quantitatively mimicked by "undersampling" the stimulus. (vii) Surprisingly, in some strabismics, and in the periphery, at relatively high spatial frequencies, vernier thresholds appear to lose their contrast dependence, suggesting the possibility that there may be qualitative differences between the normal fovea and these degraded visual systems. (viii) This contrast saturation can be mimicked by "undersampling" the target, or by introducing strips of mean luminance between the two vernier gratings, thus mimicking a "scotoma". Taken together with the preceding paper, our results suggest that the extra loss in position acuity of strabismic amblyopes and the normal periphery may be a consequence of noise at a second stage of processing, which selectively degrades position but not contrast discrimination.

Human luminance pattern-vision mechanisms: masking experiments require a new model

A widely used model of simultaneous luminance pattern masking is based on mechanisms that sum inputs linearly and produce a response that is an S-shaped function of that sum. This model makes two predictions about masking: (1) Changing the masker spatial waveform will shift the threshold-versus-masker contrast function horizontally by a multiplicative constant. (2) Adding a second fixed-contrast masker will shift this function horizontally by an additive constant. Experimental tests do not support these predictions. The results can be explained by a new model that incorporates broadband divisive inhibition, consistent with physiology.

The spatial tuning of chromatic mechanisms identified by simultaneous masking

We have investigated the spatial transfer characteristics of the mechanisms sensitive to color in the human visual system using a method of simultaneous spatial masking with isoluminant chromatic stimuli. The test stimuli were Gaussian enveloped red-green gratings of three spatial frequencies in the lowpass region of the color domain (0.25, 0.5 and 1 c/deg). The masking stimuli were red-green gratings at the orientation and phase of the test, presented at the same spatial frequency, and at +/- 1, and +/- 2 octaves from its spatial frequency. We obtained test contrast threshold as a function of mask contrast for a wide range of mask contrasts (TvC functions). Tuning functions were derived from linear fits of the masking data, by taking the mask contrast that doubled the minimum test threshold at each spatial frequency. Chromatic tuning functions show bandpass characteristics for all test spatial frequencies examined with an average full bandwidth at half-height of 2.6 octaves, which is similar to the luminance bandwidths obtained under comparable conditions. Thus, our results suggest that the color contrast sensitivity function is the upper envelope of a range of bandpass mechanisms whose peaks extend to very low spatial frequencies.

Visual processing delays alter the perceived spatial form of moving gratings

This study shows that there are delays in processing high spatial frequencies relative to low frequencies, and that these may affect the perceived brightness profile of drifting waveforms. The stimuli were complex waveforms consisting of 2-3 sinusoidal components, either drifting or stationary. The phase of the components was varied until the brightness profile of the waveform appeared as a square, triangle, ramp or bar. The results indicate that stationary waveforms are perceived veridically, but drifting waveforms are not. The harmonics of a drifting complex wave must be phase advanced, relative to the fundamental, in order to cancel motion-induced waveform distortions. This suggests that during visual processing the harmonics must be phase delayed, indicating that they are being processed more slowly than the fundamental. The most significant delays appear to be those between the fundamental and its second and third harmonic. Furthermore, the results show that the magnitude of the delays is dependent on the phase relationship between the components at perceptually significant points in the waveform: delays are less when the components are in sine phase than when they are in cosine phase. Separate experiments show that the detectability of phase shifts is least when the components are in sine phase. Together, these results may explain why drifting "sharp-edged" stimuli are not perceptually distorted: the human visual system appears to be relatively insensitive to phase shifts around square-wave phase and may therefore tolerate differences in the processing times of certain harmonics. A discussion of the possible origin of these processing delays is presented, together with the hypothesis that frequency dependent delays may reflect the spatiotemporal inseparability of cortical visual units.

Can sinusoidal vernier acuity be predicted by contrast discrimination?

A test-pedestal approach, with a test grating superimposed on a masking pedestal, was used to compare sinusoidal grating vernier acuity and contrast discrimination thresholds. The goal is to develop a simple model for vernier acuity without assumptions about underlying mechanisms. In the contrast discrimination task, subjects were asked to detect contrast increments in the presence of a base pedestal. In the vernier task, a test grating shifted by 90 deg relative to the pedestal grating was added to one-half of the pedestal grating to produce a vernier offset. When expressed in the same contrast units and compared under optimal conditions, vernier and contrast discrimination thresholds agree well at spatial frequencies between 2 and 20 c/deg and at pedestal contrasts above 10 times detection threshold. Thus, under these conditions, contrast discrimination predicts grating vernier acuity. To account for the discrepancies between vernier thresholds and contrast just noticeable difference (JND) when conditions deviate from optimal, one needs to make assumptions about the underlying mechanisms.

Visibility, timing and vernier acuity

To investigate the relationship between contrast detection and vernier acuity for abutting targets, the effects of varying target exposure duration (12-2000 msec) on vernier and contrast detection thresholds for long, thin lines and sinusoidal gratings (1 and 8 c/deg), were measured. Vernier thresholds decreased with both increasing exposure duration and increasing target contrast. Predictions made for equally visible targets show that the effect of exposure duration on vernier thresholds is almost completely accounted for by its effect on target visibility. Vernier thresholds and contrast detection thresholds for line targets were also measured in the presence of a spatiotemporal mask, for different exposure durations. Again, once the effect of this mask on target visibility was accounted for, there was virtually no remaining effect of exposure duration on vernier thresholds. The results of these experiments suggest that similar spatial mechanisms mediate both contrast detection thresholds and vernier thresholds for abutting targets; and that the processes involved in target detection and the extraction of relative position information are limited by the same factors.

Electro-physiological investigation of edge-selective mechanisms of human vision

This study investigates the spatial and temporal characteristics of human visual mechanisms that respond selectively to the polarity of edges. The technique was to record steady-state visual evoked-potentials (VEPs) while visually stimulating with a sawtooth waveform (a series of edges of the same polarity) periodically reversing in contrast (and hence edge-polarity) at a suitable frequency. To ensure that phase-locked VEPs resulted from polarity reversal (rather than local luminance modulation) the stimuli were randomly jittered to a new position between each contrast reversal. The jittered stimulus elicited strong and reliable second-harmonic modulation, usually about one-fifth the amplitude of standard VEPs under similar conditions. The amplitude and extrapolated thresholds of polarity-specific VEPs (relative to standard VEPs) did not vary with eccentricity (up to 10 degrees) or with stimulus orientation. The dependency on spatial frequency was similar to that of standard VEPs, but the polarity-specific VEPs tended to peak at lower temporal frequencies. Perhaps the clearest difference in the two types of VEPs was in the estimated response latency, about 140 msec for the polarity VEPs, compared with 90 msec for standard VEPs.

Contrast adaptation and contrast masking in human vision

After a preliminary study of visual evoked potentials (VEPS) to a test grating seen in the presence of masks at different orientations, psychophysical data are presented showing the effects of adaptation and of masking on thresholds for detecting the same test grating. The test is a vertical grating of spatial frequency 2 cycles per degree; adapting and masking gratings differ from the test either in orientation or in spatial frequency. The effects of adaptation and masking are explained by a single mechanism model that assumes: (i) adaptation and masking both alter the contrast response (or transducer) function of the mechanism that detects the test; (ii) masks, but not adaptors, stimulate the mechanism that detects the test; and (iii) a test is detectable when it raises response level by a constant amount. The model incorporates two distinct tuning functions, a broad adaptive contrast function and a narrow effective contrast function. It accounts adequately for all the data, including the location and size of the facilitative dip found in some masking functions, the constant slopes of the threshold elevation segments of adaptation functions and the varying slopes of masking functions. It also predicts the sometimes surprising joint effects of adaptation followed by masking and of two masks operating simultaneously.

Binocular summation in vernier acuity

Monocular and binocular abutting line vernier acuities were measured as a function of contrast. Over a range of contrasts from near the line-detection threshold to approximately 20 times threshold, binocular vernier thresholds are lower (better) than monocular thresholds by approximately 50-60%, similar to the binocular improvement found for the detection of both a thin line and a dipole. At higher contrasts the binocular advantage diminishes, apparently as a result of saturation.

Purely chromatic perception of motion in depth: two eyes as sensitive as one

Motion hyperacuity (phase) thresholds were measured for both lateral and stereoscopic oscillatory motion in both luminance and equiluminant red/green gratings of 2 cycles per degree. Thresholds for lateral chromatic motion did not exhibit the inhibitory fall-off at low temporal frequencies that was found for luminance motion. Phase thresholds for purely chromatic motion were substantially higher than those for luminance gratings, in proportion to the ratio of cone signal modulation, but they could be predicted from the corresponding contrast sensitivities for both types of stimulus. Stereomovement thresholds in luminance gratings showed the stereomovement suppression effect relative to monocular motion sensitivity previously reported for line stimuli, but purely chromatic gratings did not. Together with the lack of an inhibitory fall-off, these results imply that chromatic and luminance motion are processed by different neural pathways, and that the chrominance pathway is capable of supporting a strong percept of stereoscopic motion from purely chromatic gratings.

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.

Wallpaper illusion: cause of disorientation and falls on escalators

The wallpaper illusion, first described over a century ago, can occur when a person with normal binocular vision views a pattern that is periodic in the horizontal meridian of the visual field. Escalator trends present such a pattern. Evidence is presented favoring the view that disorientation experienced by escalator riders is caused by this illusion. Possibly some of the estimated 60,000 escalator falls occurring in the United States each year are linked to it.

Vernier acuity as line and dipole detection

The vernier judgment is commonly thought of as discriminating the displacement of a portion of a pattern. However, we have found it revealing to consider vernier stimuli in another light; as the composite of a test pattern superimposed on a masking pedestal. The pedestal is the pattern with zero spatial offset, and the test pattern is the luminance distribution which, when added to the pedestal, produces the offset. For example, a vernier offset of an edge can be generated by adding a thin line (the derivative of an edge) to one half of an edge pedestal, and a vernier offset of a line can be generated by adding a thin dipole (the derivative of a line) to one half of a line pedestal. Vernier thresholds for low contrast edge and line pedestals can be directly predicted from detection thresholds of thin lines and dipoles on uniform fields. A surprisingly simple relationship is also derived between vernier thresholds and the size of Ricco's integration zone. We have found this masking paradigm to be fruitful and believe it is relevant to all the hyperacuities, not just vernier.

Hemispheric asymmetry in the processing of high and low spatial frequencies: a facial recognition task

The research investigated the relationship between spatial frequency and visual field in a facial recognition task. Faces of neutral affect (Ekman, 1979) were tachistoscopically presented to the right or left visual field. The faces were presented alone, or masked with square wave gratings of 1, 24, or 48 cycles/degree, for a duration of 10 msec. Accuracy in recognizing each target face from a group of five served as the dependent measure. Subjects were 15 males and 15 females. ANOVA results included a frequency x visual field interaction effect (p less than .001). As was hypothesized, LVF errors were highest in the absence of low spatial frequencies, while RVF errors were highest when a higher range of spatial frequencies was removed. These results confirm that the hemispheres show a differential efficiency in processing high and low spatial frequency information in faces. They also offer empirical evidence to support the clinical findings that both hemispheres contribute to facial recognition.

Evidence for edge and bar detectors in human vision

The structure of receptive fields of human visual detectors was investigated by studying their phase response. Observers were required to discriminate between pairs of periodic stimuli that differed in phase by 180 degrees (reversed in contrast). The stimuli comprised 256 harmonics, smoothly filtered in amplitude, and congruent in phase at the origin. Reversal discrimination thresholds were measured as a function of the phase of the harmonics. Thresholds were slightly higher for phases around 45 degrees, consistent with the idea that all discriminations were mediated by independent detectors with 0 or 90 degrees phase response (assuming probability summation between them). Discrimination thresholds were also measured with a pedestal stimulus, of phase complementary to that of the test gratings. For discriminations between 0 and 180 degrees (cosine phase), or 90 and 270 degrees (sine phase), the complementary pedestal had little effect, implying independence of detectors in sine and cosine phase. However, for discrimination between 45 and 225 degrees (stimuli containing both sine and cosine components) the complementary pedestal, which also contained both sine and cosine components, facilitated greatly discrimination thresholds. The results suggest that there exist two classes of detectors, one with a Fourier phase spectrum of 0, the other with a Fourier phase spectrum of 90 degrees. This implies that the receptive fields are symmetric, one class having even-symmetry (line-detectors), the other odd-symmetry (edge-detectors).

Sensitivity loss in odd-symmetric mechanisms and phase anomalies in peripheral vision

The ability to detect, discriminate and identify spatial stimuli is much poorer in the peripheral than in the central visual field. Some deficits are eliminated by scaling stimulus size. For example, grating detectibility is roughly constant across the visual field when spatial frequency and target extent are scaled appropriately. Other deficits persist despite scaling. For instance, some readily detectable patterns are more difficult to identify peripherally than in the fovea. This deficit is caused, at least partially, by a reduced ability to encode spatial phase (or relative position). To specify the properties of foveal and peripheral phase-encoding mechanisms, we measured discrimination thresholds for compound gratings at several eccentricities. Our observations are consistent with a two-channel model of phase encoding based on even- and odd-symmetric mechanisms (see Fig. 1), but the sensitivity of the odd-symmetric mechanisms decreases dramatically with eccentricity. Thus, the loss of sensitivity in one type of mechanism may underlie the reduced ability to encode spatial phase peripherally.

Higher-harmonic adaptation and the detection of squarewave gratings

Adaptation to a high contrast sinewave grating of 1 c/deg spatial frequency causes a large increase in the contrast threshold for a 1 c/deg test grating, but fails to raise the threshold for a squarewave grating of 0.33 c/deg, although the sensitivity of the "channel" tuned to both the third and fifth harmonic components of the squarewave test grating should be thoroughly suppressed. Following sequential adaptation to sinewave gratings of 1 and 3 c/deg spatial frequency, detection of squarewave gratings at 0.33 c/deg likewise remains unaffected. In contrast, after adaptation to a 0.33 c/deg squarewave grating with missing fundamental the contrast threshold for a squarewave test grating of the same frequency is increased by 0.25 log unit, although the higher harmonic component frequencies are less affected than by sequential sinewave adaptation. The results suggest that independent spatial frequency channels detecting harmonic components are not alone sufficient to account for the visibility of low frequency squarewaves.

Evidence for spatially local computations underlying discrimination of periodic patterns in fovea and periphery

Human visual sensitivity for discriminating between, on the one hand stimuli composed of components (F) and (F + 3F) (compound detection), and on the other hand (F + 3F) and (F - 3F) (phase discrimination), was measured as a function both of stimulus contrast and eccentricity. Performance under these particular conditions was found to depend upon whether the (F) or (3F) component was dominant in the pattern. When the (F) component was high in contrast, visual performance was well modelled by an edge-blur discrimination, whereas when the (3F) component was high in contrast, visual performance was well modelled by a contrast discrimination involving local spatial features within each waveform. These conclusions were valid for both foveal and peripheral vision. The finding that these suprathreshold compound stimuli are discriminated on the basis of the local spatial features, and not on differences in their phase spectra as previously thought, allows a reinterpretation of the importance of phase coding in normal vision and of the selective loss of these discriminations that have been previously reported for peripheral vision and in amblyopia.

Development of the discrimination of spatial phase in infancy

The ability to discriminate grating patterns, containing the same spatial frequency components but in different phase relationships, has been studied in infants by comparing looking times following habituation to one pattern. The performance of 1-month-olds was compared with that of 2/3-month-old infants. Both age groups could discriminate a set of components in square-wave-phase (fundamental 0.18 c/deg) from components of the same amplitude combined in random phase. However, these compounds differ in peak-to-trough contrast, which infants of both ages could discriminate even for a constant waveform. When contrast was randomized from presentation to presentation, the older group still demonstrated discrimination, implying that they were sensitive to the pattern differences, but the younger group did not. The younger group also failed to demonstrate discrimination between the two waveforms when they were of fixed, matched, peak-to-trough contrast, indicating that the previous absence of discrimination was not simply due to distraction by the contrast variations. We conclude that 1-month-olds are insensitive to the configuration of these compound grating patterns even when they are capable of detecting their components. This loss of spatial information has some analogies with adult peripheral and amblyopic vision. Like other aspects of vision, it shows striking development between 1 and 3 months of age.

Widely separated spatial frequencies: mechanism interactions

The question of independence between spatially tuned mechanisms that respond to very different frequencies is addressed by a theoretical reconstruction of their responses to single and compound grating stimuli presented at near-threshold levels. Parameters of sensory response distributions are estimated in a two-response rating experiment, and tested against those predicted by a Signal Detection model when independent processing is assumed. Small but consistent deviations from predicted values were observed and are interpreted in terms of frequency-specific patterns of inhibition and stochastic correlation. It is further demonstrated that these interactions may in part account for the superiority of discrimination over detection found with such widely separated frequencies.

Different encoding mechanisms for phase and contrast

Phase sensitivity was assessed over a large range of exposure durations by means of a 2AFC staircase procedure where the observer had to detect the relative position of sinusoidal gratings relative to a superimposed thin, dark line. Phase discrimination thresholds decreased as a function of exposure duration although the contrast of the stimuli was weighted for equal detectability at all durations. Phase sensitivity improved markedly with contrast, as opposed to the degradation with contrast seen in contrast discrimination paradigms. The contrast and time functions of phase sensitivity both support the hypothesis that phase is processed separately from contrast by a pathway with different temporal and contrast characteristics. We propose a model where phase sensitivity depends on a luminance subtraction process with a time constant of about 130 msec.

Effects on grating detection of vertically displaced peripheral gratings

Contrast threshold for a sinusoidal target in the simultaneous presence of the vertically displaced peripheral gratings was measured as a function of the peripheral contrast and the separation. When the signal and peripheral gratings were in phase, the low-contrast peripheral gratings produced the improvement in signal threshold, while the high-contrast gratings produced threshold elevation. The facilitation effect was extended to the separation equating to 10 grating cycles, whereas the inhibition effect was restricted to the region near the border. When the two gratings were out of phase, the low-contrast peripheral gratings produced threshold elevation, while the high-contrast gratings exerted little effect on signal threshold. The results were explained in terms of spatial summation and lateral inhibition.

Opponent-movement mechanisms in human vision

A vertical grating that sinusoidally reverses contrast can be synthesized from two identical component gratings that move with equal velocities in opposite directions (leftward and rightward). Such a counterphase grating is used as a suprathreshold masking pattern. When the mask is of low spatial frequency and is modulated rapidly, a test pattern consisting of an increment of the rightward component and an equivalent simultaneous decrement of the leftward component is highly detectable compared with simultaneous increments or decrements of both components. The visibility of the opponent-movement test signal is strongly facilitated by high-contrast masks. This facilitation is accompanied by a high sensitivity for judging the direction of motion of the test. These results show that certain detection mechanisms are highly sensitive to the difference of the rightward and leftward components. However, when the mask is of threshold contrast, the rightward- and leftward-moving test components appear to be detected independently. A high-contrast grating that rapidly moves in one direction strongly masks gratings moving in the same or opposite direction; this shows that moving patterns are not detected by unidirectional mechanisms when contrast is clearly suprathreshold. The results may be explained by a model with mechanisms that are excited by one direction of motion and inhibited by the opposite direction.

Simultaneous masking between two sinusoidal gratings measured in terms of temporal sensitivity

Effects of high-contrast simultaneous masking gratings on the temporal sensitivity of signal gratings were measured as a function of masking spatial frequency, where temporal sensitivity was defined as the reciprocal of the minimum exposure duration required for a signal to be detected. The sensitivity of signal gratings was shown to be facilitated when signal frequencies and masking frequencies were separated by more than about 2 octaves but inhibited when the two frequencies were not separated this much. The results were quantitatively different from the results obtained in terms of contrast sensitivity. Psychometric functions on grating detection were shown to become steeper when the temporal sensitivity was enhanced and less steep when it was decreased.

An inherent nonlinearity in near-threshold contrast detection

We measured an essentially normal pedestal effect using stationary gaussian targets and slowly moving pedestal gratings. Since these conditions greatly reduce the information provided by the pedestal, we question whether uncertainty about the stimulus can be the main cause of the pedestal effect.

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.

Facilitatory and inhibitory after-effect of spatially localized grating adaptation

Aftereffects of spatially localized grating adaptation were measured for different locations of the adaptation grating relative to test grating. When the adaptation grating was located on or near the retinal area occupied by the test grating, contrast sensitivity was markedly reduced. When the adaptation grating was spatially separated from the test grating, contrast sensitivity was significantly increased. This aftereffect of spatially localized grating adaptation suggests that spatial-frequency-selective detectors are not spatially independent, but tonically inhibited by spatially contiguous mechanisms. Thus the adaptation of these mechanisms might cause an increase in contrast sensitivity of detectors subserving the test grating.

Binocular contrast summation--I. Detection and discrimination

Binocular summation was evaluated for contrast detection and discrimination. Monocular and binocular forced-choice psychometric functions were measured for the detection of 0.5-c/deg sine-wave gratings presented alone (simple detection), or superimposed on identical background gratings (discrimination). The dependence of detectability d' on signal contrast C could be described by: d' = (C/C')n. C' is threshold contrast, and n is an index of the steepness of the psychometric function. n was near 2 for simple detection, near 1 for discrimination, and was approximately the same for monocular and binocular viewing. Monocular thresholds were about 1.5 times binocular thresholds for detection, but the ratio dropped for suprathreshold discrimination. These results reveal a dependence of binocular summation on background contrast. For simple detection, binocular detectabilities were at least twice monocular detectabilities . For contrast discrimination, the amount of binocular summation decreased. For a 25%-contrast background, there was little or no binocular summation. It is concluded that binocular contrast summation decreases as background contrast rises.

Change in detection threshold caused by peripheral gratings: dependence on contrast and separation

The detection threshold for a sinusoidal grating in the presence of peripheral gratings was determined as a function of peripheral-grating contrast and separation between the two gratings, with phase relation as a parameter. The result showed that the peripheral gratings, in the range of low contrast, yielded a facilitatory or an inhibitory effect dependent on the phase relation, but in the range of high contrast, yielded an inhibitory effect irrespective of the phase relation. This suggests that two separate mechanisms may underlie the grating induction effect of the detection threshold.

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

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

Phase reversal discrimination

In the Fourier representation of space, the parameter of phase plays a crucial role. In this study, several experiments were performed involving discrimination of various phase relations of fundamental (2 c/deg) to second harmonic (4 c/deg) at low contrast levels. The results were consistent with a model involving four "channels", each optimally sensitive to one of the following phase relations: + cosine (bright bar), -cosine (dark bar), +sine (left edge), and -sine (right edge).

Spatial phase or luminance profile discrimination?

The ability of human observers to discriminate differences in the relative phase of the components of high contrast compound gratings has been investigated. It is found that difference of less than 10 degrees in the phase angle of the higher harmonic can be detected reliably, if sufficient practice is given. However, examination of the mechanisms involved in making "phase" discriminations suggests that observers, in most studies of phase discrimination, may not code relative phase directly in making their judgements. Indeed, it appears that the most parsimonious explanation is that the observers detect differences in the contrast of local regions of the stimuli.

Contrast matching data predicted from contrast increment thresholds

Predictions for contrast matches were generated using a model with all parameters fixed, and gave fits to contrast matching data gathered using spatially localized 0.79 octave bandwidth patterns. The model has four mechanisms, each composed of a medium-bandwidth spatial filter followed by a contrast transfer function (a nonlinear function relating mechanism response to physical contrast). Parameters for the contrast transfer functions were fixed by fitting contrast increment threshold data. The success of the predictions shows that a small number of medium-bandwidth mechanisms can account for contrast matching results. Spatial pooling was shown to become insignificant at high contrasts. Relative spatial phase was found to be important in contrast matches using sums of frequencies one octave apart. This model shows that four mechanisms are sufficient to predict contrast matches, but does not rule out the possibility of additional mechanisms or of small changes in the mechanism bandwidths.

The effect of phase structures on spatial phase discrimination

This study was concerned with the discrimination of multifrequency gratings which differed only in the relative phase of one sinewave component (the test frequency) relative to the other components (the background frequencies). The dependent variable was the contrast of the test frequency required to discriminate between the two gratings. This study found that increasing the test frequency's relative phase difference from 10 to 90 deg significantly increased an observer's contrast sensitivity. However, no overall change in contrast thresholds was measured for test gratings having a relative phase difference between 90 to 180 deg. Moreover, when the mean relative phase was changed from 0 to 45 deg, contrast thresholds did not change when discriminating between gratings having a 90 deg relative phase difference. The type of processing most likely to account for these results in discussed.

Shifts in perceived size due to masking

It has been suggested that perceived size depends upon the distribution of responses among a localized population of different size-tuned mechanisms. If so, then spatial frequency masking, which alters the distribution of responses, should produce shifts in a test pattern's perceived size. We have found this to be the case. The magnitude and direction of the shifts depend only on the frequency difference in octaves (delta omega) between mask and standard. The results are not antisymmetric about the point delta omega = 0, however, as they would be if perceived size were based purely on local size-tuning properties. Our results suggest that size perception depends both on these local properties and on the spatial distribution of mechanism responses.

Shifts in perceived size as a function of contrast and temporal modulation

It has been suggested that perceived size depends upon the distribution of responses among a localized population of different size-tuned mechanisms. If so, then manipulations which alter this distribution should also affect perceived size. We therefore studied the effects of luminance contrast and mode of temporal presentation on size perception. Both manipulations produce significant shifts in perceived size. The results suggest that at least two factors contribute to the size percept. For small and intermediate size patterns, perceived size depends primarily on the local distribution of size-tuned mechanism responses, whereas for wide patterns, the spatial distribution of mechanism responses plays a major role.

Masking by spatially-modulated gratings

Contrast- or quasi-frequency-modulated masker gratings consisting of three high frequency components (8.8, 11 and 13.2 c/deg) affect the detectability of a 2.2 c/deg signal grating, to an extent that is strongly dependent upon the relative phase between signal and masker. Unmodulated high frequency maskers have no such phase-dependent effects. This paper explores the possibility that the visual system's nonlinear response to luminance is responsible for these phenomena. A specific hypothesis is proposed according to which the effects of the spatially modulated maskers are due entirely to a distortion product at 2.2 c/deg caused by the visual nonlinearity. Although some of the predictions of this hypothesis are borne out by the experimental findings, others are contradicted.

An investigation of the ability of the human visual system to encode spatial phase relationships

Evidence is presented that the human visual system contains broad-band mechanisms capable of encoding the spatial phase relationship between a fundamental spatial frequency and higher frequencies up to its third harmonic. Compounds of a fundamental and its harmonics above the third become progressively more difficult to discriminate by means of phase information alone. Measurements were also made of the amount of spatial summation found in various detection and phase discrimination tasks using simple or compound gratings composed of a fundamental frequency (F) and its third harmonic (3F). A task requiring the discrimination of the phase relationship between a low contrast (F) and a high contrast (3F) shows less spatial summation than does a task requiring the detection of the (F) component by itself. A simple model is advanced to account for these results qualitatively. The model is based upon the hypothesis that the human visual system analyses the retinal image in patches of a range of sizes and that phase relationships may be discerned only between components that are detected by different elements of the same patch mechanism.