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

Temporal mechanisms in frontoparallel stereomotion revealed by individual differences analysis

Masking experiments, using vertical and horizontal sinusoidal depth corrugations, have suggested the existence of more than two spatial-frequency disparity mechanisms. This result was confirmed through an individual differences approach. Here, using factor analytic techniques, we want to investigate the existence of independent temporal mechanisms in frontoparallel stereoscopic (cyclopean) motion. To construct stereomotion, we used sinusoidal depth corrugations obtained with dynamic random-dot stereograms. Thus, no luminance motion was present monocularly. We measured disparity thresholds for drifting vertical (up-down) and horizontal (left-right) sinusoidal corrugations of 0.4 cyc/deg at 0.25, 0.5, 1, 2, 4, 6, and 8 Hz. In total, we tested 34 participants. Results showed a small orientation anisotropy with lower thresholds for horizontal corrugations. Disparity thresholds as a function of temporal frequency were almost constant from 0.25 up to 1 Hz, and then they increased monotonically. Principal component analysis uncovered two significant factors for vertical and two for horizontal corrugations. Varimax rotation showed that one factor loaded from 0.25 to 1-2 Hz and a second factor from 2 to 4 to 8 Hz. Direct Oblimin rotation indicated a moderate intercorrelation of both factors. Our results suggest the possible existence of two somewhat interdependent temporal mechanisms involved in frontoparallel stereomotion.

Characterizing Spatiotemporal Population Receptive Fields in Human Visual Cortex with fMRI

The use of fMRI and computational modeling has advanced understanding of spatial characteristics of population receptive fields (pRFs) in human visual cortex. However, we know relatively little about the spatiotemporal characteristics of pRFs because neurons' temporal properties are one to two orders of magnitude faster than fMRI BOLD responses. Here, we developed an image-computable framework to estimate spatiotemporal pRFs from fMRI data. First, we developed a simulation software that predicts fMRI responses to a time-varying visual input given a spatiotemporal pRF model and solves the model parameters. The simulator revealed that ground-truth spatiotemporal parameters can be accurately recovered at the millisecond resolution from synthesized fMRI responses. Then, using fMRI and a novel stimulus paradigm, we mapped spatiotemporal pRFs in individual voxels across human visual cortex in 10 participants (both females and males). We find that a compressive spatiotemporal (CST) pRF model better explains fMRI responses than a conventional spatial pRF model across visual areas spanning the dorsal, lateral, and ventral streams. Further, we find three organizational principles of spatiotemporal pRFs: (1) from early to later areas within a visual stream, spatial and temporal windows of pRFs progressively increase in size and show greater compressive nonlinearities, (2) later visual areas show diverging spatial and temporal windows across streams, and (3) within early visual areas (V1-V3), both spatial and temporal windows systematically increase with eccentricity. Together, this computational framework and empirical results open exciting new possibilities for modeling and measuring fine-grained spatiotemporal dynamics of neural responses using fMRI.

Mapping the Contrast Sensitivity of the Visual Field With Bayesian Adaptive qVFM

Current clinical evaluation, which focuses on central vision, could be improved through characterization of residual vision with peripheral testing of visual acuity, contrast sensitivity, color vision, crowding, and reading speed. Assessing visual functions in addition to light sensitivity, a comprehensive visual field map (VFM) would be valuable for detecting and managing eye diseases. In a previous study, we developed a Bayesian adaptive qVFM method that combines a global module for preliminary assessment of the VFM's shape and a local module for assessment at individual retinal locations. The method was validated in measuring the light sensitivity VFM. In this study, we extended the qVFM method to measure contrast sensitivity across the visual field. In both simulations and psychophysics, we sampled 64 visual field locations (48 x 48 deg) and compared the qVFM method with a procedure that tested each retinal location independently (qFC; Lesmes et al., 2015). In each trial, subjects were required to identify a single optotype (size: 2.5 x 2.5 deg), one of 10 filtered Sloan letters. To compare the accuracy and precision of the two methods, three simulated eyes were tested in 1,280 trials with each method. In addition, data were collected from 10 eyes (5 OS, 5 OD) of five normal observers. For simulations, the average RMSE of the estimated contrast sensitivity with the qVFM and qFC methods were 0.057 and 0.100 after 320 trials, and 0.037 and 0.041 after 1,280 trials [all in log10 units, represent as log(sensitivity)], respectively. The average SD of the qVFM and qFC estimates were 0.054 and 0.096 after 320 trials, and 0.032 and 0.041 after 1,280 trials, respectively. The within-run variability (68.2% HWCIs) were comparable to the cross-run variability (SD). In the psychophysics experiment, the average HWCI of the estimated contrast sensitivity from the qVFM and qFC methods across the visual field decreased from 0.33 on the first trial to 0.072 and 0.16 after 160, and to 0.060 and 0.10 after 320 trials. The RMSE between the qVFM and qFC estimates started at 0.26, decreased to 0.12 after 160 and to 0.11 after 320 qVFM trials. The qVFM provides an accurate, precise, and efficient mapping of contrast sensitivity across the entire visual field. The method might find potential clinical applications in monitoring vision loss, evaluating therapeutic interventions, and developing effective rehabilitation for visual diseases.

Predicting neuronal dynamics with a delayed gain control model

Visual neurons respond to static images with specific dynamics: neuronal responses sum sub-additively over time, reduce in amplitude with repeated or sustained stimuli (neuronal adaptation), and are slower at low stimulus contrast. Here, we propose a simple model that predicts these seemingly disparate response patterns observed in a diverse set of measurements-intracranial electrodes in patients, fMRI, and macaque single unit spiking. The model takes a time-varying contrast time course of a stimulus as input, and produces predicted neuronal dynamics as output. Model computation consists of linear filtering, expansive exponentiation, and a divisive gain control. The gain control signal relates to but is slower than the linear signal, and this delay is critical in giving rise to predictions matched to the observed dynamics. Our model is simpler than previously proposed related models, and fitting the model to intracranial EEG data uncovers two regularities across human visual field maps: estimated linear filters (temporal receptive fields) systematically differ across and within visual field maps, and later areas exhibit more rapid and substantial gain control. The model is further generalizable to account for dynamics of contrast-dependent spike rates in macaque V1, and amplitudes of fMRI BOLD in human V1.

Can speed be judged independent of direction?

The ability to judge speed is a fundamental aspect of visual motion processing. Speed judgments are generally assumed to depend on signals in motion-sensitive, directionally selective, neurons in areas such as V1 and MT. Speed comparisons might therefore be expected to be most accurate when they use information within a common set of directionally tuned neurons. However, there does not appear to be any published evidence on how well speeds can be compared for movements in different directions. We tested speed discrimination judgments between pairs of random-dot stimuli presented side-by-side in a series of four experiments (n = 65). Participants judged which appeared faster of a reference stimulus moving along the cardinal or oblique axis and a comparison stimulus moving either in the same direction or in a different direction. The bias (point of subjective equality) and sensitivity (Weber fraction) were estimated from individual psychometric functions fitted for each condition. There was considerable between-participants variability in psychophysical estimates across conditions. Nonetheless, participants generally made more acute comparisons between stimuli moving in the same direction than those moving in different directions, at least for conditions with an upwards reference (∼20% difference in Weber fractions). We also showed evidence for an oblique effect in speed discrimination when comparing stimuli moving in the same direction, and a bias whereby oblique motion tended to be perceived as moving faster than cardinal motion. These results demonstrate interactions between speed and direction processing, thus informing our understanding of how they are represented in the brain.

Compressive Temporal Summation in Human Visual Cortex

Combining sensory inputs over space and time is fundamental to vision. Population receptive field models have been successful in characterizing spatial encoding throughout the human visual pathways. A parallel question, how visual areas in the human brain process information distributed over time, has received less attention. One challenge is that the most widely used neuroimaging method, fMRI, has coarse temporal resolution compared with the time-scale of neural dynamics. Here, via carefully controlled temporally modulated stimuli, we show that information about temporal processing can be readily derived from fMRI signal amplitudes in male and female subjects. We find that all visual areas exhibit subadditive summation, whereby responses to longer stimuli are less than the linear prediction from briefer stimuli. We also find fMRI evidence that the neural response to two stimuli is reduced for brief interstimulus intervals (indicating adaptation). These effects are more pronounced in visual areas anterior to V1-V3. Finally, we develop a general model that shows how these effects can be captured with two simple operations: temporal summation followed by a compressive nonlinearity. This model operates for arbitrary temporal stimulation patterns and provides a simple and interpretable set of computations that can be used to characterize neural response properties across the visual hierarchy. Importantly, compressive temporal summation directly parallels earlier findings of compressive spatial summation in visual cortex describing responses to stimuli distributed across space. This indicates that, for space and time, cortex uses a similar processing strategy to achieve higher-level and increasingly invariant representations of the visual world.SIGNIFICANCE STATEMENT Combining sensory inputs over time is fundamental to seeing. Two important temporal phenomena are summation, the accumulation of sensory inputs over time, and adaptation, a response reduction for repeated or sustained stimuli. We investigated these phenomena in the human visual system using fMRI. We built predictive models that operate on arbitrary temporal patterns of stimulation using two simple computations: temporal summation followed by a compressive nonlinearity. Our new temporal compressive summation model captures (1) subadditive temporal summation, and (2) adaptation. We show that the model accounts for systematic differences in these phenomena across visual areas. Finally, we show that for space and time, the visual system uses a similar strategy to achieve increasingly invariant representations of the visual world.

Bar-like S-cone stimuli reveal the importance of an intermediate temporal filter

The relative involvement of different temporal frequency-selective filters underlying detection of chromatic stimuli was studied. Diverse spectral stimuli were used, namely flashed blue and yellow light spots, wide bars, and narrow bars. The stimuli were temporally modulated in luminance having constant wavelength. Although the bar-like stimuli apparently reduced the sensitivity at short and long wavelengths, the cone-opponent mechanism still remained responsible for the actual stimulus detection at different temporal frequencies. The bar-like stimuli increased sensitivity for temporal frequencies around 3-6 Hz, revealing involvement of an intermediate temporal frequency-selective filter in detection, the so-called transient-1 filter. A probability summation model for the method of adjustment was developed that assumes that detection depends on the properties of the temporal filters underlying the temporal frequency-sensitivity curve. The model supports the notion that at least two temporal frequency-selective filters are necessary to account for the shape of the sensitivity curves obtained for blue bar-like stimuli.

Higher order color mechanisms: a critical review

A large number of studies, using a wide variety of experimental techniques, have investigated the "higher-order" color mechanisms proposed by Krauskopf and colleagues in 1986. Results reviewed here come from studies of chromatic discrimination at threshold, habituation, classification images, spatial alignment and orientation effects, and noise masking. The bulk of the evidence has been taken to support the existence of multiple, linear color mechanisms in addition to (or after) the three putative low-level cardinal mechanisms. But there remain disconcerting inconsistencies in the results of noise masking experiments, and the results of chromatic discrimination experiments clearly show that there are a very limited number of labeled-line mechanisms near threshold. No consensus on higher order mechanisms has been reached even after more than 20 years of study.

Two temporal channels in human V1 identified using fMRI

Human visual sensitivity to a fairly broad class of dynamic stimuli can be modeled accurately using two temporal channels. Here, we analyze fMRI measurements of the temporal step response to spatially uniform stimuli to estimate these channels in human primary visual cortex (V1). In agreement with the psychophysical literature, the V1 fMRI temporal responses are modeled accurately as a mixture of two (transient and sustained) channels. We derive estimates of the relative contributions from these two channels at a range of eccentricities. We find that all portions of V1 contain a significant transient response. The central visual field representation includes a significant sustained response, but the amplitude of the sustained channel signal declines with eccentricity. The sustained signals may reflect the emphasis on pattern recognition and color in the central visual field; the dominant transient response in the visual periphery may reflect responses in the human visual attention system.

Distinct perceptual grouping pathways revealed by temporal carriers and envelopes

S. E. Guttman, L. A. Gilroy, and R. Blake (2005) investigated whether observers could perform temporal grouping in multi-element displays where each local element was stochastically modulated over time along one of several potential dimensions--or "messenger types"--such as contrast, position, orientation, or spatial scale. Guttman et al.'s data revealed that grouping discards messenger type and therefore support a single-pathway model that groups elements with similar temporal waveforms. In the current study, we carried out three experiments in which temporal-grouping information resided either in the carrier, the envelope, or the combined carrier and envelope of each messenger's timecourse. Results revealed that grouping is highly specific for messenger type if carrier envelopes lack grouping information but largely messenger nonspecific if carrier envelopes contain grouping information. These imply that temporal grouping is mediated by several messenger-specific carrier pathways as well as by a messenger-nonspecific envelope pathways. Findings also challenge simple temporal-filtering accounts of perceptual grouping (E. H. Adelson & H. Farid, 1999).

Only two phase mechanisms, ±cosine, in human vision

We evaluated the proposal that there exist detectors of the following four cardinal phases in human vision: +cosine, -cosine, +sine, and -sine. First, we assessed whether there was evidence that these cardinal phases were processed by independent 'labeled lines,' using a discrimination at detection threshold paradigm. Second, we assessed whether suprathreshold phase discrimination was best at phases intermediate between these cardinal values. Third, we tried to replicate previous evidence showing that an absence of facilitation occurs only between cosine pedestals and sine tests (or vice-versa). In all three experimental approaches we found no compelling evidence for four cardinal phase groupings. We did however find evidence for independent detectors for pure increments and decrements (+/-cosine). We suggest that phase discrimination, whether at threshold or suprathreshold, is mediated by mechanisms that encode the relative positions and contrasts of local increments and decrements within the stimulus.

Second-order spatial frequency and orientation channels in human vision

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

Psychophysical estimation of speed discrimination. I. Methodology

Thresholds were assessed for a speed discrimination task with a pair of luminance-defined drifting gratings. The design and results of a series of experiments dealing in general with speed discrimination are described. Results show that for a speed discrimination task using drifting gratings, simultaneous presentation of the pair of gratings (spatially separated) was preferred over sequential presentation (temporally separated) in order to minimize the effects of eye movements and tracking. An interstimulus interval of at least 1000 ms was necessary to prevent motion aftereffects on subsequently viewed stimuli. For the two reference speeds tested of 2 and 8 deg/s using identical spatial frequency or randomizing spatial frequency for the pair of gratings did not affect speed discrimination thresholds. Implementing a staircase method of estimating thresholds was preferred over the method of constant stimuli or the method of limits. The results of these experiments were used to define the methodology for an investigation of aging and motion perception. These results will be of interest and use to psychophysicists designing and implementing speed discrimination paradigms.

Temporal detection in human vision: dependence on eccentricity

Studies of human perception of time-varying luminance often aim to estimate either temporal impulse response shapes or temporal modulation transfer functions (MTFs) of putative temporal processing mechanisms. Previously, temporal masking data have been used to estimate the properties and numbers of these temporal mechanisms in central vision for 1 cycle per degree (cpd) targets [Fredericksen and Hess (1998)]. The same methods have been used to explore how these properties change with stimulus energy [Fredericksen and Hess (1997)] and spatial frequency [Fredericksen and Hess (1999)]. We present here analyses of the properties of temporal mechanisms that detect temporal variations of luminance in peripheral vision. The results indicate that a two-filter model provides the best model for our masking data, but that no multiple filter model provides an acceptable fit across the range of parameters varied in this study. Single-filter modelling shows differences between processing mechanisms at 1 cpd in central vision and those that operate eccentrically. We find evidence that this change is because of differences in relative sensitivities of the mechanisms, and to differences in fundamental mechanism impulse responses.

The minimum temporal thresholds for motion detection of grating patterns

The minimum temporal thresholds for absolute motion detection were measured for sinusoidal grating patterns in foveal vision. Test patterns of relatively low temporal frequencies and low velocities were examined. The thresholds clearly decreased with test velocities rather than with test temporal frequencies. Modified velocity-time reciprocity was observed (i.e. the relationship between test velocity and temporal thresholds was described by a simple equation including two constants which indicate temporal and spatial limits). The temporal constant was about 35 ms and the spatial constant was about 1 min of arc. These constants are thought to provide the basic constraints on motion detection.

Velocity discrimination in scotopic vision

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

Temporal detection in human vision: dependence on spatial frequency

In the study of perception of temporal changes in luminance, it is customary to model perceptual performance as based on one or more linear filters. The task is then to estimate the temporal impulse responses or the representation of the impulse response in the frequency domain. Previously, temporal masking data have been used to estimate the properties and numbers of these temporal mechanisms (filters) in central vision for 1-cycle-per-degree (cpd) targets [Vision Res. 38, 1023 (1998)]. The same methods have been used to explore how properties of the estimated filters change with stimulus contrast energy [J. Opt. Soc. Am. A 14, 2557 (1997)]. We present estimated properties for temporal mechanisms that detect low spatial-frequency patterns. The results indicate that two filters provide the best model for performance when mask contrast is significant. There are also differences between properties for mechanisms that detect signal spatial frequencies of 1 cpd and 1/3 cpd. The sensitivity of the low-pass mechanism relative to the bandpass mechanism is reduced at 1/3 cpd, consistent with previous findings.

Temporal resolution deficits in the visual fields of MS patients

We assessed the relationship between temporal resolution and MS-induced neuropathy. A diagnostic strategy comprising assessments of temporal resolution at 16 points in the extra-foveal visual field up to 12 degrees from the fovea was first compared with foveal temporal resolution and with a standard VEP procedure in the same MS patients. At the group level, foveal temporal resolution was less sensitive to demyelination than the 16-point diagnostic strategy, the detection rate of which was comparable to that of the VEP procedure. Cross-sensitivity of the VEP and the 16-point diagnostic procedure was low. Subsequently, the average severity of MS-induced temporal resolution deficits was studied at three retinal loci of the same size but different eccentricities. Foveal deficits were not significantly greater than more peripheral deficits within the central 12 degrees.

Temporal sensitivity of human luminance pattern mechanisms determined by masking with temporally modulated stimuli

Target contrast thresholds were measured using vertical spatial Gabor targets in the presence of full field maskers of the same spatial frequency and orientation. In the first experiment both target and masker were 2 cpd. The target was modulated at a frequency of 1 or 10 Hz and the maskers varied in temporal frequency from 1 to 30 Hz and in contrast from 0.03 to 0.50. In the second experiment both target and masker had a spatial frequency of 1, 5 or 8 cpd. The target was modulated at 7.5 Hz and the same set of maskers was used as in the first experiment. The results are not consistent with a widely used model that is based on mechanisms in which excitation is summed linearly and the sum is transformed by an S-shaped nonlinear excitation-response function. A new model of human pattern vision mechanisms, which has excitatory and divisive inhibitory inputs, describes the results well. Parameters from the best fit of the new model to the results of the first experiment show that the 1 Hz and 10 Hz targets were detected by mechanisms with temporal low-pass and band-pass excitatory sensitivity, respectively. Fits to the second experiment suggest that at 1 cpd, the excitatory tuning of the detecting mechanism is band-pass. At 5 and 8 cpd, the mechanisms are excited by a broad range of temporal frequencies. Mechanism sensitivity to divisive inhibition depends on temporal frequency in the same general way as sensitivity to excitation. Mechanisms are more broadly tuned to divisive inhibition than to excitation, except when the target temporal frequency is high.

Estimating multiple temporal mechanisms in human vision

When studying human ability to perceive temporal changes in luminance it is customary to estimate either temporal impulse response shapes or temporal modulation transfer functions, the representation of the impulse response in the frequency domain. The advantages and limitations of previous methods are summarized. We then describe an approach based on use of an impulse response basis set that resolves some of those limitations. We next present psychophysical results for spatiotemporal signal detection in spatiotemporal noise, together with an economical model of performance. The model is based on accepted notions of psychophysical detection mechanisms and the filter basis set described in the first part of the paper. The best-fitting model requires only eight parameters, as opposed to the 198 parameters required to separately fit each psychometric function, and captures both qualitative and quantitative properties of the psychophysical data. Finally, the best-fitting model indicates that only two temporal filters are necessary to describe the performance of each of three subjects under the specific stimulus conditions employed here.

Temporal detection in human vision: dependence on stimulus energy

We have previously proposed and evaluated an economical model of human performance in tasks requiring spatiotemporal signal detection in spatiotemporal noise [Vision Research (to be published)]. The model was successful in describing human psychophysical performance and provides a means for comparing temporal filters (mechanisms) employed under different stimulus conditions. We present investigations into how estimates of temporal mechanisms depend on the contrast energy of the stimulus. Temporal-sensitivity changes result in covariation of the cutoff and peak frequencies of the low-pass and bandpass mechanisms, respectively, with stimulus energy. The results indicate that sensitivity to high temporal frequencies increases as stimulus energy increases, commensurate with extent physiological evidence in cat and primate.

Red-green and achromatic temporal filters: a ratio model predicts contrast-dependent speed perception

We simultaneously measured detection and identification performance by using isoluminant red-green (RG) and achromatic flickering stimuli and fitted these data with a modified line-element model that does not make high-threshold assumptions. The modeling shows that detection and identification data are adequately described by postulating only two underlying temporal filters each for RG and achromatic vision, even when more than two threshold classifications are evident. We use a spatial frequency of 1.5 cycles per degree (c/deg) and compare the derived temporal impulse response functions with those obtained previously with the use of 0.25 c/deg stimuli under otherwise identical conditions [J. Opt. Soc. Am. A 13, 1969 (1996)]. We find that at 1.5 c/deg the luminance impulse response functions peak later and integrate out to longer times compared with those measured at 0.25 c/deg. For RG stimuli, although their relative overall sensitivities change, the impulse response functions are similar across spatial frequency, indicating a constancy of chromatic temporal properties across spatial scales. In a second experiment, we measured RG and achromatic flicker discrimination over a wide range of suprathreshold contrasts. These data suggest a common nonlinear contrast response function operating after initial temporal filtering. Using a ratio model of speed perception in which both RG and achromatic filters are combined at a common motion site, we can predict (1) the perceived slowing of RG stimuli compared with the perceived drift of achromatic drifting stimuli, (2) the contrast dependency of speed perception for RG and achromatic drifting stimuli, and (3) how this dependency changes with base speed. Thus we conclude that there is no need to postulate separate mechanisms for fast and slow motion [Nature (London) 367, 268 (1994)], since a unified ratio model can explain both RG and achromatic contrast-speed dependency.

What is the denominator for contrast normalisation?

The perceived speed of 1 c/deg sinusoidal gratings of contrast 0.02 was measured in the presence of high contrast (0.50) 1 c/deg sinusoidal gratings (called modifiers). The modifiers drifted or were counterphase modulated at various temporal frequencies. The presence of a modifier with temporal frequencies (0 and 3 Hz) lower than the low contrast moving grating decreased its perceived speed while the presence of modifiers with higher temporal frequencies (8, 12 and 16 Hz) increased its perceived speed. A modifier of the same temporal frequency (6 Hz) as the standard grating had no effect upon the perceived speed of the low contrast gratings. Moving modifiers are more effective than counterphase flickering modifiers in biasing the perceived speed of low contrast gratings if they move in the same direction as the test grating and less effective if they move in the opposite direction. Finally, a modifier presented in an annulus surrounding the test grating is more effective than a modifier presented in a circular patch above or below the test grating in raising the perceived speed of low contrast gratings. This suggests that perceived speed depends on the ratio of low and high temporal frequency signals averaged over a significant area of the visual field.

Temporal mechanisms underlying flicker detection and identification for red-green and achromatic stimuli

We have simultaneously measured detection and temporal frequency identification for both red-green isoluminant and achromatic stimuli over a range of temporal frequencies for two observers. Results show that temporal frequency identification can be made along the temporal frequency dimension for both red-green and achromatic stimuli at contrasts close to detection threshold. In general, temporal frequency identification was better for the achromatic than for the red-green stimuli; however, the level of chromatic identification performance was still sufficient to permit us to reject the notion that the red-green mechanism embodies a single temporal filter. We have developed a model based on signal detection theory that assumes that detection and identification both depend on the properties of the temporal filters underlying each mechanism. From this we have derived putative underlying shapes and sensitivities for the temporal filters of the red-green and achromatic mechanisms that comprise a low-pass and a bandpass filter for red-green color vision and two bandpass filters for luminance vision. Finally, we suggest that the relative perceived slowing of isoluminant stimuli may be accounted for by a common motion analysis subserved by different front-end temporal filters for red-green and achromatic motion signals.

Temporal and spatial frequency tuning of the flicker motion aftereffect

The motion aftereffect (MAE) was used to study the temporal and spatial frequency selectivity of the visual system at supra-threshold contrasts. Observers adapted to drifting sine-wave gratings of a range of spatial and temporal frequencies. The magnitude of the MAE induced by the adaptation was measured with counterphasing test gratings of a variety of spatial and temporal frequencies. Independently of the spatial or temporal frequency of the adapting grating, the largest MAE was found with slowly counterphasing test gratings (at approximately 0.125-0.25 Hz). The largest MAEs were also found when the test grating was of similar spatial frequency to that of the adapting grating, even at very low spatial frequencies (0.125 c/deg). These data suggest that MAEs are dominated by a single, low-pass temporal frequency mechanism and by a series of band-pass spatial frequency mechanisms. The band-pass spatial frequency tuning even at low spatial frequencies suggests that the "lowest adaptable channel" concept [Cameron et al. (1992). Vision Research, 32, 561-568] may be an artifact of disadvantaged low spatial frequencies using static test patterns.

A biologically plausible model of early visual motion processing. I: theory and implementation

A model of local image encoding is described which explicitly incorporates quantitative data about the number density, bandwidth and receptive field organisation of neurons involved in motion detection. The model solves the problem of extracting local velocity on the basis of inputs tuned to spatiotemporal frequency and sensitive to contrast. The spatiotemporally tuned, opponent motion filters are followed by a compressive non-linearity and comprise a first stage. The inter-stage signals are interpreted as those from single neurons and the second stage is modelled as a neural-network layer. The second stage uses semilinear units and models the effect of lateral, on-centre off-surround, intra-layer connections. Characterisation of the first stage leads to a clarification of the concept of the psychophysical 'channel' and its relation to physiological data. The quantitative parametrisation of the model allows the simulation of several psychophysical phenomena which are reported in a companion paper.

Evidence of spatial and temporal channels in the correlational structure of human spatiotemporal contrast sensitivity

1. The statistical correlation of detection thresholds for pairs of stimuli should be higher for stimuli detected by the same mechanism than for stimuli detected by different mechanisms--a property that can be used to probe the visual mechanisms that underlie detection. 2. Correlation of contrast sensitivities for pairs of spatiotemporal stimuli is approximately a linear function of spatial or temporal frequency separation in octaves. Using the slope of this function as an index of neural processing gave results consistent with: more spatial mechanisms than temporal; more spatial mechanisms at low temporal frequencies than at high; and at least two temporal mechanisms active at spatial frequencies up to 22.6 cycles deg-1. 3. This method of analysing sensitivity data is insensitive to experimental conditions and applicable to any sensory detection task mediated by tuned channels. In addition to being applicable to psychophysical sensitivity measurements, it may also be useful in analysing some kinds of electrophysiological measurements that pool the responses from many active mechanisms (such as evoked potentials).

A covariance structure analysis of flicker sensitivity

We tested whether linear structural models of the mechanisms underlying flicker sensitivity could reproduce the variance-covariance matrix of temporal contrast sensitivity data. Monocular sensitivities to frequencies between 2.5 and 45 Hz were measured for 124 subjects, ages 18-88 yr. Exploratory factor analyses revealed that both a two-mechanism and a three-mechanism model could adequately account for the data. Furthermore, confirmatory factor analyses and full structural equation models, using age as an explanatory variable, supported both models, with the three-factor model giving a somewhat better representation of the data. Parsimony favors the two-mechanism model. But patterns of loss associated with pre-exudative age-related maculopathy are more easily understood in terms of three underlying mechanisms.

A unified account of three apparent motion illusions

We discuss three motion illusions, the fluted square wave illusion, the reverse phi illusion and the Pantle illusion. In these illusions reversed apparent motion is either induced or eliminated by the introduction of a blank inter-frame-interval between the frames of the apparent motion sequence. In order to simulate these effects with the multi-channel gradient model we had to introduce low-pass spatial filters and second-order temporal differentiating filters. These illusions have been used as evidence of multiple motion mechanisms. Here we demonstrate that they can be considered as emergent properties of a single computational strategy.

The processing of temporal modulation at different levels of retinal illuminance

How does our temporal vision change as the mean illuminance reduces? We have examined the processing of near-threshold temporal information for a range of illuminance values (2850--0.15 phot td). At high illuminance, the modulation transfer function can be shown to be mediated via three underlying temporal filters that vary in sensitivity with spatial frequency. As the mean illuminance decreases these channels appear to change their sensitivity. Even at the lowest (scotopic) illuminance levels we were able to find evidence for at least two channels mediating detection threshold. There are also changes in the tuning properties of these channels such that the processing of high temporal frequencies is differentially compromised, resulting in a reduction in the flicker fusion limit of each channel, and a shift in the peak of the band-pass channel. The slope of the fall-off in sensitivity at high temporal frequencies is unaffected by test spatial frequency at each illuminance level, suggesting its limiting factor is one that is insensitive to spatial frequency. We propose that the changes in the tuning of the temporal filters occur because of an early (e.g. photoreceptor) change in the response dynamics, or by interactions between photoreceptors, rather than changes at or beyond the level of the channel response.

Suprathreshold temporal-frequency discrimination in the fovea and the periphery

To address the question of whether temporal-frequency information in the fovea and the periphery is processed in fundamentally different ways we measured temporal-frequency-discrimination thresholds for spatiotemporally narrow-band stimuli presented at suprathreshold contrast. Temporal-frequency-discrimination thresholds are similar (within a factor of 2) at the fovea and at 30 degrees in the periphery. We use a line-element approach and three spatiotemporally separable temporal mechanisms to model foveal and peripheral data with the same degree of fidelity. These findings suggest that not only are the front-end temporal mechanisms in the fovea and periphery likely to be similar but also the way in which their outputs are combined at more central sites is the same.

Intracranial hypertension in a dieting patient

We report a case of encephalopathy with paranoid psychosis in association with intracranial hypertension. This occurred in a patient whose diet consisted almost solely of walnuts, ginseng tea, and vitamin A supplements. The patient was found to be severely iron- and vitamin B12-deficient. She was vitamin A toxic. Venous sinus thrombosis was also present. Symptoms remitted with serial lumbar punctures, normalization of diet, and repletion of vitamin B12 and iron stores. Physicians should be alerted to the possibility of a potentially confusing clinical presentation with coexistent and seemingly mutually exclusive neurologic conditions in patients with extremely restricted or fad diets.

Antagonistic comparison of temporal frequency filter outputs as a basis for speed perception

The prevailing view of motion detection in human vision is that the retinal image is convolved with each of a set of spatiotemporal filters and that perceived speed emerges from a process of pooling the outputs of these filters. Such a system can operate only if multiple filters exist; ideally the filters should also be fairly narrowly tuned in both spatial and temporal frequency. These constraints are met in the case of spatial frequency. But several studies suggest that multiple, finely tuned temporal filters do not exist; instead just two (perhaps three) broadly-tuned temporal mechanisms can be identified. We report some experiments concerning the effects of adaptation to motion on perceived speed. It is shown that perceived speed is increased by adaptation in some circumstances and decreased in others. We then present a computational model in which a temporal frequency code, on which perceived speed is presumed to be based, is derived by a process of antagonistic comparison of the responses of two psychophysically-plausible, broadly-tuned temporal mechanisms. The model, which includes the effects of adaptation to motion upon the sensitivities of the filters and the subsequent comparison of their sensitivities, is shown to give a good fit to the empirical data.

Perceived contrast as a function of adaptation duration

We measured how the perceived contrast of a sinusoidal grating fades as a function of time. Measurements were made for a range of temporal and spatial frequencies and eccentricities. Patterns of high temporal and low spatial frequency exhibited a greater and more rapid loss of apparent contrast (fade) than those of medium frequencies. The rate and amount of fading for a subgroup of moderate frequencies increased when presented peripherally rather than foveally. Further measurements revealed that gratings of disparate spatial frequencies, but with the same threshold sensitivity, exhibit very different fading characteristics but equal threshold elevation. We conclude that the differential loss of apparent contrast is not an artefact of differing proximities to threshold, nor can it be accounted for by differences in the adaptability of underlying spatio-temporal mechanisms at threshold. The differences in fading may thus reflect either a difference in the adaptability of underlying channels above threshold or a differential contribution of such channels to perceived contrast.

Abnormalities of visual function in hereditary motor and sensory neuropathy

Visual function was studied in a group of 15 patients with hereditary motor and sensory neuropathy (HMSN). Psychophysical measures of luminance and chromatic threshold and temporal contrast sensitivity were undertaken, together with visual evoked potentials (VEPs), visual fields and clinical neuro-ophthalmological examination. A patchy loss of visual function was found in individual cases of HMSN. In the group analysis there was evidence of a selective loss of luminance threshold and temporal contrast sensitivity at low temporal frequencies; the VEP P100 latency was not significantly prolonged. The losses of visual function in HMSN were discussed and compared with visual losses in multiple sclerosis, which had been detected using identical experimental techniques.

Peripheral temporal frequency channels code frequency and speed inaccurately but allow accurate discrimination

Perceived temporal frequency is vastly underestimated in the peripheral visual field, as all temporal frequencies above 10 Hz are perceived as flickering at 10 Hz even after scaling for acuity. Varying the contrast and spatial frequency of the peripheral pattern four-fold have negligible effects on the perceived flicker rate. Speed and auditory matching experiments also support this finding. Despite the saturation of perceived temporal frequency, frequency discrimination beyond 10 Hz was as accurate as in the fovea. By using a temporal masking paradigm, we obtained threshold elevation data that could be accounted for by three overlapping, broadly tuned temporal channels peaking at 5.5, 12 and 22 Hz. Based on these temporal frequency channels, we proposed that the visual system uses a line-element scheme for mediating temporal frequency discrimination, but adopts a weighted-average method for determining perceived temporal frequency. In the peripheral visual field, the weight assigned to the highest temporal channel is much larger than those assigned to the lower frequency channels.

Orientation bandwidth: the effect of spatial and temporal frequency

The orientation bandwidths of psychophysically defined channels of human vision were estimated by two techniques for a wide range of spatial and temporal frequencies. The first technique was an adaptation paradigm, where the subjects' ability to see patterns of various orientations was measured before and after adapting to a high contrast pattern. The second technique evaluated subjects' ability to discriminate between two gratings of different orientations in relation to their ability to detect the patterns. Bandwidths were unaffected by temporal frequency at high spatial frequencies but increased with temporal frequency at low spatial frequencies. Bandwidths increased modestly with decreasing spatial frequency at low temporal frequencies but more drastically at high temporal frequencies. Both techniques gave similar results except for patterns with very low spatial and high temporal frequencies. In this region the stimulus appears "spatial-frequency doubled" which may be used as a cue for the orientation discrimination task.

Is the visual field temporally homogeneous?

We asked the question "is the visual field temporally homogeneous when the well known spatial inhomogeneity is taken into account?" Our results show that the visual field exhibits inhomogeneity for stimuli of low spatial frequency for which the spatial inhomogeneity is minimal. This inhomogeneity takes the form of a reduction in sensitivity for stimuli of low temporal frequency in the periphery and an enhancement of sensitivity for stimuli of high temporal frequency in the periphery. The low temporal frequency loss in the periphery is post-receptoral and must involve a selective loss of sensitivity of the low pass filter. The enhanced high frequency sensitivity may be post-receptoral or purely receptoral. The consequence of such an inhomogeneity for subsequent stages of visual processing is discussed.

Two temporal channels or three? A re-evaluation

The initial filtering of the image by the human visual system involves only a small number of temporal filters. Several studies suggest there are in fact only two, but some suggest that a third filter, sensitive to high frequencies, exists, at least at low spatial frequencies. This conclusion is derived in part from the observation that temporal frequency discrimination performance is better at very high (30-40 Hz) than at medium (20 Hz) temporal frequencies. We show that this apparent improvement at high frequencies is not real but is an artifact of differences in the rate of perceptual fading as a function of temporal frequency. Using suprathreshold counterphase gratings and a stimulus duration of 1.5 sec we replicated the finding of an improvement at high frequencies at a low (0.5 c/deg) spatial frequency. But when duration was reduced to 300 msec, to minimize fading cues, this improvement disappeared. Similarly, at 4 c/deg, the improvement was present at 3 sec duration but absent at 1.5 sec or less. Direct evidence that this effect of duration reflects differences in the ability to use fading cues was obtained in an experiment in which naive subjects were instructed to discriminate on the basis of fading: at high temporal frequencies and long durations performance was as good or better than for subjects instructed to use frequency; at short durations performance on this task was poor. Thus, the claim that a third temporal channel exists may need to be re-evaluated.

Effects of flicker modulation depth on the detection of changes in target location

Response times to a change in location of a small, low contrast target in a uniform flickering field were investigated under a range of flicker modulation depths. Increasing depth of modulation gave an increased response time for modulation depths from 0% (no flicker, to approx. 35%. Further increases in modulation depth had only a marginal effect on response time. It is shown that this effect is not due to flicker adaptation. The functional form of the modulation dependence is qualitatively similar to that reported by Badcock and Smith (1989, Vision Research, 29, 803-808), but shows a large difference in the modulation at which a levelling of performance occurred. It is shown that this difference is consistent with the presence of a third temporal filter, as proposed by Mandler and Makous (1984, Vision Research, 24, 1881-1887).

Temporal frequency filters in the human peripheral visual field

The temporal filtering properties of the human peripheral field were investigated by means of measuring: (1) modulation transfer functions for a range of spatial frequencies at four visual field locations (0, 10, 30 and 50 degrees), (2) the contrast of a masking stimulus required to extinguish the visibility of just suprathreshold probes. Results suggest that the number of temporal filters governing detection threshold is dependent upon both eccentricity and spatial frequency. For near-foveal viewing three temporal filters were found (one low-pass and two band-pass), whereas at far eccentricities only one was found (band-pass). A similar result was obtained by modeling the modulation transfer function by simply scaling the sensitivities of three independently derived filters. Our data suggest that (1) changes in the modulation transfer function with respect to spatial frequency and eccentricity can be adequately explained by the changes in sensitivity of a small number of spatio-temporal separable filters; (2) the peripheral field is not merely a coarser version of the fovea but has qualitative differences which may be thought to emphasize the transient properties of the stimulus.

Temporal properties of human visual filters: number, shapes and spatial covariation

The temporal properties of the foveal visual filters were revealed using a method which is a variant on previously used noise masking paradigms. This enables the temporal properties of the mechanisms underlying threshold detection of a spatio-temporal probe to be measured. In accord with recent suggestions these results support the existence of three temporal mechanisms. The evidence for the third, higher temporal mechanism is only persuasive at low spatial frequencies. Furthermore, the results suggest that although there is some degree of spatio-temporal covariation in the filtering properties either of individual filters or across the filter population, the well known spatio-temporal covariation in human detection sensitivity is adequately explained by a sensitivity scaling of individual temporal filters with approximately invariant temporal properties.

Visual space-time interactions: effects of adapting to spatial frequencies on temporal sensitivity

To study how adaptation to spatial frequency patterns affects temporal sensitivity in vision, observers were selectively adapted for 4 min to either a high- or a low-spatial-frequency sinusoidal grating (12 and 2 cpd, respectively). Their sensitivities to modulation of a blurred patch at high or low temporal frequencies (12 Hz and 2 Hz, respectively) were measured, before and after the adaptation period, by using the yes/no task of signal detection theory. The data consistently indicated that spatial adaptation differentially affected the observers' sensitivities to temporal signals. Specifically, when the observers were adapted to low spatial frequencies, their sensitivity to low temporal frequencies was reduced; when they were adapted to high spatial frequencies, their sensitivity to high temporal frequencies was increased. These results have implications for the psychophysical measurements of temporal and spatial sensitivity, as well as for the issue of the separability of spatial and temporal properties of individual channels.

Figure and ground in space and time: 1. Temporal response surfaces of perceptual organization

The figure-ground organization of an ambiguous bipartite pattern can be manipulated by altering the temporal-frequency content of the two regions of the pattern. Ambiguous patterns in which the two regions of each pattern contained sine-wave gratings of either 8, 4, 1, or 0.5 cycles deg-1 undergoing contrast reversal at rates of 0, 3.75, 7.5, or 15 Hz were tested for figure-ground organization under conditions of equated space-averaged and time-averaged luminance and perceived contrast. All combinations of temporal-frequency differences between the two regions were tested at each spatial frequency. The data are reported for two levels of temporal resolution (15 and 30 s). The pattern region with the relatively higher temporal frequency tended to be seen as the background a higher percentage of the viewing time. There were significant linear trends for the appearance as background of the region of higher temporal frequency with respect to the magnitude of the temporal-frequency difference between the two regions of each pattern for all spatial frequencies and data intervals except the final 15 s interval of the lowest (0.5 cycle deg-1) spatial-frequency condition.

Spatial and temporal frequency in figure-ground organization

Figure-ground organization of an ambiguous pattern can be manipulated by the spatial and temporal frequency content of the two regions of the pattern. Controlling for space-averaged luminance and perceived contrast, we tested patterns in which the two regions of the ambiguous pattern contained sine-wave gratings of 8, 4, 1, or 0.5 cycles per degree (cpd) undergoing on:off flicker at the rates of 0, 3.75, 7.5, or 15 Hz. For a full set of combinations of temporal frequency differences, with each spatial frequency the higher temporal frequency was seen as background for more of the viewing time. For two spatial frequency combinations, 1 and 4 cpd, and 1 and 8 cpd, tested under each of the four temporal frequencies, the lower spatial frequency region was seen as the background for more of the viewing time. When the effects of spatial and temporal frequency were set in opposition, neither was predominant in determining perceptual organization. It is suggested that figure-ground organization may parallel the sustained-transient response characteristics of the visual system.

The contrast sensitivity gradient across the human visual field: with emphasis on the low spatial frequency range

The regional variation of contrast sensitivity along the greater extent of each of the four principal hemi-meridia of the normal human eye was determined under photopic conditions using horizontally-orientated sinusoidal grating stimuli. The stimuli were well localized in space and frequency, and special attention was paid to the low spatial frequency range. The results confirm that contrast sensitivity is maximal for central vision for all test spatial stimuli. Extra-foveal fall-off in sensitivity can be represented as a linear function of eccentricity if the latter is expressed in relative units (i.e. periods of the stimulus). The regional variation parameter depends upon whether the horizontal or vertical field is tested and upon the spatial frequency of stimulation. The visible spatial frequency range (0.05-24 c/deg) can be approximately described by just three different rules. The fact that more than one rule is found bears upon current models of the functional organization of the visual system.

Further evidence for a broadband, isotropic mechanism sensitive to high-velocity stimuli

Spatial frequency and orientation selectively, the most prominent properties of image-processing in the striate cortex, are not uniform throughout the spatiotemporal frequency domain. Some current models include one "transient" mechanism at very high velocities (i.e. low spatial and high temporal frequencies), and multiple "sustained" mechanisms elsewhere in the spatiotemporal frequency domain, but they do not consider the parameter of orientation. On the basis of earlier, orthogonal masking experiments, we concluded that the high-velocity mechanism is sensitive to a broad band of spatial frequencies, and has little or no orientation selectivity. In the present study we use pattern adaptation to measure the spatiotemporal properties of this mechanism. In other experiments, we attempt to relate it to the direction-selective motion detectors that also respond at high velocities. Finally we compare the pattern-adaptation results to the results of orthogonal subthreshold summation experiments in the same region of high temporal and low spatial frequencies.