Christopher W. Tyler

Bayesian adaptive estimation of psychometric slope and threshold.

We introduce a new Bayesian adaptive method for acquisition of both threshold and slope of the psychometric function. The method updates posterior probabilities in the two-dimensional parameter space of psychometric functions and makes predictions based on the expected mean threshold and slope values. On each trial it sets the stimulus intensity that maximizes the expected information to be gained by completion of that trial. The method was evaluated in computer simulations and in a psychophysical experiment using the two-alternative forced-choice (2AFC) paradigm. Threshold estimation within 2 dB (23%) precision requires less than 30 trials for a typical 2AFC detection task. To get the slope estimate with the same precision takes about 300 trials.

Spatial frequency sweep VEP : visual acuity during the first year of life

The grating acuity of 197 infants from 1 week to 53 weeks of age was measured using the visual evoked potential (VEP) in response to counterphase grating stimulation. The gratings were presented as a 10 sec spatial frequency sweep which spanned the acuity limit. The amplitude and phase of the second harmonic response were extracted by discrete Fourier analysis. The VEP amplitude versus spatial frequency function showed narrow spatial frequency tuning with amplitude peaks at one or more spatial frequencies. The phase of the response at medium to high spatial frequencies was generally constant at a spatial frequency peak, followed by a progressive phase lag with increasing spatial frequency. Grating acuity was estimated by linear extrapolation to zero microvolts of the highest spatial frequency peak in the VEP amplitude versus spatial frequency function. This visual acuity estimate increased from a mean of 4.5 c/deg during the first month to about 20 c/deg at 8-13 months of age. The VEP acuities at 1 month are a factor of three to five higher than previously reported for pattern reversal or pattern appearance stimuli. By 8 months VEP grating resolution was not reliably different from adult levels in the same apparatus.

Psychophysical isolation of movement sensitivity by removal of familiar position cues.

To isolate differential motion sensitivity from the contaminating effects of position sensitivity, we used a field of random dots undergoing a differential shearing motion. Movement threshold amplitude vs temporal frequency showed a slope of −1 on double-logarithmic coordinates, confirming that the detection was based on motion rather than on positional information. A comparison of motion and position sensitivity showed both to be very high, each requiring a differential displacement of only 5 sec arc. In comparison to position sensitivity, motion sensitivity showed a 10-fold superiority at the lowest spatial frequencies tested and a poorer sensitivity at higher spatial frequencies. We conclude that the random-dot stimulus can isolate motion- from position-sensitive mechanisms and that motion comprises a distinct form of sensitivity, not derivable from the measured forms of position sensitivity.

Development of contrast sensitivity in the human infant

Contrast sensitivity and grating acuity were measured using the sweep VEP method in a group of 48 infants from 2 to 40 weeks of age and in a group of 10 adults. Sinusoidal gratings were reversed in contrast at 12 alternations per sec at a space-average luminance of 220 cd/m2. During 10 sec trials, either the contrast or the spatial frequency was increased in a series of 19 steps. Thresholds were estimated by extrapolation of the VEP response functions to zero amplitude. The contrast threshold at low spatial frequencies developed rapidly from 7% contrast at 2-3 weeks to an asymptote of 0.5% at 9 weeks. For adults, maximum sensitivity at low spatial frequencies was 0.32-0.22%. The sweep VEP estimate of grating acuity showed a gradual increase in spatial frequency with age, starting at 5 c/deg during the first month and reaching 16.3 c/deg at 8 months. The mean adult acuity was 31.9 c/deg. There appeared to be two phases in the development of contrast sensitivity and acuity. Between 4 and 9 weeks overall contrast sensitivity increased by a factor of 4-5 at all spatial frequencies. Beyond 9 weeks, contrast sensitivity at low spatial frequencies remained constant, while sensitivity increased systematically at higher spatial frequencies.

Signal detection theory in the 2AFC paradigm: attention, channel uncertainty and probability summation

Neural implementation of classical High-Threshold Theory reveals fundamental flaws in its applicability to realistic neural systems and to the two-alternative forced-choice (2AFC) paradigm. For 2AFC, Signal Detection Theory provides a basis for accurate analysis of the observers attentional strategy and effective degree of probability summation over attended neural channels. The resulting theory provides substantially different predictions from those of previous approximation analyses. In additive noise, attentional probability summation depends on the attentional model assumed. (1) For an ideal attentional strategy in additive noise, summation proceeds at a diminishing rate from an initial level of fourth-root summation for the first few channels. The maximum improvement asymptotes to about a factor of 4 by a million channels. (2) For a fixed attention field in additive noise, detection is highly inefficient at first and approximates fourth-root summation through the summation range. (3) In physiologically plausible root-multiplicative noise, on the other hand, attentional probability summation mimics a linear improvement in sensitivity up to about ten channels, approaching a factor of 1000 by a million channels. (4) Some noise sources, such as noise from eye movements, are fully multiplicative and would prevent threshold determination within their range of effectiveness. Such results may require reappraisal of previous interpretations of detection behavior in the 2AFC paradigm.

New look at Bloch's law for contrast

It has been commonly reported that the temporal integration of grating contrast proceeds more slowly as spatial frequency is increased. Such results have been based on the critical duration for sensitivity to contrast pulses varying in duration, but the analyses have not assumed full integration at short durations and have neglected the effects of probability summation over time. To take such effects into account, we discuss a class of analytical models based on nonlinear temporal integration. On the assumption that the temporal impulse response of the visual system determines contrast integration over time, we develop both a high-threshold model and a signal-detection approach involving multiple and independent nonlinear signal detectors with a time-limited integration span. The redefined critical durations predicted by the models and verified by the data are about 35 msec and vary by no more than 10 msec across spatial frequency. This variation is entirely attributable to a change in the strength of inhibition with spatial frequency, and the analysis implies that the excitatory component is constant at all spatial frequencies, contrary to previous accounts.

Measurement of spatial contrast sensitivity with the swept contrast VEP

Contrast response functions (CRFs) for the VEP were obtained with a Discrete Fourier Transform (DFT) technique employing swept contrast gratings. VEP CRFs in infants were found to have a form similar to those observed in adults, being linear functions of log contrast over a range of near-threshold contrasts. CRFs with low and high contrast lobes were present in infants, as they are in adults. Contrast thresholds were estimated by extrapolation of the CRF to zero microvolts. The effects of additive EEG noise and of the DFT data window on the shape of the measured CRF are considered. For large signals, the measured CRF is nearly independent of the additive noise, but at small signal values additive noise introduces a small bias towards larger amplitudes. The VEP signal-plus-noise distribution was modeled as a family of Rice distributions in order to evaluate the effects of bias on the estimates of threshold. The amount of bias depends inversely upon the slope of the CRF. The amount of bias introduced by a smoothing window also depends upon slope of the CRF as well as the sweep rate. The combined effects of additive noise and window bias were such that the total bias was nearly independent of CRF slope. Sweep VEP contrast thresholds were shown empirically to be unaffected by changes in the range of contrast swept.

The foveal confluence in human visual cortex

The human visual system devotes a significant proportion of its resources to a very small part of the visual field, the fovea. Foveal vision is crucial for natural behavior and many tasks in daily life such as reading or fine motor control. Despite its significant size, this part of cortex is rarely investigated and the limited data have resulted in competing models of the layout of the foveal confluence in primate species. Specifically, how V2 and V3 converge at the central fovea is the subject of debate in primates and has remained “terra incognita” in humans. Using high-resolution fMRI (1.2 × 1.2 × 1.2 mm3) and carefully designed visual stimuli, we sought to accurately map the human foveal confluence and hence disambiguate the competing theories. We find that V1, V2, and V3 are separable right into the center of the foveal confluence, and V1 ends as a rounded wedge with an affine mapping of the foveal singularity. The adjacent V2 and, in contrast to current concepts from macaque monkey, also V3 maps form continuous bands (∼5 mm wide) around the tip of V1. This mapping results in a highly anisotropic representation of the visual field in these areas. Unexpectedly, for the centermost 0.75°, the cortical representations for both V2 and V3 are larger than that of V1, indicating that more neuronal processing power is dedicated to second-level analysis in this small but important part of the visual field.

Predominantly extra-retinotopic cortical response to pattern symmetry

Symmetry along one or more axes is a key property of objects and biological organisms. We report on a bilateral visual region of occipital cortex that responds strongly to the presence of multiple symmetries in the viewed image. The stimuli consisted of random dots organized in fourfold and onefold mirror-symmetric patterns, against random control stimuli. The contrast between symmetric and random patterns produced negligible or inconsistent activation of the primary visual projection area V1 or of other medial occipital projection areas. However, there was strong symmetry-specific activation in extra-retinotopic lateral occipital cortex. The high level of activation in this region of cortex may represent part of a general class of computations that require integration of information across a large span of the visual field.

Multiple spatial-frequency tuning of electrical responses from human visual cortex.

SummaryHuman occipital potentials evoked by stimulation with a counterphase flickering grating were recorded by a digital narrowband filter technique. The data showed a surprising degree of narrow tuning to particular spatial frequencies in addition to the expected narrow temporal frequency tuning. At each temporal frequency, there could be two or more peaks of response to different spatial frequencies, each distinct from the whole field flicker response. Variations in this multiple spatial frequency tuning were investigated as a function of luminance, electrode location, and temporal frequency for several observers. The results are interpreted in terms of many stimulus-specific resonant neural circuits within the brain, and suggest that it is possible to make a highly detailed exploration of the responses of neural circuits to visual stimulation.