Mark A. Georgeson

Binocular contrast vision at and above threshold

A fundamental problem for any visual system with binocular overlap is the combination of information from the two eyes. Electrophysiology shows that binocular integration of luminance contrast occurs early in visual cortex, but a specific systems architecture has not been established for human vision. Here, we address this by performing binocular summation and monocular, binocular, and dichoptic masking experiments for horizontal 1 cycle per degree test and masking gratings. These data reject three previously published proposals, each of which predict too little binocular summation and insufficient dichoptic facilitation. However, a simple development of one of the rejected models (the twin summation model) and a completely new model (the two-stage model) provide very good fits to the data. Two features common to both models are gently accelerating (almost linear) contrast transduction prior to binocular summation and suppressive ocular interactions that contribute to contrast gain control. With all model parameters fixed, both models correctly predict (1) systematic variation in psychometric slopes, (2) dichoptic contrast matching, and (3) high levels of binocular summation for various levels of binocular pedestal contrast. A review of evidence from elsewhere leads us to favor the two-stage model.

Sensitivity to modulations of luminance and contrast in visual white noise: separate mechanisms with similar behaviour

Human vision can detect spatiotemporal information conveyed by first-order modulations of luminance and by second-order, non-Fourier modulations of image contrast. Models for second-order motion have suggested two filtering stages separated by a rectifying nonlinearity. We explore here the encoding of stationary first-order and second-order gratings, and their interaction. Stimuli consisted of 2-D binary, broad-band, static, visual noise sinusoidally modulated in luminance (LM, first-order) or contrast (CM, second-order). Modulation thresholds were measured in a two-interval forced-choice staircase procedure. Sensitivity curves for LM and CM had similar shape as a function of spatial frequency, and as a function of the size of a circular Gaussian blob of modulation. Weak background gratings present in both intervals produced order-specific facilitation: LM background facilitated LM detection (the dipper function) and CM facilitated CM detection. LM did not facilitate CM, nor vice-versa, neither in-phase nor out-of-phase, and this is strong evidence that LM and CM are detected via separate mechanisms. This conclusion was further supported by an experiment on the detection of LM/CM mixtures. From a general mathematical model and a specific computer simulation we conclude that a single mechanism sensitive to both LM and CM cannot predict the pattern of results for mixtures, while a model containing separate pathways for LM and CM, followed by energy summation, does so successfully and is quantitatively consistent with the finding of order-specific facilitation.

The effect of spatial adaptation on perceived contrast

Perceived contrast was assessed by contrast-matching between adjacent sinusoidal gratings of the same spatial frequency (3 cycles/degree), before and after adaptation to gratings of various contrasts. On logarithmic axes, the effect of adaptation was large for test contrasts below the adapting contrast, but absent for test contrasts higher than the adapting contrast. This result rules out a simple gain-reduction hypothesis, in which adaptation would attenuate all test contrasts by the same proportion. Instead, results for all combinations of adapting and test contrast levels (including threshold elevation) conformed fairly closely to a simple subtractive rule: any test contrast presented after adaptation behaved as if one-third of the adapting contrast were subtracted from it. Though not exact, this may be a useful descriptive rule. Deviations from the simple rule may be explained by increased variance in the visual response at high adapting contrasts, combined with nonlinearity at low test contrasts. A subtractive effect at the psychophysical level does not necessarily conflict with evidence for contrast gain reduction at the single-cell level.

Temporal properties of spatial contrast vision

The temporal characteristics of spatial contrast vision at and above threshold were assessed psychophysically using sinusoidal gratings and a contrast-matching method. Temporal frequency response curves became flatter as contrast level increased. An impulse response model was fitted to these flicker data, and used to make predictions about temporal integration and two-pulse summation. The predictions fitted the experimental data well, except under conditions where the Broca-Sulzer effect occurred. The latter was not predicted by the biphasic impulse response that otherwise worked well. Temporal filtering became moderately transient and operated over a shorter time-scale as contrast increased, and above threshold temporal properties varied little with spatial frequency. The data and modelling supported the idea that subjects exploited probability summation at threshold while using a peak detection criterion above threshold. Systematic visual field asymmetries in contrast perception are also described. Single- and multiple-channel models of temporal processing are discussed.

Does early non-linearity account for second-order motion?

A contrast-modulated (CM) pattern is formed when a modulating or envelope function imposes local contrast variations on a higher-frequency carrier. Motion may be seen when the envelope drifts across a stationary carrier and this has been attributed to a second-order pathway for motion. However, an early compressive response to luminance (e.g. in the photoreceptors) would introduce a distortion product at the modulating frequency. We used a nulling method to measure the distortion product, and then asked whether this early distortion could account for perception of second-order motion. The first stimulus sequence consisted of alternate frames of CM (100% modulation) and luminance-modulated (LM) patterns. Carriers were either 2-D binary noise (4 x 4 min arc dots) or a 4 c/deg grating, both modulated at 0.6 c/deg. The carrier was stationary while the phase of the modulating signal (LM alternating with CM) stepped successively through 90 degrees to the left or right. Motion was seen in a direction opposite to the phase stepping, consistent with early compressive distortion that induces an out-of-phase LM component into the CM stimulus. We measured distortion amplitude by adding LM to the CM frames to null the perceived motion. Distortion increased as the square of carrier contrast, as predicted by the compressive transducer. It also increased with modulation drift rate, implying that the transducer is time-dependent, not static. Thus early compressive non-linearity does induce first-order artefacts into second-order stimuli. Nevertheless this does not account for second-order motion, since perceived motion of second-order sequences (CM in every frame) could in general not be nulled by adding LM components. We conclude that two pathways for motion do exist.

Facilitation and masking of briefly presented gratings: time-course and contrast dependence.

We measured two-alternative forced-choice contrast thresholds for briefly presented sinusoidal gratings in the presence of superimposed masking gratings of various contrasts, and at a range of onset asynchronies. Facilitation (lower thresholds) occurred when the mask was simultaneous, in-phase, and near-threshold, but was abolished at asynchronies of 50 msec or more and by presenting the test grating as a brief contrast reversal instead of a pulse. We argue that facilitation requires temporal summation of responses within the same neural channels, but our results do not distinguish between transducer and uncertainty models. Masking (threshold elevation) occurred over a broader range of asynchronies, and was not abolished by test contrast reversal. Masking and facilitation probably depend on different processes with different time-courses. The occurrence of masking at asynchronies outside the range of temporal summation suggests that a static, compressive transducer does not, in general, account for masking. Brief masking and prolonged contrast adaptation are very similar in magnitude, and as a function of contrast and relative spatial frequency. Masking and adaptation may have a common origin, but differ in speed of recovery.

Sensitivity to contrast modulation: the spatial frequency dependence of second-order vision.

We consider the overall shape of the second-order modulation sensitivity function (MSF). Because second-order modulations of local contrast or orientation require a carrier signal, it is necessary to evaluate modulation sensitivity against a variety of carriers before reaching a general conclusion about second-order sensitivity. Here we present second-order sensitivity functions for new carrier types (low pass (1/f) noise, and high pass noise) and demonstrate that, when first-order artefacts have been accounted for, the shape of the resulting MSFs are similar to one another and to those for white and broad band noise. They are all low pass with a likely upper frequency limit in the range 10-20 c/deg, suggesting that detection of second-order stimuli is relatively insensitive to the structure of the carrier signal. This result contrasts strongly with that found for (first-order) luminance modulations of the same noise types. Here the noise acts as mask and each noise type masks most those frequencies that are dominant in its spectrum. Thus the shape of second-order MSFs are largely independent of the spectrum of their noise carrier, but first-order CSFs depend on the spectrum of an additive noise mask. This provides further evidence for the separation of first- and second-order vision and characterises second-order vision as a low pass mechanism.

Human vision combines oriented filters to compute edges

The experiments examined the perceived spatial structure of plaid patterns, composed of two or three sinusoidal gratings of the same spatial frequency, superimposed at different orientations. Perceived structure corresponded well with the pattern of zero crossings in the output of a circular spatial filter applied to the image. This lends some support to Marr & Hildreth’s (Proc. R. Soc. Lond. B 207, 187 (1980)) theory of edge detection as a model for human vision, but with a very different implementation. The perceived structure of two-component plaids was distorted by prior exposure to a masking or adapting grating, in a way that was perceptually equivalent to reducing the contrast of one of the plaid components. This was confirmed by finding that the plaid distortion could be nulled by increasing the contrast of the masked or adapted component. A corresponding reduction of perceived contrast for single gratings was observed after adaptation and in some masking conditions. I propose the outlines of a model for edge finding in human vision. The plaid components are processed through cortical, orientationselective filters that are subject to attenuation by forward masking and adaptation. The outputs of these oriented filters are then linearly summed to emulate circular filtering, and zero crossings (zcs) in the combined output are used to determine edge locations. Masking or adapting to a grating attenuates some oriented filters more than others, and although this changes only the effective contrast of the components, it results in a geometric distortion at the zc level after different filters have been combined. The orientation of zcs may not correspond at all with the orientation of Fourier components, but they are correctly predicted by this two-stage model. The oriented filters are not ‘orientation detectors’, but are precursors to a more subtle stage that locates and represents spatial features.

Channels for spatial frequency selection and the detection of single bars by the human visual system

Abstract Contrast sensitivities for a range of sinusoidal grating frequencies and a range of single bar widths were measured in 4 subjects. Unadapted contrast sensitivity was compared with that following adaptation to sinusoidal gratings of 5.5 or 16 cycles/deg, or bars of 7.5 or 1.25 min width, at 1.5 log units above threshold. Adaptation to both these sinusoids produced frequency specific elevation of threshold for sinusoids, whereas adaptation to 5.5 cycles/deg gratings uniformly elevated the bar threshold, and adaptation to 16 cycles/deg did not affect the bar threshold. Adaptation to bars produced no width specific adaptation in the bar sensitivity function, but elevated the threshold for bars of all widths, as well as elevating the threshold for sinusoids of all frequencies. Bar width and spatial frequency are not equivalent, and there is no evidence for width selective channels. Bars seem to be detected when their frequency components most easily detected by the visual system (near 5 cycles/deg) rise above their independent thresholds.

Motion contrast: a new metric for direction discrimination

The Adelson-Bergen energy model (Adelson, E. H., & Bergen, J. R. (1985). Spatiotemporal energy models for the perception of motion. Journal of the Optical Society of America A, 2, 284-299) is a standard framework for understanding first-order motion processing. The opponent energy for a given input is calculated by subtracting one directional energy measure (EL) from its opposite (ER), and its sign indicates the direction of motion of the input. Our observers viewed a dynamic sequence of gratings (1 c/deg) equivalent to the sum of two gratings moving in opposite directions with different contrasts. The ratio of contrasts was varied across trials. We found that opponent energy was a very poor predictor of direction discrimination performance. Heeger (1992). Normalization of cell responses in cat striate cortex. Visual Neuroscience, 9, 181-197) has suggested that divisive inhibition amongst striate cells requires a contrast gain control in the energy model. A new metric can be formulated in the spirit of Heegers model by normalising the opponent energy (EL - ER) with flicker energy, the sum of the directional motion energies (EL + ER). This new measure, motion contrast (EL - ER)/(EL + ER), was found to be a good predictor of direction discrimination performance over a wide range of contrast levels, but opponent energy was not. Discrimination thresholds expressed as motion contrast were around 0.5 +/- 0.1 for the sampled drifting gratings used in our experiments. We show that the dependence on motion contrast, and the threshold of about 0.5, can be predicted by a modified opponent energy model based on current knowledge of the response functions and response variance of cortical cells.