Contrast discrimination with sinusoidal gratings of different spatial frequency

Subjective and objective measures of visual awareness converge

Within consciousness research, the most appropriate assessment of visual awareness is matter of a controversial debate: Subjective measures rely on introspections of the observer related to perceptual experiences, whereas objective measures are based on performance of the observer to accurately detect or discriminate the stimulus in question across a series of trials. In the present study, we compared subjective and objective awareness measurements across different stimulus feature and contrast levels using a temporal two-alternative forced choice task. This task has the advantage to provide an objective psychophysical performance measurement, while minimizing biases from unconscious processing. Thresholds based on subjective ratings with the Perceptual Awareness Scale (PAS) and on performance accuracy were determined for detection (stimulus presence) and discrimination (letter case) tasks at high and low stimulus contrast. We found a comparable pattern of thresholds across tasks and contrasts for objective and subjective measurements of awareness. These findings suggest that objective performance measures based on accuracy and subjective ratings of the visual experience can provide similar information on the feature-content of a percept. The observed similarity of thresholds validates psychophysical and subjective approaches to awareness as providing converging and thus most likely veridical measures of awareness.

Linking perceived to physical contrast: Comparing results from discrimination and difference-scaling experiments

Psychophysical approaches that allow us to estimate how perceived stimulus intensity is linked to physical intensity are import tools for studying nonlinear transformations of visual signals within different visual pathways. Here, we investigated how stimulus contrast is encoded in achromatic and chromatic pathways using simple grating stimuli. We compared two experimental approaches to this question: contrast discrimination (increment detection thresholds measured on contrast pedestals) and the maximum likelihood difference scaling (MLDS) approach introduced by Maloney and Yang (2003). The results of both experiments are expressed using simple models that include a transducer function mapping physical contrast to an internal signal the observer uses in making judgments, and an estimate of the variability of this representation (internal "noise"). We found that the transducers derived from both experiments have a similar form, but occupy different ranges of physical contrast in different stimulus conditions, reflecting difference in contrast sensitivity. This is consistent with past discrimination results, and in the difference-scaling case provides new evidence supporting the idea that suprathreshold chromatic and achromatic contrast are processed similarly, once differences in contrast sensitivity are taken into account. Model estimates of internal noise were higher in the difference-scaling experiment than the discrimination experiment, a finding we attribute to a difference in task complexity. Finally, we fit an alternative version of the MLDS model in which internal noise increased with response level. This alternative was no better at predicting holdout data in a cross-validation analysis than the original constant-variance model.

Contrast Sensitivity on 1/f Noise Is More Greatly Impacted by Older Age for the Fovea Than Parafovea

SIGNIFICANCE

Contrast sensitivity changes across the visual field with age and is often measured clinically with various forms of perimetry on plain backgrounds. In daily life, the visual scene is more complicated, and therefore, the standard clinical measures of contrast sensitivity may not predict a patient's visual experience in more natural environments.

PURPOSE

This study aims to determine whether contrast thresholds in older adults are different from younger adults when measured on a 1/f noise background (a nonuniform background whose spatial frequency content is similar to those present in the natural vision environments).

METHODS

Twenty younger (age range, 20 to 35 years) and 20 older adults (age range, 61 to 79 years) with normal ocular health were recruited. Contrast thresholds were measured for a Gabor patch of 6 cycles per degree (sine wave grating masked by a Gaussian envelope of standard deviation 0.17°) presented on 1/f noise background (root-mean-square contrast, 0.05 and 0.20) that subtended 15° diameter of the central visual field. The stimulus was presented at four eccentricities (0°, 2°, 4°, and 6°) along the 45° meridian in the noise background, and nine contrast levels were tested at each eccentricity. The proportion of correct responses for detecting the target at each eccentricity was obtained, and psychometric functions were fit to estimate the contrast threshold.

RESULTS

Older adults demonstrate increased contrast thresholds compared with younger adults. There was an eccentricity-dependent interaction with age, with the difference between groups being highest in the fovea compared with other eccentricities. Performance was similar for the two noise backgrounds tested.

CONCLUSIONS

Our results revealed a strong eccentricity dependence in performance between older and younger adults, highlighting age-related differences in the contrast detection mechanisms between fovea and parafovea for stimuli presented on nonuniform backgrounds.

Classification images for contrast discrimination

Contrast discrimination measures the smallest difference in contrast (the threshold) needed to successfully tell two stimuli apart. The contrast discrimination threshold typically increases with contrast. However, for low spatial frequency gratings the contrast threshold first increases, but then starts to decrease at contrasts above about 50%. This behaviour was originally observed in contrast discrimination experiments using dark spots as stimuli, suggesting that the contrast discrimination threshold for low spatial frequency gratings may be dominated by responses to the dark parts of the sinusoid. This study measures classification images for contrast discrimination experiments using a 1 cycle per degree sinusoidal grating at contrasts of 0, 25%, 50% and 75%. The classification images obtained clearly show that observers emphasize the darker parts of the sinusoidal grating (i.e. the troughs), and this emphasis increases with contrast. At 75% contrast, observers almost completely ignored the bright parts (peaks) of the sinusoid, and for some observers the emphasis on the troughs is already evident at contrasts as low as 25%. Analysis using a Hammerstein model suggests that the bias towards the dark parts of the stimulus is due to an early nonlinearity, perhaps similar to that proposed by Whittle.

What Do Contrast Threshold Equivalent Noise Studies Actually Measure? Noise vs. Nonlinearity in Different Masking Paradigms

The internal noise present in a linear system can be quantified by the equivalent noise method. By measuring the effect that applying external noise to the system's input has on its output one can estimate the variance of this internal noise. By applying this simple "linear amplifier" model to the human visual system, one can entirely explain an observer's detection performance by a combination of the internal noise variance and their efficiency relative to an ideal observer. Studies using this method rely on two crucial factors: firstly that the external noise in their stimuli behaves like the visual system's internal noise in the dimension of interest, and secondly that the assumptions underlying their model are correct (e.g. linearity). Here we explore the effects of these two factors while applying the equivalent noise method to investigate the contrast sensitivity function (CSF). We compare the results at 0.5 and 6 c/deg from the equivalent noise method against those we would expect based on pedestal masking data collected from the same observers. We find that the loss of sensitivity with increasing spatial frequency results from changes in the saturation constant of the gain control nonlinearity, and that this only masquerades as a change in internal noise under the equivalent noise method. Part of the effect we find can be attributed to the optical transfer function of the eye. The remainder can be explained by either changes in effective input gain, divisive suppression, or a combination of the two. Given these effects the efficiency of our observers approaches the ideal level. We show the importance of considering these factors in equivalent noise studies.

Four theorems on the psychometric function

In a 2-alternative forced-choice (2AFC) discrimination task, observers choose which of two stimuli has the higher value. The psychometric function for this task gives the probability of a correct response for a given stimulus difference, . This paper proves four theorems about the psychometric function. Assuming the observer applies a transducer and adds noise, Theorem 1 derives a convenient general expression for the psychometric function. Discrimination data are often fitted with a Weibull function. Theorem 2 proves that the Weibull “slope” parameter, , can be approximated by , where is the of the Weibull function that fits best to the cumulative noise distribution, and depends on the transducer. We derive general expressions for and , from which we derive expressions for specific cases. One case that follows naturally from our general analysis is Pelli's finding that, when , . We also consider two limiting cases. Theorem 3 proves that, as sensitivity improves, 2AFC performance will usually approach that for a linear transducer, whatever the actual transducer; we show that this does not apply at signal levels where the transducer gradient is zero, which explains why it does not apply to contrast detection. Theorem 4 proves that, when the exponent of a power-function transducer approaches zero, 2AFC performance approaches that of a logarithmic transducer. We show that the power-function exponents of 0.4–0.5 fitted to suprathreshold contrast discrimination data are close enough to zero for the fitted psychometric function to be practically indistinguishable from that of a log transducer. Finally, Weibull reflects the shape of the noise distribution, and we used our results to assess the recent claim that internal noise has higher kurtosis than a Gaussian. Our analysis of for contrast discrimination suggests that, if internal noise is stimulus-independent, it has lower kurtosis than a Gaussian.

Probability summation--a critique

This Discussion Paper seeks to kill off probability summation, specifically the high-threshold assumption, as an explanatory idea in visual science. In combination with a Weibull function of a parameter of about 4, probability summation can accommodate, to within the limits of experimental error, the shape of the detectability function for contrast, the reduction in threshold that results from the combination of widely separated grating components, summation with respect to duration at threshold, and some instances, but not all, of spatial summation. But it has repeated difficulty with stimuli below threshold, because it denies the availability of input from such stimuli. All the phenomena listed above, and many more, can be accommodated equally accurately by signal-detection theory combined with an accelerated nonlinear transform of small, near-threshold, contrasts. This is illustrated with a transform that is the fourth power for the smallest contrasts, but tends to linear above threshold. Moreover, this particular transform can be derived from elementary properties of sensory neurons. Probability summation cannot be regarded as a special case of a more general theory, because it depends essentially on the 19th-century notion of a high fixed threshold. It is simply an obstruction to further progress.

Paradoxical psychometric functions ("swan functions") are explained by dilution masking in four stimulus dimensions

The visual system dissects the retinal image into millions of local analyses along numerous visual dimensions. However, our perceptions of the world are not fragmentary, so further processes must be involved in stitching it all back together. Simply summing up the responses would not work because this would convey an increase in image contrast with an increase in the number of mechanisms stimulated. Here, we consider a generic model of signal combination and counter-suppression designed to address this problem. The model is derived and tested for simple stimulus pairings (e.g. A + B), but is readily extended over multiple analysers. The model can account for nonlinear contrast transduction, dilution masking, and signal combination at threshold and above. It also predicts nonmonotonic psychometric functions where sensitivity to signal A in the presence of pedestal B first declines with increasing signal strength (paradoxically dropping below 50% correct in two-interval forced choice), but then rises back up again, producing a contour that follows the wings and neck of a swan. We looked for and found these "swan" functions in four different stimulus dimensions (ocularity, space, orientation, and time), providing some support for our proposal.

The slope of the psychometric function and non-stationarity of thresholds in spatiotemporal contrast vision

The slope of the two-interval, forced-choice psychometric function (e.g. the Weibull parameter, β) provides valuable information about the relationship between contrast sensitivity and signal strength. However, little is known about how or whether β varies with stimulus parameters such as spatiotemporal frequency and stimulus size and shape. A second unresolved issue concerns the best way to estimate the slope of the psychometric function. For example, if an observer is non-stationary (e.g. their threshold drifts between experimental sessions), β will be underestimated if curve fitting is performed after collapsing the data across experimental sessions. We measured psychometric functions for 2 experienced observers for 14 different spatiotemporal configurations of pulsed or flickering grating patches and bars on each of 8 days. We found β≈3 to be fairly constant across almost all conditions, consistent with a fixed nonlinear contrast transducer and/or a constant level of intrinsic stimulus uncertainty (e.g. a square law transducer and a low level of intrinsic uncertainty). Our analysis showed that estimating a single β from results averaged over several experimental sessions was slightly more accurate than averaging multiple estimates from several experimental sessions. However, the small levels of non-stationarity (SD≈0.8dB) meant that the difference between the estimates was, in practice, negligible.

A reevaluation of achromatic spatio-temporal vision: Nonoriented filters are monocular, they adapt, and can be used for decision making at high flicker speeds

Masking, adaptation, and summation paradigms have been used to investigate the characteristics of early spatio-temporal vision. Each has been taken to provide evidence for (i) oriented and (ii) nonoriented spatial-filtering mechanisms. However, subsequent findings suggest that the evidence for nonoriented mechanisms has been misinterpreted: those experiments might have revealed the characteristics of suppression (eg, gain control), not excitation, or merely the isotropic subunits of the oriented detecting mechanisms. To shed light on this, we used all three paradigms to focus on the 'high-speed' corner of spatio-temporal vision (low spatial frequency, high temporal frequency), where cross-oriented achromatic effects are greatest. We used flickering Gabor patches as targets and a 2IFC procedure for monocular, binocular, and dichoptic stimulus presentations. To account for our results, we devised a simple model involving an isotropic monocular filter-stage feeding orientation-tuned binocular filters. Both filter stages are adaptable, and their outputs are available to the decision stage following nonlinear contrast transduction. However, the monocular isotropic filters (i) adapt only to high-speed stimuli-consistent with a magnocellular subcortical substrate-and (ii) benefit decision making only for high-speed stimuli (ie, isotropic monocular outputs are available only for high-speed stimuli). According to this model, the visual processes revealed by masking, adaptation, and summation are related but not identical.

A common contrast pooling rule for suppression within and between the eyes

Recent work has revealed multiple pathways for cross-orientation suppression in cat and human vision. In particular, ipsiocular and interocular pathways appear to assert their influence before binocular summation in human but have different (1) spatial tuning, (2) temporal dependencies, and (3) adaptation after-effects. Here we use mask components that fall outside the excitatory passband of the detecting mechanism to investigate the rules for pooling multiple mask components within these pathways. We measured psychophysical contrast masking functions for vertical 1 cycle/deg sine-wave gratings in the presence of left or right oblique (±45 deg) 3 cycles/deg mask gratings with contrast C%, or a plaid made from their sum, where each component (i) had contrast 0.5Ci%. Masks and targets were presented to two eyes (binocular), one eye (monoptic), or different eyes (dichoptic). Binocular-masking functions superimposed when plotted against C, but in the monoptic and dichoptic conditions, the grating produced slightly more suppression than the plaid when Ci ≥ 16%. We tested contrast gain control models involving two types of contrast combination on the denominator: (1) spatial pooling of the mask after a local nonlinearity (to calculate either root mean square contrast or energy) and (2) “linear suppression” (Holmes & Meese, 2004, Journal of Vision4, 1080–1089), involving the linear sum of the mask component contrasts. Monoptic and dichoptic masking were typically better fit by the spatial pooling models, but binocular masking was not: it demanded strict linear summation of the Michelson contrast across mask orientation. Another scheme, in which suppressive pooling followed compressive contrast responses to the mask components (e.g., oriented cortical cells), was ruled out by all of our data. We conclude that the different processes that underlie monoptic and dichoptic masking use the same type of contrast pooling within their respective suppressive fields, but the effects do not sum to predict the binocular case.

Effects of Luminance Ratio in a Liquid-Crystal Display on Discrimination of Separation by Elderly People

In a 2006 study the influence of spacing between vertical lines, exposure time, and number of vertical lines on visual performance was identified. The present study further explored the effects of luminance ratio on discrimination of separation. Analysis showed the luminance ratio of target vertical lines affected the visual performance of both younger and elderly people. The luminance ratio was greater, as was accuracy; however, accuracy might not become greater when the luminance ratio was too high. Further, the effect of the number of vertical lines on accuracy was significant, as was consistent with the 2006 study. Two interactive two-way effects were found, group × luminance ratio and luminance ratio × number of vertical lines.

Collinear facilitation: Effect of additive and multiplicative external noise

The detectability of a Gabor patch is improved by the presence of collinear flanking Gabors, this phenomenon is termed collinear facilitation. In experiment 1, we investigate the effects of adding 2D spatial luminance noise as a means of investigating different transects through the suprathreshold contrast space to see whether facilitation is ubiquitous throughout the contrast domain or whether it is confined to absolute contrast threshold. The results show that adding luminance noise abolishes the facilitation, showing it is confined to absolute threshold. In experiment 2, we assess whether 2nd order stimuli exhibit collinear facilitation and whether 1st order flanks can induce facilitation in 2nd order stimuli and vice versa. Our results suggest that collinear facilitation, albeit weaker, does occur for some 2nd order stimuli but we did not find any 1st/2nd order interactions, suggesting separate 1st/2nd order cortical processing streams, at least at the level at which this phenomenon occurs. Our two main findings, namely the lack of facilitation at suprathreshold contrasts and its presence for 2nd order processing argue against it playing a pivotal role in contour integration which does occur at all contrasts but not for these 2nd order stimuli.

Remote facilitation in the Fourier domain

To explore spatial interactions between visual mechanisms in the Fourier domain we measured detection thresholds for vertical and horizontal sine-wave gratings (4.4 deg diameter) over a range of spatial frequencies (0.5-23 c/deg) in the presence of grating and plaid masks with component contrasts of 8%, orientations of +/-45 degrees and a spatial frequency of 1c/deg. The mask suppressed the target grating over a range of +/-1 octave, and the plaid produced more suppression than the grating, consistent with summation of mask components in a broadly tuned contrast gain pool. At greater differences in spatial frequency ( approximately 3 octaves), the plaid and grating masks both produced about 3 dB of facilitation (they reduced detection thresholds by a factor of about square root 2). At yet further distances ( approximately 4 octaves) the masks had no effect. The facilitation cannot be attributed to a reduction of uncertainty by the mask because (a) it occurs for mask components that have very different spatial frequencies and orientations from the test and (b) the large stimulus size and central fixation point mean there was no spatial uncertainty that could be reduced. We suggest the results are due to long-range sensory interactions (in the Fourier domain) between mask and test-channels. The effects could be due to either direct facilitation or disinhibition.

Psychophysical evidence for two routes to suppression before binocular summation of signals in human vision

Visual mechanisms in primary visual cortex are suppressed by the superposition of gratings perpendicular to their preferred orientations. A clear picture of this process is needed to (i) inform functional architecture of image-processing models, (ii) identify the pathways available to support binocular rivalry, and (iii) generally advance our understanding of early vision. Here we use monoptic sine-wave gratings and cross-orientation masking (XOM) to reveal two cross-oriented suppressive pathways in humans, both of which occur before full binocular summation of signals. One is a within-eye (ipsiocular) pathway that is spatially broadband, immune to contrast adaptation and has a suppressive weight that tends to decrease with stimulus duration. The other pathway operates between the eyes (interocular), is spatially tuned, desensitizes with contrast adaptation and has a suppressive weight that increases with stimulus duration. When cross-oriented masks are presented to both eyes, masking is enhanced or diminished for conditions in which either ipsiocular or interocular pathways dominate masking, respectively. We propose that ipsiocular suppression precedes the influence of interocular suppression and tentatively associate the two effects with the lateral geniculate nucleus (or retina) and the visual cortex respectively. The interocular route is a good candidate for the initial pathway involved in binocular rivalry and predicts that interocular cross-orientation suppression should be found in cortical cells with predominantly ipsiocular drive.

Spatial and temporal dependencies of cross-orientation suppression in human vision

A well-known property of orientation-tuned neurons in the visual cortex is that they are suppressed by the superposition of an orthogonal mask. This phenomenon has been explained in terms of physiological constraints (synaptic depression), engineering solutions for components with poor dynamic range (contrast normalization) and fundamental coding strategies for natural images (redundancy reduction). A common but often tacit assumption is that the suppressive process is equally potent at different spatial and temporal scales of analysis. To determine whether it is so, we measured psychophysical cross-orientation masking (XOM) functions for flickering horizontal Gabor stimuli over wide ranges of spatio-temporal frequency and contrast. We found that orthogonal masks raised contrast detection thresholds substantially at low spatial frequencies and high temporal frequencies (high speeds), and that small and unexpected levels of facilitation were evident elsewhere. The data were well fit by a functional model of contrast gain control, where (i) the weight of suppression increased with the ratio of temporal to spatial frequency and (ii) the weight of facilitatory modulation was the same for all conditions, but outcompeted by suppression at higher contrasts. These results (i) provide new constraints for models of primary visual cortex, (ii) associate XOM and facilitation with the transient magno- and sustained parvostreams, respectively, and (iii) reconcile earlier conflicting psychophysical reports on XOM.

Does a Bayesian model of V1 contrast coding offer a neurophysiological account of human contrast discrimination?

The dipper effect for contrast discrimination provides strong evidence that the underlying neural response is accelerating at low contrasts and saturating at high contrasts. The contrast-response functions of V1 neurons do have this sigmoidal shape, but individual neurons do not generally have a dynamic range wide enough to account for the dipper effect. This paper presents a Bayesian model of neurons in monkey V1, whose contrast-response function is described by a modified Naka-Rushton with multiplicative noise. It is shown that a model of groups of twelve or more neurons gives a reasonable explanation of the psychophysical data of two observers, but there is a large systematic error which is apparently due to the shape of the distribution of the monkey's sensitivity parameter, c50. A further model provides a better fit to the data by sacrificing strict adherence to V1 neuronal parameters and, instead using an arbitrary bimodal c50 distribution, perhaps reflecting differences between M- and P-cells.

The effects of amplitude-spectrum statistics on foveal and peripheral discrimination of changes in natural images, and a multi-resolution model

Psychophysical thresholds were measured for discriminating small changes in spatial features of naturalistic scenes (morph sequences), for foveal and peripheral vision, and under M-scaling. Sensitivity was greatest for scenes with near natural Fourier amplitude slope, perhaps implying that human vision is optimised for natural scene statistics. A low-level model calculated differences in local contrast between pairs of images within a few spatial frequency channels with bandwidth like neurons in V1. The model was "customised" to each observer's contrast sensitivity function for sinusoidal gratings, and it could replicate the "U-shaped" relationships between discrimination threshold and spectral slope, and many differences between picture sets and observers. A single-channel model and an ideal-observer analysis both failed to capture the U-shape.

Masking effect produced by Mach bands on the detection of narrow bars of random polarity

Difficulties arise in measuring masking by Mach bands because very-low-contrast signals distort the bands. [J. Opt. Soc. Am. A 17, 1147 (2000).] Adding narrow luminance increments (bright bars) in the dark Mach band widens the dark band; adding decrements (dark bars) narrows the dark band, and conversely in the bright bands. Randomizing signal polarity prevents observers from using the distortion of the Mach bands as a cue to the presence of the signal. We measured (two-alternative-forced-choice) Mach bands' masking of randomly selected bright (incremental) or dark (decremental) bars. Detection was worse in both dark and bright Mach bands than on the neighboring plateaus. Separate analysis of trials containing only one polarity signal revealed 9-cycle/deg oscillations in performance as a function of location. Oscillations in the two polarities were approximately 180 degrees out of phase.

Contrast discrimination with pulse trains in pink noise

Detection performance was measured with sinusoidal and pulse-train gratings. Although the 2.09-cycles-per-degree pulse-train, or line, grating contained at least eight harmonics all at equal contrast, it was no more detectable than its most detectable component. The addition of broadband pink noise designed to equalize the detectability of the components of the pulse train made the pulse train approximately a factor of 4 more detectable than any of its components. However, in contrast-discrimination experiments, with a pedestal or masking grating of the same form and phase as the signal and with 15% contrast, the noise did not affect the discrimination performance of the pulse train relative to that obtained with its sinusoidal components. We discuss the implications of these observations for models of early vision, in particular the implications for possible sources of internal noise.