Modeling pedestal experiments with amplitude instead of contrast

Contrast discrimination in images of natural scenes

Contrast discrimination determines the threshold contrast required to distinguish between two suprathreshold visual stimuli. It is typically measured using sine-wave gratings. We first present a modification to Barten's semi-mechanistic contrast discrimination model to account for spatial frequency effects and demonstrate how the model can successfully predict visual thresholds obtained from published classical contrast discrimination studies. Contrast discrimination functions are then measured from images of natural scenes, using a psychophysical paradigm based on that employed in our previous study of contrast detection sensitivity. The proposed discrimination model modification is shown to successfully predict discrimination thresholds for structurally very different types of natural image stimuli. A comparison of results shows that, for normal contrast levels in natural scene viewing, contextual contrast detection and discrimination are approximately the same and almost independent of spatial frequency within the range of 1-20 c/deg. At higher frequencies, both sensitivities decrease in magnitude due to optical limitations of the eye. The results are discussed in relation to current image quality models.

Single additive mechanism predicts lateral interactions effects-computational model

The mechanism underlying the lateral interactions (LI) phenomenon is still an enigma. Over the years, several groups have tried to explain the phenomenon and suggested models to predict its psychophysical results. Most of these models comprise both inhibitory and facilitatory mechanisms for describing the LI phenomenon. Their studies' assumption that a significant inhibition mechanism exists is based on the classical interpretation of the threshold elevation perceived in psychophysical experiments. In this work, we suggest a different interpretation of the threshold elevation obtained experimentally. Our model proposes and demonstrates how a facilitatory additive mechanism can solely predict both the facilitation and "inhibition" aspects of the phenomenon, without the need for an additional inhibitory mechanism, at least for the two flankers' configurations. Though the model is simple it succeeds to predict the LI effect under a large variety of stimuli configurations and parameters. The model is in agreement with both classical and recent psychophysical and neurophysiological results. We suggest that the LI mechanism plays a role in creating an educated guess to form a continuation of gratings and textures based on the surrounding visual stimuli.

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.

Defining the detection mechanisms for symmetric and rectified flicker stimuli

Symmetric flicker modulates about a background light level and effects no change in the time-average luminance. Rectified flicker is achieved by modulating a luminance-increment and results in both a flickering component and an increase in the time-averaged luminance (luminance-pedestal) above the adapting background light level. We studied the effect that changes in adapting light level and local luminance (within the area of the flickering target) have on thresholds. We measured thresholds for single and multiple cycles of flicker over a range of adapting light levels (Threshold versus Intensity paradigm) and defined their gain as a function of luminance-pedestal amplitude (Threshold versus Amplitude paradigm). The dynamics of symmetric and rectified flicker responses were determined using a Stimulus Onset Asynchrony paradigm. The data show rectified flicker thresholds differ from symmetric flicker thresholds due to two factors that can be contrast-dependent or contrast-independent: (1) local adaptation, which varies with stimulus duration and (2) surround interactions that depend on adapting light level. The dynamics of the thresholds for symmetric and rectified flicker stimuli suggest the detection mechanisms occur early in the visual pathways, involving the magnocellular pathway.

Effect of noise on the contrast detection threshold in visual perception

It has recently been shown that noise can improve the detection of stimuli in several sensory modalities. We herein investigated whether visual contrast detection sensitivity can be improved by adding a certain amount of noise. The contrast detection thresholds of a light changing brightness periodically were measured either with or without overlapping noise in 22 normal participants. Sinusoidal modulating light at 1 or 15 Hz was used as a signal. White noise was used to produce random flickering light as the noise. Participants were required to detect any changes in the brightness of the signal with or without noise. The contrast detection threshold, which was measured using a psychophysical method, decreased at around the threshold level of the noise intensity. The maximum facilitatory effect was obtained at a noise intensity of 5 dB. This effect was consistently observed regardless of the frequency of the signal (1 and 15 Hz). These findings indicate that noise can improve the signal detection in human visual perception.

A noisy transform predicts saccadic and manual reaction times to changes in contrast

One of the most important factors affecting the time taken to respond to a visual stimulus is contrast, and studies of reaction time can provide precise, quantitative information about the underlying signal processing. In this study we measured both saccadic and manual reaction times to step increments in target contrast. Our results over a range of initial contrasts are consistent with a simple model consisting of a noisy logarithmic transducer followed by a rise-to-threshold accumulator. A systematic comparison with previous contrast-processing models also shows that the commonly used method of linear regression may not be a particularly sensitive tool in deciding between them. We found similar parameters for the contrast processor in both saccadic and manual reaction times, as might be expected if a common target detection stage precedes each type of reaction.

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.

Flanker effects in peripheral contrast discrimination--psychophysics and modeling

We studied lateral interactions in the periphery by measuring how contrast discrimination of a peripheral Gabor patch is affected by flankers. In the psychophysical experiments, two Gabor targets appeared simultaneously to the left and right of fixation (4 degrees eccentricity). Observers reported which contrast was higher (spatial 2-alternative-forced-choice). In different conditions, Gabor flankers of different orientation, phase, and contrast were present above and below the two targets, at a distance of three times the spatial Gabor period. The data show that collinear flanks impair discrimination performance for low pedestal contrasts but have no effect for high pedestal contrasts. The transition between these two result patterns occurs typically at a pedestal contrast which is similar to the flanker contrast. For orthogonal flanks, we find facilitation at low pedestal contrasts, and suppression at intermediate contrasts. We account for this complex interaction pattern by a model that assumes that flankers can provide additive input to the target unit, and that they further contribute to the target's gain control, but only in a limited range of pedestal contrasts; once the target contrast exceeds a critical value, inhibition becomes subtractive rather than divisive. We further make specific propositions on how this model could be implemented at the neuronal level and show that a simple integrate and fire unit that receives time-modulated inhibition behaves in a fashion strikingly similar to the model inferred from the psychophysical data.

Interactions between flicker thresholds and luminance pedestals

We investigated the interactions between flicker thresholds and luminance pedestals using threshold versus contrast (TvC) and method of constant stimuli paradigms. High amplitude luminance pedestals were found to elevate flicker thresholds, but low amplitude luminance pedestals were unable to reduce flicker thresholds. Luminance pedestals elevated flicker thresholds more at low temporal frequencies. A simple model based on local light adaptation was able to capture the general form of the TvC functions. Our results suggest that flicker thresholds derived in the presence of a luminance pedestal (luminance-pedestal flicker) may vary from those obtained by modulating about a mean luminance (mean-modulated flicker).

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.

Texture luminance judgments are approximately veridical

This paper investigates intensity coding in human vision. Specifically, we address the following question: how do different luminances influence the perceived total luminance of a composite image? We investigate this question using a paradigm in which the observer attempts to judge, with feedback, which of two texture patches has higher total luminance. All patches are composed of nine luminances, ranging linearly from 0 (black) to a maximum luminance (white: 160 cd/m(2) in one condition; 20.2 cd/m(2) in another condition). Luminance histograms of the patches being compared are experimentally varied to derive, for each luminance nu, the impact exerted by texture elements (texels) of luminance nu on texture luminance judgments. We find that impact is approximately proportional to texel luminance; That is, a texture element exerts, on average, an impact on texture brightness (i.e. perceived texture luminance) that is proportional to its (the texel's) luminance. The only exception occurs for texels of maximal luminance, which surprisingly exert an impact that is slightly, but significantly, less than that exerted by texels of the next lower luminance. We conclude that visual intensity coding for purposes of assessing overall luminance of inhomogeneous patches is approximately veridical. In particular, texture luminance judgments are not mediated by a significant, compressive nonlinearity.

Pattern detection in the presence of maskers that differ in spatial phase and temporal offset: threshold measurements and a model

Four experiments are described in which brief Gabor patterns are detected in the presence of full-field gratings or Gabor patterns that are superimposed in space, but vary in spatial phase and temporal offset (SOA). E1: Threshold versus masker contrast (TvC) functions were determined for relative phases of 0, 90, 180 and 270 degrees at SOA = 0. For 0 degree relative phase, TvC functions decrease (facilitation) and then increase (masking) as contrast increases. For 90 degrees, there is little or no facilitation and thresholds increase with masker contrast. For 180 degrees, the form of the TvC function varies with observer and conditions. E2: Like E1, except that maskers are Gabor patterns. TvC functions are similar in form to those for full-field maskers, but there is less masking. E3: Forward masking. TvC functions were determined for relative phases of 0, 90, and 180 degrees at SOA = -33 ms. The forms of the TvC functions for 0 and 180 degrees are reversed relative to those at SOA = 0. E4: TvP (threshold versus phase) functions were determined for SOA's of -100, -67, -33, 0 and 33 ms at a constant masker contrast of 0.063. Masking occurs at all relative phases. For simultaneous and backward masking, the threshold is minimum for a relative phase of 0 and maximum at 180 degrees. For forward masking, the form of the function is inverted. A model of pattern masking and facilitation (Foley, J. M. (1994a) Journal of the Optical Society of America A, 11, 1710-1719) is extended to account for masker phase and SOA effects. The model assumes four mechanisms tuned to phases 90 degrees apart, and divisively inhibited by stimuli of all phases. Performance depends on the detection strategy of the observer.

Nonlinearities of near-threshold contrast transduction

The existence of analytic threshold nonlinearities was probed with 2AFC incremental threshold functions for both local and extended test patterns on stationary matched pedestals of the same and opposite sign. In contrast to the facilitation effect with same-sign pedestals, sensitivity with opposite-sign pedestals first deteriorated up to the mask detection level, abruptly improved and then deteriorated again. Analytic solutions for the transducer function with additive noise were derived to account for the incremental data in all conditions. The results for positive difference-of-Gaussian (DoG) stimuli (whose increment made the central spot lighter) and for 10 c deg-1 Gabor stimuli were consistent with accurate hard-threshold behavior with best-fitting d' powers from 17 to 358. The 10 c deg-1 data further implied that contrast gain control was operating throughout the subthreshold range. The results for negative DoGs (whose increment corresponds to the darkening of the central spot) and 2 c deg-1 Gabor profiles were consistent with mild nonlinearities having d' powers of 1.6-3. Significant differences between the nonlinearities for positive and negative DoGs indicate that only a small portion, if any, of the near-threshold nonlinearity could be attributed to uncertainty. Our analysis suggests that, with low spatial frequency gratings, detection was based on those bars that become darker; with high-frequency gratings, on the bars that become brighter.

Transducer model produces facilitation from opposite-sign flanks

Small spots, lines and Gabor patterns can be easier to detect when they are superimposed upon similar spots, lines and Gabor patterns. Traditionally, such facilitation has been understood to be a consequence of nonlinear contrast transduction. Facilitation has also been reported to arise from non-overlapping patterns with opposite sign. We point out that this result does not preclude the traditional explanation for superimposed targets. Moreover, we find that facilitation from opposite-sign flanks is weaker than facilitation from same-sign flanks. Simulations with a transducer model produce opposite-sign facilitation.

Effect of background components on spatial-frequency masking

Previous studies of spatial-frequency masking and adaptation have shown that the contrast-detection threshold elevates maximally when the test spatial frequency is the same as the masking (or adapting) frequency but changes only slightly when they are separated by two or more octaves. At low spatial frequencies, however, the peak of the threshold-elevation function does not obey this rule: there is a well-established peak shift in the threshold-elevation functions toward higher spatial frequencies. We investigated whether this shift might be due to the masking effects caused by the background field, which contributes energy at the very low end of the spectrum. We first measured the effect of a 3-cycles/deg (c/deg) mask on detection of a range of test frequencies, compared with unmasked detection thresholds. We then measured the combined effect of a 2-c/deg and a 3-c/deg mask on detection, compared with detection with just the 2-c/deg mask. The comparison in the second case still tests the effect of the 3-c/deg mask, but the presence of the hidden 2-c/deg mask causes the peak masking effect to shift toward higher frequencies. This result provides a proof of concept for the hypothesis that the peak shift at low spatial frequencies is caused by the low-frequency energy in the background field, which is present in both masked and unmasked conditions. A five-parameter quantitative model of frequency masking is presented that describes the pure contrast-detection function, the frequency-masking functions at mask frequencies of 0.25, 0.5, 2, and 3 c/deg, and the peak-shift phenomenon.

Color and luminance detection and discrimination asymmetries and interactions

We investigated the nature of color and luminance processes under threshold and suprathreshold conditions in normal trichromatic observers. Detection and discrimination contours as well as threshold-vs-contrast (Tvc) functions were measured in the Derrington-Krauskopf-Lennie (DKL) color space using a masking paradigm. Such contours revealed substantial threshold asymmetries along the three cardinal axes for excursions of opposite polarity along a single axis (e.g. "red" vs "green"). The detection threshold asymmetry was significant for the "blue" and "yellow" (P < 0.05) and luminance increments and decrements (P < 0.01). For suprathreshold discrimination contours the polarity of these asymmetries reversed but remained significant for "blue" and "yellow" (P < 0.001) and luminance increments and decrements (P < 0.01). No significant differences were found between the "red" and "green" cardinal axes under either condition. The discrimination contours also indicated that suprathreshold performance had variable masking along the different axes. A characteristic Tvc curve was found in all cardinal directions except "yellow". The Tvc for "yellow" differed from the other cardinal directions by showing no masking after the initial facilitation and by giving a greater saturating response as a function of contrast. We considered whether the state of retinal adaptation had any role in producing the asymmetries.

Detection facilitation by collinear stimuli in humans: dependence on strength and sign of contrast

We measured detection of a thin vertical line (target) in the presence of a slightly thicker collinear, adjacent line (inducer). Sign and strength of contrast of the inducer were varied. Test lines could be either bright or dark. Detection thresholds were obtained through a temporal two-alternative forced-choice (2AFC) procedure with the method of constant stimuli. When target and inducer had equal contrast polarity, low thresholds of target lines were observed for low inducer contrasts and increased with increasing inducer contrast. With opposite contrast polarity of target and inducer, thresholds were high for low inducer contrasts and decreased for increasing contrast thereof. Our results support the hypothesis that cortical mechanisms with different sensitivity to the sign and strength of contrast participate in the detection facilitation of line contours.

The effect of white and filtered noise on contrast detection thresholds

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

Contrast discrimination function: spatial cuing effects

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

Fourier models and the loci of adaptation

First measures of sensitivity and the need for a model to interpret them are addressed. Then modeling in the Fourier domain is promoted by a demonstration of how much an approach explains spatial sensitization and its dependence on luminance. Then the retinal illuminance and receptor absorptions produced by various stimuli are derived to foster interpretation of the neural mechanisms underlying various psychophysical phenomena. Finally, the sequence and the anatomical loci of the processes controlling visual sensitivity are addressed. It is concluded that multiplicative adaptation often has effects identical to response compression followed by subtractive adaptation and that, perhaps as a consequence, there is no evidence of retinal gain changes in human cone vision until light levels are well above those available in natural scenes and in most contemporary psychophysical experiments; that contrast gain control fine tunes sensitivity to patterns at all luminances; and that response compression, modulated by subtractive adaptation, predominates in the control of sensitivity in human cone vision.

Implicit masking constrained by spatial inhomogeneities

Human contrast sensitivities to gratings were measured within windows of 3, 9.1 and 61.5 deg at spatial differences down to the nominal frequency of 0 c/deg (i.e., a uniform field), and the resulting curves were related to the Fourier spectra of the corresponding windows and of spatial inhomogeneities in the visual pathway. The data show that sensitivity approaches an asymptote about 1.5 log units below peak sensitivity as spatial frequency decreases, the so-called low frequency cut. Computations show that the fundamentals of the test files used here were detected and not their harmonics, and control experiments suggest that the edges of the gratings did not affect detection of the gratings. Most of the low frequency cut could be attributed to masking by the harmonics of the windows within which the gratings were introduced. The added contribution of the inhomogeneities in the retinal distribution of cones accounts for the remainder of the low frequency cut observed with the two smaller windows, and adding the effects of the inhomogeneities to the distribution of parvocellular ganglion cells accounts for the remainder of the low frequency attenuation with the largest field. Therefore, the attenuation of sensitivity to low frequencies that gives the contrast sensitivity curve its bandpass shape can be attributed entirely to implicit masking, i.e., to masking by the Fourier spectrum of the window within the test grating is presented, after further spreading by retinal inhomogeneities.

Isolation and interaction of ON and OFF pathways in human vision: contrast discrimination at pattern offset

Pattern contrast discrimination is typically studied with simultaneous onset of the base contrast (C) and added contrast (delta C) patterns. I measured contrast discrimination functions at pattern offset. A brief (30 msec) localized, spatially narrow-band D6 test stimulus was delta C. The onset of delta C was simultaneous with the offset of a large, 500 msec cosine pattern (the base contrast C). The D6 was either positive or negative contrast, and was masked by either positive or negative contrast, i.e., a light or dark bar of the cosine pattern. Stimuli were 3 cpd. Discrimination of negative delta C at the offset of positive contrast followed a "dipper" function, as if the OFF pathway were isolated. A dipper function was also obtained for a positive delta C at the offset of negative contrast (ON pathway isolation). But same-polarity delta C and C yield a monotonic discrimination function ("bumper" function) at the offset of C, suggesting inhibitory interaction. These discrimination functions for same-and opposite-polarity delta C and C are the reverse of functions obtained at pattern onset. Manipulations of temporal asynchrony between patterns and manipulations of pattern polarity are thus functionally equivalent in determining the form of the contrast discrimination function. In a second experiment, I determined delta C at times before and after the offset of a high-contrast C and manipulated pattern polarity. The time course of threshold change is different for same vs opposite-polarity test and mask. The results suggest that interaction between ON and OFF pathways is delayed relative to the masking process within a pathway. Interaction between pathways may function to improve temporal resolution by suppressing persistence of neural response in the complementary pathway. The present pattern polarity and temporal asynchrony effects on the contrast discrimination function also decisively falsify the "uncertainty" hypothesis for low-contrast threshold facilitation (the dipper).

Facilitation of luminance grating detection by induced gratings

Grating induction causes a homogeneous test field surrounded by sinewave gratings to possess an induced counterphase grating [McCourt M. E. (1982). Vision Research, 22, 119]. There is currently no consensus about the stage of visual processing at which illusory phenomena such as simultaneous brightness contrast are signaled. We measured the masking efficacy of induced gratings by measuring contrast detection thresholds for targets (sinewave luminance gratings) added in phase to both real and induced gratings which were matched in apparent contrast. At spatial frequencies below c. 0.5 c/deg, target detection and discrimination were comparably facilitated by both real and induced low-contrast pedestals (0.5-2%). At higher spatial frequencies (above 1.0 c/deg) facilitation continued to be observed for targets added in-phase to real grating pedestals, but occurred only for targets added out-of-phase with induced pedestal gratings. Higher inducing frequencies by themselves were not responsible for the observed phase shift of facilitation, however, since both real and induced pedestals produced similar target contrast discrimination functions when inducing frequency was varied by manipulating viewing distance (which holds the ratio of inducing grating period and test field height constant). The results imply the existence of at least two types of lateral interactive processes: one producing in-phase facilitation, and a second producing out-of-phase facilitation. The relative contribution of each process depends upon the ratio of inducing grating period and test field height.

Zero frequency masking and a model of contrast sensitivity

Stimulating the visual system tends to desensitize it to certain stimulus properties. Such desensitization is usually called adaptation or masking, but the distinction between the two is unclear. Nonspecific desensitization by light is usually regarded as adaptation, whereas pattern-specific desensitization is typically considered masking. Here we unify the treatment of such desensitizing phenomena by handling both in the spatial frequency domain. The amount of adapting light in a stimulus is represented in the spatial frequency domain by the component at zero frequency. To determine whether such adapting light acts like other components in the spatial frequency domain, we compared the effect of masking by the zero frequency component with the effects of masking by components at other frequencies. We show that the zero frequency component acts like other masking components, decreasing sensitivity to nearby test frequencies and thereby producing the insensitivity to low spatial frequencies that gives the contrast sensitivity curve its band-pass shape at high light levels. Treating light adaptation as masking by the zero frequency component leads to a general model that describes visual sensitivity to test gratings of varying spatial frequency at varying mean luminance, in the presence (or absence) of masking gratings of varying spatial frequency. Individual components of the model provide insight into visual processing at the system level.