Inverse modeling of human contrast response

Mathematical singularities found in the Signal Detection Theory (SDT) based analysis of the 2-Alternative-Forced-Choice (2AFC) method [Katkov, M., Tsodyks, M., & Sagi, D. (2006a). Analysis of two-alternative force-choice Signal Detection Theory model. Journal of Mathematical Psychology, 50, 411-420; Katkov, M., Tsodyks, M., & Sagi, D. (2006b). Singularities in the inverse modeling of 2AFC contrast discrimination data. Vision Research, 46, 256-266; Katkov, M., Tsodyks, M., & Sagi, D. (2007). Singularities explained: Response to Klein. Vision Research, doi:10.1016/j.visres.2006.10.030] imply that contrast discrimination data obtained with the 2AFC method cannot always be used to reliably estimate the parameters of the underlying model (internal response and noise functions) with a reasonable number of trials. Here we bypass this problem with the Identification Task (IT) where observers identify one of N contrasts. We have found that identification data varies significantly between experimental sessions. Stable estimates using individual session data showed Contrast Response Functions (CRF) with high gain in the low contrast regime and low gain in the high contrast regime. Noise Amplitudes (NA) followed a decreasing function of contrast at low contrast levels, and were practically constant above some contrast level. The transition between these two regimes corresponded approximately to the position of the dipper in the Threshold versus Contrast (TvC) curves that were computed using the estimated parameters and independently measured using 2AFC.     

A local measure for modeling contrast discrimination: response to Katkov, Tsodyks and Sagi

Katkov, et al. [Katkov, M., Tsodyks, M., & Sagi, D. (2007). Singularities explained: Response to Klein. Vision Research, preceding article] commented on my comments [Klein, S. A. (2006). Separating transducer nonlinearities and multiplicative noise in contrast discrimination. Vision Research, 46, 4279-4293] regarding fitting the Kontsevich, et al. [Kontsevich, L. L., Chen, C. C., & Tyler, C. W. (2002). Separating the effects of response nonlinearity and internal noise psychophysically. Vision Research, 42, 1771-1784] contrast discrimination data. Klein [Klein, S. A. (2006). Separating transducer nonlinearities and multiplicative noise in contrast discrimination. Vision Research, 46, 4279-4293] focused on the question of whether the singularity associated with the constant noise model makes it difficult to reject that model. The present paper acknowledges the presence of a singularity but shows that even in the presence of a strong singularity and using a reasonable number of 2AFC trials, it is possible to not only reject the constant noise hypothesis, but also to place confidence limits on estimates of the magnitude of the multiplicative noise. Our analysis is based on measuring contrast discrimination among triplet of contrast levels.     

Perceptual learning in contrast discrimination and the (minimal) role of context

Unlike most visual tasks, contrast discrimination has been reported to be unchanged by practice (Dorais & Sagi, 1997; Adini, Sagi, & Tsodyks, 2002), unless practice is undertaken in the presence of flankers (context-enabled learning, Adini et al., 2002). Here we show that under experimental conditions nearly identical to those in the no-flanker practice experiment of Adini et al. (2002), practice significantly improved contrast discrimination. Moreover, in a separate experiment, we found that practice without flankers can improve contrast discrimination to a level only reached with flankers in Adini et al. (2002), but further practice with flankers produces no further improvement of contrast discrimination. These results call into question whether the "context-enabled learning" proposed by Adini et al. (2002) is different from regular contrast learning without flankers. In separate experiments, we found that contrast learning is tuned to spatial frequency, orientation, retinal location, and, unexpectedly, contrast. We also replicated Sagi, Adini, Tsodyks, and Wilkonsky's (2003) more recent finding that no regular contrast learning occurs if reference contrasts are randomly interleaved (contrast roving), and further demonstrated that flankers have no effect on contrast learning under contrast roving, another piece of evidence equating "context-enabled learning" to regular contrast learning. The contrast specificity of learning and the lack of learning under contrast roving provide new evidence in favor of a multiple contrast-selective channels model of contrast discrimination, and against saturating transducer models and multiplicative noise models.     

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 observer's 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.     

Probability summation for multiple patches of luminance modulation

When components of a compound pattern stimulate different visual mechanisms, psychophysical performance typically improves by a small amount consistent with probability summation amongst independent detectors. Here we extend previous summation experiments by (i) plotting full psychometric functions; and (ii) using compound stimuli with components that varied in up to three stimulus dimensions: spatial frequency (1, 4, 5 or 11 c/deg), orientation (0 degrees, +/-45 degrees ), and position. Stimulus components were isolated circular sine-phase patches of grating centred on up to four corners of an imaginary square surrounding a fixation-point. Combinations of component patches produced compound stimuli made from up to 16 components that differed in various combinations of the three stimulus dimensions. Other than when the spatial frequency was 11 c/deg, results were well described using: (i) probabilistic summation of individual psychometric functions; (ii) the Quick pooling formula; and (iii) the signal detection analysis for 2IFC developed by Tyler and Chen (2000) [Signal detection theory in the 2AFC paradigm: attention, channel uncertainty and probability summation (under review)]. We conclude that in general, nonlinear spatial summation is consistent with probabilistic summation across independent detecting mechanisms that vary in spatial frequency (a range of at least 1-5 c/deg), orientation (a range of 90 degrees ) and position (a range of at least 24 cycles at 4 c/deg). In further experiments, results were found to be consistent with probability summation for pairs of orthogonally oriented step-edge stimuli and a matrix of randomly oriented 11 c/deg sine-wave patches. This casts doubt on the generality of a recent suggestion that local interactions between colinearly oriented detectors within a spatial neighbourhood of around four cycles may contribute to nonlinear spatial summation [Bonneh & Sagi, 1998; Vision Research, 38, 3541-3553].     

Why luminance discrimination may be better than detection

Signal Detection Theory (SDT) predicts that the presence of uncertainty will diminish the observer's sensitivity to visual signals, and increase the exponent of the psychometric function. The first prediction has been confirmed previously with spatial and chromatic uncertainty. The second prediction is confirmed in this paper.The psychometric function is commonly found to be a positive accelerating function of intensity. This has been explained by two competing theories: the uncertainty hypothesis and the nonlinear transducer theory.A second experiment is conducted to distinguish between these theories. The results of this experiment are inconsistent with the nonlinear transducer theory.     

Combining cues in contour orientation discrimination

The perceived orientation of a Gabor-patch contour is determined, in part, by shifts in carrier phase between the patches [Popple, A. V. & Sagi, D., 2000. A Fraser illusion without local cues? Vision Research, 40, 873-878; Popple, A. V. & Levi, D. M., 2000a. A new illusion demonstrates long-range processing. Vision Research, 40, 2545-2549; Popple, A. V. & Levi, D. M., 2000b. Amblyopes see true alignment where normal observers see illusory tilt. Proceedings of the National Academy of Sciences of the United States of America, 97, 11667-11672]. Here we show that perceived orientation results from the combination of at least three stimulus cues: (1) patch orientation, (2) contour envelope orientation, and (3) between-patches orientation, which is a function of phase-shifts. In a series of three experiments, we investigated how these three cues were combined. The data are consistent with weighted cue combination.     

Sensory and decisional factors in motion-induced blindness

The processes underlying motion-induced blindness (MIB) are widely debated. Ultimately, however, they must reduce to a sensitivity drop and/or to an upward shift of the decision criterion. The first possibility was tested by assessing the detection threshold for a contrast (or luminance) increment applied to the MIB target under its visible and suppressed phases. This was performed over a whole range of reference target contrasts (yielding the standard Threshold vs. Contrast [TvC] function) with a 2AFC staircase procedure. The second possibility was tested with a Yes/No procedure, allowing the assessment of both the sensitivities (d') and decision criteria (c) yielded by four contrast increments applied to a fixed reference target contrast (the psychometric function). The 2AFC procedure yielded a global upward shift of the TvC function of about 5.3 dB (a factor of 1.84) under the suppressed phase. The Yes/No procedure yielded a commensurate d' drop (of about 0.8 sigma) under the suppressed phase with no change in the slope of the psychometric function and an upward shift of c of about 0.7 sigma. The presently observed vertical shift (in log-log coordinates) of the TvC function in the suppressed phase is indicative of a divisive inhibition occurring after the transducing stage. The invariance of the psychometric function slope under the visible and suppressed MIB phases supports this conclusion. The present experiments cannot settle the issue of whether the upward shift of the decision criteria is yet another cause of the MIB or a consequence of its underlying inhibitory process. Instead, they make clear that MIB (and perhaps other unstable perceptual phenomena) is associated with both sensory and decisional processes.     

Concurrent measurement of perceived speed and speed discrimination threshold using the method of single stimuli

Velocity matching using the method of Constant Stimuli shows that perceived velocity varies with contrast [Thompson, P. (1982). Perceived rate of movement depends upon contrast. Vision Research, 22, 377-380]. Random contrast jitter would therefore be expected to increase the slopes of psychometric functions, and thus the velocity discrimination threshold. However, McKee, S., Silverman, G., and Nakayama, K. [(1986) Precise velocity discrimination despite random variation in temporal frequency. Vision Research, 26, 609-620] found no effect of contrast jitter on thresholds, using the method of single stimuli. To determine whether this apparent discrepancy is due to the difference in methodology, or to the different ranges of temporal frequencies used in the two studies, we used the method of single stimuli to measure psychometric functions at three different velocities (0.5, 2.0 and 4.0 degrees/s). We found that contrast jitter increased thresholds at low but not at high velocities. Separate analysis of the psychometric functions at each contrast level showed that increases in contrast increased perceived velocity at low standard speeds (0.5 degree/s) but not at high. We conclude that the effect of contrast on perceived speed is real, and not a methodological artefact, but that it is found only at low temporal frequencies.     

Stereopsis-dependent deficits in maximum motion displacement in strabismic and anisometropic amblyopia

Direction discrimination thresholds for maximum motion displacement (D(max)) have been previously reported to be abnormal in amblyopic children [Ho, C. S., Giaschi, D. E., Boden, C., Dougherty, R., Cline, R., & Lyons, C. (2005). Deficient motion perception in the fellow eye of amblyopic children. Vision Research, 45, 1615-1627; Ho, C. S., & Giaschi, D. E. (2006). Deficient maximum motion displacement in amblyopia. Vision Research, 46, 4595-4603]. We looked at D(max) thresholds for random dot kinematograms (RDKs) biased toward low- or high-level motion mechanisms. D(max) is thought to be limited, for high-level motion mechanisms, by the efficiency of object feature tracking and probability of false matches. To reduce the influence of low-level mechanisms, we determined thresholds also for a high-pass filtered version of the RDKs. Performance did not significantly differ between strabismic and anisometropic groups with amblyopia, although both groups performed significantly worse than the age-matched control group. D(max) thresholds were higher for children with poor stereoacuity. This was significant in both anisometropic and strabismic groups, and more robust for high-pass filtered RDKs than for unfiltered RDKs. The results imply that impairment of the extra-striate dorsal stream is a likely part of the neural deficit underlying both strabismic and anisometropic amblyopia. This deficit appears to be more dependent on extent of binocularity than etiology. Our findings suggest a possible relationship between fine stereopsis, coarse stereopsis, and motion correspondence mechanisms.     

Binocular contrast detection with unequal monocular illuminance

Binocular summation was measured in eight normal subjects by means of psychometric functions for contrast detection. An average 47% increase in binocular over monocular performance was obtained. Our data agreed with the simple summation model of Signal Detection Theory (Legge, 1984). Binocular psychometric functions were also measured when the sensitivity of one eye was decreased by means of a 1.0 neutral density (ND) filter. We found that binocular detectability in this case was reduced to below that of the better eye. This binocular inhibition was seen in all subjects. The slope of a contrast detection function gives a measure of the rate of change in detectability with contrast. If the slopes of two functions are equal, then the difference in detectability between these functions remains constant for all the contrast values used. When the slopes of the measured functions were analysed, no significant differences were found under any of the testing conditions. This indicates that the magnitude of summation (with equal monocular sensitivities), and of inhibition (with unequal monocular sensitivities), remains constant across the range of stimulus contrasts. The clinical implications of binocular inhibition are discussed.     

Learning motion discrimination with suppressed and un-suppressed MT

Perceptual learning of motion direction discrimination is generally thought to rely on the middle temporal area of the brain (MT/V5). A recent study investigating learning of motion discrimination when MT was psychophysically suppressed found that learning was possible with suppressed MT, but only when the task was sufficiently easy [Lu, H., Qian, N., Liu, Z. (2004). Learning motion discrimination with suppressed MT. Vision Research 44, 1817-1825]. We investigated whether this effect was indeed due to MT suppression or whether it could be explained by task difficulty alone. By comparing learning of motion discrimination when MT was suppressed vs. un-suppressed, at different task difficulties, we found that task difficulty alone could not explain the effects. At the highest difficulty, learning was not possible with suppressed MT, confirming [Lu, H., Qian, N., Liu, Z. (2004). Learning motion discrimination with suppressed MT. Vision Research 44, 1817-1825]. In comparison, learning was possible with un-suppressed MT at the same difficulty level. At the intermediate task difficulty, there was a clear learning disadvantage when MT was suppressed. Only for the easiest level of difficulty, did learning become equally possible for both suppressed and un-suppressed conditions. These findings suggest that MT plays an important role in learning to discriminate relatively fine differences in motion direction.     

Concordant eye movement and motion parallax asymmetries in esotropia

The role of eye movements in the perception of depth from motion was investigated in esotropia. Elevated motion parallax thresholds have been shown in strabismus [Thompson, A. M., & Nawrot, M. (1999). Abnormal depth perception from motion parallax in amblyopic observers. Vision Research, 39, 1407-1413] suggesting a global deficit in depth perception involving both stereopsis and motion. However, this motion parallax deficit in strabismus might be better explained by the role that eye movements play in motion parallax [Nawrot, M., & Joyce, L. (2006). The pursuit theory of motion parallax. Vision Research, 46, 4709-4725]. Esotropia is associated with asymmetric pursuit and optokinetic response eye movements [Demer, J. L., & von Noorden, G. K. (1988). Optokinetic asymmetry in esotropia. Journal of Pediatric Ophthalmology and Strabismus, 25, 286-292; Schor, C. M., & Levi, D. M. (1980). Disturbances of small-field horizontal and vertical optokinetic nystagmus in amblyopia. Investigative Ophthalmology and Visual Science, 19, 851-864; Tychsen, L., & Lisberger, S. G. (1986). Maldevelopment of visual motion processing in humans who had strabismus with onset in infancy. The Journal of Neuroscience, 6, 2495-2508; [Westall, C. A., Eizenman, M., Kraft, S. P., Panton, C. M., Chatterjee, S., & Sigesmund, D. (1998). Cortical binocularity and monocular optokinetic asymmetry in early-onset esotropia. Investigative Ophthalmology and Visual Science, 39, 1352-1360.]. The first experiment demonstrates that the motion parallax deficit in esotropia mirrors the pursuit eye movement asymmetry: in the direction of normal pursuit, esotropic observers had normal depth from motion parallax. A second set of experiments, conducted in normal observers, demonstrates that this motion parallax deficit is not a secondary problem due to the retinal slip created by inadequate pursuit. These results underscore the role of pursuit eye movements in the perception of depth from motion parallax.     

The effect of spatial layout on motion segmentation

We present a series of experiments exploring the effect of the stimulus spatial configuration on speed discrimination and two different types of segmentation, for random dot patterns. In the first experiment, we find that parsing the image produces a decrease of speed discrimination thresholds such as was first shown by Verghese and Stone [Verghese, P., & Stone, L. (1997). Spatial layout affects speed discrimination threshold. Vision Research, 37(4), 397-406; Verghese, P., & Stone, L. S. (1996). Perceived visual speed constrained by image segmentation. Nature, 381, 161-163] for sinusoidal gratings. In the second experiment, we study how the spatial configuration affects the ability of a subject in localizing an illusory contour defined by two surfaces with different speeds. Results show that the speed difference necessary to localize the contour decreases as the stimulus patches are separated. The third experiment involves transparency. Our results show a little or null effect for this condition. We explain the first and second experiment in the framework of the model of Bravo and Watamaniuk [Bravo, M., & Watamaniuk, S. (1995). Evidence for two speed signals: a coarse local signal for segregation and a precise global signal for discrimination. Vision Research, 35(12), 1691-1697] who proposed that motion computation consists in, at least, two stages: a first computation of coarse local speeds followed by an integration stage. We propose that the more precise estimate of speed obtained from the integration stage is used to produce a new refined segmentation of the image perhaps, through a feedback loop. Our data suggest that this third stage would not apply to the processing of transparency.     

Accuracy of identification of grating contrast by human observers: Bayesian models of V1 contrast processing show correspondence between discrimination and identification performance

This paper presents the results of a contrast identification study, where accuracy in identification is quantified as mutual information between stimulus contrast and observer's response. The stimulus was a set of 2-8 gratings, spanning the range of visible contrasts. Gratings from the set were presented individually for 500 ms, and the observer had to respond by giving the number label corresponding to the contrast of the grating presented. Mutual information increased with set size up to a maximum of around 2.35 bits, i.e., only 5 clearly identifiable contrasts. Set sizes greater than 5 showed a plateau or decline in performance. These data were well fit by Bayesian models of V1 contrast coding, with the parameters obtained by fitting the contrast discrimination results of Chirimuuta and Tolhurst [Chirimuuta, M., & Tolhurst, D. J. (2005). Does a Bayesian model of V1 contrast coding offer a neurophysiological account of human contrast discrimination? Vision Research].     

Attentional shifts between surfaces: effects on detection and early brain potentials

Two consecutive events transforming the same illusory surface in transparent motion (brief changes in direction) can be discriminated with ease, but a prolonged interference ( approximately 500 ms) on the discrimination of the second event arises when different surfaces are concerned [Valdes-Sosa, M., Cobo, A., & Pinilla, T. (2000). Attention to object files defined by transparent motion. Journal of Experimental Psychology: Human Perception and Performance, 26(2), 488-505]. Here we further characterise this phenomenon and compare it to the attentional blink AB [Shapiro, K.L., Raymond, J.E., & Arnell, K.M. (1994). Attention to visual pattern information produces the attentional blink in RSVP. Journal of Experimental Psychology: Human Perception and Performance, 20, 357-371]. Similar to the AB, reduced sensitivity (d') was found in the two-surface condition. However, the two-surface cost was associated with a reduced N1 brain response in contrast to reports for AB [Vogel, E.K., Luck, S.J., & Shapiro, K. (1998). Electrophysiological evidence for a postperceptual locus of suppression during the attentional blink. Journal of Experimental Psychology: Human Perception and Performance, 24(6), 1656-1674]. The results from this study indicate that the two-surface cost corresponds to competitive effects in early vision. Reasons for the discrepancy with the AB study are considered.     

Two cases requiring external reinforcement in perceptual learning

The role of external reinforcement is an issue of much debate and uncertainty in perceptual learning research. Although it is commonly acknowledged that external reinforcement, such as performance feedback, can aid in perceptual learning (M. H. Herzog & M. Fahle, 1997), there are many examples in which it is not required (K. Ball & R. Sekuler, 1987; M. Fahle, S. Edelman, & T. Poggio, 1995; A. Karni & D. Sagi, 1991; S. P. McKee & G. Westheimer, 1978; L. P. Shiu & H. Pashler, 1992). Additionally, learning without external reinforcement can occur even for stimuli that are irrelevant to the subject's task (A. R. Seitz & T. Watanabe, 2003). It has been thus hypothesized that internal reinforcement can serve a similar role as external reinforcement in learning (M. H. Herzog & M. Fahle, 1998; A. Seitz & T. Watanabe, 2005). This idea suggests that perceptual learning should occur in the absence of external reinforcement provided that easy exemplars are utilized as a basis for the subject to generate internal reinforcement. Here, we report results from two studies that show that this is not always the case. In the first study, subjects participated in two sessions of a motion direction discrimination task with low-contrast dots moving in directions separated by 90 degrees. In the second study, subjects participated in 12 orientation-discrimination sessions using oriented bars (oriented either 70 degrees or 110 degrees) that were masked by spatial noise. Trials of different signal levels (yielding psychometric functions ranging from chance to ceiling) were randomly interleaved. In both studies, subjects experiencing external reinforcement showed significant learning, whereas subjects receiving no external reinforcement failed to show learning. We conclude that while internal reinforcement is an important learning signal, the presence of easy exemplars is not sufficient to generate reinforcement signals.     

Naming versus matching and the stability of unique hues

It is known that there is a distortion of hue and saturation in the peripheral visual field. In a previous study, when an asymmetric matching paradigm was used, four hues in the blue, red, yellow and green regions of colour space were unchanged and these were referred to as peripherally invariant (Parry et al., J Opt Soc Am A, 23, 2006, 1586). Three of these invariant hues were similar to unique blue, red and yellow. However, for most observers there was a marked difference between unique and invariant green. To investigate this apparent paradox, we have measured unique hues using a range of eccentricities and colourimetric purities. An asymmetric matching and a 4‐AFC paradigm were used to establish peripherally invariant and unique hues, respectively. In the asymmetric matching task the observer matched a peripheral spot with a para‐foveal spot, for 24 different hues at 18° eccentricity. In the 4‐AFC paradigm, 41 hues were presented 20 times at three purities (0.5, 0.75 and 1.0) and three eccentricities (18°, 10° and 1°). The observer had to name the hues as red, blue, green or yellow. Unique hues were found to be constant with eccentricity and purity. The unique green, established with 4‐AFC, was found to differ from the invariant green, determined using the matching task. However, red, blue and yellow invariant hues correspond well with unique hues. The data suggest that different mechanisms mediate the matching of green compared with the identification of unique hues. This is similar to the difference between detection and discrimination of spectral stimuli: the detection process is dominated by the cone opponent mechanisms and is most sensitive, whereas more central processes, serving unique hues, influence discrimination.