Binocular summation improves performance to defocus-induced blur

PURPOSE. To assess whether there are any advantages of binocular over monocular vision under blur conditions. METHODS. We measured the effect of defocus, induced by positive lenses, on the pattern reversal Visual Evoked Potential (VEP) and on visual acuity (VA). Monocular (dominant eye) and binocular VEPs were recorded from thirteen volunteers (average age: 28±5 years, average spherical equivalent: -0.25±0.73 D) for defocus up to 2.00 D using positive powered lenses. VEPs were elicited using reversing 10 arcmin checks at a rate of 4 reversals/second. The stimulus subtended a circular field of 7 degrees with 100% contrast and mean luminance 30 cd/m2. VA was measured under the same conditions using ETDRS charts. All measurements were performed at 1m viewing distance with best spectacle sphero-cylindrical correction and natural pupils. RESULTS. With binocular stimulation, amplitudes and implicit times of the P100 component of the VEPs were greater and shorter, respectively, in all cases than for monocular stimulation. Mean binocular enhancement ratio in the P100 amplitude was 2.1 in-focus, increasing linearly with defocus to be 3.1 at +2.00 D defocus. Mean peak latency was 2.9 ms shorter in-focus with binocular than for monocular stimulation, with the difference increasing with defocus to 8.8 ms at +2.00 D. As for the VEP amplitude, VA was always better with binocular than with monocular vision, with the difference being greater for higher retinal blur. CONCLUSIONS. Both subjective and electrophysiological results show that binocular vision ameliorates the effect of defocus. The increased binocular facilitation observed with retinal blur may be due to the activation of a larger population of neurons at close-to-threshold detection under binocular stimulation.

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. © 2007 IBRO.

Binocular summation of contrast remains intact in strabismic amblyopia

PURPOSE. Strabismic amblyopia is typically associated with several visual deficits, including loss of contrast sensitivity in the amblyopic eye and abnormal binocular vision. Binocular summation ratios (BSRs) are usually assessed by comparing contrast sensitivity for binocular stimuli (sens BIN) with that measured in the good eye alone (sensGOOD), giving BSR = sensBIN/sensGOOD. This calculation provides an operational index of clinical binocular function, but does not assess whether neuronal mechanisms for binocular summation of contrast remain intact. This study was conducted to investigate this question. METHODS. Horizontal sine-wave gratings were used as stimuli (3 or 9 cyc/deg; 200 ms), and the conventional method of assessment (above) was compared with one in which the contrast in the amblyopic eye was adjusted (normalized) to equate monocular sensitivities. RESULTS. In nine strabismic amblyopes (mean age, 32 years), the results confirmed that the BSR was close to unity when the conventional method was used (little or no binocular advantage), but increased to approximately √2 or higher when the normalization method was used. The results were similar to those for normal control subjects (n = 3; mean age, 38 years) and were consistent with the physiological summation of contrast between the eyes. When the normal observers performed the experiments with a neutral-density (ND) filter in front of one eye, their performance was similar to that of the amblyopes in both methods of assessment. CONCLUSIONS. The results indicate that strabismic amblyopes have mechanisms for binocular summation of contrast and that the amblyopic deficits of binocularity can be simulated with an ND filter. The implications of these results for best clinical practice are discussed. Copyright © Association for Research in Vision and Ophthalmology.

Binocular summation at contrast threshold:a new look

Contrast sensitivity is better with two eyes than one. The standard view is that thresholds are about 1.4 (v2) times better with two eyes, and that this arises from monocular responses that, near threshold, are proportional to the square of contrast, followed by binocular summation of the two monocular signals. However, estimates of the threshold ratio in the literature vary from about 1.2 to 1.9, and many early studies had methodological weaknesses. We collected extensive new data, and applied a general model of binocular summation to interpret the threshold ratio. We used horizontal gratings (0.25 - 4 cycles deg-1) flickering sinusoidally (1 - 16 Hz), presented to one or both eyes through frame-alternating ferroelectric goggles with negligible cross-talk, and used a 2AFC staircase method to estimate contrast thresholds and psychometric slopes. Four naive observers completed 20 000 trials each, and their mean threshold ratios were 1.63, 1.69, 1.71, 1.81 - grand mean 1.71 - well above the classical v2. Mean ratios tended to be slightly lower (~1.60) at low spatial or high temporal frequencies. We modelled contrast detection very simply by assuming a single binocular mechanism whose response is proportional to (Lm + Rm) p, followed by fixed additive noise, where L,R are contrasts in the left and right eyes, and m, p are constants. Contrast-gain-control effects were assumed to be negligible near threshold. On this model the threshold ratio is 2(?1/m), implying that m=1.3 on average, while the Weibull psychometric slope (median 3.28) equals 1.247mp, yielding p=2.0. Together, the model and data suggest that, at low contrasts across a wide spatiotemporal frequency range, monocular pathways are nearly linear in their contrast response (m close to 1), while a strongly accelerating nonlinearity (p=2, a 'soft threshold') occurs after binocular summation. [Supported by EPSRC project grant GR/S74515/01]

Contrast masking in strabismic amblyopia: attenuation, noise, interocular suppression and binocular summation

To investigate amblyopic contrast vision at threshold and above we performed pedestal-masking (contrastdiscrimination) experiments with a group of eight strabismic amblyopes using horizontal sinusoidal gratings (mainly 3 c/deg) in monocular, binocular and dichoptic configurations balanced across eye (i.e. five conditions). With some exceptions in some observers, the four main results were as follows. (1) For the monocular and dichoptic conditions, sensitivity was less in the amblyopic eye than in the good eye at all mask contrasts. (2) Binocular and monocular dipper functions superimposed in the good eye. (3) Monocular masking functions had a normal dipper shape in the good eye, but facilitation was diminished in the amblyopic eye. (4) A less consistent result was normal facilitation in dichoptic masking when testing the good eye, but a loss of this when testing the amblyopic eye. This pattern of amblyopic results was replicated in a normal observer by placing a neutral density filter in front of one eye. The two-stage model of binocular contrast gain control [Meese, T.S., Georgeson, M.A. & Baker, D.H. (2006). Binocular contrast vision at and above threshold. Journal of Vision 6, 1224--1243.] was `lesioned' in several ways to assess the form of the amblyopic deficit. The most successful model involves attenuation of signal and an increase in noise in the amblyopic eye, and intact stages of interocular suppression and binocular summation. This implies a behavioural influence from monocular noise in the amblyopic visual system as well as in normal observers with an ND filter over one eye.

Neuronal convergence in early contrast vision: binocular summation is followed by response nonlinearity and area summation

We assessed summation of contrast across eyes and area at detection threshold ( C t). Stimuli were sine-wave gratings (2.5 c/deg) spatially modulated by cosine- and anticosine-phase raised plaids (0.5 c/deg components oriented at ±45°). When presented dichoptically the signal regions were interdigitated across eyes but produced a smooth continuous grating following their linear binocular sum. The average summation ratio ( C t1/([ C t1+2]) for this stimulus pair was 1.64 (4.3 dB). This was only slightly less than the binocular summation found for the same patch type presented to both eyes, and the area summation found for the two different patch types presented to the same eye. We considered 192 model architectures containing each of the following four elements in all possible orders: (i) linear summation or a MAX operator across eyes, (ii) linear summation or a MAX operator across area, (iii) linear or accelerating contrast transduction, and (iv) additive Gaussian, stochastic noise. Formal equivalences reduced this to 62 different models. The most successful four-element model was: linear summation across eyes followed by nonlinear contrast transduction, linear summation across area, and late noise. Model performance was enhanced when additional nonlinearities were placed before binocular summation and after area summation. The implications for models of probability summation and uncertainty are discussed.

Binocular summation, binocular fusion and the transition to diplopia

The visual system combines spatial signals from the two eyes to achieve single vision. But if binocular disparity is too large, this perceptual fusion gives way to diplopia. We studied and modelled the processes underlying fusion and the transition to diplopia. The likely basis for fusion is linear summation of inputs onto binocular cortical cells. Previous studies of perceived position, contrast matching and contrast discrimination imply the computation of a dynamicallyweighted sum, where the weights vary with relative contrast. For gratings, perceived contrast was almost constant across all disparities, and this can be modelled by allowing the ocular weights to increase with disparity (Zhou, Georgeson & Hess, 2014). However, when a single Gaussian-blurred edge was shown to each eye perceived blur was invariant with disparity (Georgeson & Wallis, ECVP 2012) – not consistent with linear summation (which predicts that perceived blur increases with disparity). This blur constancy is consistent with a multiplicative form of combination (the contrast-weighted geometric mean) but that is hard to reconcile with the evidence favouring linear combination. We describe a 2-stage spatial filtering model with linear binocular combination and suggest that nonlinear output transduction (eg. ‘half-squaring’) at each stage may account for the blur constancy.

Binocular combination at threshold: temporal filtering and summation of signals in separate ON and OFF channels

How does the brain combine spatio-temporal signals from the two eyes? We quantified binocular summation as the improvement in 2AFC contrast sensitivity for flickering gratings seen by two eyes compared with one. Binocular gratings in-phase showed sensitivity up to 1.8 times higher, suggesting nearly linear summation of contrasts. The binocular advantage decreased to 1.4 at lower spatial and higher temporal frequencies (0.25 cycle deg-1, 30 Hz). Dichoptic, antiphase gratings showed only a small binocular advantage, by a factor of 1.1 to 1.2, but no evidence of cancellation. We present a signal-processing model to account for the contrast-sensitivity functions and the pattern of binocular summation. It has linear sustained and transient temporal filters, nonlinear transduction, and half-wave rectification that creates ON and OFF channels. Binocular summation occurs separately within ON and OFF channels, thus explaining the phase-specific binocular advantage. The model also accounts for earlier findings on detection of brief antiphase flashes and the surprising finding that dichoptic antiphase flicker is seen as frequency-doubled (Cavonius et al, 1992 Ophthalmic and Physiological Optics 12 153 - 156). [Supported by EPSRC project GR/S74515/01].

Linear binocular combination of responses to contrast modulation:contrast-weighted summation in first- and second-order vision

Binocular combination for first-order (luminancedefined) stimuli has been widely studied, but we know rather little about this binocular process for spatial modulations of contrast (second-order stimuli). We used phase-matching and amplitude-matching tasks to assess binocular combination of second-order phase and modulation depth simultaneously. With fixed modulation in one eye, we found that binocularly perceived phase was shifted, and perceived amplitude increased almost linearly as modulation depth in the other eye increased. At larger disparities, the phase shift was larger and the amplitude change was smaller. The degree of interocular correlation of the carriers had no influence. These results can be explained by an initial extraction of the contrast envelopes before binocular combination (consistent with the lack of dependence on carrier correlation) followed by a weighted linear summation of second-order modulations in which the weights (gains) for each eye are driven by the first-order carrier contrasts as previously found for first-order binocular combination. Perceived modulation depth fell markedly with increasing phase disparity unlike previous findings that perceived first-order contrast was almost independent of phase disparity. We present a simple revision to a widely used interocular gain-control theory that unifies first- and second-order binocular summation with a single principle-contrast-weighted summation-and we further elaborate the model for first-order combination. Conclusion: Second-order combination is controlled by first-order contrast.

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. © 2006 ARVO.

Binocular interaction:Contrast matching and contrast discrimination are predicted by the same model

How do signals from the 2 eyes combine and interact? Our recent work has challenged earlier schemes in which monocular contrast signals are subject to square-law transduction followed by summation across eyes and binocular gain control. Much more successful was a new 'two-stage' model in which the initial transducer was almost linear and contrast gain control occurred both pre- and post-binocular summation. Here we extend that work by: (i) exploring the two-dimensional stimulus space (defined by left- and right-eye contrasts) more thoroughly, and (ii) performing contrast discrimination and contrast matching tasks for the same stimuli. Twenty-five base-stimuli made from 1 c/deg patches of horizontal grating, were defined by the factorial combination of 5 contrasts for the left eye (0.3-32%) with five contrasts for the right eye (0.3-32%). Other than in contrast, the gratings in the two eyes were identical. In a 2IFC discrimination task, the base-stimuli were masks (pedestals), where the contrast increment was presented to one eye only. In a matching task, the base-stimuli were standards to which observers matched the contrast of either a monocular or binocular test grating. In the model, discrimination depends on the local gradient of the observer's internal contrast-response function, while matching equates the magnitude (rather than gradient) of response to the test and standard. With all model parameters fixed by previous work, the two-stage model successfully predicted both the discrimination and the matching data and was much more successful than linear or quadratic binocular summation models. These results show that performance measures and perception (contrast discrimination and contrast matching) can be understood in the same theoretical framework for binocular contrast vision. © 2007 VSP.

Nonlinearities in the binocular combination of luminance and contrast

We studied the rules by which visual responses to luminous targets are combined across the two eyes. Previous work has found very different forms of binocular combination for targets defined by increments and by decrements of luminance, with decrement data implying a severe nonlinearity before binocular combination. We ask whether this difference is due to the luminance of the target, the luminance of the background, or the sign of the luminance excursion. We estimated the pre-binocular nonlinearity (power exponent) by fitting a computational model to ocular equibrightness matches. The severity of the nonlinearity had a monotonic dependence on the signed difference between target and background luminance. For dual targets, in which there was both a luminance increment and a luminance decrement (e.g. contrast), perception was governed largely by the decrement. The asymmetry in the nonlinearities derived from the subjective matching data made a clear prediction for visual performance: there should be more binocular summation for detecting luminance increments than for detecting luminance decrements. This prediction was confirmed by the results of a subsequent experiment. We discuss the relation between these results and luminance nonlinearities such as a logarithmic transform, as well as the involvement of contemporary model architectures of binocular vision.

Suppression and summation in contrast gain control for human vision

Over the last ten years our understanding of early spatial vision has improved enormously. The long-standing model of probability summation amongst multiple independent mechanisms with static output nonlinearities responsible for masking is obsolete. It has been replaced by a much more complex network of additive, suppressive, and facilitatory interactions and nonlinearities across eyes, area, spatial frequency, and orientation that extend well beyond the classical recep-tive field (CRF). A review of a substantial body of psychophysical work performed by ourselves (20 papers), and others, leads us to the following tentative account of the processing path for signal contrast. The first suppression stage is monocular, isotropic, non-adaptable, accelerates with RMS contrast, most potent for low spatial and high temporal frequencies, and extends slightly beyond the CRF. Second and third stages of suppression are difficult to disentangle but are possibly pre- and post-binocular summation, and involve components that are scale invariant, isotropic, anisotropic, chromatic, achromatic, adaptable, interocular, substantially larger than the CRF, and saturated by contrast. The monocular excitatory pathways begin with half-wave rectification, followed by a preliminary stage of half-binocular summation, a square-law transducer, full binocular summation, pooling over phase, cross-mechanism facilitatory interactions, additive noise, linear summation over area, and a slightly uncertain decision-maker. The purpose of each of these interactions is far from clear, but the system benefits from area and binocular summation of weak contrast signals as well as area and ocularity invariances above threshold (a herd of zebras doesn't change its contrast when it increases in number or when you close one eye). One of many remaining challenges is to determine the stage or stages of spatial tuning in the excitatory pathway.

Interocular masking and summation indicate two stages of divisive contrast gain control

Our understanding of early spatial vision owes much to contrast masking and summation paradigms. In particular, the deep region of facilitation at low mask contrasts is thought to indicate a rapidly accelerating contrast transducer (eg a square-law or greater). In experiment 1, we tapped an early stage of this process by measuring monocular and binocular thresholds for patches of 1 cycle deg-1 sine-wave grating. Threshold ratios were around 1.7, implying a nearly linear transducer with an exponent around 1.3. With this form of transducer, two previous models (Legge, 1984 Vision Research 24 385 - 394; Meese et al, 2004 Perception 33 Supplement, 41) failed to fit the monocular, binocular, and dichoptic masking functions measured in experiment 2. However, a new model with two-stages of divisive gain control fits the data very well. Stage 1 incorporates nearly linear monocular transducers (to account for the high level of binocular summation and slight dichoptic facilitation), and monocular and interocular suppression (to fit the profound 42 Oral presentations: Spatial vision Thursday dichoptic masking). Stage 2 incorporates steeply accelerating transduction (to fit the deep regions of monocular and binocular facilitation), and binocular summation and suppression (to fit the monocular and binocular masking). With all model parameters fixed from the discrimination thresholds, we examined the slopes of the psychometric functions. The monocular and binocular slopes were steep (Weibull ߘ3-4) at very low mask contrasts and shallow (ߘ1.2) at all higher contrasts, as predicted by all three models. The dichoptic slopes were steep (ߘ3-4) at very low contrasts, and very steep (ß>5.5) at high contrasts (confirming Meese et al, loco cit.). A crucial new result was that intermediate dichoptic mask contrasts produced shallow slopes (ߘ2). Only the two-stage model predicted the observed pattern of slope variation, so providing good empirical support for a two-stage process of binocular contrast transduction. [Supported by EPSRC GR/S74515/01]

Binocular contrast interactions:Dichoptic masking is not a single process

To decouple interocular suppression and binocular summation we varied the relative phase of mask and target in a 2IFC contrast-masking paradigm. In Experiment I, dichoptic mask gratings had the same orientation and spatial frequency as the target. For in-phase masking, suppression was strong (a log-log slope of ∼1) and there was weak facilitation at low mask contrasts. Anti-phase masking was weaker (a log-log slope of ∼0.7) and there was no facilitation. A two-stage model of contrast gain control [Meese, T.S., Georgeson, M.A. and Baker, D.H. (2006). Binocular contrast vision at and above threshold. Journal of Vision, 6: 1224-1243] provided a good fit to the in-phase results and fixed its free parameters. It made successful predictions (with no free parameters) for the anti-phase results when (A) interocular suppression was phase-indifferent but (B) binocular summation was phase sensitive. Experiments II and III showed that interocular suppression comprised two components: (i) a tuned effect with an orientation bandwidth of ∼±33° and a spatial frequency bandwidth of >3 octaves, and (ii) an untuned effect that elevated threshold by a factor of between 2 and 4. Operationally, binocular summation was more tightly tuned, having an orientation bandwidth of ∼±8°, and a spatial frequency bandwidth of ∼0.5 octaves. Our results replicate the unusual shapes of the in-phase dichoptic tuning functions reported by Legge [Legge, G.E. (1979). Spatial frequency masking in human vision: Binocular interactions. Journal of the Optical Society of America, 69: 838-847]. These can now be seen as the envelope of the direct effects from interocular suppression and the indirect effect from binocular summation, which contaminates the signal channel with a mask that has been suppressed by the target. © 2007 Elsevier Ltd. All rights reserved.