Dr Daniel Baker

Published conference abstracts (25)

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• Baker, Meese, Georgeson & Hess (2011). How much of noise masking derives from noise? Perception, 40(S): 51.

In masking studies, external luminance noise is often used to estimate an observer’s level of internal (neural) noise. However, the standard noise model fails three important empirical tests: noise does not fully linearise the slope of the psychometric function, masking occurs even when the noise is identical in both 2AFC intervals, and double pass consistency is too low. This implies the involvement of additional processes such as suppression from contrast gain control or increased uncertainty, either of which invalidate estimates of equivalent internal noise. We propose that jittering the target contrast (cf Cohn, 1976 Journal of the Optical Society of America 66 1426–1428) provides a ’cleaner’ source of noise because it excites only the detecting mechanism. We compare the jitter condition to masking from 1D and 2D (white and pink) pixel noise, pedestals and orthogonal masks, in double pass masking and (novel) contrast matching experiments. The results show that contrast jitter produced the strongest masking, greatest double pass consistency, and no suppression of perceived contrast: just as the standard model of noise masking predicts (and unlike pixel noise). We attribute the remainder of the masking from pixel noise to contrast gain control, raising concerns about its use in equivalent noise masking experiments.

• Baker & Meese (2011). Varying extrinsic uncertainty affects the slope and position of the psychometric function for contrast detection and contrast discrimination. Perception, 40: 113.

The slope of the psychometric function for contrast detection is controlled by nonlinear contrast transduction or uncertainty, or a combination of the two. For contrast discrimination, the pedestal removes intrinsic uncertainty, and contrast gain control reduces the effective exponent; both processes result in a shallower slope of the psychometric function. Manipulating extrinsic uncertainty experimentally should affect both threshold and slope but, despite its theoretical importance, this test has not been performed previously at both detection threshold and above. Here we manipulated spatial uncertainty for detection and discrimination of a pair of horizontal 4 cycles deg-1 Gabor patches placed equidistant from a central fixation point on the circumference of a virtual circle. In a temporal 2AFC paradigm, there were 1, 2, 4, or 8 possible locations for the target pairs, indicated by low contrast rings. The level of uncertainty was fixed within a block of trials, with target contrast levels determined by the method of constant stimuli. For contrast discrimination, the experiment was identical except that pedestals were presented in all locations on every trial. Thresholds and slopes increased with extrinsic uncertainty for both detection and discrimination. However, the threshold effect was greater for discrimination than for detection, confirming our prediction that intrinsic uncertainty is greater at threshold than above. We report estimated levels of intrinsic uncertainty for a range of transducer exponents (1: 3). A detailed understanding of the effects of intrinsic and extrinsic uncertainty are critical for examining effects such as collinear facilitation, for which uncertainty reduction is a common explanation.

• Baldwin, Meese & Baker (2011). Retinal inhomogeneity and the witch's hat: contrast sensitivity declines as a bilinear function of eccentricity in each direction. Perception, 40: 112.

The logarithm of contrast sensitivity has been described as a linear function of retinal eccentricity for a visual field of 120 deg (Pointer and Hess, 1989 Vision Research 29 1133-1151). Here we ask whether this is a suitable account for the central 9 deg of the visual field where most contrast sensitivity experiments are performed. We measured contrast detection thresholds for oriented cosine-phase log-Gabor stimuli with a spatial frequency of 4 cycles/deg and bandwidths of 1.6 octaves and 25°. Four meridians were tested (-45°, 0°, 45° and 90°), each with four stimulus orientations (-45°, 0°, 45° and 90°). Eccentricity was sampled in steps of 6 cycles, and 1.5 cycles in a subsample of conditions. In almost every case, we found that the initial sensitivity loss with eccentricity was steep (average = 1.1 dB/cycle), becoming shallower (average = 0.4 dB/cycle, similar to previous reports) after a critical point: a behaviour that was nicely described by a bi-linear equation. This equation also improved the fit to the Pointer and Hess results. Sensitivity to the entire central visual field was estimated by elliptical interpolation between bi-linear fits to each of the four cardinal half-meridians. This produced a sensitivity surface shaped like a "witch's hat", and made good predictions for the results for the oblique meridians. By testing other spatial frequencies, we aim to determine whether the location of the hat's brim is a fixed visual angle (as might be expected on anatomical grounds) or a fixed number of stimulus cycles.

• Baker, Meese & Georgeson (2010). 'Dilution masking', negative d-prime and nonmonotonic psychometric functions for eyes, space and time. Perception, 39(S): 7.

Recent work investigated contrast-interactions using targets and pedestals constructed from stimulus pairs (A, B) that were interdigitated across the domain of interest. It suggested similar gain-control frameworks for summation and suppression of contrast in the domains of space, time, ocularity and orientation. One of the properties of this framework is ‘dilution masking’. This is different from each of the well-known processes of ‘within-channel’ and ‘cross-channel’ masking and it derives from the integration of relevant target and pedestal regions (A) with uninformative pedestal regions (B). It makes a surprising prediction when the pedestal contrast in the target region (A) is reduced to 0%. If suppression between A and B is strong, the model’s contrast-response first decreases for small target contrast-increments before increasing to threshold as target contrast approaches the high mask contrast. This predicts a non-monotonic psychometric function, where discrimination performance drops below 50% correct in 2AFC, implying negative d’. We have confirmed the existence of this paradoxical ‘trough’ empirically in contrast-masking experiments for interdigitated (A, B) stimuli in each of three stimulus domains: space, time (flicker) and ocularity. But in the orientation domain, where cross-orientation suppression is relatively weak, the effect is not found, consistent with the gain-control model.

• Meese & Baker (2010). Summation and suppression of luminance contrast across eyes, space, time and orientation: the equation of the visual brain. Perception, 39(S): 6.

To understand summation of visual signals we also need to understand the opposite process: suppression. To investigate both processes we measured triplets of dipper functions for targets and pedestals involving interdigitated stimulus pairs (A, B) within each domain of interest (task: detect A on A; A on A+B; A+B on A+B). Previous work showed that summation and suppression operate over the full contrast range for the domains of ocularity (A and B are left and right eyes) and space (A and B are adjacent neighbourhoods). Here we include orientation and time domains and a contrast-matching task. Temporal stimuli were 15Hz counter-phase sine-wave gratings, where A, B were the positive and negative phases of the oscillation. For orientation, we used orthogonally oriented contrast patches (A, B) whose sum was an isotropic difference-of-Gaussians. Results from all four domains could be understood within a common framework: summation operates independently within the excitatory and suppressive pathways of a contrast gain control equation. Subtle differences across conditions were explained by variable strengths of divisive suppression. For example, contrast-matching confirmed that A+B has greater perceived contrast than A in the orientation domain but not the spatial domain, suggesting cross-orientation suppression is weaker than spatial suppression.

• Baker, Georgeson, Wallis & Meese (2010). Difference between target and background luminance determines the rule for binocular combination. Perception, 39(8): 1149.

Binocular combination of luminance can be investigated by matching binocularly unequal target stimuli to binocularly equal standards. Such experiments typically produce quasi-linear equibrightness contours, which fold back at the extremes owing to Fechner's paradox (Levelt, 1965 British Journal of Psychology 56 1 - 13). For decrements against a bright background, however, Anstis and Ho (1998 Vision Research 38 523 - 539) reported highly nonlinear functions which imply a winner-take-all rule. Are these very different findings due to the sign of the contrast, the luminance of the target, the luminance of the background, or all three? We performed binocular matching experiments for increments on a black background (<0.01 cd/m²), and either increments, decrements, or both (a light-dark edge) against a grey background (~10 cd/m²). Stimuli were uniform or bipartite discs (diameter 1 deg) or a Gabor patch (1 cycle/deg), and matches were obtained by measuring the point of subjective equality with a 2IFC staircase procedure. Results showed that grey backgrounds were associated with nonlinear combination across eyes, which was particularly severe (close to winner-take-all) for high-contrast decrements, consistent with Anstis and Ho (1998). For increments on a black background, combination was nonlinear at low target luminances (<=2 cd/m²) but became increasingly linear towards higher luminances (>2 cd/m²). Fitting a generic model of binocular combination reveals that the exponent governing summation is inversely related to the (signed) difference between the luminance of the target and that of the background.

• Baldwin, Meese & Baker (2010). Loss of contrast sensitivity at 4 cycles/deg depends on eccentricity and meridian but not grating orientation for the central 9 deg of the visual field. Perception, 39(8): 1151.

Surprisingly, there has been no detailed study of the relation between contrast sensitivity and stimulus orientation across the central visual field. Here we measured contrast detection thresholds for cosine-phase log-Gabor stimuli with a spatial frequency of 4 cycles/deg, duration of 100 ms and bandwidths of 1.6 octaves and 25 deg. There were 4 meridians (-45°, 0°, 45°, 90°), 4 stimulus orientations (45°, 0°, 45°, 90°) and 4 eccentricities (0°, ±1.5°, ±3°, ±4.5°), giving a total of 100 conditions in a randomised blocked design. To reduce extrinsic uncertainty, a low contrast ring (diameter of 0.75 deg) was presented continuously at the appropriate position in the visual field, where it surrounded the stimulus. A similar ring in the centre of the display aided fixation. We found no evidence for the meridional resolution effect of Rovamo et al (1982 Investigative Ophthalmology & Visual Science 23 666-670) or the oblique effect. For two observers, ASB and DHB, the loss of sensitivity with eccentricity averaged 0.6 and 0.82 dB per cycle, respectively; a little more severe than previous reports. In general, sensitivity declined less rapidly for the horizontal meridian than for the vertical meridian for each stimulus orientation. The sensitivity functions were slightly concave on log-linear axes and preliminary analysis attributed the anisotropy to the initial slopes of bi-linear fits - the second parts of the slopes being fairly uniform. These results will help to constrain the interpretation of previous and future studies addressing the details of spatial integration of contrast in the central visual field.

• Georgeson, Meese & Baker (2010). Detecting contrast differences in binocular and dichoptic vision: we use monocular or binocular channels, whichever gives the MAX response. Journal of Vision, 10(7): 350.

Two eyes are often better than one. Models based on binocular summation of signals from each eye, with interocular contrast gain control and a single binocular output channel, account well for detection, discrimination and perception of monocular and binocular contrast. We now ask whether monocular signals also remain available to perception. Horizontal 1c/deg sine-wave gratings of contrast C were presented to both eyes for 200ms in 2AFC discrimination tasks, to determine whether contrast increments (C+dC) in one eye were more difficult to detect when accompanied by contrast decrements (C-dC) in the other eye. Summation or averaging over the two eyes should make these opposite changes cancel. Results consistently showed no cancellation. Binocular increments or decrements were more detectable than monocular ones, but thresholds for the hybrid increment/decrement condition were close to those for monocular contrast increment (on the binocular pedestal). Since the binocular channel must suffer cancellation, its absence here implies that monocular signals can remain available to perception and decision, alongside the combined binocular response. Despite this, monocular decrements of contrast on a binocular pedestal were unusually difficult to detect. An extended version of our 2-stage gain-control model (Meese, Georgeson & Baker, Journal of Vision 2006), now incorporating left-eye, right-eye and binocular channels, accurately explained the patterns of threshold variation over at least 7 distinct forms of dipper function. Importantly, the model observer is assumed to pick only the MAX response across the 3 types of channel. This normally arises from the binocular channel, which can thus occlude useful information in the monocular channels. But when the pedestal gratings are out-of-phase in the 2 eyes, interocular suppression wipes out the binocular response, and monocular channels mediate the task. This switch from binocular to monocular responses may be the early, local bias for binocular rivalry.

• Baker & Meese (2010). Area summation of contrast is scale invariant and occurs over at least 8 carrier cycles. Perception, 39: 273-274.
  

Classical studies of area summation – in which detection thresholds are measured as a function of target diameter – confound summation of signal with summation of internal noise, and are compromised by retinal inhomogeneity. A “swiss cheese” stimulus recently introduced by Meese & Summers (2007; Proc Biol Sci, 274, 2891-2900) was designed to avoid these problems by keeping target diameter constant and modulating the contrast of interdigitated ‘check’ regions. This approach has revealed substantial area summation at and above detection threshold. Here, we investigate the spatial limits of this integration process over a range of carrier frequencies (1 – 16c/deg) and modulator frequencies (0.25 – 32cycles/check). We used two experimental designs: a simple method in which component ‘check’ thresholds were compared with those for their linear sum, and a normalization method in which the strength of each component in the compound stimulus depended on its detectability. The second design was of particular benefit for large check sizes (low spatial frequency modulators). Plotting results as functions of carrier cycles per check revealed contrast summation to be scale invariant for both designs. Summation remained strong (~6dB) up to at least 4cycles/check, implying linear physiological summation over 8 carrier cycles or more, and declined monotonically for larger check sizes. We consider area summation models involving spatial filtering, nonlinear transduction, linear summation over a fixed region, and Minkowski summation over multiple regions. These analyses support our conclusion that physiological summation of contrast occurs over a minimum of 8 carrier cycles after the initial stage of linear spatial filtering.

• Baker & Graf (2009). Surround motion affects speed encoding at an early stage of processing. Perception, 38(S): 9. 

Surround motion can strongly modulate the perceived speed of a central stimulus, yet the mechanisms behind this process are unknown. Using translating gratings (1 cycle deg^-1, 1 deg s^-1) surrounded by filtered noise textures, we conducted experiments to measure spatiotemporal tuning, contrast dependency and envelope properties of surround modulation in two directions. Plotted in terms of relative surround speed, perceived (matched) speed followed a sigmoidal function, saturating at the fastest speeds, ruling out a simple differencing process. Effect size increased with temporal frequency (speed * SF) and showed some spatial frequency tuning. Reductions in perceived speed saturated as a function of surround contrast and were constant with envelope blur. Perceived speed increases were weaker for sharper envelopes, but increased with surround contrast. We then asked whether surround effects occur before or after pattern motion computation. Using plaid stimuli with components ±45°, we measured the PSE for global plaid direction with and without surrounds drifting along the motion axis of one component. We observed substantial shifts (up to 20°) in the perceived plaid direction, consistent with surround-induced perceived speed changes. No effect was found for a grating drifting in the pattern direction. This suggests that surround effects occur before pattern integration in extra-striate areas (MT).

• Baker & Graf (2009). Binocular rivalry favors naturalistic stimuli in space and time. Journal of Vision, 9(8): 292.
  

The spatiotemporal structure of natural images has characteristic amplitude and phase spectra. For example, the distribution of spatial and temporal frequency information is proportional to 1/f^α, where f is frequency and α has a value near unity. The visual system seems optimized to these properties, with discrimination performance and gain control mechanisms most efficient when α≈1 (e.g. McDonald & Tadmor, 2006, Vis Res, 46: 3098-3104). Here, we ask if binocular rivalry is sensitive to properties typical of natural scenes. We used filtered 2D noise (tinted red or blue to aid identification) and varied the value of α in either the spatial or temporal domain in two separate experiments. All stimuli were equated for RMS contrast and presented dichoptically in counterbalanced, pairwise factorial combination (2 experiments, 15 unique pairs each, 4 observers, 5 repetitions, 1-min trials). We found that stimuli for which α=1 showed the greatest predominance in both the spatial and temporal domains. We compare these findings to perceived contrast measurements for the same stimuli, and the total contrast energy in each image after passing through a model contrast sensitivity function. We conclude that the strong contrast dependency of rivalry is the mechanism by which binocular vision is optimized for viewing natural images. Additionally, we compared rivalry between natural and phase-scrambled images. With stimuli equated for total energy, images with natural phase structure were dominant for 70% of the trial duration (averaged over 8 images and 6 observers for a total of 576 1-min trials). We ruled out the effects of bias using a simulated rivalry condition, which produced an average natural image dominance of 50% (i.e. no bias). This evidence indicates that binocular rivalry is preferentially sensitive to the properties of natural images across space, time and phase.

• Meese, Georgeson, Baker, Holmes, Challinor & Summers (2009). Suppression and summation in contrast gain control for human vision. Perception, 38, 627.
  

Over the last ten years our understanding of the ascending visual pathway 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 receptive field (CRF). A review of a substantial body of psychophysical work performed by others and ourselves, 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 probably pre- and post-binocular summation and involve components that are: spatiotemporally invariant, isotropic, adaptable, achromatic and dichoptic; isotropic and chromatic; anisotropic and achromatic; substantially larger than the CRF, orientation tuned 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 followed by ocularity and area invariances (fractal object contrasts don't change when you close one eye or get closer) owing to the suppressive gain control. One of many remaining challenges is to determine the stage or stages of spatial tuning in the excitatory pathway.

• Baker & Graf (2009). The effect of eye-movements and surround motion on bistable plaids. Perception, 38, 459-460

Perceived motion of drifting plaid stimuli is bistable over a wide range of component angles and spatial frequencies (Hupé, J-M. & Rubin, N., 2003, Vision Res, 43: 531-548). Perception alternates between coherent pattern motion and transparent component motion. Given previous findings associating saccades with percept transitions for some bistable stimuli (van Dam, L.C.J. & van Ee, R., 2006, Vision Res, 46: 787-799), we explored the relationship between perceived plaid motion and eye-movements in ten observers. Besides a standard plaid motion condition, during which observers were instructed to fixate centrally, we also included two surround motion conditions (moving dots with speed and direction consistent with the coherent or transparent percept), and two guided eye-movement conditions, where observers tracked a moving fixation point. Observers reported their percept continuously as coherent or transparent using a mouse (60s trial duration). Behaviourally, surround motion and guided eye-movements biased the proportion of coherent/transparent percepts by 5-10%. This occurred largely through extending the durations of percepts directionally congruent with the surround motion or guided eye-movements. Saccades were longer and more numerous in the surround motion or guided eye-movement direction. For all conditions, a number of perceptual transition reports were preceded by blinks, giving a measure of observer response lag (500-1000ms). Saccades congruent with percept direction showed a different pattern, following perceptual transitions. We conclude that i) percept changes elicit eye-movements in the direction of the percept, ii) saccades can prolong an existing percept and iii) surround motion might capture eye-movements, which in turn influence perception.

• Baker & Graf (2008). A common factor underlying binocular rivalry and dichoptic masking. Perception, 37(S), 1.

When incompatible images are shown to the two eyes, two empirical phenomena are observed: monocular detection thresholds are elevated (dichoptic masking) and the perceived image changes over time (binocular rivalry) . It has recently been shown (van Boxtel et al, 2007, Journal of Vision, 7, 14-3) that these two phenomena have similar perceptual dynamics when images are presented successively. Here, we report a common underlying factor between rivalry and dichoptic masking during simultaneous presentation. Using orthogonal Gabor patches (2cpd) we measured threshold elevation for dichoptic masking, as well as the mean dominance duration of binocular rivalry, in a group of 41 subjects. Both threshold elevation and dominance durations varied substantially across observers, and were highly correlated (r=0.44, p<0.01) such that stronger dichoptic masking was associated with longer dominance durations. Within subjects, we also varied the angle between dichoptic Gabors, producing a similar pattern of results. These findings are accounted for by a single computational model in which the weight of interocular suppression determines both threshold elevation and dominance durations.

• Graf & Baker (2008). Rivalry alternations bind together along entire contours. Perception, 37(S), 100.

Dominance periods in binocular rivalry can be influenced by contextual information and spatial relationships. Recently, Alais et al (2006, Vis Res, 46: 1473-1487) demonstrated that pairs of collinear elements tend to alternate together, suggesting a mechanism (contour integration) by which image features may be bound together during rivalry. To investigate this, we constructed curved monocular contours of between one and five Gabor elements (4cpd) equidistant from fixation in either the left or right hemifield, and rivalling with binary noise. Observers reported when all Gabors were either present or absent, giving an index of alternation coherency. Elements consistent with a continuous contour were coherent for a greater proportion of trials than expected by chance (calculated as 2/2ⁿ; n is number of elements). Elements orthogonal to the contour were less coherent, though still greater than chance, whereas reported coherence for randomly oriented elements was at chance. These effects disappeared (or reversed) when successive elements were presented to different eyes, indicating that the binding effects are eye-specific.

• Summers, Meese & Baker (2008). Luminance contrast is summed across eyes before space. Perception, 37, 314.

Here we assess whether summation of contrast occurs over eyes and space conjointly. Stimuli were sine-wave gratings (2.5 cycles deg-1) spatially modulated by cosine- and anticosine-phase plaids. This produced patchy gratings where patches were placed at the centres of either the `black' or `white' checks of a notional checkerboard. One eye was presented with pedestal patches in one of these locations (eg `black') and the other eye was presented with pedestal patches in the other locations (eg `white'). Contrast increments were presented to one or both eyes (single or dual increments, respectively). Conventional dipper functions were found, but the dual increments were shifted downwards by 4.8 dB. 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 space, (iii) linear or accelerating contrast transduction, and (iv) additive Gaussian stochastic noise. Formal equivalences reduced this to 48 different models, only 4 of which were consistent with our empirical estimates of summation ratios and slopes of the psychometric functions. 2 of these were rejected by considerations outside the present work. Our preferred model was: linear summation across eyes followed by nonlinear contrast transduction, linear summation across space, and late noise. Results were inconsistent with a MAX operator across eyes but a MAX operator across space remains a viable alternative for the stimulus conditions here. In any case, suprathreshold pooling of contrast across different regions of the retina in different eyes is a property of human vision at threshold and above.

• Baker & Graf (2008). Perceived and true speeds have the same effect on binocular rivalry. Perception, 37, 310-311.

The relative dominance of gratings engaged in binocular rivalry can be influenced by their surroundings. For drifting stimuli, central gratings opposing the background motion are more dominant (Paffen et al, 2004 Vision Research 44 1635-1639). Such centre-surround stimulus configurations can, however, produce a profound change in perceived speed (Norman et al, 1996 Perception 25 815-830). We used rivalling orthogonal Gabor patches (1 cycle deg-1, 100% contrast, ±45deg), drifting at 0.5 deg s-1, embedded in a noise texture drifting at the same speed. Varying the direction of the noise affected the dominance of each grating in the direction expected from previous work. We then used a spatial 2AFC task to match the speed of a noise-embedded Gabor (standard) with that of a Gabor surrounded by mean luminance (test). As expected, background motion produced substantial changes in perceived speed; at least by a factor of two for all subjects. Lastly, we simulated the context experiment by using gratings (surrounded by mean luminance) moving at different physical speeds, as determined by the matching data. We found the same pattern of dominance as for the context experiment. This suggests that perceived and true speeds influence rivalry in the same manner, perhaps at the same neural locus. Since direction-tuned suppressive and facilitatory surround processes occur in area MT, these findings imply a key role for this brain area in rivalry, through either modulating signals directly or by feedback to earlier visual areas.

• Baker, Meese, Patel & Sarwar (2007). Interocular suppression is scale invariant, but ipsiocular suprression is weighted by flicker speed. Perception, 36(S), 60.

In human and cat there are two routes to suppression for orthogonal masks: a broadband, non-adaptable, ipsiocular pathway, and a more narrowband, adaptable interocular pathway. We investigated the strength of both types of suppression in humans across spatio-temporal scale using orthogonal pairs of superimposed Gabor patches (mask and target) flickering at four spatial (0.5, 1, 2, 4 cycles deg-1) and two temporal (4 and 15 Hz) frequencies. Mask and target were presented to the same eye or different eyes in 2IFC cross-orientation masking experiments. Masking functions were normalized to baseline detection thresholds and fit by a two-stage model of contrast gain control (Meese et al, 2006 Journal of Vision 6 1224 - 1243) developed to accommodate cross-orientation masking. The weight of ipsiocular suppression was proportional to the square-root of stimulus speed (TF/SF), as in the binocular case (Meese and Holmes, 2007 Proceedings of the Royal Society of London, Series B 274 127 - 136). However, dichoptic-masking functions superimposed, showing that the interocular, presumably cortical, process is scale-invariant. These findings have implications for studies of amblyopia, binocular rivalry, and single-cell physiology.

• Baker, Meese & Patryas (2007). Binocular summation is more tightly tuned to spatial frequency, orientation and spatial phase than interocular suppression. Perception, 36(9), 1401.

Binocular vision involves at least two interactions between the eyes: interocular suppression and binocular summation. Both contribute to dichoptic masking, but the second also contributes to facilitation. Here we used a 2AFC contrast-masking paradigm and horizontal 1 cycle deg target gratings (200 ms) to characterise the spatial properties of these two processes. In experiment 1, dichoptic masks were the same as the target but were either in-phase or out-of-phase. For in-phase masking, suppression was strong (log-log slope of ~1) at moderate mask contrasts and above, and there was weak facilitation at low mask contrasts. Anti-phase masking was weaker (log-log slope of ~0.6) and there was no facilitation. The in-phase function set the parameters of our model (Meese et al, 2006 Journal of Vision 6 1224-1243), which predicted the anti-phase function when binocular summation was selective for phase, but interocular suppression was not. In experiment 2, the spatial frequency and orientation tuning of both processes were measured with the use of high-contrast dichoptic masks. By using masks in-phase and out-of-phase with the target we were able to decouple the masking produced by the two processes. Interocular suppression had an orientation bandwidth of ±30deg, and a spatial frequency bandwidth >2 octaves. Binocular summation was much more narrowly tuned with an orientation bandwidth of ±7.5deg, and a spatial frequency bandwidth of <0.5 octave. Our results replicate the unusual shape of dichoptic tuning functions reported by Legge (1979 Journal of the Optical Society of America 69 838-847), which can now be seen as the envelope of two processes (interocular suppression and binocular summation).

• Baker, Meese, Mansouri & Hess (2007). Monoptic, dichoptic and binocular masking in strabismic amblyopia. Perception, 36(2), 302.

Contrast vision in strabismic amblyopia is characterised by (i) threshold elevation in the amblyopic eye, (ii) poor binocular summation at threshold, and (iii) abnormal dichoptic masking (Harrad and Hess, 1992 Vision Research 32 2135-2150). We develop this here by reporting contrast masking functions for five strabismic amblyopes. Patches of horizontal grating with spatial frequencies of 0.5 or 3 cycles deg-1 were presented to the same (monoptic, left and right), different (dichoptic, left and right), or both (binocular) eyes (five conditions in total). All subjects had higher thresholds in the amblyopic eye and typically showed substantial levels of dichoptic masking in each eye. Otherwise, the subjects fell into two groups. In one group (n=2), small levels of dichoptic facilitation were found, similar to normal observers (Meese et al, 2006 Journal of Vision 6 1224 - 1243). The results from this group were strikingly similar to those of a normal observer with a neutral density filter in front of one eye. In all cases, the loss of binocular summation could be attributed to the low sensitivity in the affected eye. The other group (n=3) showed no evidence of dichoptic facilitation and their loss of binocular summation could not be attributed to a loss of contrast sensitivity in the affected eye. One possibility is that their eyes operate independently, with perceived stimulus strength determined by the most active ocular channel (be that mask or test), resulting in dichoptic masking (without suppression) and no binocular summation. Our findings suggest that the visual architectures amongst strabismic amblyopes might vary considerably.

• Baker & Meese (2006). Cross-orientation suppression occurs before binocular summation: evidence from masking and adaptation. Journal of Vision, 6(6), 821.

The threshold elevation produced by a grating mask with very dissimilar orientation from a target is sometimes called cross-orientation suppression (XOS). Once thought to be a single process within visual cortex, recent single-cell studies suggest earlier processes specific to eye of origin (e.g. Li et al. 2005, J Neurophysiol, 94(2), 1645-1650). Here, we investigate interocular XOS psychophysically using 1c/deg horizontal test gratings and cross-oriented masks. Masking functions for monoptic and dichoptic masks did not superimpose when plotted against contrast (0%-45%@200ms; Experiment 1) or duration (25-400ms@45%; Experiment 2). For example, monoptic XOS decreased and dichoptic XOS increased, as functions of duration. These results reject models in which XOS occurs only after binocular summation because such models predict that dichoptic and monoptic masking are identical. An unexpected finding was that a monoptic + dichoptic mask condition produced less masking than the dichoptic mask alone, suggesting interocular suppression of the mask components prior to dichoptic XOS. In Experiment 3, we found that dichoptic, but not monoptic, masking was reduced by adapting to the mask, consistent with cat physiology and a cortical locus for dichoptic masking. We propose a quantitative model of all our data where XOS is: (i) non-adaptable (and possibly precortical) for the monoptic case and (ii) adaptable (and presumably cortical) for the dichoptic case. This model also explains the finding that binocular XOS does not adapt (Foley & Chen, 1997, Vis Res, 37(19), 2779-2788) because in that condition, the adaptable contribution to XOS is negligible due to the interocular suppression described above.

• Baker & Meese (2006). Monoptic and dichoptic cross-orientation masking are not the same mechanism. Perception, 35(3), 421.

In monoptic and dichoptic masking paradigms, test and mask stimuli are presented to the same and different eyes, respectively. By using mask and test stimuli that are sufficiently different not to excite the same detecting mechanism, suppressive processes can be investigated without the complicating problem of excitatory summation. In the case of binocular stimulation, this type of experiment has led to the concept of contrast gain control by a broad-band pool of suppressive mechanisms [eg Foley, 1994 Journal of the Optical Society of America A 11 1710 - 1719]. One possibility is that broad-band suppression occurs after binocular summation, in which case cross-orientation masking for monoptic and dichoptic conditions should be identical. We tested this prediction on three observers by measuring contrast masking functions at two different stimulus durations (50 ms and 200 ms), for horizontal patches of 1 cycle/deg test grating in the presence of either an orthogonal 1 cycle/deg mask or an oblique 3 cycles/deg mask. We also measured masking as a function of stimulus duration (25 ms to 400 ms) for zero and high-contrast masks (45%). We found that: (i) masking increased as a function of mask contrast, and (ii) monoptic and dichoptic masking decreased and increased as functions of duration, respectively. In no case did monoptic and dichoptic masking functions superimpose. These results suggest a scheme in which cross-orientation suppression occurs within and between the eyes, and where both of these effects must impact before binocular summation. These results and conclusions show some parallels with recent reports for two different processes of cross-orientation suppression at a cellular level (eg Li et al, 2005 Journal of Neurophysiology 94 1645 - 1650).

• Meese, Georgeson & Baker (2005). Interocular masking and summation indicate two stages of divisive contrast gain control. Perception, 34(S), 42-43.
  

  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 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 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 beta ~3 - 4) at very low mask contrasts and shallow (beta ~1.2) at all higher contrasts, as predicted by all three models. The dichoptic slopes were steep (beta ~3 - 4) at very low contrasts, and very steep (beta > 5.5) at high contrasts (confirming Meese et al, loco cit.). A crucial new result was that intermediate dichoptic mask contrasts produced shallow slopes (beta ~2). 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.

• Baker, Meese & Georgeson (2005). Contrast discrimination with simultaneous monocular and dichoptic masks, Perception. 34(S), 202.

In experiments reported elsewhere at this conference, we have revealed two striking results concerning binocular interactions in a masking paradigm. First, at low mask contrasts, a dichoptic masking grating produces a small facilitatory effect on the detection of a similar test grating. Second, the psychometric slope for dichoptic masking starts high (Weibull beta~4) at detection threshold, becomes low (beta~1.2) in the facilitatory region, and then unusually steep at high mask contrasts (beta > 5.5). Neither of these results is consistent with Legge's (1984 Vision Research 24 385 - 394) model of binocular summation, but they are predicted by a two-stage gain control model in which interocular suppression precedes binocular summation. Here, we pose a further challenge for this model by using a 'twin-mask' paradigm (cf Foley, 1994 Journal of the Optical Society of America A 11 1710 - 1719). In 2AFC experiments, observers detected a patch of grating (1 cycle/deg, 200 ms) presented to one eye in the presence of a pedestal in the same eye and a spatially identical mask in the other eye. The pedestal and mask contrasts varied independently, producing a two-dimensional masking space in which the orthogonal axes (10 x 10 contrasts) represent conventional dichoptic and monocular masking. The resulting surface (100 thresholds) confirmed and extended the observations above, and fixed the six parameters in the model, which fitted the data well. With no adjustment of parameters, the model described performance in a further experiment where mask and test were presented to both eyes. Moreover, in both model and data, binocular summation was greater than a factor of root 2 at detection threshold. We conclude that this two-stage nonlinear model, with interocular suppression, gives a good account of early binocular processes in the perception of contrast.

• Georgeson, Meese & Baker (2005). Binocular summation, dichoptic masking and contrast gain control. Journal of Vision, 5(8), 797.

We consider a classical question - how signals from the two eyes are combined - in the context of contemporary models of contrast gain control. In 2AFC experiments, observers had to detect the presence of a test grating (1 c/deg, 200 ms) in one or both eyes, in the presence or absence of a similar masking ('pedestal') grating in one or both eyes. We found a high degree of binocular summation when pedestal contrast was low or zero, while at higher contrasts we confirmed Legge's (1984) paradoxical finding that there was no advantage for detecting binocular contrast increments over purely monocular ones. In a new variant, however, we found that, on a binocular pedestal, binocular increments were better detected than monocular ones. This implies that there is binocular summation of test signals even in the suprathreshold task. Importantly, there is also binocular summation of suppressive (gain control) signals: monocular increments were harder to detect on a binocular pedestal than on a monocular one. The pattern of results can be largely, but not completely, understood through a binocular version of the standard gain control equation: Resp(binoc) = (Lp +Rp)/(sq+Lq+Rq), expressing the output of a binocular channel to contrasts L,R in the left and right eyes, with p,q,s constant (p~2.4, q~2). With additive noise, this mechanism correctly predicts the high thresholds and unusually steep, step-like psychometric functions that we observed in dichoptic masking (test in one eye, pedestal in the other). But this mechanism under-estimates both facilitation and binocular summation at low contrasts, so we shall consider what modifications are needed. Viable options include more than one output channel, and more than one stage at which nonlinear transduction and gain control operate.

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Last updated 22/08/11