Revealing the influence of bias in a letter acuity identification task: A noisy template model.

In clinical testing of visual acuity, it is often assumed that performance reflects sensory abilities and observers do not exhibit strong biases for or against specific letters, but this assumption has not been extensively tested. We re-analyzed single-letter identification data as a function of letter size, spanning the resolution threshold, for 10 Sloan letters at central and paracentral visual field locations. Individual observers showed consistent letter biases across letter sizes. Preferred letters were named much more often and others less often than expected (group averages ranged from 4% to 20% across letters, where the unbiased rate was 10%). In the framework of signal detection theory, we devised a noisy template model to distinguish biases from differences in sensitivity. When bias varied across letter templates the model fitted very well - much better than when sensitivity varied without bias. The best model combined both, having substantial biases and small variations in sensitivity across letters. The over- and under-calling decreased at larger letter sizes, but this was well-predicted by template responses that had the same additive bias for all letter sizes: with stronger inputs (larger letters) there was less opportunity for bias to influence which template gave the biggest response. The neural basis for such letter bias is not known, but a plausible candidate is the letter-recognition machinery of the left temporal lobe. Future work could assess whether such biases affect clinical measures of visual performance. Our analyses so far suggest very small effects in most settings.

Contrast adaptation and interocular transfer in cortical cells: A re-analysis & a two-stage gain-control model of binocular combination.

How do V1 cells respond to, adapt to, and combine signals from the two eyes? We tested a simple functional model that has monocular and binocular stages of divisive contrast gain control (CGC) that sit before, and after, binocular summation respectively. Interocular suppression (IOS) was another potential influence on contrast gain. Howarth, Vorobyov & Sengpiel (2009, Cerebral Cortex, 19, 1835-1843) studied contrast adaptation and interocular transfer in cat V1 cells. In our re-analysis we found that ocular dominance (OD) and contrast adaptation at a fixed test contrast were well described by a re-scaling of the unadapted orientation tuning curve - a simple change in response gain. We compared six variants of the basic model, and one model fitted the gain data notably better than the others did. When the dominant eye was tested, adaptation reduced cell response gain more when that eye was adapted than when the other eye was adapted. But when the non-dominant eye was tested, adapting either eye gave about the same reduction in overall gain, and there was an interaction between OD and adapting eye that was well described by the best-fitting model. Two key features of this model are that signals driving IOS arise 'early', before attenuation due to OD, while suppressive CGC signals are 'late' and so affected by OD. We show that late CGC confers a functional advantage: it yields partial compensation for OD, which should reduce ocular imbalance at the input to binocular summation, and improve the cell's sensitivity to variation in stereo disparity.

Interocular difference thresholds are mediated by binocular differencing, not summing, channels.

Patterns in the two eyes' views that are not identical in hue or contrast often elicit an impression of luster, providing a cue for discriminating them from perfectly matched patterns. Here we attempt to determine the mechanisms for detecting interocular differences in luminance contrast, in particular in relation to the possible contributions of binocular differencing and binocular summing channels. Test patterns were horizontally oriented multi-spatial-frequency luminance-grating patterns subject to variable amounts of interocular difference in grating phase, resulting in varying degrees of local interocular contrast difference. Two types of experiment were conducted. In the first, subjects discriminated between a pedestal with an interocular difference that ranged upward from zero (i.e., binocularly correlated) and a test pattern that contained a bigger interocular difference. In the second type of experiment, subjects discriminated between a pedestal with an interocular difference that ranged downward from a maximum (i.e., binocularly anticorrelated) and a test pattern that contained smaller interocular difference. The two types of task could be mediated by a binocular differencing and a binocular summing channel, respectively. However, we found that the results from both experiments were well described by a simpler model in which a single, linear binocular differencing channel is followed by a standard nonlinear transducer that is expansive for small signals but strongly compressive for large ones. Possible reasons for the lack of involvement of a binocular summing channel are discussed in the context of a model that incorporates the responses of both monocular and binocular channels.

Binocular summation revisited: Beyond √2.

Our ability to detect faint images is better with two eyes than with one, but how great is this improvement? A meta-analysis of 65 studies published across more than 5 decades shows definitively that psychophysical binocular summation (the ratio of binocular to monocular contrast sensitivity) is significantly greater than the canonical value of √2. Several methodological factors were also found to affect summation estimates. Binocular summation was significantly affected by both the spatial and temporal frequency of the stimulus, and stimulus speed (the ratio of temporal to spatial frequency) systematically predicts summation levels, with slow speeds (high spatial and low temporal frequencies) producing the strongest summation. We furthermore show that empirical summation estimates are affected by the ratio of monocular sensitivities, which varies across individuals, and is abnormal in visual disorders such as amblyopia. A simple modeling framework is presented to interpret the results of summation experiments. In combination with the empirical results, this model suggests that there is no single value for binocular summation, but instead that summation ratios depend on methodological factors that influence the strength of a nonlinearity occurring early in the visual pathway, before binocular combination of signals. Best practice methodological guidelines are proposed for obtaining accurate estimates of neural summation in future studies, including those involving patient groups with impaired binocular vision. (PsycINFO Database Record (c) 2018 APA, all rights reserved).

Adaptation to interocular difference.

Patterns in the two eyes' views that are not identical in hue or contrast often elicit an impression of luster, providing a cue for discriminating them from perfectly matched patterns. Here we ask whether the mechanism for detecting interocular differences (IDs) is adaptable. Our stimuli were horizontally oriented multispatial-frequency grating patterns that could be subject to varying degrees of ID through the introduction of interocular phase differences in the grating components. Subjects adapted to patterns that were either correlated, uncorrelated, monocular (one eye only), or anticorrelated. Following adaptation, thresholds for detecting IDs were measured using a staircase procedure. It was found that ID thresholds were elevated following adaptation to uncorrelated, monocular, and anticorrelated but not correlated patterns. Threshold elevation was found to be maximal when the orientations of the adaptor and test gratings were the same, and when their spatial frequencies were similar. The results support the existence of a specialized mechanism for detecting IDs, the most likely candidate being the binocular differencing channel proposed in previous studies.

Luminance gradient at object borders communicates object location to the human oculomotor system.

The locations of objects in our environment constitute arguably the most important piece of information our visual system must convey to facilitate successful visually guided behaviour. However, the relevant objects are usually not point-like and do not have one unique location attribute. Relatively little is known about how the visual system represents the location of such large objects as visual processing is, both on neural and perceptual level, highly edge dominated. In this study, human observers made saccades to the centres of luminance defined squares (width 4 deg), which appeared at random locations (8 deg eccentricity). The phase structure of the square was manipulated such that the points of maximum luminance gradient at the square's edges shifted from trial to trial. The average saccade endpoints of all subjects followed those shifts in remarkable quantitative agreement. Further experiments showed that the shifts were caused by the edge manipulations, not by changes in luminance structure near the centre of the square or outside the square. We conclude that the human visual system programs saccades to large luminance defined square objects based on edge locations derived from the points of maximum luminance gradients at the square's edges.

Brightening and Dimming Aftereffects at Low and High Luminance.

Adaptation to a spatially uniform field that increases or decreases in luminance over time yields a "ramp aftereffect", whereby a steady, uniform luminance appears to dim or brighten, and an appropriate non-uniform test field appears to move. We measured the duration of this aftereffect of adaptation to ascending and descending luminance for a wide range of temporal frequencies and luminance amplitudes. Three types of luminance ramp profiles were used: linear, logarithmic, and exponential. The duration of the motion aftereffect increased as amplitude increased, regardless of the frequency, slope, or ramp profile of the adapting pattern. At low luminance, this result held for ascending luminance adaptation, but the duration of the aftereffect was significantly reduced for descending luminance adaptation. This reduction in the duration of the aftereffect at low luminance is consistent with differential recruitment of temporally tuned cells of the ON and OFF pathways, but the relative independence of the effect from temporal frequency is not.

Direction discrimination thresholds in binocular, monocular, and dichoptic viewing: Motion opponency and contrast gain control.

We studied the binocular organization of motion opponency and its relationship to contrast gain control. Luminance contrast thresholds for discriminating direction of motion were measured for drifting Gabor patterns (target) presented on counterphase flickering Gabor patterns (pedestal). There were four presentation conditions: binocular, monocular, dichoptic, and half-binocular. For the half-binocular presentation, the target was presented to one eye while pedestals were presented to both eyes. In addition, to test for motion opponency, we studied two increment and decrement conditions, in which the target increased contrast for one direction of movement but decreased it for the opposite moving component of the pedestal. Threshold versus pedestal contrast functions showed a dipper shape, and there was a strong interaction between pedestal contrast and test condition. Binocular thresholds were lower than monocular thresholds but only at low pedestal contrasts. Monocular and half-binocular thresholds were similar at low pedestal contrasts, but half-binocular thresholds became higher and closer to dichoptic thresholds as pedestal contrast increased. Adding the decremental target reduced thresholds by a factor of two or more-a strong sign of opponency-when the decrement was in the same eye as the increment or the opposite eye. We compared several computational models fitted to the data. Converging evidence from the present and previous studies (Gorea, Conway, & Blake, 2001) suggests that motion opponency is most likely to be monocular, occurring before direction-specific binocular summation and before divisive, binocular gain control.

Binocular functional architecture for detection of contrast-modulated gratings.

Combination of signals from the two eyes is the gateway to stereo vision. To gain insight into binocular signal processing, we studied binocular summation for luminance-modulated gratings (L or LM) and contrast-modulated gratings (CM). We measured 2AFC detection thresholds for a signal grating (0.75c/deg, 216ms) shown to one eye, both eyes, or both eyes out-of-phase. For LM and CM, the carrier noise was in both eyes, even when the signal was monocular. Mean binocular thresholds for luminance gratings (L) were 5.4dB better than monocular thresholds - close to perfect linear summation (6dB). For LM and CM the binocular advantage was again 5-6dB, even when the carrier noise was uncorrelated, anti-correlated, or at orthogonal orientations in the two eyes. Binocular combination for CM probably arises from summation of envelope responses, and not from summation of these conflicting carrier patterns. Antiphase signals produced no binocular advantage, but thresholds were about 1-3dB higher than monocular ones. This is not consistent with simple linear summation, which should give complete cancellation and unmeasurably high thresholds. We propose a three-channel model in which noisy monocular responses to the envelope are binocularly combined in a contrast-weighted sum, but also remain separately available to perception via a max operator. Vision selects the largest of the three responses. With in-phase gratings the binocular channel dominates, but antiphase gratings cancel in the binocular channel and the monocular channels mediate detection. The small antiphase disadvantage might be explained by a subtle influence of background responses on binocular and monocular detection.

Contrast and lustre: A model that accounts for eleven different forms of contrast discrimination in binocular vision.

Our goal here is a more complete understanding of how information about luminance contrast is encoded and used by the binocular visual system. In two-interval forced-choice experiments we assessed observers' ability to discriminate changes in contrast that could be an increase or decrease of contrast in one or both eyes, or an increase in one eye coupled with a decrease in the other (termed IncDec). The base or pedestal contrasts were either in-phase or out-of-phase in the two eyes. The opposed changes in the IncDec condition did not cancel each other out, implying that along with binocular summation, information is also available from mechanisms that do not sum the two eyes' inputs. These might be monocular mechanisms. With a binocular pedestal, monocular increments of contrast were much easier to see than monocular decrements. These findings suggest that there are separate binocular (B) and monocular (L,R) channels, but only the largest of the three responses, max(L,B,R), is available to perception and decision. Results from contrast discrimination and contrast matching tasks were described very accurately by this model. Stimuli, data, and model responses can all be visualized in a common binocular contrast space, allowing a more direct comparison between models and data. Some results with out-of-phase pedestals were not accounted for by the max model of contrast coding, but were well explained by an extended model in which gratings of opposite polarity create the sensation of lustre. Observers can discriminate changes in lustre alongside changes in contrast.

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

UNLABELLED: Binocular combination for first-order (luminance-defined) 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 fusion, suppression and diplopia for blurred edges.

PURPOSE: (1) To devise a model-based method for estimating the probabilities of binocular fusion, interocular suppression and diplopia from psychophysical judgements, (2) To map out the way fusion, suppression and diplopia vary with binocular disparity and blur of single edges shown to each eye, (3) To compare the binocular interactions found for edges of the same vs opposite contrast polarity. METHODS: Test images were single, horizontal, Gaussian-blurred edges, with blur B = 1-32 min arc, and vertical disparity 0-8.B, shown for 200 ms. In the main experiment, observers reported whether they saw one central edge, one offset edge, or two edges. We argue that the relation between these three response categories and the three perceptual states (fusion, suppression, diplopia) is indirect and likely to be distorted by positional noise and criterion effects, and so we developed a descriptive, probabilistic model to estimate both the perceptual states and the noise/criterion parameters from the data. RESULTS: (1) Using simulated data, we validated the model-based method by showing that it recovered fairly accurately the disparity ranges for fusion and suppression, (2) The disparity range for fusion (Panum's limit) increased greatly with blur, in line with previous studies. The disparity range for suppression was similar to the fusion limit at large blurs, but two or three times the fusion limit at small blurs. This meant that diplopia was much more prevalent at larger blurs, (3) Diplopia was much more frequent when the two edges had opposite contrast polarity. A formal comparison of models indicated that fusion occurs for same, but not opposite, polarities. Probability of suppression was greater for unequal contrasts, and it was always the lower-contrast edge that was suppressed. CONCLUSIONS: Our model-based data analysis offers a useful tool for probing binocular fusion and suppression psychophysically. The disparity range for fusion increased with edge blur but fell short of complete scale-invariance. The disparity range for suppression also increased with blur but was not close to scale-invariance. Single vision occurs through fusion, but also beyond the fusion range, through suppression. Thus suppression can serve as a mechanism for extending single vision to larger disparities, but mainly for sharper edges where the fusion range is small (5-10 min arc). For large blurs the fusion range is so much larger that no such extension may be needed.

Enhanced text spacing improves reading performance in individuals with macular disease.

The search by many investigators for a solution to the reading problems encountered by individuals with no central vision has been long and, to date, not very fruitful. Most textual manipulations, including font size, have led to only modest gains in reading speed. Previous work on spatial integrative properties of peripheral retina suggests that 'visual crowding' may be a major factor contributing to inefficient reading. Crowding refers to the fact that juxtaposed targets viewed eccentrically may be difficult to identify. The purpose of this study was to assess the combined effects of line spacing and word spacing on the ability of individuals with age-related macular degeneration (ARMD) to read short passages of text that were printed with either high (87.5%) or low contrast (17.5%) letters. Low contrast text was used to avoid potential ceiling effects and to mimic a possible reduction in letter contrast with light scatter from media opacities. For both low and high contrast text, the fastest reading speeds we measured were for passages of text with double line and double word spacing. In comparison with standard single spacing, double word/line spacing increased reading speed by approximately 26% with high contrast text (p < 0.001), and by 46% with low contrast text (p < 0.001). In addition, double line/word spacing more than halved the number of reading errors obtained with single spaced text. We compare our results with previous reading studies on ARMD patients, and conclude that crowding is detrimental to reading and that its effects can be reduced with enhanced text spacing. Spacing is particularly important when the contrast of the text is reduced, as may occur with intraocular light scatter or poor viewing conditions. We recommend that macular disease patients should employ double line spacing and double-character word spacing to maximize their reading efficiency.

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

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

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

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

Mach bands and multiscale models of spatial vision: the role of first, second, and third derivative operators in encoding bars and edges.

Ernst Mach observed that light or dark bands could be seen at abrupt changes of luminance gradient in the absence of peaks or troughs in luminance. Many models of feature detection share the idea that bars, lines, and Mach bands are found at peaks and troughs in the output of even-symmetric spatial filters. Our experiments assessed the appearance of Mach bands (position and width) and the probability of seeing them on a novel set of generalized Gaussian edges. Mach band probability was mainly determined by the shape of the luminance profile and increased with the sharpness of its corners, controlled by a single parameter (n). Doubling or halving the size of the images had no significant effect. Variations in contrast (20%-80%) and duration (50-300 ms) had relatively minor effects. These results rule out the idea that Mach bands depend simply on the amplitude of the second derivative, but a multiscale model, based on Gaussian-smoothed first- and second-derivative filtering, can account accurately for the probability and perceived spatial layout of the bands. A key idea is that Mach band visibility depends on the ratio of second- to first-derivative responses at peaks in the second-derivative scale-space map. This ratio is approximately scale-invariant and increases with the sharpness of the corners of the luminance ramp, as observed. The edges of Mach bands pose a surprisingly difficult challenge for models of edge detection, but a nonlinear third-derivative operation is shown to predict the locations of Mach band edges strikingly well. Mach bands thus shed new light on the role of multiscale filtering systems in feature coding.

The effect of interocular phase difference on perceived contrast.

Binocular vision is traditionally treated as two processes: the fusion of similar images, and the interocular suppression of dissimilar images (e.g. binocular rivalry). Recent work has demonstrated that interocular suppression is phase-insensitive, whereas binocular summation occurs only when stimuli are in phase. But how do these processes affect our perception of binocular contrast? We measured perceived contrast using a matching paradigm for a wide range of interocular phase offsets (0-180°) and matching contrasts (2-32%). Our results revealed a complex interaction between contrast and interocular phase. At low contrasts, perceived contrast reduced monotonically with increasing phase offset, by up to a factor of 1.6. At higher contrasts the pattern was non-monotonic: perceived contrast was veridical for in-phase and antiphase conditions, and monocular presentation, but increased a little at intermediate phase angles. These findings challenge a recent model in which contrast perception is phase-invariant. The results were predicted by a binocular contrast gain control model. The model involves monocular gain controls with interocular suppression from positive and negative phase channels, followed by summation across eyes and then across space. Importantly, this model--applied to conditions with vertical disparity--has only a single (zero) disparity channel and embodies both fusion and suppression processes within a single framework.

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.

Sun and sky: Does human vision assume a mixture of point and diffuse illumination when interpreting shape-from-shading?

People readily perceive smooth luminance variations as being due to the shading produced by undulations of a 3-D surface (shape-from-shading). In doing so, the visual system must simultaneously estimate the shape of the surface and the nature of the illumination. Remarkably, shape-from-shading operates even when both these properties are unknown and neither can be estimated directly from the image. In such circumstances humans are thought to adopt a default illumination model. A widely held view is that the default illuminant is a point source located above the observer's head. However, some have argued instead that the default illuminant is a diffuse source. We now present evidence that humans may adopt a flexible illumination model that includes both diffuse and point source elements. Our model estimates a direction for the point source and then weights the contribution of this source according to a bias function. For most people the preferred illuminant direction is overhead with a strong diffuse component.

Response normalization and blur adaptation: data and multi-scale model.

Adapting to blurred or sharpened images alters perceived blur of a focused image (M. A. Webster, M. A. Georgeson, & S. M. Webster, 2002). We asked whether blur adaptation results in (a) renormalization of perceived focus or (b) a repulsion aftereffect. Images were checkerboards or 2-D Gaussian noise, whose amplitude spectra had (log-log) slopes from -2 (strongly blurred) to 0 (strongly sharpened). Observers adjusted the spectral slope of a comparison image to match different test slopes after adaptation to blurred or sharpened images. Results did not show repulsion effects but were consistent with some renormalization. Test blur levels at and near a blurred or sharpened adaptation level were matched by more focused slopes (closer to 1/f) but with little or no change in appearance after adaptation to focused (1/f) images. A model of contrast adaptation and blur coding by multiple-scale spatial filters predicts these blur aftereffects and those of Webster et al. (2002). A key proposal is that observers are pre-adapted to natural spectra, and blurred or sharpened spectra induce changes in the state of adaptation. The model illustrates how norms might be encoded and recalibrated in the visual system even when they are represented only implicitly by the distribution of responses across multiple channels.