Fourth-root summation of contrast over area: No end in sight when spatially inhomogeneous sensitivity is compensated by a witch's hat.

Measurements of area summation for luminance-modulated stimuli are typically confounded by variations in sensitivity across the retina. Recently we conducted a detailed analysis of sensitivity across the visual field (Baldwin, Meese, & Baker, 2012) and found it to be well described by a bilinear "witch's hat" function: Sensitivity declines rapidly over the first eight cycles or so, but more gently thereafter. Here we multiplied luminance-modulated stimuli (4 cycles/degree gratings and "Swiss cheeses") by the inverse of the witch's hat function to compensate for the inhomogeneity. This revealed summation functions that were straight lines (on double log axes) with a slope of -1/4 extending to ≥33 cycles, demonstrating fourth-root summation of contrast over a wider area than has previously been reported for the central retina. Fourth-root summation is typically attributed to probability summation, but recent studies have rejected that interpretation in favor of a noisy energy model that performs local square-law transduction of the signal, adds noise at each location of the target, and then sums over signal area. Modeling shows our results to be consistent with a wide field application of such a contrast integrator. We reject a probability summation model, a quadratic model, and a matched template model of our results under the assumptions of signal detection theory. We also reject the high threshold theory of contrast detection under the assumption of probability summation over area.

Area summation of first- and second-order modulations of luminance.

To extend our understanding of the early visual hierarchy, we investigated the long-range integration of first- and second-order signals in spatial vision. In our first experiment we performed a conventional area summation experiment where we varied the diameter of (a) luminance-modulated (LM) noise and (b) contrast-modulated (CM) noise. Results from the LM condition replicated previous findings with sine-wave gratings in the absence of noise, consistent with long-range integration of signal contrast over space. For CM, the summation function was much shallower than for LM suggesting, at first glance, that the signal integration process was spatially less extensive than for LM. However, an alternative possibility was that the high spatial frequency noise carrier for the CM signal was attenuated by peripheral retina (or cortex), thereby impeding our ability to observe area summation of CM in the conventional way. To test this, we developed the "Swiss cheese" stimulus of Meese and Summers (2007) in which signal area can be varied without changing the stimulus diameter, providing some protection against inhomogeneity of the retinal field. Using this technique and a two-component subthreshold summation paradigm we found that (a) CM is spatially integrated over at least five stimulus cycles (possibly more), (b) spatial integration follows square-law signal transduction for both LM and CM and (c) the summing device integrates over spatially-interdigitated LM and CM signals when they are co-oriented, but not when cross-oriented. The spatial pooling mechanism that we have identified would be a good candidate component for a module involved in representing visual textures, including their spatial extent.

A two-stage model of orientation integration for Battenberg-modulated micropatterns.

The visual system pools information from local samples to calculate textural properties. We used a novel stimulus to investigate how signals are combined to improve estimates of global orientation. Stimuli were 29 × 29 element arrays of 4 c/deg log Gabors, spaced 1° apart. A proportion of these elements had a coherent orientation (horizontal/vertical) with the remainder assigned random orientations. The observer's task was to identify the global orientation. The spatial configuration of the signal was modulated by a checkerboard pattern of square checks containing potential signal elements. The other locations contained either randomly oriented elements ("noise check") or were blank ("blank check"). The distribution of signal elements was manipulated by varying the size and location of the checks within a fixed-diameter stimulus. An ideal detector would only pool responses from potential signal elements. Humans did this for medium check sizes and for large check sizes when a signal was presented in the fovea. For small check sizes, however, the pooling occurred indiscriminately over relevant and irrelevant locations. For these check sizes, thresholds for the noise check and blank check conditions were similar, suggesting that the limiting noise is not induced by the response to the noise elements. The results are described by a model that filters the stimulus at the potential target orientations and then combines the signals over space in two stages. The first is a mandatory integration of local signals over a fixed area, limited by internal noise at each location. The second is a task-dependent combination of the outputs from the first stage.

Blobs versus bars: psychophysical evidence supports two types of orientation response in human color vision.

The classic hypothesis of Livingstone and Hubel (1984, 1987) proposed two types of color pathways in primate visual cortex based on recordings from single cells: a segregated, modular pathway that signals color but provides little information about shape or form and a second pathway that signals color differences and so defines forms without the need to specify their colors. A major problem has been to reconcile this neurophysiological hypothesis with the behavioral data. A wealth of psychophysical studies has demonstrated that color vision has orientation-tuned responses and little impairment on form related tasks, but these have not revealed any direct evidence for nonoriented mechanisms. Here we use a psychophysical method of subthreshold summation across orthogonal orientations for isoluminant red-green gratings in monocular and dichoptic viewing conditions to differentiate between nonoriented and orientation-tuned responses to color contrast. We reveal nonoriented color responses at low spatial frequencies (0.25-0.375 c/deg) under monocular conditions changing to orientation-tuned responses at higher spatial frequencies (1.5 c/deg) and under binocular conditions. We suggest that two distinct pathways coexist in color vision at the behavioral level, revealed at different spatial scales: one is isotropic, monocular, and best equipped for the representation of surface color, and the other is orientation-tuned, binocular, and selective for shape and form. This advances our understanding of the organization of the neural pathways involved in human color vision and provides a strong link between neurophysiological and behavioral data.

Object Image Size Is a Fundamental Coding Dimension in Human Vision: New Insights and Model.

In previous psychophysical work we found that luminance contrast is integrated over retinal area subject to contrast gain control. If different mechanisms perform this operation for a range of superimposed retinal regions of different sizes, this could provide the basis for size-coding. To test this idea we included two novel features in a standard adaptation paradigm to discount more pedestrian accounts of repulsive size-aftereffects. First, we used spatially jittering luminance-contrast adaptors to avoid simple contour displacement aftereffects. Second, we decoupled adaptor and target spatial frequency to avoid the well-known spatial frequency shift aftereffect. Empirical results indicated strong evidence of a bidirectional size adaptation aftereffect. We show that the textbook population model is inappropriate for our results, and develop our existing model of contrast perception to include multiple size mechanisms with divisive surround-suppression from the largest mechanism. For a given stimulus patch, this delivers a blurred step-function of responses across the population, with contrast and size encoded by the height and lateral position of the step. Unlike for textbook population coding schemes, our human results (N = 4 male, N = 4 female) displayed two asymmetries: (i) size aftereffects were greatest for targets smaller than the adaptor, and (ii) on that side of the function, results did not return to baseline, even when targets were 25% of adaptor diameter. Our results and emergent model properties provide evidence for a novel dimension of visual coding (size) and a novel strategy for that coding, consistent with previous results on contrast detection and discrimination for various stimulus sizes.

Blurring the boundary between models and reality: Visual perception of scale assessed by performance.

One of the primary jobs of visual perception is to build a three-dimensional representation of the world around us from our flat retinal images. These are a rich source of depth cues but no single one of them can tell us about scale (i.e., absolute depth and size). For example, the pictorial depth cues in a (perfect) scale model are identical to those in the real scene that is being modelled. Here we investigate image blur gradients, which derive naturally from the limited depth of field available for any optical device and can be used to help estimate visual scale. By manipulating image blur artificially to produce what is sometimes called fake tilt shift miniaturization, we provide the first performance-based evidence that human vision uses this cue when making forced-choice judgements about scale (identifying which of an image pair was a photograph of a full-scale railway scene, and which was a 1:76 scale model). The orientation of the blur gradient (relative to the ground plane) proves to be crucial, though its rate of change is less important for our task, suggesting a fairly coarse visual analysis of this image parameter.

The attenuation surface for contrast sensitivity has the form of a witch's hat within the central visual field.

Over the full visual field, contrast sensitivity is fairly well described by a linear decline in log sensitivity as a function of eccentricity (expressed in grating cycles). However, many psychophysical studies of spatial visual function concentrate on the central ±4.5 deg (or so) of the visual field. As the details of the variation in sensitivity have not been well documented in this region we did so for small patches of target contrast at several spatial frequencies (0.7-4 c/deg), meridians (horizontal, vertical, and oblique), orientations (horizontal, vertical, and oblique), and eccentricities (0-18 cycles). To reduce the potential effects of stimulus uncertainty, circular markers surrounded the targets. Our analysis shows that the decline in binocular log sensitivity within the central visual field is bilinear: The initial decline is steep, whereas the later decline is shallow and much closer to the classical results. The bilinear decline was approximately symmetrical in the horizontal meridian and declined most steeply in the superior visual field. Further analyses showed our results to be scale-invariant and that this property could not be predicted from cone densities. We used the results from the cardinal meridians to radially interpolate an attenuation surface with the shape of a witch's hat that provided good predictions for the results from the oblique meridians. The witch's hat provides a convenient starting point from which to build models of contrast sensitivity, including those designed to investigate signal summation and neuronal convergence of the image contrast signal. Finally, we provide Matlab code for constructing the witch's hat.

Zero-dimensional noise: the best mask you never saw.

The transmission of weak signals through the visual system is limited by internal noise. Its level can be estimated by adding external noise, which increases the variance within the detecting mechanism, causing masking. But experiments with white noise fail to meet three predictions: (a) noise has too small an influence on the slope of the psychometric function, (b) masking occurs even when the noise sample is identical in each two-alternative forced-choice (2AFC) interval, and (c) double-pass consistency is too low. We show that much of the energy of 2D white noise masks extends well beyond the pass-band of plausible detecting mechanisms and that this suppresses signal activity. These problems are avoided by restricting the external noise energy to the target mechanisms by introducing a pedestal with a mean contrast of 0% and independent contrast jitter in each 2AFC interval (termed zero-dimensional [0D] noise). We compared the jitter condition to masking from 2D white noise in double-pass masking and (novel) contrast matching experiments. Zero-dimensional noise produced the strongest masking, greatest double-pass consistency, and no suppression of perceived contrast, consistent with a noisy ideal observer. Deviations from this behavior for 2D white noise were explained by cross-channel suppression with no need to appeal to induced internal noise or uncertainty. We conclude that (a) results from previous experiments using white pixel noise should be re-evaluated and (b) 0D noise provides a cleaner method for investigating internal variability than pixel noise. Ironically then, the best external noise stimulus does not look noisy.

Theory and data for area summation of contrast with and without uncertainty: evidence for a noisy energy model.

Contrast sensitivity improves with the area of a sine-wave grating, but why? Here we assess this phenomenon against contemporary models involving spatial summation, probability summation, uncertainty, and stochastic noise. Using a two-interval forced-choice procedure we measured contrast sensitivity for circular patches of sine-wave gratings with various diameters that were blocked or interleaved across trials to produce low and high extrinsic uncertainty, respectively. Summation curves were steep initially, becoming shallower thereafter. For the smaller stimuli, sensitivity was slightly worse for the interleaved design than for the blocked design. Neither area nor blocking affected the slope of the psychometric function. We derived model predictions for noisy mechanisms and extrinsic uncertainty that was either low or high. The contrast transducer was either linear (c(1.0)) or nonlinear (c(2.0)), and pooling was either linear or a MAX operation. There was either no intrinsic uncertainty, or it was fixed or proportional to stimulus size. Of these 10 canonical models, only the nonlinear transducer with linear pooling (the noisy energy model) described the main forms of the data for both experimental designs. We also show how a cross-correlator can be modified to fit our results and provide a contemporary presentation of the relation between summation and the slope of the psychometric function.

A psychophysical performance-based approach to the quality assessment of image processing algorithms.

Image processing algorithms are used to improve digital image representations in either their appearance or storage efficiency. The merit of these algorithms depends, in part, on visual perception by human observers. However, in practice, most are assessed numerically, and the perceptual metrics that do exist are criterion sensitive with several shortcomings. Here we propose an objective performance-based perceptual measure of image quality and demonstrate this by comparing the efficacy of a denoising algorithm for a variety of filters. For baseline, we measured detection thresholds for a white noise signal added to one of a pair of natural images in a two-alternative forced-choice (2AFC) paradigm where each image was selected randomly from a set of n = 308 on each trial. In a series of experimental conditions, the stimulus image pairs were passed through various configurations of a denoising algorithm. The differences in noise detection thresholds with and without denoising are objective perceptual measures of the ability of the algorithm to render noise invisible. This was a factor of two (6dB) in our experiment and consistent across a range of filter bandwidths and types. We also found that thresholds in all conditions converged on a common value of PSNR, offering support for this metric. We discuss how the 2AFC approach might be used for other algorithms including compression, deblurring and edge-detection. Finally, we provide a derivation for our Cartesian-separable log-Gabor filters, with polar parameters. For the biological vision community this has some advantages over the more typical (i) polar-separable variety and (ii) Cartesian-separable variety with Cartesian parameters.

Contrast summation across eyes and space is revealed along the entire dipper function by a "Swiss cheese" stimulus.

Previous contrast discrimination experiments have shown that luminance contrast is summed across ocular (T. S. Meese, M. A. Georgeson, & D. H. Baker, 2006) and spatial (T. S. Meese & R. J. Summers, 2007) dimensions at threshold and above. However, is this process sufficiently general to operate across the conjunction of eyes and space? Here we used a "Swiss cheese" stimulus where the blurred "holes" in sine-wave carriers were of equal area to the blurred target ("cheese") regions. The locations of the target regions in the monocular image pairs were interdigitated across eyes such that their binocular sum was a uniform grating. When pedestal contrasts were above threshold, the monocular neural images contained strong evidence that the high-contrast regions in the two eyes did not overlap. Nevertheless, sensitivity to dual contrast increments (i.e., to contrast increments in different locations in the two eyes) was a factor of ∼1.7 greater than to single increments (i.e., increments in a single eye), comparable with conventional binocular summation. This provides evidence for a contiguous area summation process that operates at all contrasts and is influenced little, if at all, by eye of origin. A three-stage model of contrast gain control fitted the results and possessed the properties of ocularity invariance and area invariance owing to its cascade of normalization stages. The implications for a population code for pattern size are discussed.

Contrast integration over area is extensive: a three-stage model of spatial summation.

Classical studies of area summation measure contrast detection thresholds as a function of grating diameter. Unfortunately, (i) this approach is compromised by retinal inhomogeneity and (ii) it potentially confounds summation of signal with summation of internal noise. The Swiss cheese stimulus of T. S. Meese and R. J. Summers (2007) and the closely related Battenberg stimulus of T. S. Meese (2010) were designed to avoid these problems by keeping target diameter constant and modulating interdigitated checks of first-order carrier contrast within the stimulus region. This approach has revealed a contrast integration process with greater potency than the classical model of spatial probability summation. Here, we used Swiss cheese stimuli to investigate the spatial limits of contrast integration over a range of carrier frequencies (1-16 c/deg) and raised plaid modulator frequencies (0.25-32 cycles/check). Subthreshold summation for interdigitated carrier pairs remained strong (∼4 to 6 dB) up to 4 to 8 cycles/check. Our computational analysis of these results implied linear signal combination (following square-law transduction) over either (i) 12 carrier cycles or more or (ii) 1.27 deg or more. Our model has three stages of summation: short-range summation within linear receptive fields, medium-range integration to compute contrast energy for multiple patches of the image, and long-range pooling of the contrast integrators by probability summation. Our analysis legitimizes the inclusion of widespread integration of signal (and noise) within hierarchical image processing models. It also confirms the individual differences in the spatial extent of integration that emerge from our approach.

Spatially extensive summation of contrast energy is revealed by contrast detection of micro-pattern textures.

Vision must analyze the retinal image over both small and large areas to represent fine-scale spatial details and extensive textures. The long-range neuronal convergence that this implies might lead us to expect that contrast sensitivity should improve markedly with the contrast area of the image. But this is at odds with the orthodox view that contrast sensitivity is determined merely by probability summation over local independent detectors. To address this puzzle, I aimed to assess the summation of luminance contrast without the confounding influence of area-dependent internal noise. I measured contrast detection thresholds for novel Battenberg stimuli that had identical overall dimensions (to clamp the aggregation of noise) but were constructed from either dense or sparse arrays of micro-patterns. The results unveiled a three-stage visual hierarchy of contrast summation involving (i) spatial filtering, (ii) long-range summation of coherent textures, and (iii) pooling across orthogonal textures. Linear summation over local energy detectors was spatially extensive (as much as 16 cycles) at Stage 2, but the resulting model is also consistent with earlier classical results of contrast summation (J. G. Robson & N. Graham, 1981), where co-aggregation of internal noise has obscured these long-range interactions.

Orientation masking and cross-orientation suppression (XOS): implications for estimates of filter bandwidth.

Most contemporary models of spatial vision include a cross-oriented route to suppression (masking from a broadly tuned inhibitory pool), which is most potent at low spatial and high temporal frequencies (T. S. Meese & D. J. Holmes, 2007). The influence of this pathway can elevate orientation-masking functions without exciting the target mechanism, and because early psychophysical estimates of filter bandwidth did not accommodate this, it is likely that they have been overestimated for this corner of stimulus space. Here we show that a transient 40% contrast mask causes substantial binocular threshold elevation for a transient vertical target, and this declines from a mask orientation of 0° to about 40° (indicating tuning), and then more gently to 90°, where it remains at a factor of ∼4. We also confirm that cross-orientation masking is diminished or abolished at high spatial frequencies and for sustained temporal modulation. We fitted a simple model of pedestal masking and cross-orientation suppression (XOS) to our data and those of G. C. Phillips and H. R. Wilson (1984) and found the dependency of orientation bandwidth on spatial frequency to be much less than previously supposed. An extension of our linear spatial pooling model of contrast gain control and dilution masking (T. S. Meese & R. J. Summers, 2007) is also shown to be consistent with our results using filter bandwidths of ±20°. Both models include tightly and broadly tuned components of divisive suppression. More generally, because XOS and/or dilution masking can affect the shape of orientation-masking curves, we caution that variations in bandwidth estimates might reflect variations in processes that have nothing to do with filter bandwidth.

Cross-orientation masking is speed invariant between ocular pathways but speed dependent within them.

In human (D. H. Baker, T. S. Meese, & R. J. Summers, 2007b) and in cat (B. Li, M. R. Peterson, J. K. Thompson, T. Duong, & R. D. Freeman, 2005; F. Sengpiel & V. Vorobyov, 2005) there are at least two routes to cross-orientation suppression (XOS): a broadband, non-adaptable, monocular (within-eye) pathway and a more narrowband, adaptable interocular (between the eyes) pathway. We further characterized these two routes psychophysically by measuring the weight of suppression across spatio-temporal frequency for cross-oriented pairs of superimposed flickering Gabor patches. Masking functions were normalized to unmasked detection thresholds and fitted by a two-stage model of contrast gain control (T. S. Meese, M. A. Georgeson, & D. H. Baker, 2006) that was developed to accommodate XOS. The weight of monocular suppression was a power function of the scalar quantity 'speed' (temporal-frequency/spatial-frequency). This weight can be expressed as the ratio of non-oriented magno- and parvo-like mechanisms, permitting a fast-acting, early locus, as benefits the urgency for action associated with high retinal speeds. In contrast, dichoptic-masking functions superimposed. Overall, this (i) provides further evidence for dissociation between the two forms of XOS in humans, and (ii) indicates that the monocular and interocular varieties of XOS are space/time scale-dependent and scale-invariant, respectively. This suggests an image-processing role for interocular XOS that is tailored to natural image statistics-very different from that of the scale-dependent (speed-dependent) monocular variety.

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 degrees ). 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.

A common contrast pooling rule for suppression within and between the eyes.

Recent work has revealed multiple pathways for cross-orientation suppression in cat and human vision. In particular, ipsiocular and interocular pathways appear to assert their influence before binocular summation in human but have different (1) spatial tuning, (2) temporal dependencies, and (3) adaptation after-effects. Here we use mask components that fall outside the excitatory passband of the detecting mechanism to investigate the rules for pooling multiple mask components within these pathways. We measured psychophysical contrast masking functions for vertical 1 cycle/deg sine-wave gratings in the presence of left or right oblique ( 16%. We tested contrast gain control models involving two types of contrast combination on the denominator: (1) spatial pooling of the mask after a local nonlinearity (to calculate either root mean square contrast or energy) and (2) (Holmes & Meese, 2004, Journal of Vision 4, 1080-1089), involving the linear sum of the mask component contrasts. Monoptic and dichoptic masking were typically better fit by the spatial pooling models, but binocular masking was not: it demanded strict linear summation of the Michelson contrast across mask orientation. Another scheme, in which suppressive pooling followed compressive contrast responses to the mask components (e.g., oriented cortical cells), was ruled out by all of our data. We conclude that the different processes that underlie monoptic and dichoptic masking use the same type of contrast pooling within their respective suppressive fields, but the effects do not sum to predict the binocular case.

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 (contrast discrimination) experiments with a group of eight strabismic amblyopes using horizontal sinusoidal gratings (mainly 3c/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.

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).