Border effects on brightness: a review of findings, models and issues

Isolation of brightness induction effects on target patches from adjacent surrounds and remote backgrounds

The brightness (perceived intensity) of a region of visual space depends on its luminance and on the luminance of nearby regions. This phenomenon is called brightness induction and includes both brightness contrast and assimilation. Historically, and on a purely descriptive level, brightness contrast refers to a directional shift in target brightness away from the brightness of an adjacent region while assimilation refers to a brightness shift toward that of an adjacent region. In order to understand mechanisms, it is important to differentiate the descriptive terms contrast and assimilation from the optical and/or neural processes, often similarly named, which cause the effects. Experiment 1 isolated the effect on target patch (64 cd/m2) matching luminance (brightness) of six surround-ring widths (0.1°–24.5°) varied over 11 surround-ring luminances (32–96 cd/m2). Using the same observers, Experiment 2 examined the effect of the identical surround-ring parameters on target patch matching luminance in the presence of a dark (0.0 cd/m2) and a bright (96 cd/m2) remote background. By differencing the results of Experiment 1 (the isolated effect of the surround-ring) from those of Experiment 2 (the combined effect of the surround-ring with the dark and bright remote background) we further isolated the effect of the remote background. The results reveal that surround-rings and remote backgrounds produce brightness contrast effects in the target patch that are of the same or opposite polarity depending on the luminance polarity of these regions relative to target patch luminance. The strength of brightness contrast from the surround-ring varied with surround-ring luminance and width. Brightness contrast (darkening) in the target from the bright remote background was relatively constant in magnitude across all surround-ring luminances and increased in magnitude with decreasing surround-ring width. Brightness contrast (brightening) from the isolated dark remote background also increased in magnitude with decreasing surround-ring width: however, despite some regional flattening of the functions due to the fixed luminance of the dark remote background, induction magnitude was much reduced in the presence of a surround-ring of greater luminance than the target patch indicating a non-linear interaction between the dark remote background and surround-ring luminance.

The SSVEP tracks attention, not consciousness, during perceptual filling-in

Research on the neural basis of conscious perception has almost exclusively shown that becoming aware of a stimulus leads to increased neural responses. By designing a novel form of perceptual filling-in (PFI) overlaid with a dynamic texture display, we frequency-tagged multiple disappearing targets as well as their surroundings. We show that in a PFI paradigm, the disappearance of a stimulus and subjective invisibility is associated with increases in neural activity, as measured with steady-state visually evoked potentials (SSVEPs), in electroencephalography (EEG). We also find that this increase correlates with alpha-band activity, a well-established neural measure of attention. These findings cast doubt on the direct relationship previously reported between the strength of neural activity and conscious perception, at least when measured with current tools, such as the SSVEP. Instead, we conclude that SSVEP strength more closely measures changes in attention.

A multiple-response frequency-tagging paradigm measures graded changes in consciousness during perceptual filling-in

Perceptual filling-in (PFI) occurs when a physically present visual target disappears from conscious perception, with its location filled-in by the surrounding visual background. These perceptual changes are complete, near instantaneous, and can occur for multiple separate locations simultaneously. Here, we show that contrasting neural activity during the presence or absence of multi-target PFI can complement other findings from multistable phenomena to reveal the neural correlates of consciousness (NCC). We presented four peripheral targets over a background dynamically updating at 20 Hz. While participants reported on target disappearances/reappearances via button press/release, we tracked neural activity entrained by the background during PFI using steady-state visually evoked potentials (SSVEPs) recorded in the electroencephalogram. We found background SSVEPs closely correlated with subjective report, and increased with an increasing amount of PFI. Unexpectedly, we found that as the number of filled-in targets increased, the duration of target disappearances also increased, suggesting that facilitatory interactions exist between targets in separate visual quadrants. We also found distinct spatiotemporal correlates for the background SSVEP harmonics. Prior to genuine PFI, the response at the second harmonic (40 Hz) increased before the first (20 Hz), which we tentatively link to an attentional effect, while no such difference between harmonics was observed for physically removed stimuli. These results demonstrate that PFI can be used to study multi-object perceptual suppression when frequency-tagging the background of a visual display, and because there are distinct neural correlates for endogenously and exogenously induced changes in consciousness, that it is ideally suited to study the NCC.

On a lightness phenomenon

This work demonstrates a lightness phenomenon useful to extend the notion of "belongingness," which is crucial to explain a class of illusions that include simultaneous lightness contrast, the Koffka-Benussi ring, the Benary cross, and the White effect. These phenomena manifest some kind of dissimilarity, difference, or change responsible for the perceived contrast. The dissimilarity is related to the "belongingness" of the crucial gray elements (i) to a unique or separated/divided object, as in the Koffka-Benussi ring, or (ii) to the figure or to the background, as in the Benary and White effects. If we plausibly assume that differences and changes are biologically important to be detected and if necessary highlighted, then any visible difference might induce a contrast effect. This is the main hypothesis demonstrated by the lightness phenomenon based on checks grouped vertically, split in two upper and lower halves, and segregated from the homogeneous gray background. The checks are alternated and vertically/horizontally reversed in the upper and lower halves of the pattern. Despite the constant visual organization and in spite of the identical local contrast within each check, the inner area of the elements of the upper group appears darker than the one of the lower group. The visible dissimilarity, although not related to the notion of belongingness, is sufficient to elicit a clear lightness difference.

Interactions of flicker and motion

We present a series of novel observations about interactions between flicker and motion that lead to three distinct perceptual effects. We use the term flicker to describe alternating changes in a stimulus' luminance or color (i.e. a circle that flickers from black to white and visa-versa). When objects flicker, three distinct phenomena can be observed: (1) Flicker Induced Motion (FLIM) in which a single, stationary object, appears to move when it flickers at certain rates; (2) Flicker Induced Motion Suppression (FLIMS) in which a moving object appears to be stationary when it flickers at certain rates, and (3) Flicker-Induced Induced-Motion (FLIIM) in which moving objects that are flickering induce another flickering stationary object to appear to move. Across four psychophysical experiments, we characterize key stimulus parameters underlying these flicker-motion interactions. Interactions were strongest in the periphery and at flicker frequencies above 10 Hz. Induced motion occurred not just for luminance flicker, but for isoluminant color changes as well. We also found that the more physically moving objects there were, the more motion induction to stationary objects occurred. We present demonstrations that the effects reported here cannot be fully accounted for by eye movements: we show that the perceived motion of multiple stationary objects that are induced to move via flicker can appear to move independently and in random directions, whereas eye movements would have caused all of the objects to appear to move coherently. These effects highlight the fundamental role of spatiotemporal dynamics in the representation of motion and the intimate relationship between flicker and motion.

Dissecting the influence of the collinear and flanking bars in White's effect

In White's effect equiluminant test patches placed on the black and white bars of a square-wave grating appear different in brightness. The illusion has generated intense interest because the direction of the brightness effect does not correlate with the amount of black or white border in contact with the test patch, or in its general vicinity. Therefore, unlike brightness induction effects such as simultaneous contrast, White's effect is not consistent with explanations based on contrast or assimilation that depend solely on the relative amounts of black and white surrounding the test patches. We independently manipulated the luminance of the collinear and flanking bars to investigate their influence on test patch matching luminance (brightness). The inducing grating was a 0.5c/d square-wave and test patches measured 1.0° in width and either 0.5° or 3.0° in height. Test patches measuring 0.5° in height had more extensive contact with the collinear bars and test patches measuring 3.0° in height had more extensive contact with the flanking bars. The luminance of the collinear (or flanking) bars assumed twenty values from 3.2 to 124.8cd/m(2), while the luminance of the flanking (or collinear) bars remained white (124.8cd/m(2)) or black (3.2cd/m(2)). Under these conditions the influence of the collinear and flanking bars was found to be purely in the direction of contrast. The effect was dominated by contrast from the collinear bars (which results in White's effect), however, the influence of the flanking bars was also in the contrast direction. The data elucidate the luminance relationships between the collinear and flanking bars which produce the behavior associated with White's effect as well as that associated with "the inverted White effect" which is akin to simultaneous contrast.

Luminance gradient configuration determines perceived lightness in a simple geometric illusion

Accurate perception of surface reflectance poses a significant computational problem for the visual system. The amount of light reflected by a surface is affected by a combination of factors including the surface's reflectance properties and illumination conditions. The latter are not limited by the strength of the illuminant but also include the relative placement of the light illuminating the surface, the orientation of the surface and its 3d shape, all of which result in a pattern of luminance gradients across the surface. In this study we explore how luminance gradients contribute to lightness perception. We introduce a novel, simple lightness illusion. It consists of six separate checks, organized in rows of two. Each check has a negative luminance gradient across it. The top and the bottom rows are the same: with the darker check on the left, and the lighter check on the right. Two checks in the middle row are identical; however, the check on the right appears darker than the check on the left. As there are no shared borders between the checks, simultaneous contrast cannot explain the effect. However, there are multiple possible explanations including spatial filtering (Blakeslee and McCourt, 2004) or some higher-order mechanism such as perceptual grouping or amodal completion. Here, we explore these possibilities by manipulating the luminance configurations and the gradient slopes of the checks.

Enhancement of backlight-scaled images

Switching the liquid crystal display (LCD) backlight of a portable multimedia device to a low power level saves energy but results in poor image quality especially for the low-luminance image areas. In this paper, we propose an image enhancement algorithm that overcomes such effects of dim LCD backlight by taking the human visual property into consideration. It boosts the luminance of image areas below the perceptual threshold while preserving the contrast of the other image areas. We apply the just noticeable difference theory and decompose an image into an HVS response layer and a background luminance layer. The boosting and compression processes, which enhance the visibility of the low-luminance image areas, are carried out in the background luminance layer to avoid luminance gradient reversal and over-compensation. The contrast of the processed image is further enhanced by exploiting the Craik-O'Brein-Cornsweet visual illusion. Experimental results are provided to show the performance of the proposed algorithm.

Brightness induction magnitude declines with increasing distance from the inducing field edge

Brightness induction refers to a class of visual illusions where the perceived intensity of a region of space is influenced by the luminance of surrounding regions. These illusions are significant because they provide insight into the neural organization and processing strategies employed by the visual system. The nature of these processing strategies, however, has long been debated. Here we investigate the spatial characteristics of grating induction as a function of the distance from the inducing field edge to evaluate the viability of various competing models. In particular multiscale spatial filtering models and homogeneous filling-in models make very different predictions in regard to the magnitude of induction as a function of this distance. Filling-in explanations predict that the brightness/lightness of the filled-in region will be homogeneous, whereas multiscale filtering predicts a fall-off in induction magnitude with distance from the inducing field edge. Induction magnitude was measured using a narrow probe version of the quadrature-phase motion-cancellation paradigm (Blakeslee & McCourt, 2011) and a point-by-point brightness matching paradigm (Blakeslee & McCourt, 1997, 1999; McCourt, 1994). Both techniques reveal a decrease in the magnitude of induction with increasing distance from the inducing edge. A homogeneous filling-in mechanism cannot explain the induced structure in the test fields of these stimuli. The results argue strongly against filling-in mechanisms as well as against any mechanism that posits that induction is homogeneous. The structure of the induction is, however, well accounted for by the multiscale filtering (ODOG) model of Blakeslee and McCourt (1999). These results support models of brightness/lightness, such as filtering models, which preserve these gradients of induction.

A new taxonomy for perceptual filling-in

Perceptual filling-in occurs when structures of the visual system interpolate information across regions of visual space where that information is physically absent. It is a ubiquitous and heterogeneous phenomenon, which takes place in different forms almost every time we view the world around us, such as when objects are occluded by other objects or when they fall behind the blind spot. Yet, to date, there is no clear framework for relating these various forms of perceptual filling-in. Similarly, whether these and other forms of filling-in share common mechanisms is not yet known. Here we present a new taxonomy to categorize the different forms of perceptual filling-in. We then examine experimental evidence for the processes involved in each type of perceptual filling-in. Finally, we use established theories of general surface perception to show how contextualizing filling-in using this framework broadens our understanding of the possible shared mechanisms underlying perceptual filling-in. In particular, we consider the importance of the presence of boundaries in determining the phenomenal experience of perceptual filling-in.

Lightness, brightness and transparency: a quarter century of new ideas, captivating demonstrations and unrelenting controversy

The past quarter century has witnessed considerable advances in our understanding of Lightness (perceived reflectance), Brightness (perceived luminance) and perceived Transparency (LBT). This review poses eight major conceptual questions that have engaged researchers during this period, and considers to what extent they have been answered. The questions concern 1. the relationship between lightness, brightness and perceived non-uniform illumination, 2. the brain site for lightness and brightness perception, 3 the effects of context on lightness and brightness, 4. the relationship between brightness and contrast for simple patch-background stimuli, 5. brightness "filling-in", 6. lightness anchoring, 7. the conditions for perceptual transparency, and 8. the perceptual representation of transparency. The discussion of progress on major conceptual questions inevitably requires an evaluation of which approaches to LBT are likely and which are unlikely to bear fruit in the long term, and which issues remain unresolved. It is concluded that the most promising developments in LBT are (a) models of brightness coding based on multi-scale filtering combined with contrast normalization, (b) the idea that the visual system decomposes the image into "layers" of reflectance, illumination and transparency, (c) that an understanding of image statistics is important to an understanding of lightness errors, (d) Whittle's logW metric for contrast-brightness, (e) the idea that "filling-in" is mediated by low spatial frequencies rather than neural spreading, and (f) that there exist multiple cues for identifying non-uniform illumination and transparency. Unresolved issues include how relative lightness values are anchored to produce absolute lightness values, and the perceptual representation of transparency. Bridging the gap between multi-scale filtering and layer decomposition approaches to LBT is a major task for future research.

A biologically inspired algorithm for the recovery of shading and reflectance images

We present an algorithm for separating the shading and reflectance images of photographed natural scenes. The algorithm exploits the constraint that in natural scenes chromatic and luminance variations that are co-aligned mainly arise from changes in surface reflectance, whereas near-pure luminance variations mainly arise from shading and shadows. The novel aspect of the algorithm is the initial separation of the image into luminance and chromatic image planes that correspond to the luminance, red-green, and blue-yellow channels of the primate visual system. The red-green and blue-yellow image planes are analysed to provide a map of the changes in surface reflectance, which is then used to separate the reflectance from shading changes in both the luminance and chromatic image planes. The final reflectance image is obtained by reconstructing the chromatic and luminance-reflectance-change maps, while the shading image is obtained by subtracting the reconstructed luminance-reflectance image from the original luminance image. A number of image examples are included to illustrate the successes and limitations of the algorithm.

Cortical processing of a brightness illusion

Several brightness illusions indicate that borders can affect the perception of surfaces dramatically. In the Cornsweet illusion, two equiluminant surfaces appear to be different in brightness because of the contrast border between them. Here, we report the existence of cells in monkey visual cortex that respond to such an "illusory" brightness. We find that luminance responsive cells are located in color-activated regions (cytochrome oxidase blobs and bridges) of primary visual cortex (V1), whereas Cornsweet responsive cells are found preferentially in the color-activated regions (thin stripes) of second visual area (V2). This colocalization of brightness and color processing within V1 and V2 suggests a segregation of contour and surface processing in early visual pathways and a hierarchy of brightness information processing from V1 to V2 in monkeys.

A unified theory of brightness contrast and assimilation incorporating oriented multiscale spatial filtering and contrast normalization

Brightness induction includes both contrast and assimilations effects. Brightness contrast occurs when the brightness of a test region shifts away from the brightness of adjacent regions. Brightness assimilation refers to the opposite situation in which the brightness of the test region shifts toward that of the surrounding regions. Interestingly, in the White effect [Perception 8 (1979) 413] the direction of the induced brightness change does not correlate with the amount of black or white border in contact with the gray test patch. This has led some investigators to reject spatial filtering explanations not only for the White effect but for brightness perception in general. Instead, these investigators have offered explanations based on a variety of junction analyses and/or perceptual organization schemes. Here, these approaches are challenged with a critical set of new psychophysical measurements that determined the magnitude of the White effect, the shifted White effect [Perception 10 (1981) 215] and the checkerboard illusion [R.L. DeValois, K.K. DeValois, Spatial Vision, Oxford University Press, NY, 1988] as a function of inducing pattern spatial frequency and test patch height. The oriented difference-of-Gaussians (ODOG) computational model of Blakeslee and McCourt [Vision Res. 39 (1999) 4361] parsimoniously accounts for the psychophysical data, and illustrates that mechanisms based on junction analysis or perceptual inference are not required to explain them. According to the ODOG model, brightness induction results from linear spatial filtering with an incomplete basis set (the finite array of spatial filters in the human visual system). In addition, orientation selectivity of the filters and contrast normalization across orientation channels are critical for explaining some brightness effects, such as the White effect.

Building surfaces from borders in Areas 17 and 18 of the cat

Several brightness illusions indicate that borders can dramatically affect the perception of adjoining surfaces. In the Craik-O'Brien-Cornsweet illusion, in particular, two equiluminant surfaces can appear different in brightness due to the contrast border between them. Although the psychophysical nature of this phenomenon has been well characterized, the neural circuitry underlying this effect is unexplored. Here, we have asked whether there are cells in visual cortex which respond to edge-induced illusory brightness percepts such as the Cornsweet. Using optical imaging and single unit recordings methods, we have studied responses of the primary (Area 17) and second (Area 18) visual cortical areas of the anesthetized cat to both real luminance change and Cornsweet brightness change. We find that there are indeed cells whose responses are modulated in phase with the modulation of the Cornsweet stimulus. These cells are present in both Area 17 and Area 18, but are more prevalent in Area 18. These responses are generally weak and are found even when receptive fields are distant from the contrast border. Consistent with perception, cells which respond to the Cornsweet border are modulated in antiphase to the Narrow Real (another border-induced illusory brightness stimulus). Remarkably, we also find evidence of edge-induced responses to illusory brightness change using intrinsic signal optical imaging. Both real luminance change and edge-induced brightness change produces a greater imaged response in Area 18 than in Area 17. Thus, in the absence of direct luminance stimulation, cells in visual cortex can respond to modulation of distant border contrasts. We suggest that the perception of surface brightness was encoded in the early visual cortical pathway by both surface luminance contrast signals in Area 17 (Rossi, A. F., Rittenhouse, C. D., & Paradiso, M. A. (1996). The representation of brightness in primary visual cortex. Science, 273, 1104-7) and border-induced contrast signals that predominate in Area 18.

Increased sensitivity to speed changes during adaptation to first-order, but not to second-order motion

Observers adapted to drifting patterns varying either in luminance (first-order pattern), or in contrast (second-order pattern). Sensitivity to increases or decreases in the speed of the first-order pattern increased sharply as adaptation time increased, but sensitivity to speed changes of the second-order pattern remained unchanged throughout the adaptation time. Adaptation of first-order motion mechanisms seems thus to mediate increased sensitivity to variations in speed around the adapting speed. No evidence was found for such effects of adaptation to second-order motion. The observed differences in the effects of adaptation accord well with reports of fundamental differences between after-effects to drifting first- and second-order patterns and are in harmony with models of motion perception emphasizing different mechanisms for the detection of first- and second-order motion.

Lightness from contrast: a selective integration model

As has been observed by Wallach (1948), perceived lightness is proportional to the ratio between the luminances of adjacent regions in simple disk-annulus or bipartite scenes. This psychophysical finding resonates with neurophysiological evidence that retinal mechanisms of receptor adaptation and lateral inhibition transform the incoming illuminance array into local measures of luminance contrast. In many scenic configurations, however, the perceived lightness of a region is not proportional to its ratio with immediately adjacent regions. In a particularly striking example of this phenomenon, called White's illusion, the relationship between the perceived lightnesses of two gray regions is the opposite of what is predicted by local edge ratios or contrasts. This paper offers a new treatment of how local measures of luminance contrast can be selectively integrated to simulate lightness percepts in a wide range of image configurations. Our approach builds on a tradition of edge integration models (Horn, 1974; Land & McCann, 1971) and contrast/filling-in models (Cohen & Grossberg, 1984; Gerrits & Vendrik 1970; Grossberg & Mingolla, 1985a, 1985b). Our selective integration model (SIM) extends the explanatory power of previous models, allowing simulation of a number of phenomena, including White's effect, the Benary Cross, and shading and transparency effects reported by Adelson (1993), as well as aspects of motion, depth, haploscopic, and Gelb induced contrast effects. We also include an independently derived variant of a recent depthful version of White's illusion, showing that our model can inspire new stimuli.

An empirical explanation of the cornsweet effect

A long-standing puzzle in vision is the assignment of illusory brightness values to visual territories based on the characteristics of their edges (the Craik-O'Brien-Cornsweet effect). Here we show that the perception of the equiluminant territories flanking the Cornsweet edge varies according to whether these regions are more likely to be similarly illuminated surfaces having the same material properties or unequally illuminated surfaces with different properties. Thus, if the likelihood is increased that these territories are surfaces with similar reflectance properties under the same illuminant, the Craik-O'Brien-Cornsweet effect is diminished; conversely, if the likelihood is increased that the adjoining territories are differently reflective surfaces receiving different amounts of illumination, the effect is enhanced. These findings indicate that the Craik-O'Brien-Cornsweet effect is determined by the relative probabilities of the possible sources of the luminance profiles in the stimulus.

The missing-fundamental illusion at isoluminance

The missing-fundamental illusion describes how a square wave with its fundamental Fourier component removed appears as a square wave. This illusion is normally explained with reference to the bandpass nature of the luminance-contrast-sensitivity function, together with a 'default-to-square-wave' rule. Since the chromatic-contrast-sensitivity function is low-pass, we should not expect a missing-fundamental illusion at isoluminance. Using a simultaneous-detection-and-identification paradigm to eliminate contrast as a cue to discrimination, we nevertheless found that chromatic missing fundamentals and square waves could not be separately identified at detection threshold: just under twice the contrast required to detect the stimuli was needed to identify them. To test whether this was due to insufficiently narrow chromatic-channel bandwidths, we measured detection and identification thresholds for chromatic F and 3F sine-wave gratings. In this case identification was possible almost at detection threshold, suggesting that channel bandwidth limitations were not the critical factor. It is suggested that the weak missing-fundamental illusion observed at isoluminance probably reflects the operation of mechanisms similar to those that are responsible for the chromatic Craik-Cornsweet illusion.

A multiscale spatial filtering account of the White effect, simultaneous brightness contrast and grating induction

Blakeslee and McCourt ((1997) Vision Research, 37, 2849-2869) demonstrated that a multiscale array of two-dimensional difference-of-Gaussian (DOG) filters provided a simple but powerful model for explaining a number of seemingly complex features of grating induction (GI), while simultaneously encompassing salient features of brightness induction in simultaneous brightness contrast (SBC), brightness assimilation and Hermann Grid stimuli. The DOG model (and isotropic contrast models in general) cannot, however, account for another important group of brightness effects which includes the White effect (White (1979) Perception, 8, 413-416) and the demonstrations of Todorovic ((1997) Perception, 26, 379-395). This paper introduces an oriented DOG (ODOG) model which differs from the DOG model in that the filters are anisotropic and their outputs are pooled nonlinearly. The ODOG model qualitatively predicts the appearance of the test patches in the White effect, the Todorovic demonstration, GI and SBC, while quantitatively predicting the relative magnitudes of these brightness effects as measured psychophysically using brightness matching. The model also accounts for both the smooth transition in test patch brightness seen in the White effect (White & White (1985) Vision Research, 25, 1331-1335) when the relative phase of the test patch is varied relative to the inducing grating, and for the spatial variation of brightness across the test patch as measured using point-by-point brightness matching. Finally, the model predicts intensive aspects of brightness induction measured in a series of Todorovic stimuli as the arms of the test crosses are lengthened (Pessoa, Baratoff, Neumann & Todorokov (1998) Investigative Ophthalmology and Visual Science, Supplement, 39, S159), but fails in one condition. Although it is concluded that higher-level perceptual grouping factors may play a role in determining brightness in this instance, in general the psychophysical results and ODOG modeling argue strongly that the induced brightness phenomena of SBC, GI, the White effect and the Todorovic demonstration, primarily reflect early-stage cortical filtering operations in the visual system.

A two-dimensional model of brightness perception based on spatial filtering consistent with retinal processing

We have applied a multiple scale, 2-D model of brightness perception to a broad range of brightness phenomena. The filters encapsulate only processing that is well established to occur in retinal ganglion cells. Their outputs are then combined in the simplest way compatible with the earliest levels of cortical processing. Not only essential features of a number of the phenomena but also more subtle shading effects are reproduced. Because of the retinal nature of this model, these results would appear to support previous speculation that much of the ground work for brightness perception is performed at the retinal level.

Brightness with and without perceived transparency: when does it make a difference?

Subjects matched the brightness of test patches whose inner (adjacent) surrounds appeared either as transparent overlays on a wider background that included the test patch or as regions differing in reflectance from the test patch and the outer surround. In the above configurations the luminance and spatial extent of the inner surround was identical, thus controlling for the effects of surround luminance. Configuration condition had a significant effect on test-patch brightness. In general, test-patch brightness was significantly elevated under conditions favouring the interpretation of the stimulus as including a transparent overlay. The largest effect occurred for the configuration in which the perception of transparency was supported by stereo depth cues. The brightness effect was mediated by the virtual transmittance of the transparent overlay, increasing in magnitude with decreasing transmittance. Further, the effect of transparency on brightness was greatest for test-patch luminances near to those of their immediate surrounds.

Similar mechanisms underlie simultaneous brightness contrast and grating induction

The experiments explore whether the mechanism(s) underlying grating induction (GI) can also account for simultaneous brightness contrast (SBC). At each of three test field heights (1, 3 and 6 deg), point-by-point brightness matches were obtained from two subjects for test field widths of 32 deg (GI condition), 14, 12, 8, 6, 3 and 1 deg. The point-by-point brightness matches were quantitatively compared, using GI condition matches as a standard, to assess systematic alterations in the structure and average magnitude of brightness and darkness induction within the test fields as a function of changing test field height and width. In the wider test fields induction structure was present and was generally well-accounted for by the GI condition sinewave predictions. As test field width decreased the sinewave amplitude of the induced structure in the test field decreased (i.e., flattened), and eventually became negative (i.e., showed a reverse cusping) at the narrower test field widths. As expected, both subjects showed a decrease in overall levels of brightness and darkness induction with increasing test field height. For any particular test field height, however, relative brightness increased with decreasing test field width. This brightness increase began at larger test field widths as test field height increased. The results are parsimoniously accounted for by the output of a weighted, octave-interval array of seven difference-of-gaussian filters. This array of filters differs from those previously employed to model various aspects of spatial vision in that it includes filters tuned to much lower spatial frequencies. The two-dimensional output of this same array of filters also accounts for the GI demonstrations of Zaidi [(1989) Vision Research, 29, 691-697], Shapley and Reid's [(1985) Proceedings of the National Academy of Sciences USA, 82, 5983-5986] contrast and assimilation demonstration, and the induced spots seen at the street intersections of the Hermann Grid. The physiological plausibility of the filter array explanation of brightness induction is discussed, along with a consideration of its relationship to other models of brightness perception.

Mach bands: how many models are possible? Recent experimental findings and modeling attempts

Mach bands are illusory bright and dark bands seen where a luminance plateau meets a ramp, as in half-shadows or penumbras. A tremendous amount of work has been devoted to studying the psychophysics and the potential underlying neural circuitry concerning this phenomenon. A number of theoretical models also have been proposed, originating in the seminal studies of Mach himself. The present article reviews the main experimental findings after 1965 and the main recent theories of early vision that have attempted to account for the effect. It is shown that the different theories share working principles and can be grouped into three classes: (a) feature-based; (b) rule-based; and (c) filling-in. In order to evaluate individual proposals, it is necessary to consider them in the larger picture of visual science and to determine how they contribute to the understanding of vision in general.

Facilitation of luminance grating detection by induced gratings

Grating induction causes a homogeneous test field surrounded by sinewave gratings to possess an induced counterphase grating [McCourt M. E. (1982). Vision Research, 22, 119]. There is currently no consensus about the stage of visual processing at which illusory phenomena such as simultaneous brightness contrast are signaled. We measured the masking efficacy of induced gratings by measuring contrast detection thresholds for targets (sinewave luminance gratings) added in phase to both real and induced gratings which were matched in apparent contrast. At spatial frequencies below c. 0.5 c/deg, target detection and discrimination were comparably facilitated by both real and induced low-contrast pedestals (0.5-2%). At higher spatial frequencies (above 1.0 c/deg) facilitation continued to be observed for targets added in-phase to real grating pedestals, but occurred only for targets added out-of-phase with induced pedestal gratings. Higher inducing frequencies by themselves were not responsible for the observed phase shift of facilitation, however, since both real and induced pedestals produced similar target contrast discrimination functions when inducing frequency was varied by manipulating viewing distance (which holds the ratio of inducing grating period and test field height constant). The results imply the existence of at least two types of lateral interactive processes: one producing in-phase facilitation, and a second producing out-of-phase facilitation. The relative contribution of each process depends upon the ratio of inducing grating period and test field height.

A contrast- and luminance-driven multiscale network model of brightness perception

A neural network model of brightness perception is developed to account for a wide variety of data, including the classical phenomenon of Mach bands, low- and high-contrast missing fundamental, luminance staircases, and non-linear contrast effects associated with sinusoidal waveforms. The model builds upon previous work on filling-in models that produce brightness profiles through the interaction of boundary and feature signals. Boundary computations that are sensitive to luminance steps and to continuous luminance gradients are presented. A new interpretation of feature signals through the explicit representation of contrast-driven and luminance-driven information is provided and directly addresses the issue of brightness "anchoring". Computer simulations illustrate the model's competencies.

Contrast-matching analysis of grating induction and suprathreshold contrast perception

The effect that induced gratings [Vision Res. 22, 119 (1982)] exert on the perceived contrast of standard gratings situated within a 0.5 degrees test field was assessed for two observers by a contrast-matching procedure. Five levels of inducing-grating contrast, CI, ranged from 0.0 to 0.75. Functions relating matching contrast, CM, to standard-grating contrast, CS, were obtained at four levels of inducing-grating contrast across a range of standard contrasts, -0.90 < or = CS < or = +0.90, where the sign denotes the spatial phase of the standard relative to the inducing grating. The matching functions possessed three distinct limbs separated by two inflection points; the limb between the inflection points represents a region of high contrast gain. Another measure, canceling contrast, was obtained at the four levels of inducing contrast by variation of CS until the test field appeared spatially homogeneous. Induction magnitude measured in terms of canceling contrast, CC, grew approximately linearly with CI, such that CC = 0.819 (CI). Induction magnitude determined from matching-contrast data obtained for homogeneous test fields (i.e., CM for CS = 0.0) grew as a decelerating function of inducing-grating contrast, such that CM = 0.308(CI]1.8 + 0.096), effectively asymptoting at a contrast of approximately 0.275 for CI > or = 0.50. When the difference between the absolute values of matching and standard contrast, magnitude of CM-magnitude of CS, is plotted against the ratio of standard to inducing-grating contrast, CS/CI, the resulting functions are generally biphasic, revealing regions of both contrast overmatching (i.e., magnitude of CM > magnitude of CS) and contrast undermatching, magnitude of CM < magnitude of CS. A four parameter model is presented that accounts for many features of the raw matching functions and that is mathematically similar to Semmelroth's account of the crispening effect in brightness matching [J. Opt. Soc. Am. 60, 1685 (1970)]. The model describes matching contrast, CM, as the weighted sum of two nonlinear contrast-response functions whose inputs are CS and CS-CI. The results are discussed relative to the crispening effect (the effect of contrast adaptation on perceived contrast) and to similarities and differences in luminance and contrast-domain visual processing.

A multi-channel approach to brightness coding

A model of brightness coding is presented which is shown to predict the appearance of a number of classical brightness phenomena. The model is known as MIDAAS which stands for Multiple Independent Descriptions Averaged Across Scale. In common with many other approaches to brightness perception MIDAAS imputes to local feature detectors a central role in the computation of brightness. It also explicitly recognises the crucial importance to brightness perception of feature detectors operating at different spatial scales. The unique and definitive feature of the model however is the supposition that each scale of spatial filtering operates as if to generate its own description of the pattern of brightness relationships in the image. The final percept is then provided by the composite of those individual brightness descriptions. It is shown that MIDAAS provides a good account of a variety of Mach band phenomena, the conditions under which the Missing Fundamental illusion is observed, the effect of occluding bars on the apparent contrast of step edges, the Chevreul illusion, simultaneous brightness contrast and the non-linear appearance of high contrast sinusoidal gratings. The advantages of MIDAAS over other approaches to brightness perception is discussed, as well as its current limitations.

An orientation anisotropy in induced brightness

It is shown that an orientation anisotropy exists for the magnitude of induced brightness in a cruciform stimulus consisting of a grey test patch positioned at the intersection of two inducing bars, one black and one white, oriented at right angles to each other. When the cruciform was oriented such that the white bar was horizontal, the grey patch appeared darker than when the same cruciform was oriented such that the white bar was vertical. The contribution of the black and white inducing bars towards the brightness of the test patch was investigated. A simple mathematical function, which took into account both the contribution of the two component inducing bars and the orientation anisotropy, was fitted to the data. No consistent orientation anisotropy was found with inducing stimuli at oblique orientations.