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

Comparing the spatial-frequency response of first-order and second-order lateral visual interactions: grating induction and contrast-contrast

The magnitudes of two suprathreshold lateral spatial-interaction effects--grating induction and contrast--contrast--were compared with regard to their dependence upon inducing-grating spatial frequency. Both effects cause the contrast of target stimuli embedded in surrounding patterns to be matched nonveridically. The magnitudes of each effect were measured in a common unit that indexed the degree of nonveridical contrast matching across a large range of target-grating contrasts (+/- 0.80). Grating induction was a low-pass effect with respect to spatial frequency, whereas contrast-contrast was bandpass, peaking at approximately 4.0 cycles deg(-1). The magnitude of grating induction exceeded that of contrast--contrast, both overall and at their optimal frequencies (0.03125 and 4.0 cycles deg(-1), respectively); the two effects are equipotent at an inducing-grating spatial frequency of 1.0 cycle deg(-1). A significant negative correlation between the magnitudes of the two effects suggests a link whereby activation of second-order normalization mechanisms may inhibit first-order mechanisms.

Oriented multiscale spatial filtering and contrast normalization: a parsimonious model of brightness induction in a continuum of stimuli including White, Howe and simultaneous brightness contrast

The White effect [Perception 8 (1979) 413] cannot be simply explained as due to either brightness contrast or brightness assimilation because 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 abandon spatial filtering explanations not only for the White effect but for brightness perception in general. Offered instead are explanations based on a variety of junction analyses and/or perceptual organization schemes which in the case of the White effect are usually based on T-junctions. Recently, Howe [Perception 30 (2001) 1023] challenged T-junction based explanations with a novel variation of White's effect in which the T-junctions were constant while the brightness effect was eliminated or reversed, and proposed an alternative explanation in terms of illusory contours. The present study argues that an analysis at the level of illusory contours is not necessary and that a much simpler spatial filtering based explanation is sufficient. Brightness induction was measured in a set of stimuli chosen to illustrate the relationship between the Howe stimulus [Perception 30 (2001) 1023], the White stimulus [Perception 8 (1979) 413] and the classical simultaneous brightness contrast (SBC) stimulus. The White stimulus and the SBC stimulus occupy opposite ends of a continuum of stimuli in which the Howe stimulus is the mid-point. The psychophysical measurements were compared with the predictions of the oriented difference-of-Gaussians (ODOG) computational model of Blakeslee and McCourt [Vision Research 39 (1999) 4361]. The ODOG model parsimoniously accounted for both the direction and relative magnitude of the brightness effects suggesting that more complex mechanisms are not required to explain them.

Lightness perception: seeing one color through another

A newly described and dramatic visual illusion suggests that the retinal image is decomposed by the brain into overlapping layers, not into contiguous frameworks of illumination.

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.

Brightness induction: Unequal spatial integration with increments and decrements

Modern theories of brightness induction include an influence from regions that do not share a border with the target. This study tested whether the spatial range of neural integration is the same with incremental versus decremental contrast edges in relatively remote parts of the background. Using an asymmetric matching task, observers set the brightness of a comparison ring, within its own uniform surround, to match the brightness of a test ring within a contiguous surround and a noncontiguous background. The measurements showed that the area of integration depended on the incremental versus decremental contrast polarity at the edge between the surround and background. This implies that brightness induction from an inhomogeneous background must consider the polarity of contrast edges within the whole scene.

Straightness as a cue for luminance edge interpretation

In order to determine the reflectance of a surface, it is necessary to discount luminance changes produced by illumination variation, a process that requires the visual system to respond differently to luminance changes that are due to illumination and reflectance. It is known that various cues can be used in this process. By measuring the strength of lightness illusions, we find evidence that straightness is, used as a cue: When a boundary is straight rather than curved, it has a greater tendency to be discounted, as if it were an illumination edge. The strongest illusions occur when a boundary has high contrast and has multiple X-junctions that preserve a consistent contrast ratio.

Influence of target size and luminance on the White-Todorovic effect

Variants of a lightness effect described by [Todorovic's, D. (1997). Lightness and junctions. Perception, 26, 379] were studied to quantify the failure of lightness constancy as a function of target luminance and target size. Todorovic's effect is similar to White's effect. Simultaneous lightness contrast appears to operate selectively between stimuli belonging to the same perceptual group, and not between stimuli of equal proximity belonging to different perceptual groups. We found that mid-gray targets grouped with a white contextual stimulus were matched on average to a darker-than-veridical gray. Those grouped with a black contextual stimulus were matched on average veridically. This is consistent with 'anchoring' effects observed in simple two-stimulus displays. However, target luminance had an effect that was not captured by mid-level target luminance data or data averaged across target luminances. For both white and black contextual stimuli, light-gray targets were matched to a darker-than-veridical gray and the direction of this error shifted toward the lighter-than-veridical direction as the luminance of the target was lowered. The result was a constant difference between the perceived lightnesses of targets presented with white and black contextual stimuli. Target size had no effect on perceived lightness. These data imply that the Todorovic-White effect can be characterized as lightness assimilation rather than as lightness contrast. By accounting for compression as well as the Todorovic-White effect, assimilation is the more general explanation.

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.

Chromatic assimilation: spread light or neural mechanism?

Chromatic assimilation is the shift in color appearance of a test field toward the appearance of nearby light. Possible explanations of chromatic assimilation include wavelength independent spread light, wavelength-dependent chromatic aberration and neural summation. This study evaluated these explanations by measuring chromatic assimilation from a concentric-ring pattern into an equal-energy-white background, as a function of the inducing rings' width, separation, chromaticity and luminance. The measurements showed, in the s direction, that assimilation was observed with different inducing-ring widths and separations when the inducing luminance was lower or higher than the test luminance. In general, the thinner the inducing rings and the smaller their separation, the stronger the assimilation in s. In the l direction, either assimilation or contrast was observed, depending on the ring width, separation and luminance. Overall, the measured assimilation could not be accounted for by the joint contributions from wavelength-independent spread light and wavelength-dependent chromatic aberration. Spatial averaging of neural signals explained the assimilation in s reasonably well, but there were clear deviations from neural spatial averaging for the l direction.

Mechanisms of contrast induction in heterogeneous displays

This study examines how judgments of a region's contrast are influenced by components of a heterogeneous surround. Each stimulus comprised a 5x5 grid of squares in a homogeneous background of fixed mean luminance, with the central square the target. On a given trial, the task was to judge (with feedback) whether the (Weber) contrast of the target was 0.04 or -0.04 (relative to the background); the contrasts assigned (in random order) to the 24 surrounding squares were drawn from the values -0.98, -0.33, 0.33, 0.98 in conformity to one of nine pre-chosen histograms. Presentations were brief (80 ms) in one condition and long (800 ms) in another. A novel psychophysical method was used to estimate the impact exerted on judged target contrast (JTC) by a given contrast in a given grid position. Results were similar for four observers. For both display durations, the four squares sharing an edge with the target influenced JTC 2.4-9 times more than any other surrounding squares. In long presentations, abutting squares of extreme contrast repelled target contrast: squares of contrast -0.98 (0.98) increased (decreased) JTC. However, lower contrast abutting squares attracted target contrast: squares of contrast -0.33 (0.33) decreased (increased) JTC. This central finding can be explained by supposing that: (a) JTC is strongly correlated with the average boundary contrast from surround to target, as registered by linear, edge-selective neurons, and, crucially, (b) the responses of these neurons are themselves subject to lateral inhibition from the rectified responses of other similarly tuned neurons. Finally, in brief presentations, a polarity-specific asymmetry was observed: the two positive abutting-square contrasts continued to influence JTC as they did in long presentations, but contrasts -0.33 and -0.98 ceased to exert much impact, suggesting that lateral influences on target appearance propagate more quickly from positive than from negative contrast abutting regions.

Quantitative properties of achromatic color induction: an edge integration analysis

Edge integration refers to a hypothetical process by which the visual system combines information about the local contrast, or luminance ratios, at luminance borders within an image to compute a scale of relative reflectances for the regions between the borders. The results of three achromatic color matching experiments, in which a test and matching ring were surrounded by one or more rings of varying luminance, were analyzed in terms of three alternative quantitative edge integration models: (1) a generalized Retinex algorithm, in which achromatic color is computed from a weighted sum of log luminance ratios, with weights free to vary as a function of distance from the test (Weighted Log Luminance Ratio model); (2) an elaboration of the first model, in which the weights given to distant edges are reduced by a percentage that depends on the log luminance ratios of borders lying between the distant edges and the target (Weighted Log Luminance Ratio model with Blockage); and (3) an alternative modification of the first model, in which Michelson contrasts are substituted for log luminance ratios in the achromatic color computation (Weighted Michelson Contrast model). The experimental results support the Weighted Log Luminance Ratio model over the other two edge integration models. The Weighted Log Luminance Ratio model is also shown to provide a better fit to the achromatic color matching data than does Wallach's Ratio Rule, which states that the two disks will match in achromatic color when their respective disk/ring luminance ratios are equal.

Brightening prospects for early cortical coding of perceived luminance: a high-density electrical mapping study

Establishing the computational rules and neural substrates of brightness coding is a topic of both historical and contemporary interest. Two major classes of explanations for brightness illusions, such as brightness contrast, can be traced to Hering and Helmholtz. Hering's legacy is a low-level account in which brightness contrast results from obligatory lateral inhibitory interactions occurring at some level(s) in the visual system. Helmholtz offered a high-level account, positing a causal role for factors such as perceptual grouping, inferred illumination, and the extraction of surface properties such as orientation and reflectance. The tension between these theoretical viewpoints persists unabated to date. Intracranial electrophysiological recordings have revealed that brightness is represented in the firing rates of striate neurons, a fact consistent with low-level explanations. However, since the time-course of brightness-related responses relative to the onset of striate activity is undisclosed, it remains possible that striate activation might be temporally and causally secondary to higher-level computational processes. Knowledge of the timing of brightness-related neural activity is thus crucial to both constrain and adjudicate between these competing theories. We utilize high-density electrophysiological recording and a tachistoscopic brightness discrimination task to measure the time-course and scalp topography of brightness-related electrical potentials in human observers. Brightness perception is correlated with electrical activity at the earliest stages of visual cortical processing. These findings are interpreted to support Hering's low-level account of brightness for White's effect, and the results are discussed in the context of current theories of brightness perception.

The statistical structure of natural light patterns determines perceived light intensity

The same target luminance in different contexts can elicit markedly different perceptions of brightness, a fact that has long puzzled vision scientists. Here we test the proposal that the visual system encodes not luminance as such but rather the statistical relationship of a particular luminance to all possible luminance values experienced in natural contexts during evolution. This statistical conception of vision was validated by using a database of natural scenes in which we could determine the probability distribution functions of co-occurring target and contextual luminance values. The distribution functions obtained in this way predict target brightness in response to a variety of challenging stimuli, thus explaining these otherwise puzzling percepts. That brightness is determined by the statistics of natural light patterns implies that the relevant neural circuitry is specifically organized to generate these probabilistic responses.

Perceiving the intensity of light

The relationship between luminance (i.e., the photometric intensity of light) and its perception (i.e., sensations of lightness or brightness) has long been a puzzle. In addition to the mystery of why these perceptual qualities do not scale with luminance in any simple way, "illusions" such as simultaneous brightness contrast, Mach bands, Craik-O'Brien-Cornsweet edge effects, and the Chubb-Sperling-Solomon illusion have all generated much interest but no generally accepted explanation. The authors review evidence that the full range of this perceptual phenomenology can be rationalized in terms of an empirical theory of vision. The implication of these observations is that perceptions of lightness and brightness are generated according to the probability distributions of the possible sources of luminance values in stimuli that are inevitably ambiguous.

BOLD fMRI and psychophysical measurements of contrast response to broadband images

We have measured the relationship between image contrast, perceived contrast, and BOLD fMRI activity in human early visual areas, for natural, whitened, pink noise, and white noise images. As root-mean-square contrast increases, BOLD response to natural images is stronger and saturates more rapidly than response to the whitened images. Perceived contrast and BOLD fMRI responses are higher for pink noise than for white noise patterns, by the same ratio as between natural and whitened images. Spatial phase structure has no measurable effect on perceived contrast or BOLD fMRI response. The fMRI and perceived contrast response results can be described by models of spatial frequency response in V1, that match the contrast sensitivity function at low contrasts, and have more uniform spatial frequency response at high contrasts.

Brightness assimilation in bullseye displays

In simultaneous brightness contrast displays, a gray target square G(B) bordered by black appears brighter than an identical gray target square G(W) bordered by white. Here we demonstrate that this effect can be reversed if G(B) is surrounded by bands that alternate outward from black to white, while G(W) is surrounded by bands that alternate outward from white to black. With these simple "bullseye" displays assimilation generally occurs--G(B) appears darker than G(W). Experiments 1 and 2 used a 2AFC design with a 2.2 s display duration. The results of these experiments indicate that (i) substantial assimilation occurs for target Weber contrasts (relative to the gray background) of -0.25, 0, and 0.25, but assimilation was maximal when target contrast was -0.25 and decreased as target contrast increased, (ii) assimilation effects were the same whether the width of the four surround bands was 20% of the target or 40% of the target, and (iii) assimilation occurs with as few as 2 surround-bands and the magnitude of the effect increases slightly as the number of bands increase. When experiment 1 was re-run using the method of matching (experiment 3), however, the results changed dramatically: (moderate) assimilation effects were found only when target contrast was -0.25; when target contrast was 0.25, there was a brightness contrast effect; when target contrast was 0, there was no illusion. Assimilation effects in bullseye displays are not predicted by the CSF model described in DeValois and DeValois [Spatial Vision, Oxford University Press, New York, 1988], the anchoring model of Gilchrist et al. [Psychological Review, 106(4) (1999) 795], or Blakeslee and McCourt's [Vision Research 39 (1999) 4361] ODOG model. We propose that this assimilation effect is the result of a contrast inhibition mechanism similar to that proposed by Chubb et al. [Proceedings for the National Academy of Science, vol. 86, 1989, p. 9631] to underlie contrast effects.

Natural image statistics mediate brightness 'filling in'

Although the human visual system can accurately estimate the reflectance (or lightness) of surfaces under enormous variations in illumination, two equiluminant grey regions can be induced to appear quite different simply by placing a light-dark luminance transition between them. This illusion, the Craik-Cornsweet-O'Brien (CCOB) effect, has been taken as evidence for a low-level 'filling-in' mechanism subserving lightness perception. Here, we present evidence that the mechanism responsible for the CCOB effect operates not via propagation of a neural signal across space but by amplification of the low spatial frequency (SF) structure of the image. We develop a simple computational model that relies on the statistics of natural scenes actively to reconstruct the image that is most likely to have caused an observed series of responses across SF channels. This principle is tested psychophysically by deriving classification images (CIs) for subjects' discrimination of the contrast polarity of CCOB stimuli masked with noise. CIs resemble 'filled-in' stimuli; i.e. observers rely on portions of the stimuli that contain no information per se but that correspond closely to the reported perceptual completion. As predicted by the model, the filling-in process is contingent on the presence of appropriate low SF structure.

Influences of motion and depth on brightness induction: an illusory transparency effect?

To experiments were performed to investigate whether motion and binocular disparity influence brightness induction, and whether the effects of motion and binocular disparity, if any, interact with each other. In order to introduce motion, textured backgrounds were used as the inducing field. The results showed that motion and/or crossed disparity reduce brightness induction, whereas uncrossed disparity increases it. The effect of motion and the effect of disparity are independent of each other and additive, which suggests that, to the extent that brightness induction reflects segmentation of objects, motion and binocular disparity serve independently to segment objects from their background. The difference between the effects of crossed and uncrossed disparity can be explained by what we call 'illusory transparency'.

A fair test of the effect of a shadow-incompatible luminance gradient on the simultaneous lightness contrast

Shadow-compatibility of simultaneous lightness contrast is discussed by Alexander D Logvinenko and Paola Bressan, with examples claiming to provide a test of the hypothesis.

Does the bandpass linear filter response predict gradient lightness induction? A reply to Fred Kingdom

It is argued that lightness illusions induced by luminance gradient cannot be accounted for by the response of a bandpass linear filter as recently claimed by Kingdom (Perception 28 929-934).

Perceptual organization and White's illusion

The apparent lightness of a surface can be strongly modulated by the spatial context in which it is embedded. Early theories of such context dependence emphasized the role of low-level mechanisms that sense border contrast, whereas a number of recent authors have emphasized the role of perceptual organization in determining perceived lightness. One of the simplest and most theoretically challenging lightness illusions was described by White. This illusion has been explained with a variety of different models, ranging from low-level filter outputs to computations underlying the extraction of mid-level representations of surfaces. Here, I present a new method for determining the organizational forces that shape this illusion. I show that the spatial context of White's pattern not only transforms the apparent lightness of homogeneous target patches. but can also induce dramatic inversions of figure-ground relationships of textured target regions. These phenomena provide new evidence for the role of scission in causing the lightness illusion experienced in White's effect.

Perception of brightness and brightness illusions in the macaque monkey

Recent physiological studies show that neural responses correlated with the perception of brightness are found in cortical area V1 but not earlier in the visual pathway (Kayama et al., 1979; Reid and Shapley, 1989; Squatrito et al., 1990; Komatsu et al., 1996; Rossi et al., 1996; MacEvoy et al., 1998; Rossi and Paradiso, 1999; Hung et al., 2001; Kinoshita and Komatsu, 2001; MacEvoy and Paradiso, 2001). However, these studies are based on comparisons of neural responses in animals with brightness perception in humans. Very little is known about the perception of brightness in animals typically used in physiological experiments. In this study, we quantify brightness discrimination, brightness induction, and White's effect in macaque monkeys. The results show that, qualitatively and quantitatively, the perception of brightness in macaques and humans is quite similar. This similarity may be an indication of common underlying neural computations in the two species.

Induction in variants of White's effect: common or separate mechanisms?

In White's display the gray target surrounded more by black than white appears darker than the target of the same physical luminance surrounded more by white than black. Several subsequent studies have shown that this effect occurs only when the luminance of the test regions lies between the minimum and maximum luminance values of the inducing stripes. With targets either lighter or darker than both inducing stripes, the direction of the effect is reversed and the effect is known as the 'inverted' White's effect. Views differ on whether the classical and inverted White's effects are mediated by common or separate underlying mechanisms. We varied the aspect ratio of the test and inducing regions in the classical and inverted White's effects. Consistent with previously reported findings, we found that the direction of the classical effect did not depend on the amount of black or white border in immediate contact with the test patch. On the other hand, perceived lightness in the inverted White's effect was affected by such variations, suggesting that induction in classical and inverted White's configurations is governed by different mechanisms. These results confirm the critical importance of the interaction between luminance and geometric relationships in induced brightness.

Perceptual organization overcomes the effects of local surround in determining simultaneous lightness contrast

Lightness induction can occur on the basis of the immediate surround of a region (local interactions) and also on the basis of global factors of perceptual organization. The experiments reported in this article used novel displays that made it possible to differentiate the contributions of these two kinds offactors. The experiments demonstrated, for the first time, that when higher-level factors act contemporaneously with lower-level factors, the contrast effect induced by the global-organization principle of perceptual belongingness overcomes the effect due to retinal lateral inhibition.

A multiscale spatial filtering account of the Wertheimer-Benary effect and the corrugated Mondrian

Blakeslee and McCourt [Blakeslee, B., & McCourt, M.E. (1997). Similar mechanisms underlie simultaneous brightness contrast and grating induction. 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 including the White effect [White, M. (1997). A new effect of pattern on perceived lightness. Perception, 8, 413-416] and a variant of SBC [Todorovic, D. (1997). Lightness and junctions. Perception, 26, 379-395]. Blakeslee and McCourt [Blakeslee, B., McCourt, M.E. (1999). A multiscale spatial filtering account of the White effect, simultaneous brightness contrast and grating induction. Vision Research, 39, 4361-4377] developed a modified version of the model, an oriented (ODOG) model, which differed from the DOG model in that the filters were anisotropic and their outputs were pooled nonlinearly. Using this model, they were able to account for both groups of induction effects. The present paper examines two additional sets of brightness illusions that cannot be explained by isotropic contrast models. Psychophysical brightness matching is employed to quantitatively measure the size of the brightness effect for two Wertheimer-Benary stimuli [Benary, W. (1924). Beobachtungen zu einem experiment uber helligkeitskontrast. Psychologische Forschung, 5, 131-142; Todorovic, D. (1997). Lightness and junctions. Perception, 26, 379-395] and for low- and high-contrast versions of corrugated Mondrian stimuli [Adelson, E.H. (1993). Perceptual organization and the jugdement of brightness. Science, 262, 2042-2044; Todorovic, D. (1997). Lightness and junctions. Perception, 26, 379-395]. Brightness matches are obtained on both homogeneous and checkerboard matching backgrounds. The ODOG model qualitatively predicts the appearance of the test patches in the Wertheimer-Benary stimuli and corrugated Mondrian stimuli. In addition, it quantitatively predicts the relative magnitudes of the corrugated Mondrian effects in the various conditions. In general, the psychophysical results and ODOG modeling argue strongly that like SBC, GI, the White effect and Todorovic's SBC demonstration, induced brightness in Wertheimer-Benary stimuli and in the corrugated Mondrian primarily reflects early-stage filtering operations in the visual system.

Classical and inverted White's effects

In classical White's effect, intermediate-luminance targets appear lighter when they interrupt the dark stripes of a grating and darker when they interrupt the light stripes. The effect is reversed when targets are of double-increment or double-decrement luminance, relative to the luminances of grating stripes. To find a common explanation for classical and inverted effects, we ran two experiments. In experiment 1, we utilised intermediate-target displays to show that perceived transparency dominates over occlusion only when the target luminance is close to the luminances of top regions. This result weakens transparency-based accounts of White's effect. In experiment 2, we varied grating contrast and target luminance to measure the classical effect in seven intermediate-target cases, as well as the inverted effect in four double-increment and four double-decrement cases. Both types of effect are explained by a common model, based on assimilation to the top region and contrast with the interrupted region, weighted by adjacency along the luminance continuum.