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Article  |   January 2016
Robust brightness enhancement across a luminance range of the glare illusion
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Journal of Vision January 2016, Vol.16, 10. doi:10.1167/16.1.10
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      Hideki Tamura, Shigeki Nakauchi, Kowa Koida; Robust brightness enhancement across a luminance range of the glare illusion. Journal of Vision 2016;16(1):10. doi: 10.1167/16.1.10.

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Abstract

The glare illusion refers to brightness enhancement and the perception of a self-luminous appearance that occurs when a central region is surrounded by a luminance gradient. The center region appears to be a light source, with its light dispersing into the surrounding region. If the luminous edge is critical for generating the illusion, modulating the perceived luminance of the image, and switching its appearance from luminous to nonluminous, would have a strong impact on lightness and brightness estimation. Here, we quantified the illusion in two ways, by assessing brightness enhancement and examining whether the center region appeared luminous. Thus, we could determine whether the two effects occurred jointly or independently. We examined a wide luminance range of center regions, from 0 to 200% relative to background. Brightness enhancement in the illusion was observed for a wide range of luminances (20% to 200% relative to background), while a luminous-white appearance was observed when the center region luminance was 145% of the background. These results exclude the possibility that brightness enhancement occurs because the stimuli appear self-luminous. We suggest that restoring the original image intensity precedes the perceptual process of lightness estimation.

Introduction
Lightness estimation of objects within scenes is an important function of our visual system. The perception of lightness is related to the proportion of reflected light from a surface (Kingdom, 1997). This lightness percept can be categorized, such as by the descriptive terms white, gray, or black. Since the Middle Ages, numerous reports, such as those of Alhazen, and later by Helmholz and Hering (Kingdom, 1997), have described lightness perception and its basis. Current vision researchers have built upon such works (Gilchrist, 2006). To estimate the lightness of an object's surface, several cues are available, such as its luminance, spatially adjacent stimuli, three-dimensional configuration, and texture statistics (Adelson, 1993; Anderson & Winawer, 2005; Gilchrist, 2006; Knill & Kersten, 1991). Based on these cues, the visual system could estimate the mapping between the retinal output and reflectance, which is required for lightness perception (Adelson, 2000; Gilchrist, 2006; Murray, 2013). 
Numerous studies have addressed lightness perception and illumination estimation (Adelson, 2000; Adelson & Pentland, 1996; Arend & Goldstein, 1987; Gilchrist, 2006; Kingdom, 2011; Land & McCann, 1971). One hypothesis is that lightness perception describes how the visual system decomposes images into separate layers based on illumination geometry, shading due to shape, and surface albedo (Gilchrist, 2006). These three components correspond to the physical attributes of scenes, and are indispensable for rendering objects in computer graphics. If two of them, such as illumination and shape, are clearly defined, the other component, in this case, reflectance, can be determined theoretically. However, if the target object is self-luminous, this calculation is not possible. Thus, it is important to know how humans discriminate self-luminous from nonluminous surfaces. 
A stimulus that is higher in luminance than its surroundings has a luminous appearance (Bonato & Gilchrist, 1994; Evans, 1959; Gilchrist et al., 1999; Radonjić, Allred, Gilchrist, & Brainard, 2011; Uchikawa, Koida, Meguro, Yamauchi, & Kuriki, 2001). The contrast between an object and its surroundings is important for lightness and brightness perception. The physiological basis of this function is lateral inhibition in the retina (Cornsweet, 1970; Shapley & Enroth-Cugell, 1984; Walraven, Enroth-Cugell, Hood, MacLeod, & Schnapf, 1990) and higher-order cortical mechanisms (Boyaci, Fang, Murray, & Kersten, 2007; Haynes, Lotto, & Rees, 2004; Kinoshita & Komatsu, 2001; MacEvoy & Paradiso, 2001; Roe & Ts'o, 1995; Shevell, Holliday, & Whittle, 1992; Whittle, 1994). If circumstances exist whereby a luminous appearance is not explicable by the contrast model, these would potentially assist our understanding of lightness/brightness perception mechanisms. 
The glare illusion is an optical illusion in which brightness enhancement and self-luminosity occur for a bright central region relative to the equiluminant surface (Agostini & Galmonte, 2002; Zavagno, 1999). It has a surrounding gradient that mimics the spread of intense light due to atmospheric or ocular dispersion (Kakimoto, Matsuoka, Nishita, Naemura, & Harashima, 2005; Spencer, Shirley, Zimmerman, & Greenberg, 1995). Figure 1A shows examples of the glare illusion. In the figure's top right, the central circles appear relatively bright and self-luminous due to their annular blur, even though the central region has the same luminance as the circle with no annular blur, directly below. The glare illusion is very robust across various displays, and even occurs in printed images. As early as the Renaissance period, painters such as Tintoretto and Rembrandt employed blur to produce the appearance of self-luminosity (Zavagno & Massironi, 1997). Perceived self-luminosity induced by annular blur has been frequently used as a stimulus in psychological experiments (Correani, Scott-Samuel, & Leonards, 2006; Hanada, 2012; Keil, 2007; Yoshida, Ihrke, Mantiuk, & Seidel, 2008; Zavagno, Annan, & Caputo, 2004; Zavagno & Caputo, 2001, 2005), including fMRI studies (Leonards, Troscianko, Lazeyras, & Ibanez, 2005). Further, such blur is widely used in computer graphics to represent an intense light source or specular reflection (Nakamae, Kaneda, Okamoto, & Nishita, 1990; Rokita, 1993; Shinya, Saito, & Takahashi, 1989; Spencer et al., 1995). This illusion raises questions about how our visual system integrates contextual information when evaluating lightness or brightness, and how self-luminosity is judged. 
Figure 1
 
Stimuli used in this study. (A) Examples of glare stimuli (top) and reference stimuli (bottom). The luminance of a central circle and surrounding inducer were modulated from dark to light (left to right). Circles in the same column have the same intensity (luminance). (B) Screen appearance: The sample and reference stimuli were placed to the left and right of the central fixation point, respectively. (C) Luminance profiles of Glow (blue), Halo (green), and Uniform (red) stimuli. The annulus is labeled as “inducer,” the inner circle as “patch,” and the surrounding uniform area covering the remaining display as “background.” In this example, the luminance of the center patch was 160 cd/m2. The background was always 100 cd/m2 irrespective of sample intensity.
Figure 1
 
Stimuli used in this study. (A) Examples of glare stimuli (top) and reference stimuli (bottom). The luminance of a central circle and surrounding inducer were modulated from dark to light (left to right). Circles in the same column have the same intensity (luminance). (B) Screen appearance: The sample and reference stimuli were placed to the left and right of the central fixation point, respectively. (C) Luminance profiles of Glow (blue), Halo (green), and Uniform (red) stimuli. The annulus is labeled as “inducer,” the inner circle as “patch,” and the surrounding uniform area covering the remaining display as “background.” In this example, the luminance of the center patch was 160 cd/m2. The background was always 100 cd/m2 irrespective of sample intensity.
Measurement of the effect of visual illusions has been considered important in neuroscience (Eagleman, 2001). It is possible to measure illusions consistently in animals as well as humans (Kelley & Kelley, 2014). Thus, quantitative measurement of the illusion is important in order to evaluate similarities in perception across species and to understand the neurophysiological basis of our visual system. 
Zavagno and Caputo (2001) measured self-luminosity thresholds of the glare illusion by modulating the luminance of the central and inducing regions and found that the illusion occurred even when the central region was darker than the white background. Yoshida et al. (2008) measured the amount of brightness enhancement in the glare illusion. Subjects perceived the central region in the illusion as 20% to 35% brighter than the reference white. These two studies implicitly assumed that two ways exist to quantify the glare illusion, namely via self-luminosity thresholds and by assessing the amount of brightness enhancement. Further, it was assumed that these two attributes can be measured separately. 
In this study, we asked how the illusion elicits two kinds of perceptual effect—brightness enhancement and a self-luminous appearance—and whether they are elicited either jointly or independently. To test this, we modulated the stimulus intensity while keeping the background stimulus constant and asked the subjects to report perceived brightness and to provide a categorical judgment of appearance. Does the glare illusion induce a brighter, self-luminous appearance for both dark and bright stimuli, and what luminance level effectively induces the illusion? If the illusion is observed at specific range, do the two aspects of the illusion appear jointly? 
Methods
Subjects
Subjects were eight naïve volunteers aged from 22 to 25 years (average 22.8 years, seven males and one female). They had normal or corrected-to-normal acuity and normal trichromatic color vision. All experimental protocols were approved by the institutional review board of Toyohashi University of Technology with respect to the use of humans in experiments. Informed consent was obtained from all participants. 
Apparatus
Stimuli were displayed on a 27-inch (screen size 596 × 335 mm) liquid crystal display (LCD; CG276, EIZO, Ishikawa, Japan) with a resolution of 2,560 × 1,440 pixels, calibrated by ColorCAL II (Cambridge Research Systems, Ltd., Kent, UK). Stimulus presentation was controlled by MATLAB using Psychtoolbox 3.0 (Brainard, 1997) on a desktop computer (Precision T7500, Dell, Austin, TX). Subjects observed the stimuli binocularly, while seated on a chair facing the display with the head secured on a chin rest to keep a constant distance from the display (1340 mm). The only luminous object present in the room was the LCD monitor. 
Stimuli
Figure 1B shows the screen layout in both experiments. The stimulus on the left is an example of an image that evokes the glare illusion. That is, the central circle is surrounded by a luminance gradient extending toward the periphery of the annulus. The stimulus on the right is a reference where the center patch is surrounded by an annulus of uniform luminance. The diameters of the outer and inner stimulus boundary were 9° and 3.4° of visual angle, respectively. Two stimuli were simultaneously displayed 5.5° to the left and right of the fixation point. The background was uniform, with a luminance of 100 cd/m2
Figure 1C illustrates the luminance profiles of the three types of stimuli used in this study. Center patches of the three stimuli were the same, but the surrounding inducers were different. Glow had a linear profile, which modulated from zero on the outer boundary to the highest luminance adjacent to the central region. Halo had a similar profile as Glow but the direction of the gradient was reversed. Halo was used to examine the effect of contrast polarity and to reduce visual adaptation to Glow. Uniform had a spatially uniform profile, with a luminance of 44% of the central region. The value of 44% was arbitrarily determined. We also used a uniform black inducer in an additional experiment for comparison (Appendix, Additional experiment 1). After taking into account the number of pixels, the mean inducer luminance of Glow and Halo compared to the center patch was 41% and 59%, respectively. All stimuli were achromatic gray (CIE: x = 0.290, y = 0.331). 
Procedure
Experiment 1: Brightness comparison
Two stimuli were presented while participants were fixating; they were asked to report which of the two stimuli had the brighter central region. The two stimuli were presented horizontally to the left and right of the fixation point; one was the sample and the other was the reference. The sample was selected randomly from three profiles (Glow, Halo, and Uniform), and the reference was always Uniform. The horizontal position of the sample was randomly switched. 
There were 18 luminance levels: 0, 5, 10, 15, 20, 30, 40, 50, 60, 70, 80, 90, 100, 120, 140, 160, 180, and 200 cd/m2. Both the sample and reference in each trial had the same luminance. We also used other reference stimuli with 20% higher (bright reference) or 20% lower (dark reference) luminance. In this case, both center and annulus luminance varied together while the contrast between center and annulus was kept constant. 
At the beginning of the experiment, the background and a fixation point were displayed and remained throughout the experiment. After three minutes of adaptation, the first trial was started by a mouse click. Stimuli were presented for 0.3 s, after which only the background was shown. The subject then responded with a right or left mouse click to indicate which stimulus was brighter. The next trial began following a further click. One session was composed of 648 trials (2 repeats × 2 positions × 18 luminance levels × 3 profiles × 3 references), and all conditions were randomly ordered. Each subject participated in four sessions; thus, each condition was repeated eight times. In the analysis, we combined the data for the two horizontal positions, thus providing 16 repeats per condition. 
Experiment 2: Categorical labeling
After three minutes of adaptation to the background, a single stimulus was displayed either to the right or to the left of the center. Stimulus position was switched on every trial. Subjects were asked to report the appearance of the central region of the stimulus using four categories: black, gray, white, or luminous-white. The response was recorded by keyboard. There was no fixation point, and the subjects were allowed to freely view the stimuli. We also conducted the additional experiment to confirm that the responses were stable even when eye position was controlled (see Appendix, Additional experiment 2). The luminance profiles of the stimuli consisted of Glow, Halo, and Uniform. There were 21 luminance levels, ranging from 0 to 200 cd/m2
The stimulus appeared after the key press and was displayed until a response was obtained (the mean response time was 1.05 s). The next trial started following a further key press. One session was composed of 504 trials (4 trials × 2 positions × 21 luminance levels × 3 profiles) and all conditions were randomly intermingled. Each subject participated only in one session. 
Results (Experiment 1)
Brightness enhancement was observed across almost the entire range of target luminance (Figure 2A). Significant enhancements of Glow compared to chance (50%) were observed from 20 to 200 cd/m2 (p < 0.05, binomial test), which included both higher and lower luminance values than the background luminance (100 cd/m2). The probability never reached 100% at any luminance level. This was due to individual differences in the luminance level inducing brightness enhancement (Supplemental Figure 1). The majority of observers (n = 6) showed monotonically increasing functions, while other observers showed a maximum response probability at specific luminance levels (50 to 100 cd/m2). Two observers did not show 100% probability even at the most effective luminance level; nevertheless, the response was significantly higher than chance. In the low luminance range, the probabilities were distributed around 50% or slightly below. This significant negative bias was observed in at least two observers. Halo also showed significant brightness enhancement at several luminance levels (60 and 80 to 200 cd/m2, p < 0.05, binomial test); however, its probabilities were lower than those of Glow. No significant effects were observed for the Uniform control. 
Figure 2
 
Brightness enhancement in the glare illusion. (A) The horizontal axis indicates the luminance of the center patch, and the vertical axis the probability of the sample appearing brighter than the equiluminant reference uniform stimulus. Filled symbols indicate a significant difference from chance (50%). Response probabilities for each subject were calculated, and averages and standard errors among subjects were obtained. Error bars represent the standard error of the mean across all eight subjects. (B) Response probabilities for a dark (−20%) reference condition. (C) Response probabilities for a bright (+20%) reference condition. (D) Example psychometric function at a luminance level of 120 cd/m2. Response probabilities for three reference conditions with a fitted logistic function are shown. (E) Brightness enhancement quantified by the point of subjective equality (PSE). Symbols are the same as in A. Data were clipped to 100% or −25% if the function returned values greater than 100% or less than −25%, respectively. Filled symbols indicate goodness-of-fit of the psychometric functions. (F) Means and standard errors of significant PSEs for each condition.
Figure 2
 
Brightness enhancement in the glare illusion. (A) The horizontal axis indicates the luminance of the center patch, and the vertical axis the probability of the sample appearing brighter than the equiluminant reference uniform stimulus. Filled symbols indicate a significant difference from chance (50%). Response probabilities for each subject were calculated, and averages and standard errors among subjects were obtained. Error bars represent the standard error of the mean across all eight subjects. (B) Response probabilities for a dark (−20%) reference condition. (C) Response probabilities for a bright (+20%) reference condition. (D) Example psychometric function at a luminance level of 120 cd/m2. Response probabilities for three reference conditions with a fitted logistic function are shown. (E) Brightness enhancement quantified by the point of subjective equality (PSE). Symbols are the same as in A. Data were clipped to 100% or −25% if the function returned values greater than 100% or less than −25%, respectively. Filled symbols indicate goodness-of-fit of the psychometric functions. (F) Means and standard errors of significant PSEs for each condition.
Similar trends were observed for the different reference conditions (Figure 2B, C). The largest response was observed for the Glow condition, followed by Halo and Uniform. For the bright reference condition (Figure 2C), responses for Glow were still greater than chance, indicating that the magnitude of brightness enhancement for Glow was still higher than the 20% increase in luminance of the reference. Responses for Halo were slightly lower than chance, indicating that the magnitude of brightness enhancement for Halo did not attain the 20% increase in luminance of the reference. 
By combining the data from the three reference conditions, we obtained psychometric functions for each luminance level (Figure 2D). The response probabilities obtained for the three reference levels were then fit to a maximum-likelihood logistic function. With this function, we could estimate the brightness enhancement quantitatively. The point of subjective equality (PSE) between the Glow and Uniform reference was calculated as the luminance ratio between the midpoint of the function and zero. The observed PSEs were 30%. Similar calculations were performed for each sample luminance (Figure 2E). The average PSE was 42.8% (Figure 2F) when we included data showing good fit (slope significantly different from zero, p < 0.05 by MATLAB glmfit). The average PSEs of Halo and Uniform were 8.5% and 2.1%, respectively. 
The number of samples in the present study was relatively small for calculating psychometric functions (i.e., there were only three reference levels). Therefore, to validate whether the PSEs were estimated appropriately, we performed an additional experiment that used more reference levels (specifically, seven) for one luminance of the target stimulus (120 cd/m2, see Supplemental Figure 2). The observed PSE was 31% of the luminance ratio, i.e., almost identical to that in the main experiment (Figure 2E). Thus, we conclude that the observed PSEs in the main experiment were reliable. 
Results (Experiment 2)
We found that the Glow stimulus (Figure 3A) was perceived as self-luminous between 100 and 200 cd/m2, while very few self-luminous percepts were reported for Halo and Uniform stimuli, even at 200 cd/m2. We calculated the response probabilities of the four alternatives at each luminance level and fit cumulative Gaussian functions via a maximum-likelihood estimation procedure. Using these functions, we determined the categorical thresholds corresponding to the 50% probability level. Note that in Figure 3A, the four responses—black, gray, white, and luminous-white—are vertically stacked. The threshold between white and luminous-white responses occurred at 145 cd/m2, a clearly lower luminance than for the other two stimuli. The thresholds for the Halo and Uniform conditions were 248 cd/m2 and 243 cd/m2, respectively. 
Figure 3
 
Categorical response probability. The horizontal axis indicates the luminance of central circle, and the vertical axis the response probability for each category. A, B, and C show the response for the Glow, Halo, and Uniform conditions, respectively. The categorical responses black, gray, white, and luminous-white increased in probability from low to high luminance. For example, gray, white, and luminous-white responses were observed with approximately equal probability at 120 cd/m2 for the Glow condition. Functions are cumulative Gaussians, fit via a maximum likelihood method. Crosses indicate 50% probability points of each function.
Figure 3
 
Categorical response probability. The horizontal axis indicates the luminance of central circle, and the vertical axis the response probability for each category. A, B, and C show the response for the Glow, Halo, and Uniform conditions, respectively. The categorical responses black, gray, white, and luminous-white increased in probability from low to high luminance. For example, gray, white, and luminous-white responses were observed with approximately equal probability at 120 cd/m2 for the Glow condition. Functions are cumulative Gaussians, fit via a maximum likelihood method. Crosses indicate 50% probability points of each function.
Although the illusion had a strong impact on luminance at which the percept transitioned from white to luminous-white, the transition between gray and white percepts was very similar for all conditions (117 to 135 cd/m2). Thus, the thresholds between gray and white simply depended on the luminance of the central region; the surrounding annulus had limited influence. 
The transition between percepts of black and gray for Glow occurred at a slightly higher luminance than for Halo and Uniform stimuli. The majority of subjects (n = 5) showed this tendency. At low luminances, the central region of the Glow stimulus was less visible than in the other conditions due to low edge contrast between the center and annulus. 
Discussion
Comparison
We examined the effect of stimulus luminance on the glare illusion from two aspects: brightness enhancement and the induction of a self-luminous appearance. The results confirmed that the glare illusion enhanced brightness across a wide range of luminances (20% to 200% relative to the background); the resulting luminance enhancement was 40% (Experiment 1). Self-luminosity emerged when the central stimulus region was 145% of the luminance of the background (Experiment 2). 
Comparing the results of the two experiments, we found that brightness enhancement arose when the stimulus was not perceived as self-luminous. Indeed, the brightness enhancement of the glare illusion was observed even when the stimulus was categorically perceived as gray. This excludes the possibility that brightness enhancement occurs because the stimulus appears self-luminous. Zavagno and Caputo reported subjective experiences of self-luminous grays in the glare illusion (Zavagno & Caputo, 2001). However, they did not measure these subjective judgments directly. 
A shift in the categorical threshold due to the illusion was observed only for the white/luminous-white threshold and only a minor shift was observed for the gray/white threshold. In the luminance range of the gray/white threshold (120 to 130 cd/m2), glare stimuli enhanced brightness significantly. The white/luminous-white threshold varied by 68% (145 to 243 cd/m2) from Uniform to Glow; however, the quantitative effect of brightness enhancement was only 40%. These results suggest that the luminous appearance did not quantitatively match the metric evaluation of brightness. These discrepancies between brightness estimation and categorical reports might originate from independent underlying mechanisms (Witzel & Gegenfurtner, 2013). 
There was a small but significant decrease in brightness estimates for low-luminance Glow stimuli (Experiment 1), and an increased probability of black responses for these stimuli (Experiment 2). These two occurrences might share the same origin, namely invisibility of the stimulus due to low contrast at the edge of the central region, which might cause filling-in (Paradiso & Hahn, 1996): Observers might fail to experience the central region. This would reduce brightness and thus increase the probability of a black categorical judgment. 
There were differences in viewing conditions between the two experiments. First, eye positions were not controlled. In Experiment 1, the stimuli were presented in the peripheral visual field while the observers were fixating on the center of the display. In Experiment 2, observers freely moved their eyes. Second, sample presentation periods were not matched. Presentation duration was fixed at 0.3 s in Experiment 1 and open-ended in Experiment 2. The typical response time was 1 s, which was longer than the presentation duration in Experiment 1. The result might vary depending on gaze fixation and presentation time; however, brightness enhancement and the categorical labeling would appear the same across viewing conditions as demonstrated in Figure 1. To examine this, we performed an additional experiment that tested the effect of eye position on the appearance of stimuli (see Appendix, Additional experiment 2 details). As a result, observed thresholds of gray/white and white/luminous-white were the same between foveal and peripheral observation. In addition, the thresholds were the same as those in the original experiment in which eye position was not controlled. Thus, the discrepancy between brightness estimation and categorical judgments would likely persist, even if gaze were controlled in the categorical judgment task. 
Importance of the illusion
The current findings suggest that the glare illusion is not an exceptional phenomenon that is limited to the perception of self-luminosity under specific conditions, but rather a general brightness enhancement that is simply generated by a luminance gradient surrounding an object. The glare illusion induces robust brightness enhancement, which does not depend on the luminance of the central region. This is an important and useful property for both scientific and engineering fields. 
Intense lights are not only generated from self-luminous objects, but are also present as specular highlights on glossy surfaces. Thus, it is natural to assume that when an intense light is present on part of an object's surface, the surface is glossy. The spatial configuration of an image affects both its perceived lightness and glossiness (Motoyoshi, Nishida, Sharan, & Adelson, 2007; Sharan, Li, Motoyoshi, Nishida, & Adelson, 2008). Gloss perception also depends on object segmentation and three-dimensional configuration (Anderson & Kim, 2009; Kim & Anderson, 2010; Marlow, Todorović, & Anderson, 2015; Olkkonen & Brainard, 2010). Indeed, glossiness is perceived when it is generated from both bright specular highlights and dark specular “lowlights” (Kim, Marlow, & Anderson, 2012). That both bright and “dark” lights induce glossiness is consistent with the current findings that illustrate the robustness of the glare illusion. Those two perceptions might share similar mechanisms. Recently, the effect of glossiness on lightness and color perception was investigated (Granzier, Vergne, & Gegenfurtner, 2014; Olkkonen & Brainard, 2010); these interactions, and the glare illusion, might help us further understand lightness/brightness perception. 
Our current finding of constant brightness enhancement in the glare illusion is also potentially useful for computer graphics and image processing, to signify brighter and more luminous objects. The robustness of the illusion across illumination conditions is further useful if one wishes to show printed images. 
Halo
We included Halo as one of the test conditions. If Halo were not included, repeated presentations of Glow would have caused an afterimage (Anstis, Gori, & Wehrhahn, 2007) and subsequently affected the appearance of the following trial's stimulus. If the afterimage added to the sample stimulus brightness, Glow and Uniform would become similar to Uniform and Halo, reducing the illusion effect size. Indeed, we observed such effects in our preliminary experiments. We also noted interactions between the afterimage and the breathing light illusion, which was dynamically induced by the glare pattern (Anstis et al., 2007; Gori, Giora, & Agostini, 2010; Gori & Stubbs, 2006). 
Comparison with studies of Gilchrist and Zavagno
Bonato and Gilchrist (1994) reported that a target begins to appear luminous when its luminance is 1.7 times that of a reference white. The stimulus configuration used in their study was similar to the uniform condition in our experiment, in which subjects responded that the stimulus appeared white above 123.9 cd/m2, and luminous-white above the extrapolated value of 242.9 cd/m2 (Figure 3C). If we use 123.9 cd/m2 as reference white, 242.9 cd/m2 corresponds to a 1.96-fold increase. In contrast, the transition between the percepts of white and luminous-white in the Glow condition only required the stimulus luminance to be 1.23 times that of the reference white. This reduction in the threshold for the perception of self-luminosity represents the effect of the glare illusion. 
Zavagno (1999) indicated that luminosity perception occurred even when the target was darker than subjective white. Thus, there is a possibility of a “luminous-gray” response. Therefore, we should discuss whether our four available choices in Experiment 2 were appropriate. Alternatively, the subjects could be asked to respond in two steps, i.e., color naming and providing a luminosity judgment. If this response schedule was used, the luminosity threshold might be lower than suggested in our data, because our current task did not allow a “luminous-gray” response. However, the magnitude of the decrease would be limited, and it is unlikely that the threshold would drop to a very low level, such as 20 cd/m2, which corresponds to the lower limit of brightness enhancement in Experiment 1. This is because if the “true” luminosity threshold were very low, white (and nonluminous) responses would not have been observed in our original task; however, the observed data showed substantial white (and nonluminous) responses. Thus, even if the luminosity threshold decreased further in a different task, our conclusion still holds: Brightness enhancement is observed below the luminosity threshold. 
Effect of edge contrast
Both Glow and Halo stimuli had similar image statistics except for the direction of the luminance gradient. The mean luminances of the annuli were 41% (Glow), 59% (Halo), and 44% (Uniform) to the center patch. If we assume that the contrast between the center and the mean luminance of the annulus is critical in determining brightness enhancement, the largest contrast should be obtained for Glow, followed by Uniform and Halo. This order is not consistent with the observed brightness enhancement in Experiment 1. Another consideration is the adjacent contrast between center and annulus. In this case, contrast is maximal in Halo (∼100%), followed by Uniform (44%), and least in Glow (∼0%). Again, this order is not consistent with the observed data. These luminance contrasts do not explain brightness enhancement in the glare illusion, and thus other image statistics must be considered. 
Brightness enhancement was determined via comparison to the particular reference stimuli of the annulus's luminance level of 44% to the center. Thus, the use of other luminance might induce different results. Low luminance level of the uniform annulus may have resulted in increased lightness of the center, leading to less brightness enhancement in the glare stimuli, as compared to the reference dark annulus. To examine the effect of reference selection, we performed an additional experiment that was similar to Experiment 1, except for the reference, whose annulus was black. Again, the Glow condition led to significant brightness enhancement as compared with the reference; indeed, the magnitude of the brightness enhancement was almost comparable (35%, see Appendix, Additional experiment 1 details). Thus, we conclude that brightness enhancement is robust across different luminances of target and reference stimuli. 
Image restoring and glare illusion
An empirical explanation that may be applicable to the glare illusion is that it is similar to a hazy, multilayered scene (Anderson & Winawer, 2005, 2008). Blurring an intensely bright object corresponds to a convolution of the object with a point spread function, which results in a glare image. The glare illusion could be a perceptual process that restores the true image. For example, when an observer sees an object in a foggy scene, he or she would realize the true brightness of the object on coming closer to it. Once one learns the association between blurred and veridical images, it is possible to infer the true brightness of the image, even when only the blurred image is available. Similar optical effects would occur in a variety of situations such as the sun through a cloudy sky, a translucent lampshade, and defocusing the lens of our eye. The original image, which typically has a sharp outline, is always brighter than a blurred version of that image. Thus, perceived brightness would be enhanced in the glare illusion. This perceptual restoring process might be related to lightness constancy of the visual system. Since the blurring and restoring would not be limited to bright and self-luminous objects, but would also apply to surfaces with various reflectances, including those perceived as gray, it results in robust brightness enhancement in the illusion. 
Conclusion
Brightness enhancement in the glare illusion is surprisingly robust across stimulus intensities, ranging from dark to light, including subjectively gray, white, and luminous appearances. The magnitude of brightness enhancement is almost constant and corresponds to an effective increase in the luminance of at least 30%. Thus, the surrounding gradient, which was originally thought to mimic the spread of intense light, strongly and robustly increases brightness estimation even for stimuli that are not self-luminous. 
Acknowledgments
This study was supported by JSPS KAKENHI Grant Number 25135718 to KK, 22135005 to SN. HT was supported by the student fellowship program for leading graduate school at Toyohashi University of Technology. 
Commercial relationships: none. 
Email: koida@eiiris.tut.ac.jp. 
Corresponding author: Kowa Koida. 
Address: Electronics-Inspired Interdisciplinary Research Institute, Toyohashi University of Technology, Toyohashi, Aichi, Japan. 
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Appendix
Additional experiment 1: Brightness estimation with reference to a black annulus
The method was the same as that used in Experiment 1, except for the reference stimulus. In this experiment, the reference had a uniform black (0.56 cd/m2) annulus instead of gray (44% of the center region). Samples included Glow, Halo, Unif44, and Unif0. Unif44 was the same as Unif in Experiment 1. Unif0 was the control condition, in which the sample and reference were the same. Five subjects who also took part in the main experiment were the participants in this additional experiment. 
We observed robust and significant brightness enhancement in the Glow condition across the luminance range of the samples (p < 0.05, binomial test; see Figure A1). Unif44 was darker than the control, corresponding to the effect of simultaneous contrast. 
Figure A1
 
Brightness enhancement in the illusion in an additional experiment. The format is the same as Figure 2 in the main text, except for the two uniform conditions.
Figure A1
 
Brightness enhancement in the illusion in an additional experiment. The format is the same as Figure 2 in the main text, except for the two uniform conditions.
Additional experiment 2: Effect of viewing angle
The method was the same as that used in Experiment 2, with the exception of the eye control. Seven observers participated in two different view angle sessions. Firstly, in the peripheral observation session, the sample stimulus was presented on the peripheral visual field while the observers fixated on the fixation point on the screen, as in Experiment 1 in the main text. Secondly, in the foveal observation session, no fixation point was presented and the observers were asked to gaze at the center patch of the sample stimulus. The stimulus was displayed until a response was obtained. The sample stimuli were the same (Glow, Halo, and Uniform). There were six luminance levels: 0, 40, 80, 120, 160, and 200 cd/m2. Each session was composed of 144 trials (4 trials × 2 positions × 6 luminance levels × 3 profiles), and all conditions were randomly intermingled. 
The results are shown in Figure A2. The categorical responses were almost the same across viewing conditions, including the original condition of the main experiment. If differences existed, the thresholds of the original condition were slightly lower. This lowering due to eye control could help to support the main conclusion that brightness is enhanced even when its category is gray. Thus, we conclude that the difference of eye position is not critical for the categorical responses. 
Figure A2
 
The results of Additional experiment 2. (A) Categorical response probability in the foveal observation. (B) Those in the peripheral observation. The formats are the same as Figure 3 in the main text. (C) Luminance thresholds in Glow condition. Horizontal axis indicates three luminance thresholds: Black/Gray, Gray/White, and White/Luminous from the left. Each bar indicates a different view condition: Original (same as Experiment 2, free viewing), Foveal (foveal observation), and Peripheral (peripheral observation).
Figure A2
 
The results of Additional experiment 2. (A) Categorical response probability in the foveal observation. (B) Those in the peripheral observation. The formats are the same as Figure 3 in the main text. (C) Luminance thresholds in Glow condition. Horizontal axis indicates three luminance thresholds: Black/Gray, Gray/White, and White/Luminous from the left. Each bar indicates a different view condition: Original (same as Experiment 2, free viewing), Foveal (foveal observation), and Peripheral (peripheral observation).
Figure 1
 
Stimuli used in this study. (A) Examples of glare stimuli (top) and reference stimuli (bottom). The luminance of a central circle and surrounding inducer were modulated from dark to light (left to right). Circles in the same column have the same intensity (luminance). (B) Screen appearance: The sample and reference stimuli were placed to the left and right of the central fixation point, respectively. (C) Luminance profiles of Glow (blue), Halo (green), and Uniform (red) stimuli. The annulus is labeled as “inducer,” the inner circle as “patch,” and the surrounding uniform area covering the remaining display as “background.” In this example, the luminance of the center patch was 160 cd/m2. The background was always 100 cd/m2 irrespective of sample intensity.
Figure 1
 
Stimuli used in this study. (A) Examples of glare stimuli (top) and reference stimuli (bottom). The luminance of a central circle and surrounding inducer were modulated from dark to light (left to right). Circles in the same column have the same intensity (luminance). (B) Screen appearance: The sample and reference stimuli were placed to the left and right of the central fixation point, respectively. (C) Luminance profiles of Glow (blue), Halo (green), and Uniform (red) stimuli. The annulus is labeled as “inducer,” the inner circle as “patch,” and the surrounding uniform area covering the remaining display as “background.” In this example, the luminance of the center patch was 160 cd/m2. The background was always 100 cd/m2 irrespective of sample intensity.
Figure 2
 
Brightness enhancement in the glare illusion. (A) The horizontal axis indicates the luminance of the center patch, and the vertical axis the probability of the sample appearing brighter than the equiluminant reference uniform stimulus. Filled symbols indicate a significant difference from chance (50%). Response probabilities for each subject were calculated, and averages and standard errors among subjects were obtained. Error bars represent the standard error of the mean across all eight subjects. (B) Response probabilities for a dark (−20%) reference condition. (C) Response probabilities for a bright (+20%) reference condition. (D) Example psychometric function at a luminance level of 120 cd/m2. Response probabilities for three reference conditions with a fitted logistic function are shown. (E) Brightness enhancement quantified by the point of subjective equality (PSE). Symbols are the same as in A. Data were clipped to 100% or −25% if the function returned values greater than 100% or less than −25%, respectively. Filled symbols indicate goodness-of-fit of the psychometric functions. (F) Means and standard errors of significant PSEs for each condition.
Figure 2
 
Brightness enhancement in the glare illusion. (A) The horizontal axis indicates the luminance of the center patch, and the vertical axis the probability of the sample appearing brighter than the equiluminant reference uniform stimulus. Filled symbols indicate a significant difference from chance (50%). Response probabilities for each subject were calculated, and averages and standard errors among subjects were obtained. Error bars represent the standard error of the mean across all eight subjects. (B) Response probabilities for a dark (−20%) reference condition. (C) Response probabilities for a bright (+20%) reference condition. (D) Example psychometric function at a luminance level of 120 cd/m2. Response probabilities for three reference conditions with a fitted logistic function are shown. (E) Brightness enhancement quantified by the point of subjective equality (PSE). Symbols are the same as in A. Data were clipped to 100% or −25% if the function returned values greater than 100% or less than −25%, respectively. Filled symbols indicate goodness-of-fit of the psychometric functions. (F) Means and standard errors of significant PSEs for each condition.
Figure 3
 
Categorical response probability. The horizontal axis indicates the luminance of central circle, and the vertical axis the response probability for each category. A, B, and C show the response for the Glow, Halo, and Uniform conditions, respectively. The categorical responses black, gray, white, and luminous-white increased in probability from low to high luminance. For example, gray, white, and luminous-white responses were observed with approximately equal probability at 120 cd/m2 for the Glow condition. Functions are cumulative Gaussians, fit via a maximum likelihood method. Crosses indicate 50% probability points of each function.
Figure 3
 
Categorical response probability. The horizontal axis indicates the luminance of central circle, and the vertical axis the response probability for each category. A, B, and C show the response for the Glow, Halo, and Uniform conditions, respectively. The categorical responses black, gray, white, and luminous-white increased in probability from low to high luminance. For example, gray, white, and luminous-white responses were observed with approximately equal probability at 120 cd/m2 for the Glow condition. Functions are cumulative Gaussians, fit via a maximum likelihood method. Crosses indicate 50% probability points of each function.
Figure A1
 
Brightness enhancement in the illusion in an additional experiment. The format is the same as Figure 2 in the main text, except for the two uniform conditions.
Figure A1
 
Brightness enhancement in the illusion in an additional experiment. The format is the same as Figure 2 in the main text, except for the two uniform conditions.
Figure A2
 
The results of Additional experiment 2. (A) Categorical response probability in the foveal observation. (B) Those in the peripheral observation. The formats are the same as Figure 3 in the main text. (C) Luminance thresholds in Glow condition. Horizontal axis indicates three luminance thresholds: Black/Gray, Gray/White, and White/Luminous from the left. Each bar indicates a different view condition: Original (same as Experiment 2, free viewing), Foveal (foveal observation), and Peripheral (peripheral observation).
Figure A2
 
The results of Additional experiment 2. (A) Categorical response probability in the foveal observation. (B) Those in the peripheral observation. The formats are the same as Figure 3 in the main text. (C) Luminance thresholds in Glow condition. Horizontal axis indicates three luminance thresholds: Black/Gray, Gray/White, and White/Luminous from the left. Each bar indicates a different view condition: Original (same as Experiment 2, free viewing), Foveal (foveal observation), and Peripheral (peripheral observation).
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