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Article  |   March 2023
Attentional allocation and the pan-field color illusion
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Journal of Vision March 2023, Vol.23, 13. doi:https://doi.org/10.1167/jov.23.3.13
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      Lana Okubo, Kazuhiko Yokosawa; Attentional allocation and the pan-field color illusion. Journal of Vision 2023;23(3):13. https://doi.org/10.1167/jov.23.3.13.

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Abstract

Humans subjectively experience a scene as rendered in color across the entire visual field, a visual phenomenon called “pan-field color” (Balas & Sinha, 2007). This experience is inconsistent with the limited color sensitivity in the peripheral visual field. We investigated the effects of visual attention allocated to the peripheral visual field on the pan-field color illusion. Using “chimera” stimuli in which color was restricted to a circular central area, we assessed observers’ tendency to perceive color throughout images with achromatized peripheral regions. We separately analyzed sensitivity and response bias in judging the color content of the scene image as full-color, chimera, or gray. Using a dual-task paradigm, we manipulated observers’ attentional allocation by controlling the stimulus presentation time of the central task, making the foveal attentional load change. The slope of the foveal load-sensitivity function suggests that attention was modulated by foveal load even in the peripheral visual field. Bias was affected by the size of the central colored area, such that the tendency to answer “full-color” to the chimera image increased with eccentricity. Based on these effects of attention on sensitivity and bias, we suggest that the pan-field color illusion cannot be fully explained by the decrease of sensitivity that is modulated by attentional allocation in the periphery. Our results rather indicate that the pan-field color illusion at least partly reflects a liberal bias in peripheral vision.

Introduction
It is surprising that we effortlessly experience a rich uniform visual world in spite of limited visual acuity in the peripheral visual field (Noë, 2002). For example, peripheral vision is known to be poor relative to foveal vision in terms of color vision (Gordon & Abramov, 1977; Curcio, Sloan, Kalina, & Hendrickson, 1990), visual acuity (Anstis, 1998), and contrast sensitivity (Roorda & Williams, 1999). Nevertheless, observers generally perceive uniformity in color throughout the visual field (Balas & Sinha, 2007; Block, 2007; Haun, Tononi, Koch, & Tsuchiya, 2017; Cohen et al., 2020; Cohen & Rubenstein, 2020). Notably, it is known that this sense of color uniformity is also evoked for images without any color information in the peripheral vision. Balas and Sinha (2007) used a partly achromatic image (a “chimera” image, Figure 1) and examined the sense of uniformity by measuring the observer's tendency to misunderstand chimera images as full-color images. The phenomenon in which observers perceive colors that do not exist in the peripheral vision is called the “pan-field color illusion,” which remains an unsolved problem of visual consciousness in peripheral vision. 
Figure 1.
 
Example of a “chimera” image used by Balas and Sinha (2007). Color is restricted to a circular central region.
Figure 1.
 
Example of a “chimera” image used by Balas and Sinha (2007). Color is restricted to a circular central region.
It is known that attention plays an important role in visual consciousness. The simplest hypothesis of visual consciousness is that the features of visual signals that we pay attention to are those that are processed and reach our consciousness. Classic models of visual attention have argued that perception of features or objects requires attention (Treisman & Gelade, 1980). Human visual systems pre-attentively process basic features. Attention works as a bottleneck, and unattended features do not undergo higher level processing, which has a limited capacity (Broadbent, 1958; Treisman, 1960). This classic early selection explanation is connected to the argument that all visual processing, including conscious experience, occurs only for attended features (Cohen, Cavanagh, Chun, & Nakayama, 2012). Other psychophysical observations, such as inattentional blindness and the attentional blink, have supported the view that visual consciousness requires attention (Joseph, Chun, & Nakayama, 1997; Rensink, O'regan, & Clark, 1997). On the other hand, some researchers have proposed that attention and consciousness can be separated (Lamme, 2004; Dehaene, Changeux, Naccache, Sackur, & Sergent, 2006; Koch & Tsuchiya, 2007; Maier & Tsuchiya, 2020). For instance, if the conscious visibility of a stimulus does not depend on the attentional state, a dissociation of attention and consciousness is thought to be established (Lamme, 2004). Whether attention is necessary for consciousness continues to be debated (Dehaene et al., 2006; van Boxtel et al., 2010; Cohen, Dennett, & Kanwisher, 2016). 
Other researches have proposed that some visual processes do not necessarily need focused attention. For example, some types of visual features are perceived without attention. When we see a scene, we can rapidly identify its gist (Oliva & Torralba, 2006; but see Cohen, Alvarez, & Nakayama, 2011), extract the properties of an ensemble (Alvarez, 2011), and even classify items (Li, VanRullen, Koch, & Perona, 2002). These findings have led some researchers to add extra pathways and modes to their theories to accommodate scene processing that does not necessarily rely on attention (Treisman, 2006; Wolfe, Alvarez, Rosenholtz, Kuzmova, & Sherman, 2011). 
These facts raise a question: Does the pan-field color illusion, a visual phenomenon in which rich color is perceived in peripheral vision during observation of a scene, depend on the observer's state of visual attention? On the one hand, this illusion is directly related to scene perception, so the illusion may occur irrespective of attentional state. On the other hand, early selection theory implies that the conscious content of color would be influenced by attention. For those reasons, the role of attention in the pan-field color illusion should be investigated. 
Several recent studies have clarified the underlying mechanisms of the pan-field color illusion (Balas & Sinha, 2007; Cohen et al., 2020; Cohen & Rubenstein, 2020). Using a partly achromatic image (a “chimera” image; see Figure 1), Balas and Sinha (2007) evaluated the pan-field color illusion as the observer's tendency to misunderstand chimera images as full-color images. They hypothesized that natural scene statistics maintained in the achromatic region of the chimera image make detecting a region of impoverished color difficult, leading to the subjective experience of a fully colored image. They found that recognizable scene structure contributes to the experience of pan-field color. Recently, Cohen et al. (2020) provided a powerful demonstration of the pan-field color illusion in immersive, dynamic real-world environments using virtual reality (VR). Surprisingly, almost a third of observers failed to notice when less than 5% of the visual display was presented in color. These studies have succeeded in clarifying the important role of scene recognition in the pan-field color illusion; however, these studies did not examine the relationship between pan-field color perception and the observer's attentional state. 
The purpose of this study is to investigate the possibility that peripheral visual consciousness is affected by the attentional function of the visual system, in the case of the pan-field color illusion. To examine this hypothesis, we must control attentional allocation in the periphery. Attention can be manipulated by several methods, such as the dual-task paradigm, task instructions, and attentional blink in the rapid serial visual presentation (RSVP) task. These experimental settings exploit the fact that attention has a greatly limited capacity (Pylyshyn & Storm, 1988). In the present study, we wanted to investigate the interaction between attention and the pan-field color illusion when attention is graded. For this purpose, we adopted the dual-task paradigm (Joseph et al., 1997; Braun & Julesz, 1998; Matthews, Schröder, Kaunitz, Van Boxtel, & Tsuchiya, 2018) and gradually varied the observer's focused attention by changing task difficulty. 
Under dual-task conditions, people simultaneously perform a central attention-demanding task and a peripheral task. To quantitatively manipulate the observer's attention, we varied the difficulty of the central task using Lavie's perceptual load model of attention (Lavie & Tsal, 1994; Lavie, 1995; Lavie et al., 2004). Lavie (1995) argued that tasks that impose a high perceptual load lead to stronger focusing of attention on the task. In our study, we changed the attentional load of a central RSVP task by varying the presentation time of the characters. Because shorter presentation times result in a more difficult central task, we were able to manipulate quantitively the attention allocated to the periphery by consistently changing the foveal attentional load. 
In the peripheral task, observers were instructed to judge the color content of a presented scene image. The presented image was a full-color, chimera, or monochrome image. We measured the pan-field color illusion using observers’ “full-color” responses to the chimera image in the peripheral task (see Figure 1). Previous studies using the pan-field color illusion paradigm provided no way to assess detection sensitivity, as the two indexes – observers’ “full-color” responses to the chimera image and “chimera” responses to the full-color image – were analyzed separately (Balas & Sinha, 2007). In the present analysis, we calculated detection sensitivity (d’) and response bias (C) based on the normalized hit rate (“full-color” response rate to the full-color image) and the normalized false alarm rate (“full-color” response rate to chimera image; Green & Swets, 1966). Thus, we analyzed peripheral color perception by combining the two types of observer responses, allowing us to assess the effects of attention on detection sensitivity and on response bias separately. 
Two hypotheses on attentional allocation across the visual field
We expected that attention allocated to the periphery would decrease in proportion to the increase in eccentricity (Eriksen & James, 1986). Regarding the effect of the foveal load on attentional allocation, we expected that attentional allocation in central vision would be greater for the difficult task than for the easy task (Lavie, 1995). 
Regarding the effect of foveal load on peripheral vision, we considered two possibilities. First, the overall expenditure of resources devoted to a task may remain at a static constant even when the task difficulty changes (Kahneman, 1973; Norman & Bobrow, 1975). As a result, a more difficult central task should yield a steeper and more narrow spatial distribution of attention than an easier task, with a peak in the central visual field (LaBerge, 1983). We call this prediction the fixed resource model of attention (Figure 2A). Under this assumption, the amount of attention in the peripheral visual field (see the gray area in Figure 2A) would decrease in the higher load condition (i.e. shorter presentation time) relative to the lower load condition (i.e. longer presentation time). 
Figure 2.
 
Two hypotheses about the allocation of attention. The dotted line represents the possible distribution of attention in the lower load; the solid line represents that in the higher load. (A) A model of spatial attention with eccentricity and foveal load as variables. This is the fixed resource model, in which attention has a fixed capacity. (B) Another model of spatial attention. This is the flexible resource model, in which the available attentional resources vary depending on task difficulty.
Figure 2.
 
Two hypotheses about the allocation of attention. The dotted line represents the possible distribution of attention in the lower load; the solid line represents that in the higher load. (A) A model of spatial attention with eccentricity and foveal load as variables. This is the fixed resource model, in which attention has a fixed capacity. (B) Another model of spatial attention. This is the flexible resource model, in which the available attentional resources vary depending on task difficulty.
Alternatively, resources and capacities of specific cognitive processes, including visual attention, might have a plastic cross-domain architecture. Several cognitive processes usually work parallelly in real life by using an overlapping cortical area. Therefore, cognitive functions, such as visual attention or working memory, occasionally compete to access capacity-limited buffers from time to time (Franconeri, Alvarez, & Cavanagh, 2013). From this viewpoint, attentional resources can differ according to the task type. Indeed, additional attentional resources can be activated for the more difficult task in the dual-task condition (Müller, Mollenhauer, Rösler, & Kleinschmidt, 2005). If the expenditure of resources devoted to a central task changes, depending on the task demands, more difficult and easier central tasks should yield the same spatial distribution of attention in the peripheral visual field. We call this prediction the flexible resource model of attention (Figure 2B). Under this assumption, the amount of allocated attention in the peripheral visual field (see the gray area in Figure 2B) would remain the same under high or low load conditions. 
In Figures 2A and 2B, the amount of spatial attention in the central visual field is represented as greater when the task is difficult and less when it is easy. This assumption is based on several previous studies that have shown that higher task loads result in steeper slopes of the spatial distribution of attention (LaBerge, 1983; Lavie, 1995). In other words, in the short presentation time condition, more spatial attention is allocated to the central task than in the long presentation time condition. Even so, it should be noted that the shorter presentation time of the central RSVP task would make the central task's performance lower compared to the longer presentation time condition because the information or sensory evidence that is needed to detect the target character is accumulated over time (Ratcliff, Smith, Brown, & McKoon, 2016). Thus, the performance of the central task may not necessarily correspond to the spatial distribution of attention represented in Figures 2A and 2B; it may become poorer when the load is high and better when the load is low. 
Two hypotheses for sensitivity d′
Sensitivity d′ (d-prime) is a measure of sensitivity or discriminability derived from signal detection theory that is unaffected by response bias. It is a standardized score computed as the difference between the standard scores for the false-alarm and hit rates. Higher values of d′ indicate better discriminability and lower values reflect lower discriminability. In the latter case, observers perform a task mainly by guessing. 
Sensitivity of the peripheral task was assumed to be determined as the product of the amount of visual attention and the physiologically observed color sensitivity. As noted above, the amount of allocated attention decreases in accordance with stimulus eccentricity. Moreover, the retinal cone distribution decreases in proportion to the increase in eccentricity (Curcio et al., 1990). In tandem with the decrease of color acuity and attention in peripheral vision, we predicted that d′ on the peripheral task would decrease as the size of the colored area of the chimera image grew larger. 
In the previous section, we proposed two models of attentional allocation, the fixed and flexible resource models. Both predict that the foveal load will increase focused attention in the central visual field. The main difference between the predictions derived from the two models is whether the effects of foveal load spill over into the peripheral visual field or whether the effects are limited to the central visual field. In our experiment, if the fixed resource model holds true in case of the pan-field color illusion (see Figure 2A), d′ should decrease depending on both eccentricity and foveal load. Alternatively, if the flexible resource model (see Figure 2B) more accurately explains the pan-field color illusion, d′ should decrease depending solely on eccentricity. 
Two hypotheses for response bias C
Response bias C is an index of the human's decision-making criterion: the tendency to respond “yes” or “no.” In the present study, a value of C that falls below 0 indicates the tendency of observers to answer “full-color” to the chimera image (liberal bias), whereas a value of C above 0 indicates a tendency to answer “chimera” to the full-color image (conservative bias). 
Some researchers have argued that the perceived intactness and uniformity of a scene across the visual field is partly explained by response bias in visual perception (Rahnev, Maniscalco, Graves, Huant, De Lange, et al., 2011; Solovey, Graney, & Lau, 2015; Li, Lau, & Odegaard, 2018; Knotts, Odegaard, Lau, & Rosenthal, 2019). Intuitively, when attention is limited, observers should be more conservative in their detection judgments because they know a priori, as a result of their meta-cognitive ability, that their vision is poor without attention. On the contrary, previous studies have found that when attention is limited, participants are more likely to report “yes” in response to a stimulus that actually does not exist. This effect is known as subjective inflation in peripheral vision. Rahnev et al. (2011) examined the mechanism of this phenomenon, wherein observers exhibit liberal detection bias in the peripheral visual field. They argued that insufficient visual attention to the periphery increases the trial-by-trial variability of the internal neural response, leading to more frequent surpassing of a detection criterion. Solovey et al. (2015) also found a more liberal response bias in peripheral vision compared to the central vision, even when the performance (i.e. detection sensitivity) between the peripheral and central vision matched. In summary, response bias should be modulated by the attentional state so that less attention in the peripheral visual field causes more liberal bias. We hypothesized that this also holds true in the case of the pan-field color illusion, such that the subjective richness of color in the peripheral vision shown in the pan-field color illusion derives from such a shift of response bias. 
The predictions for response bias parallel the two proposed patterns of attentional allocation. First, a higher task load decreases attention in the peripheral visual field, leading to lower values of response bias. In other words, this prediction follows the fixed resource model of attention (see Figure 2A). A second prediction is that task load does not change the attentional state in peripheral vision, resulting in no change in response bias. In this situation, response bias would be affected only by the size of the colored area. This prediction of response bias is based on the flexible resource model of attention (see Figure 2B). We predict that the value of response bias should decrease as the size of the colored area increases, so that observers should more frequently respond “full-color” to the chimera image. This prediction is based on previous studies regarding the change of response bias in peripheral detection tasks (Rahnev et al., 2011; Solovey et al., 2015). 
Methods
Subjects
Forty-four paid participants (average age = 22.0, SD = 2.5, 26 men and 18 women) took part in this study. All participants reported having normal or corrected-to-normal visual acuity, and we administered the Ishihara test (Ishihara, 1992) to confirm that they did not have color blindness. The participants were naïve to the purpose and methods of the experiment. The experiment was approved by the ethical committees of the Graduate School of Humanities and Sociology at the University of Tokyo. Before the experiment, all observers provided written informed consent. 
Apparatus
Stimuli were displayed on a calibrated CRT monitor, 19-inch Mitsubishi Diamondtron RDF223G. The monitor was set to a spatial resolution of 1024 × 768 pixels and a refresh rate of 60 Hz. The luminance values for each color channel were measured with a luminance colorimeter BM-7 (TOPCON) and linearized. Psychtoolbox extensions (Brainard & Vision, 1997) were used for stimulus display and data collection in Matlab (Mathworks, Inc.). Subjects sat 37 cm away from the screen, using a chin rest to stabilize the head position. 
Central attentional task
In the central attentional task, participants had to detect and respond to a single target letter (one letter enclosed in a thick black frame) from a sequence of 20 to 25 letters presented at the center of the display. The number of displayed letters was uniformly distributed so that all sequence lengths occurred the same number of times for each subject. We expected that a relatively short/long stimulus presentation time would produce a high/low foveal load, thus leading to the allocation of less/more attention to the periphery (Lavie, 1995). We manipulated three levels of foveal load by setting the presentation time as 83 ms, 117 ms, or 150 ms per letter. There were 96 trials for each presentation time. Average accuracy on the RSVP task in the current dual-task was 82.7% for 83 ms, 95.5% for 117 ms, and 95.6% for 150 ms. This indicates that the shorter presentation times resulted in a more difficult task, although performance between 117 ms and 150 ms differed slightly, contrary to our expectations. Moreover, even in the most difficult condition (i.e. 83 ms condition), the percentage of correct responses exceeded 80%. This suggests that the observers succeed in paying attention to the central task. The central task stimuli were superimposed on the peripheral task stimuli. All letters were boxed in black lines to increase their visibility against the background scene image. The target letter was additionally boxed in a thick blacker line. It is known that when the feature dimension targeted in the central task (e.g. color) is a task-related feature in the peripheral task, performance on the peripheral task improves (Morrone, Denti, & Spinelli, 2002). To prevent this effect, in the present study, the target-defining feature of the central task was set as a shape (a thick black frame around the letter) instead of a color, which was related to the peripheral task. The letter frame subtended 1 degree × 1 degree of visual angle. Participants had to choose a target letter from 26 alphabet letters, so the chance level of the central task was approximately 4%. 
Peripheral color judgment task
To investigate the nature of the pan-field color illusion, we used a “chimera” image (see Figure 1) as proposed by Balas and Sinha (2007). In the present study, participants were asked to judge the color content of natural images as "full-color,” “gray,” or “chimera“ after observing full-color, chimera, or gray images. Two hundred eighty-eight unique images of natural scenes were drawn from the Nature Scene Collection (Geisler & Perry, 2011). These scenes mainly depict forest or field environments and do not contain man-made objects or people. Images subtended 48 degrees × 32 degrees of visual angle. Three types of image stimuli were generated: full-color (120 trials), gray (48 trials), and chimera images (120 trials). In the full-color stimuli, the original image was presented. In the chimera stimuli, a circular region centered on the image was selected, and saturation values outside this region were set to zero (Figure 3). The radius of the circular region ranged from 9 degrees to 25 degrees of visual angle, in steps of 4 degrees, by applying a two-dimensional Gaussian function. In other words, chimera stimuli presented five possible widths of the colored circular area. In the gray stimuli, the original red, green, blue (RGB) images were converted into hue-saturation-value (HSV) coordinates, with saturation set to zero. We wanted to make participants obtain color information from the whole scene image, but participants can distinguish between color image and chimera image by locally focusing on the presence or absence of the color on the edge of the screen. Thus, gray stimuli were added as a filler to prevent participants from judging the color of the natural scene solely based on the color of the edge of the screen. The presentation order of the scene images and the presentation time of the central task were individually randomized. In the chimera stimuli, an image and the size of the colored area it was paired with were fixed across all subjects for the technical reason of reducing system delay during the RSVP task. 
Figure 3.
 
The stimulus examples of peripheral color judgment task. The left and middle panels are examples of chimera images in which the circular central colored area was 9 degrees and 25 degrees. The right panel depicts the full-color condition.
Figure 3.
 
The stimulus examples of peripheral color judgment task. The left and middle panels are examples of chimera images in which the circular central colored area was 9 degrees and 25 degrees. The right panel depicts the full-color condition.
Procedure
Before beginning the experiment, scene stimuli that were not used in the task were presented as examples to make subjects understand what full-color, gray, and chimera images looked like. Participants were given practice under experimental conditions: 10 practice trials (with feedback) were run using stimuli that were not included at test. Upon completion, all subjects reported feeling confident in their ability to see the images and respond accurately. 
The time course of a trial is shown in Figure 4. Each trial began with a 0.5 degrees × 0.5 degrees black fixation cross presented at the center of the screen for 500 ms, followed by a 500 ms blank screen. The distractor alphabets were displayed at the center of the screen for 83 ms, 117 ms, or 150 ms per letter. This first distractor stream consisted of 5 to 10 items. The test scene image was presented at the same time as the target thick-flamed character appeared. The target character was shown for 83 ms, 117 ms, or 150 ms, followed by the 14 distractor characters displayed for 83 ms, 117 ms, or 150 ms per letter. The scene image was displayed for 150 ms, followed by a white noise mask image lasting 150 ms. We used white noise to mask the contour or edge information of the scene. Whereas the central and peripheral tasks’ stimuli appear simultaneously, the central task's characters were embedded in the scene image or noise image. After the distractor characters appeared, participants answered a single target letter using the corresponding key. The subject's response for the peripheral task was then collected, using the “4,” “5,” and “6” keys for “full-color,” “gray,” and “chimera” responses, respectively. The key assignment was counterbalanced. Breaks were scheduled every 30 trials. Subjects were instructed to focus attention on the center of the display and to try to perform both tasks as accurately as possible. Subjects first responded to the RSVP task and then to the scene color task. 
Figure 4.
 
The time course of a trial. Each letter target of the RSVP task was presented for one of three presentation times: 83 ms, 117 ms, or 150 ms. The scene image of the peripheral task appeared at the same time as the onset of the target letter. The scene image and mask image of the peripheral task were always presented for 150 ms each.
Figure 4.
 
The time course of a trial. Each letter target of the RSVP task was presented for one of three presentation times: 83 ms, 117 ms, or 150 ms. The scene image of the peripheral task appeared at the same time as the onset of the target letter. The scene image and mask image of the peripheral task were always presented for 150 ms each.
An additional 72 single-task trials were included among the dual-task trials described above. In these single-task trials, scene images were presented for 150 ms, but the central RSVP stream was not displayed, allowing us to check the observer's performance when their task was only to judge the color content of the scene. We randomly inserted the single-task trials into the dual-task trials. The results for the single-task trials are shown in Supplementary Figures S1 and S2
Results
General response tendency on the peripheral task
We intended to investigate the role of attention on the pan-field color illusion in ecologically valid conditions. In other words, we wanted to determine the effects on the pan-field color illusion when the observers’ attention was mainly directed to the central visual field, which is close to real-world viewing. For this reason, trials in which observers failed the central task were removed from this analysis. 
Figure 5A shows the general response tendency on the peripheral task. The average percentages of correct responses were 76.3% (SD = 15.1) for full-color images, 69.4% (SD = 14.0) for chimera images, and 90% (SD = 13.3) for gray images. The numbers of “full-color” responses to chimera images and “chimera” responses to full-color images were not largely different. 
Figure 5.
 
General response tendency on the peripheral task. (A) Rates of “gray,” “chimera,” and “color” responses to each type of image. (B) Rates of “gray,” “chimera,” and “color” responses to chimera images for each size of colored area.
Figure 5.
 
General response tendency on the peripheral task. (A) Rates of “gray,” “chimera,” and “color” responses to each type of image. (B) Rates of “gray,” “chimera,” and “color” responses to chimera images for each size of colored area.
In Figure 5B, the tendency of observers to report chimera images as being fully colored is shown to increase with the size of the colored area. This result supports the finding of a previous study that the proportion of “full-color” responses to chimera images grew as the ratio of the size of the chromatized region to that of achromatized region increased (Balas & Sinha, 2007). We successfully replicated the effect of the size of the colored area on the pan-field color illusion previously reported (Balas & Sinha, 2007; Cohen et al., 2020). 
Effects of foveal load on d′
Figure 6 shows mean sensitivity (d′) for the peripheral color judgment task. The d′ for performance on the color judgment task was estimated from the normalized hit rates (“full-color” responses to the full-color image) and the normalized false alarm rate (“full-color” responses to the chimera image) for each condition of foveal load. In other words, the observers’ “gray” responses were excluded from the analysis. 
Figure 6.
 
Sensitivity d′ as a function of presentation time and size of the colored area. Error bars in all panels represent ±1 standard error.
Figure 6.
 
Sensitivity d′ as a function of presentation time and size of the colored area. Error bars in all panels represent ±1 standard error.
We conducted a 3 × 5 within-subjects analysis of variance (ANOVA) on d′ scores for presentation time (83 ms, 117 ms, and 150 ms) × size of colored area (9, 13, 17, 21, and 25 degrees). This ANOVA revealed a significant main effect of presentation time (F (2, 86) = 14.3, p < 0.001, ηp2 = 0.048). To prevent type I errors with multiple planned comparisons of post hoc tests, the p values were corrected using a Bonferroni correction. Multiple comparison tests (with the Bonferroni method) showed that sensitivity of the peripheral color judgment task was lower for 83 ms than for 117 ms and 150 ms (p < 0.001). There were no significant differences between 117 ms and 150 ms (p = 0.10). The main effect of size of the colored area was also significant (F (4, 172) = 135.3, p < 0.001, ηp2 = 0.47), with sensitivity reliably lower for the larger colored area. The interaction between presentation time and the size of the colored area was also significant (F (8, 344) = 3.6, p < 0.001, ηp2 = 0.15). The analysis of simple main effects yielded significant effects of presentation time for the 9 degrees condition (F (2, 430) = 11.2, p < 0.001), 13 degrees condition (F (2, 430) = 16.7, p < 0.001), 17 degrees condition (F (2, 430) = 6.8, p < 0.01) and 25 degrees condition (F (2, 430) = 5.1, p < 0.01). Unexpectedly, the simple main effect of presentation time was not significant for the 21 degrees condition (F (2, 430) = 2.0, p = 0.14). The analysis of simple main effects also yielded significant effects of size of the colored area for all presentation time conditions (F (4, 516) = 49.1, p < 0.001, for the 83 ms condition; F (4, 516) = 66.6, p < 0.001, for the 117 ms condition; and F (4, 516) = 74.2, p < 0.001, for the 150 ms condition), indicating that sensitivity was significantly lower for the larger colored area under all presentation time conditions. 
Importantly, the higher foveal load reduced d′ on the peripheral task, suggesting that the effects of foveal load spilled over onto the peripheral visual field. This result implies that the fixed resource model of attention (see Figure 2A) more accurately predicted the effects of attention on color perception in peripheral vision compared to the flexible resource model of attention (see Figure 2B). As predicted by the fixed resource model, a more difficult central task yielded a steeper and more narrow spatial distribution of attention in the peripheral visual field. This suggests that the expenditure of resources that are devoted to peripheral color perception remains a static constant even when the task difficulty is changed, thus increasing attentional demand (Kahneman, 1973; Norman, & Bobrow, 1975). Moreover, the effects of the size of the colored area aligned with physiological data on color sensitivity (Curcio et al., 1990) and replicated previous results on attention in the peripheral visual field (Eriksen & James, 1986). 
Effects of foveal load on response bias C
Figure 7 shows the mean values of response bias (C) for performance on the peripheral color judgment task. C was estimated from the normalized hit rates and the normalized false alarm rates of performance in each condition. Values of C that fall below 0 indicate that observers tended to answer “full-color” to the chimera image; values of C greater than 0 indicate a tendency to answer “chimera” to the full-color image. 
Figure 7.
 
Response bias C as a function of presentation time and size of the colored area.
Figure 7.
 
Response bias C as a function of presentation time and size of the colored area.
We conducted a 3 × 5 within-subjects ANOVA on C for presentation time (83 ms, 117 ms, and 150 ms) × size of colored area (9, 13, 17, 21, and 25 degrees). This ANOVA revealed a significant main effect of presentation time (F (2, 86) = 9.3, p < 0.001, ηp2 = 0.03). Multiple comparison tests (with Bonferroni correction) revealed that response bias was lower for 117 ms than for 83 ms and 150 ms presentation times (p < 0.001 for 83 ms and p = 0.014 for 150 ms), and 83 ms and 150 ms did not differ significantly (p = 0.08). The main effect of size of the colored area was also significant (F (4, 172) = 135.3, p < 0.001, ηp2 = 0.49), with response bias reliably lower for larger colored areas. The interaction between presentation time and size of the colored area was also significant (F (8, 344) = 3.6, p < 0.001, ηp2 = 0.02). The analysis of simple main effects yielded significant effects of presentation time for the 17 degrees condition (F (2, 430) = 16.2, p < 0.001), 21 degrees condition (F (2, 430) = 7.7, p < 0.01), and 25 degrees condition (F (2, 430) = 3.1, p = 0.05). On the other hand, the simple main effects of presentation time were not significant for the 9 degrees and 13 degrees conditions (F (2, 430) = 0.7, p = 0.49, for the 9 degrees condition; F (2, 430) = 2.1, p = 0.13, for the 13 degrees condition). The analysis of simple main effects also yielded significant effects of the size of colored area for all presentation time conditions (F (4, 516) = 49.1, p < 0.001, for the 83 ms condition; F (4, 516) = 66.6, p < 0.001, for the 117 ms condition; and F (4, 516) = 74.2, p < 0.001, for the 150 ms conditions). 
These results suggest that C decreased as the size of the colored area consistently increased; that is, response bias shifted to a more liberal criterion as the size of the colored area grew larger. This result is in line with previous findings of a shift of response bias in peripheral vision, which leads observers to respond that they see objects more frequently (i.e. false alarm rate increases). As discussed above (see Figure 6), foveal load appeared to affect sensitivity on the peripheral task, implying that the fixed resource model of attention holds for peripheral color judgment. Thus, foveal load would also be expected to influence response bias C. To the contrary, our results for C indicate that foveal load did not consistently modulate C: the moderate foveal load produced the smallest response bias and the highest foveal load produced the largest. It also remains unclear why the effect of presentation time on C was limited to the larger colored area. We speculate that the modulation of bias by attention changed qualitatively based on the type of visual field, perifoveal versus far peripheral. We return to this effect in the Discussion section. 
Discussion
We investigated the effect of attention on the pan-field color illusion by separating response bias from sensitivity. We found color detection sensitivity to be lower with greater eccentricity of a central colored area of a stimulus image. This corresponds to established phenomena of retinal cone cell distribution (Curcio et al., 1990) and the distribution of attention (Eriksen & James, 1986). In addition, sensitivity fell as the foveal attention load increased, even in the far periphery. These results suggest that the amount of attention was constant even when task difficulty was varied, supporting the fixed resource model of attention (see Figure 2A). These findings imply that, in natural-viewing conditions, the sensitivity of color perception in the peripheral visual field is constrained by the kind of attentional-demanding task the observer is performing at the moment in the central visual field. In other words, sensitivity in perceiving the color content of a scene should differ depending on the observer's current attentional state (e.g. staring blankly at something versus actively searching for something). On the other hand, it should be noted that attention does not always have a capacity-fixed effect on color perception in the peripheral visual field. Attention exhibited characteristics of a fixed capacity in this experiment, possibly because participants’ overall cognitive resource capacity, which encompasses different functions such as attention, was approximately equal to the cognitive cost demanded by the attentional task. Our experiment artificially created a situation with a very high attentional load, but people are only occasionally placed in such situations when observing scenes. Attention might appear to have flexible resources under naturalistic conditions that often require conducting tasks other than attentional tasks (e.g. navigation) because the degree of allocating overall cognitive resources to attention and navigation, for example, changes from moment to moment. 
In our experiment, values of d′ exceeded zero even when the size of the colored area was 25 degrees. We did not measure participants' eye movements with an eye tracker in this experiment. Nevertheless, the scene was presented for only 150 ms, and we only analyzed trials in which participants correctly responded to the central task. Therefore, it can be said that their gaze was directed at the center of the screen. Given this fact, our results indicated that participants could judge whether the scene was colored or not even at 25 visual degrees. This result appears to contradict the well-known physiological finding of fewer color-responsive cone cells in the retina's periphery. However, Rosenholtz (2016) pointed out that the low density of cone cells in the peripheral visual field tends to be more exaggerated than it is. For example, there are approximately 4000 cones per mm2 at approximately 20 degrees of eccentricity (Curcio et al., 1990; Abramov, Gordon, & Chan, 1991), which would not cause color blindness. Moreover, the peripheral visual field's cone cell size is larger than that of the central visual field (Curcio et al., 1990). As a result, the spatial resolution of color might not deteriorate as much as we would expect from cone density distribution alone because the inter-cone distance also affects the spatial resolution of color. In fact, it is known that humans can perceive surprisingly rich color information in the periphery, especially if the color stimuli are complex or large-scale (Hansen, Pracejus, & Gegenfurtner, 2009; Webster, Halen, Meyers, Winkler, & Werner, 2010; Bronfman, Brezis, Jacobson, & Usher, 2014; Tyler, 2015). Future research is needed to investigate the mechanisms of color perception that are responsible for sensitivity of detection of naturalistic complex color stimuli in the case of the pan-field color illusion. 
The results also showed that increasing the colored area's size reduced sensitivity and linearly changed the response bias from neutral to liberal. We argue that the pan-field color illusion cannot be fully explained by the decrease of color sensitivity in the periphery alone. Rather, it is the shift in response bias from neutral to liberal that occurs with greater eccentricity that is presumably responsible for the pan-field color illusion. This result supports the proposed account of the response bias shift for subjective inflation on visual acuity in the periphery (Rahnev et al., 2011; Solovey et al., 2015). 
The foveal load did not consistently affect the response bias. It has been suggested that low spatial attention is associated with an increase in liberal detection bias, reflecting inflated subjective perceptual qualities, including the pan-field color illusion (Rahnev et al., 2011; Solovey et al., 2015). Based on these previous findings, we hypothesized that foveal load would affect response bias if a fixed attentional resource was used in the peripheral color judgment task (see Figure 2A). The results for the effect of foveal load in response bias did not support the prediction of the fixed resource model of attention. There are many possible reasons why the foveal load failed to change C. First, our manipulation of the presentation time might have had effects other than changing the attentional load. We always presented the scene image for 150 ms, and the presentation time of the central stimulus varied (83 ms, 117 ms, or 150 ms). The onset and offset of the central and peripheral stimuli in the 150 ms condition were always synchronized. On the other hand, the onset and offset of the central stimuli in the 83 ms and 117 ms conditions were unsynchronized with the peripheral stimuli. In these unsynchronized conditions, the judgment of color for the peripheral scene stimulus might have been hindered by the onset of the subsequent central stimuli that can attract exogenous attention. In addition to the effects of eccentricity and task load, the presence or absence of synchronization between central and peripheral stimuli might be a third factor affecting bias. Interpreting our results of bias and foveal load positively despite these shortcomings would conclude that some factors other than attention co-varied with eccentricity and made bias more liberal in pan-field color illusion. In an ordinary object detection task, the change of bias from neutral to liberal in the peripheral visual field was derived from insufficient attention to the periphery (Solovey et al., 2015). However, the observed shift of response bias in the pan-field color illusion might not have been derived solely from insufficient attention to the periphery. This argument is consistent with suggestions from other studies of pan-field color illusion in which attention was manipulated by changing the instruction (Cohen et al., 2020; Cohen & Rubenstein, 2020). So, what factors other than attention co-varied with eccentricity, making the bias more liberal? How we perceive scene structure differs significantly between the peripheral visual field and central visual field, and such differences in scene perception by visual field may produce differences in color perception by visual field as well. In fact, the observed interaction between the size of the colored area and the presentation time on C implies that the effect of foveal load on C was qualitatively different in the perifoveal region (9 visual degrees in the present study) and other peripheral regions (approximately 13 visual degrees in the present study). Specifically, it is known that summary statistics that involve low-level visual features and represent texture information presumably have a more considerable weight in peripheral visual perception than in the central visual field. Generally, these types of statistics are generally processed automatically and without attention. Balas and Sinha (2007) found that the pan-field color illusion is affected by manipulating such image statistics that involve scene perception. Given these facts, the effect of attention on color perception might also differ depending on the weight of the summary statistics for perception in each visual field. Further experiments are needed to investigate the mechanism of how the attentional load affects the criterion as a function of eccentricity. 
The results reported here raise several questions that future research could explore. First, we cannot deny the possibility that observers were aware of the peripheral desaturation, but their awareness was not accessible in their decision-making phase because of limitations on other mechanisms, such as working memory, in this task. The decrease of sensitivity and the shift of bias could be due to the differential likelihood of forgetting the correct response under different load conditions. It is known that inattentional blindness is empirically different from amnesia (Rees, Russell, Frith, & Driver, 1999). Using such methods, we could discover whether the pan-field color illusion derives from perceptual blindness. Second, we briefly presented observers with mutually unrelated images. However, during real-world viewing conditions with semantically and structurally consistent scenes, participants make saccades approximately three to four times per second (Rayner, 1998), presumably making the distribution of spatial attention change more dynamically. Besides the subjective richness in the periphery, the integration of information obtained from successive saccades is one of the main topics of perceptual constancy and continuity (Irwin, 1991; Cavanagh, Hunt, Afraz, & Rolfs, 2010). Dynamic change of attentional allocation caused by eye movements may modulate the effects of attention on the pan-field color illusion in naturalistic viewing conditions. 
Conclusions
Using the dual-task paradigm, we successfully investigated the effects of attention on sensitivity and response bias in the pan-field color illusion. Sensitivity to the content of peripheral color changed consistently with the spatial distribution of attention, which seemingly had a fixed capacity. Importantly, we found that the pan-field color illusion can be at least partly explained by the change of response bias as a function of the eccentricity of the exploited visual field. The fact that both sensitivity and response bias varied as a function of the size of the colored area suggests that the subjective richness of color in the periphery (i.e. the pan-field color illusion) is not homogeneous in the peripheral visual field but varies spatially as a function of eccentricity. 
Acknowledgments
The authors thank Takahiro Kawabe for providing fruitful discussion. 
Supported by a Grant-in-Aid for JSPS fellows (22J10016). 
Commercial relationships: none. 
Corresponding author: Lana Okubo. 
Email: lanaokubo@gmail.com. 
Address: Department of Psychology, The University of Tokyo Hongo, 7-3-1, Bunkyo-ku, Tokyo 1130032, Japan. 
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Figure 1.
 
Example of a “chimera” image used by Balas and Sinha (2007). Color is restricted to a circular central region.
Figure 1.
 
Example of a “chimera” image used by Balas and Sinha (2007). Color is restricted to a circular central region.
Figure 2.
 
Two hypotheses about the allocation of attention. The dotted line represents the possible distribution of attention in the lower load; the solid line represents that in the higher load. (A) A model of spatial attention with eccentricity and foveal load as variables. This is the fixed resource model, in which attention has a fixed capacity. (B) Another model of spatial attention. This is the flexible resource model, in which the available attentional resources vary depending on task difficulty.
Figure 2.
 
Two hypotheses about the allocation of attention. The dotted line represents the possible distribution of attention in the lower load; the solid line represents that in the higher load. (A) A model of spatial attention with eccentricity and foveal load as variables. This is the fixed resource model, in which attention has a fixed capacity. (B) Another model of spatial attention. This is the flexible resource model, in which the available attentional resources vary depending on task difficulty.
Figure 3.
 
The stimulus examples of peripheral color judgment task. The left and middle panels are examples of chimera images in which the circular central colored area was 9 degrees and 25 degrees. The right panel depicts the full-color condition.
Figure 3.
 
The stimulus examples of peripheral color judgment task. The left and middle panels are examples of chimera images in which the circular central colored area was 9 degrees and 25 degrees. The right panel depicts the full-color condition.
Figure 4.
 
The time course of a trial. Each letter target of the RSVP task was presented for one of three presentation times: 83 ms, 117 ms, or 150 ms. The scene image of the peripheral task appeared at the same time as the onset of the target letter. The scene image and mask image of the peripheral task were always presented for 150 ms each.
Figure 4.
 
The time course of a trial. Each letter target of the RSVP task was presented for one of three presentation times: 83 ms, 117 ms, or 150 ms. The scene image of the peripheral task appeared at the same time as the onset of the target letter. The scene image and mask image of the peripheral task were always presented for 150 ms each.
Figure 5.
 
General response tendency on the peripheral task. (A) Rates of “gray,” “chimera,” and “color” responses to each type of image. (B) Rates of “gray,” “chimera,” and “color” responses to chimera images for each size of colored area.
Figure 5.
 
General response tendency on the peripheral task. (A) Rates of “gray,” “chimera,” and “color” responses to each type of image. (B) Rates of “gray,” “chimera,” and “color” responses to chimera images for each size of colored area.
Figure 6.
 
Sensitivity d′ as a function of presentation time and size of the colored area. Error bars in all panels represent ±1 standard error.
Figure 6.
 
Sensitivity d′ as a function of presentation time and size of the colored area. Error bars in all panels represent ±1 standard error.
Figure 7.
 
Response bias C as a function of presentation time and size of the colored area.
Figure 7.
 
Response bias C as a function of presentation time and size of the colored area.
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