Study on the Effect of Gaze Position and Image Brightness on Peripheral Dimming Technique

: Here, we study a low-power technique for displays based on gaze tracking, called peripheral dimming. In this work, the threshold levels of the lightness reduction ratio (LRR), where people notice differences in brightness, depending on gaze positions and image brightness, are investigated. A psychophysical experiment with ﬁve gaze positions and three image brightness conditions is performed, and the estimated threshold levels are obtained. To investigate the signiﬁcance of the differences between the threshold levels, the overlap method and the Bayesian estimation (BEST) analysis are performed. The analysis results show that the difference of the threshold levels depending on the conditions is insigniﬁcant. Thus, the proposed technique can operate with a constant LRR level, regardless of the gaze position or image brightness, while maintaining the perceptual image quality. In addition, the proposed technique reduces the power consumption of virtual reality (VR) displays by 12–14% on average. We believe that the peripheral dimming technique would contribute to reducing the power of the self-luminous displays used for VR headsets with an integrated eye tracker.


Introduction
The use of displays has been steadily increasing. In particular, displays are remarkably used for mobile devices. Although long battery life is an important issue for mobile devices [1], unfortunately, the display is one of the most power-consuming parts [2,3].
Various approaches to reduce the power consumption of the display have been attempted. Among them, methods reducing the brightness of displays have been widely studied [4][5][6][7][8][9][10][11] because they are simple but effective. Brightness reduction, however, causes a degradation of image quality. Thus, it is important to balance power-saving and image quality. An image quality assessment (IQA) index is commonly used as a criterion. IQA can be categorized into objective and subjective methods. The objective IQA uses a model that can predict the quality of an image automatically. It is a relatively easy to obtain the index. Thus, there are many techniques based on objective IQAs to reach a compromise between power saving and image quality [4][5][6][7][8][9]. On the other hand, subjective evaluation is more expensive and time-consuming. However, it is the most reliable method for assessing the quality of images, as human observers are the ultimate users [12]. For this reason, methods based on subjective IQAs [10,11] have been studied less, but have achieved effective power reduction without degradation of the perceived image quality, even in more aggressive dimming conditions such as when turning off some pixels.
A low-power display technique based on subjective IQA, known as a peripheral dimming, has been studied [13]. It is based on the human visual characteristic that the visual acuity and sensitivity of the central vision are considerably higher than those of the periphery. Owing to a non-uniform distribution of photoreceptor cells in the retina, the peripheral vision has a lower resolution and sensitivity for color or brightness [14,15]. The proposed technique gradually darkens the brightness in the peripheral vision area, as shown in Figure 1a. The foveal zone is a circular area with a boundary 5 • from the fixation point, which is the inner part of a blue dashed circle, and the outer area is the peripheral zone. While the foveal zone keeps its own brightness, the brightness in the peripheral zone gradually decreases depending on the viewing angle. The amount of reduced brightness is determined based on the lightness component defined in the CIELAB color space. Figure 1b shows the lightness weight ratio depending on the viewing angle. The slope in the graph is called a lightness reduction ratio (LRR). As the LRR is higher, the lightness in the peripheral zone decreases more rapidly. We performed subjective tests for the central gaze position, as shown in Figure 1a. We obtained threshold levels of LRR (LRR TH ) where the power can be effectively saved while maintaining the perceptual image quality. In addition, LRR TH seemed to be inversely proportional to the image brightness in our previous study.
Electronics 2021, 10, x FOR PEER REVIEW 2 of 13 acuity and sensitivity of the central vision are considerably higher than those of the periphery. Owing to a non-uniform distribution of photoreceptor cells in the retina, the peripheral vision has a lower resolution and sensitivity for color or brightness [14,15]. The proposed technique gradually darkens the brightness in the peripheral vision area, as shown in Figure 1a. The foveal zone is a circular area with a boundary 5° from the fixation point, which is the inner part of a blue dashed circle, and the outer area is the peripheral zone. While the foveal zone keeps its own brightness, the brightness in the peripheral zone gradually decreases depending on the viewing angle. The amount of reduced brightness is determined based on the lightness component defined in the CIELAB color space. Figure 1b shows the lightness weight ratio depending on the viewing angle. The slope in the graph is called a lightness reduction ratio (LRR). As the LRR is higher, the lightness in the peripheral zone decreases more rapidly. We performed subjective tests for the central gaze position, as shown in Figure 1a. We obtained threshold levels of LRR (LRRTH) where the power can be effectively saved while maintaining the perceptual image quality. In addition, LRRTH seemed to be inversely proportional to the image brightness in our previous study. As the peripheral dimming technique is applied based on the user's gaze, an eye tracker should be integrated into the VR headset. Commercially available devices such as VIVE Pro Eye and FOVE VR already have integrated eye trackers [16,17]. The eye tracker is indispensable for implementing a foveated rendering technology that can reduce the computational cost and power of VR headsets [18,19]. In addition, smooth pursuit eye movement (SPEM) has been investigated for clinical diagnoses [20][21][22][23][24]. For this reason, VR headsets with eye trackers are also expected to be promising health care devices. They are also used for emotion recognition or eye fatigue [25,26]. Thus, the proposed method can contribute to lowering the power consumption of VR headsets with an eye tracker.
In the previous study, we performed a pilot test for the peripheral dimming by changing the gaze positions [27], and found that LRRTHs differed depending on the gaze position. However, because the data were not sufficient to conclude the correlation between them, we presumed that LRRTH might be related to the gaze position. This is a very critical issue for the peripheral dimming technique, which actively reacts to the user's gaze. Thus, in this study, we investigated this correlation based on more data and statistical analyses. In addition, to improve the model of LRRTH depending on image brightness, we attempted to obtain more LRRTH data under various image brightness conditions. As the peripheral dimming technique is applied based on the user's gaze, an eye tracker should be integrated into the VR headset. Commercially available devices such as VIVE Pro Eye and FOVE VR already have integrated eye trackers [16,17]. The eye tracker is indispensable for implementing a foveated rendering technology that can reduce the computational cost and power of VR headsets [18,19]. In addition, smooth pursuit eye movement (SPEM) has been investigated for clinical diagnoses [20][21][22][23][24]. For this reason, VR headsets with eye trackers are also expected to be promising health care devices. They are also used for emotion recognition or eye fatigue [25,26]. Thus, the proposed method can contribute to lowering the power consumption of VR headsets with an eye tracker.
In the previous study, we performed a pilot test for the peripheral dimming by changing the gaze positions [27], and found that LRR TH s differed depending on the gaze position. However, because the data were not sufficient to conclude the correlation between them, we presumed that LRR TH might be related to the gaze position. This is a very critical issue for the peripheral dimming technique, which actively reacts to the user's gaze. Thus, in this study, we investigated this correlation based on more data and statistical analyses. In addition, to improve the model of LRR TH depending on image brightness, we attempted to obtain more LRR TH data under various image brightness conditions.
In this paper, we focused on the following two factors: the gaze position and image brightness. A psychophysical experiment with five gaze positions and three image brightness conditions was conducted. With the statistical analysis, a quantitative model of LRR TH depending on the gaze position and image brightness was investigated.  Figure 2 shows the experimental setup. The experiment was conducted in a dark room. A 24-inch LCD monitor with a 1920 × 1080 resolution, a chin rest, an eye tracker, and a keypad were used. All of the participants fixed their heads on the chin rest. We asked them to move their gaze by rotating only their eyes, without turning their heads. The monitor was 70 cm away from the chin rest, i.e., the viewing distance was 70 cm, and the field of view (FoV) was 41.6 • × 24.1 • (horizontal × vertical). Tobii eyeX was used to monitor the participants' gaze position during the experiment. The gaze data were recorded at a sampling rate of 60 Hz. The participants answered questions by typing on a keypad.
In this paper, we focused on the following two factors: the gaze position and image brightness. A psychophysical experiment with five gaze positions and three image brightness conditions was conducted. With the statistical analysis, a quantitative model of LRRTH depending on the gaze position and image brightness was investigated. Figure 2 shows the experimental setup. The experiment was conducted in a dark room. A 24-inch LCD monitor with a 1920 × 1080 resolution, a chin rest, an eye tracker, and a keypad were used. All of the participants fixed their heads on the chin rest. We asked them to move their gaze by rotating only their eyes, without turning their heads. The monitor was 70 cm away from the chin rest, i.e., the viewing distance was 70 cm, and the field of view (FoV) was 41.6° × 24.1° (horizontal × vertical). Tobii eyeX was used to monitor the participants' gaze position during the experiment. The gaze data were recorded at a sampling rate of 60 Hz. The participants answered questions by typing on a keypad.

Conditions
In the experiment, three kinds of conditions were controlled: the gaze position, image brightness, and LRR. Firstly, there were five gaze positions: top (T), left (L), center (C), right (R), and bottom (B). As shown in Figure 3, T (or B) is vertically 5°, and L (or R) is horizontally 10° away from the screen center.  Figure 4a shows the frame images corresponding to each gaze position. To avoid the influence of color on brightness perception, monochrome images were used. The gaze position was marked by a gray cross with a size of 1° viewing angle. Figure 4b shows how to generate the frame images of the L and R gaze conditions. The source images were

Conditions
In the experiment, three kinds of conditions were controlled: the gaze position, image brightness, and LRR. Firstly, there were five gaze positions: top (T), left (L), center (C), right (R), and bottom (B). As shown in Figure 3, T (or B) is vertically 5 • , and L (or R) is horizontally 10 • away from the screen center.
In this paper, we focused on the following two factors: the gaze position and image brightness. A psychophysical experiment with five gaze positions and three image brightness conditions was conducted. With the statistical analysis, a quantitative model of LRRTH depending on the gaze position and image brightness was investigated. Figure 2 shows the experimental setup. The experiment was conducted in a dark room. A 24-inch LCD monitor with a 1920 × 1080 resolution, a chin rest, an eye tracker, and a keypad were used. All of the participants fixed their heads on the chin rest. We asked them to move their gaze by rotating only their eyes, without turning their heads. The monitor was 70 cm away from the chin rest, i.e., the viewing distance was 70 cm, and the field of view (FoV) was 41.6° × 24.1° (horizontal × vertical). Tobii eyeX was used to monitor the participants' gaze position during the experiment. The gaze data were recorded at a sampling rate of 60 Hz. The participants answered questions by typing on a keypad.

Conditions
In the experiment, three kinds of conditions were controlled: the gaze position, image brightness, and LRR. Firstly, there were five gaze positions: top (T), left (L), center (C), right (R), and bottom (B). As shown in Figure 3, T (or B) is vertically 5°, and L (or R) is horizontally 10° away from the screen center.  Figure 4a shows the frame images corresponding to each gaze position. To avoid the influence of color on brightness perception, monochrome images were used. The gaze position was marked by a gray cross with a size of 1° viewing angle. Figure 4b shows how to generate the frame images of the L and R gaze conditions. The source images were  Figure 4a shows the frame images corresponding to each gaze position. To avoid the influence of color on brightness perception, monochrome images were used. The gaze position was marked by a gray cross with a size of 1 • viewing angle. Figure 4b shows how to generate the frame images of the L and R gaze conditions. The source images were extracted from a video with a 3840 × 2160 resolution released under the Creative Commons CC0 [28]. A blue solid square represents a cropping boundary with a 1920 × 1080 resolution. By adjusting the position of the cropping boundary, images corresponding to the gaze positions were generated. After cropping, the image was converted to a grayscale image. To minimize the difference of images depending on the gaze position, the right and bottom images were made by horizontal and vertical flipping of the left and top images. To minimize the visual difference depending on the gaze condition, the visual stimulus of the foveal zone was left as unchanged as possible.
extracted from a video with a 3840 × 2160 resolution released under the Creative Commons CC0 [28]. A blue solid square represents a cropping boundary with a 1920 × 1080 resolution. By adjusting the position of the cropping boundary, images corresponding to the gaze positions were generated. After cropping, the image was converted to a grayscale image. To minimize the difference of images depending on the gaze position, the right and bottom images were made by horizontal and vertical flipping of the left and top images. To minimize the visual difference depending on the gaze condition, the visual stimulus of the foveal zone was left as unchanged as possible.  Secondly, three image brightness conditions were used. The image brightness, as mentioned above, was quantified based on the lightness defined in the CIELAB color space. To prevent the effect of the image content, we adjusted the image brightness from one source image. As shown in Figure 5a, by adjusting the lightness by ±15% from the original image (source image), two images that were brighter and darker than the original one were generated. As shown in Figure 5b, the darker, original, and brighter images had an average lightness (AL) of 52.2, 61.5, and 70.7, respectively. Thus, they were called AL50, AL60, and AL70, respectively.
Lastly, seven LRR levels were used: 0.10, 0.25, 0.40, 0.55, 0.70, 0.85, and 1.00%/degree.   Secondly, three image brightness conditions were used. The image brightness, as mentioned above, was quantified based on the lightness defined in the CIELAB color space. To prevent the effect of the image content, we adjusted the image brightness from one source image. As shown in Figure 5a, by adjusting the lightness by ±15% from the original image (source image), two images that were brighter and darker than the original one were generated. As shown in Figure 5b, the darker, original, and brighter images had an average lightness (AL) of 52.2, 61.5, and 70.7, respectively. Thus, they were called AL50, AL60, and AL70, respectively.
Lastly, seven LRR levels were used: 0.10, 0.25, 0.40, 0.55, 0.70, 0.85, and 1.00%/degree. extracted from a video with a 3840 × 2160 resolution released under the Creative Commons CC0 [28]. A blue solid square represents a cropping boundary with a 1920 × 1080 resolution. By adjusting the position of the cropping boundary, images corresponding to the gaze positions were generated. After cropping, the image was converted to a grayscale image. To minimize the difference of images depending on the gaze position, the right and bottom images were made by horizontal and vertical flipping of the left and top images. To minimize the visual difference depending on the gaze condition, the visual stimulus of the foveal zone was left as unchanged as possible.  Secondly, three image brightness conditions were used. The image brightness, as mentioned above, was quantified based on the lightness defined in the CIELAB color space. To prevent the effect of the image content, we adjusted the image brightness from one source image. As shown in Figure 5a, by adjusting the lightness by ±15% from the original image (source image), two images that were brighter and darker than the original one were generated. As shown in Figure 5b, the darker, original, and brighter images had an average lightness (AL) of 52.2, 61.5, and 70.7, respectively. Thus, they were called AL50, AL60, and AL70, respectively.

Participants
The number of participants in each session is described in Table 1. Sixteen, nineteen, and fifteen observers participated in the AL50, AL60, and AL70 sessions, respectively. They were paid about 10 USD per hour for their participation.

Procedure
The experiment consisted of three sessions in accordance with image brightness. In each session, five gaze positions with seven LRR levels were used. The AL60 session using the original image was the first one, followed by the AL50 and AL70 sessions. The experiment was designed based on the temporal two-alternative forced choice (2-AFC), which is a psychophysical method used to investigate the behavioral or perceptual responses from subjects. Two stimuli were sequentially presented and then the participants were asked to choose the brighter one between two stimuli.
Before the experiment began, all participants fixed their heads on the chin rest, and then the eye tracker was calibrated for each participant. They were asked to move their gaze without turning their heads. During the experiment, an assessment unit, as shown in Figure 6, was repeated. Each trial began with a fixation image indicating the gaze position for 3 s. The gaze position was randomly determined among the five positions. After the fixation image, the reference and test (with peripheral dimming) videos were sequentially displayed for 6 s in random order. Between two videos, a blank image was displayed for 3 s. After two visual stimuli, the participants were asked to choose the brighter one by using the keypad for 8 s. While the reference and test videos were displayed, the eye tracker recorded the gaze position. A beep sounded whenever the participant stared at an area outside 4 • from the fixation point. If the beep sounded more than three times within one assessment unit, the participant's answers were excluded from the experimental results.

Participants
The number of participants in each session is described in Table 1. Sixteen, nineteen, and fifteen observers participated in the AL50, AL60, and AL70 sessions, respectively. They were paid about 10 USD per hour for their participation.

Procedure
The experiment consisted of three sessions in accordance with image brightness. In each session, five gaze positions with seven LRR levels were used. The AL60 session using the original image was the first one, followed by the AL50 and AL70 sessions. The experiment was designed based on the temporal two-alternative forced choice (2-AFC), which is a psychophysical method used to investigate the behavioral or perceptual responses from subjects. Two stimuli were sequentially presented and then the participants were asked to choose the brighter one between two stimuli.
Before the experiment began, all participants fixed their heads on the chin rest, and then the eye tracker was calibrated for each participant. They were asked to move their gaze without turning their heads. During the experiment, an assessment unit, as shown in Figure 6, was repeated. Each trial began with a fixation image indicating the gaze position for 3 s. The gaze position was randomly determined among the five positions. After the fixation image, the reference and test (with peripheral dimming) videos were sequentially displayed for 6 s in random order. Between two videos, a blank image was displayed for 3 s. After two visual stimuli, the participants were asked to choose the brighter one by using the keypad for 8 s. While the reference and test videos were displayed, the eye tracker recorded the gaze position. A beep sounded whenever the participant stared at an area outside 4° from the fixation point. If the beep sounded more than three times within one assessment unit, the participant's answers were excluded from the experimental results. As mentioned above, each session contained five gaze conditions with seven LRRs. Each LRR condition was repeated four times i.e., four answers were obtained for each LRR, and then a correct answer rate was computed. As a result, each participant answered 140 (5 × 7 × 4) times in each session. It took about 1 h to complete one session. As mentioned above, each session contained five gaze conditions with seven LRRs. Each LRR condition was repeated four times i.e., four answers were obtained for each LRR, and then a correct answer rate was computed. As a result, each participant answered 140 (5 × 7 × 4) times in each session. It took about 1 h to complete one session.

Psychophysical Results
A psychometric function is an inferential model to estimate the threshold of the stimulus intensity statistically. It models the relationship between the stimulus intensity and the underlying probability of the responses. In this work, the response and the stimulus intensity corresponded to the correct answer rate and the LRR, respectively. The LRR level where the correct answer rate was 75% is defined as LRR TH .
The psignifit toolbox for MATLAB (version R2020a, MathWorks) presented by Schütt et al. [29] was used to fit the psychometric function to our experimental data. This tool is an open-source package for Bayesian psychometric function estimation by fitting a beta-binomial model to the correct responses at each stimulus level. It computes the posterior distributions for the parameters based on the Bayesian inference, and then estimates the psychometric function. Figure 7 shows an example outcome obtained from the tool. The red circles are the data. The blue and black curves represent the estimated posterior distribution of the threshold and the psychometric function, respectively. The red error bar represents a 95% credible interval (CI) for the threshold. The CI is a Bayesian confidence interval within which an unobserved parameter value falls with a particular probability. It is in the domain of a posterior probability distribution or a predictive distribution [30].

Psychophysical Results
A psychometric function is an inferential model to estimate the threshold of the stimulus intensity statistically. It models the relationship between the stimulus intensity and the underlying probability of the responses. In this work, the response and the stimulus intensity corresponded to the correct answer rate and the LRR, respectively. The LRR level where the correct answer rate was 75% is defined as LRRTH.
The psignifit toolbox for MATLAB (version R2020a, MathWorks) presented by Schütt et al. [29] was used to fit the psychometric function to our experimental data. This tool is an open-source package for Bayesian psychometric function estimation by fitting a betabinomial model to the correct responses at each stimulus level. It computes the posterior distributions for the parameters based on the Bayesian inference, and then estimates the psychometric function. Figure 7 shows an example outcome obtained from the tool. The red circles are the data. The blue and black curves represent the estimated posterior distribution of the threshold and the psychometric function, respectively. The red error bar represents a 95% credible interval (CI) for the threshold. The CI is a Bayesian confidence interval within which an unobserved parameter value falls with a particular probability. It is in the domain of a posterior probability distribution or a predictive distribution [30].  The average correct answer rates depending on the LRR are plotted in Figure 8a. A trend that the correct answer rate increased with increasing the LRR was observed for all conditions. Figure 8b,c shows the estimated psychometric functions fitted to the subject data and the posterior distributions for LRRTH.
The resulting LRRTHs for each condition are plotted in Figure 9. The error bar represents the 95% CI. The mean value of the obtained LRRTHs was 0.39%/degree, and they ranged from 0.3 to 0.5%/degree. The values of LRRTH slightly varied depending on both conditions of the gaze position and image brightness. To analyze the significance of the differences of LRRTHs, we compared the CI ranges. Examining the overlap among CIs is an analysis method that can quickly compare the data groups [31,32]. The 95% CI ranges are shown in Table 2. Herein, the "common" on the final row or column denotes the overlapped CI ranges for the same gaze position or image brightness condition, respectively. Under the same gaze position or image brightness condition, an overlapped CI range existed, as shown in Table 2. This verifies that the differences of LRRTH depending on each condition could be insignificant. Thus, a common LRR level can be applied, regardless of the gaze position or image brightness. However, the overlap method is one of the rough analysis methods [32], and we performed an additional analysis to verify the differences of the LRRTHs. Figure 8a-c shows the obtained subject data and the psychophysical results. The graphs in the left, center, and right columns present the results for the AL50, AL60, and AL70 conditions, respectively. The average correct answer rates depending on the LRR are plotted in Figure 8a. A trend that the correct answer rate increased with increasing the LRR was observed for all conditions. Figure 8b,c shows the estimated psychometric functions fitted to the subject data and the posterior distributions for LRR TH .
The resulting LRR TH s for each condition are plotted in Figure 9. The error bar represents the 95% CI. The mean value of the obtained LRR TH s was 0.39%/degree, and they ranged from 0.3 to 0.5%/degree. The values of LRR TH slightly varied depending on both conditions of the gaze position and image brightness. To analyze the significance of the differences of LRR TH s, we compared the CI ranges. Examining the overlap among CIs is an analysis method that can quickly compare the data groups [31,32]. The 95% CI ranges are shown in Table 2. Herein, the "common" on the final row or column denotes the overlapped CI ranges for the same gaze position or image brightness condition, respectively. Under the same gaze position or image brightness condition, an overlapped CI range existed, as shown in Table 2. This verifies that the differences of LRR TH depending on each condition could be insignificant. Thus, a common LRR level can be applied, regardless of the gaze position or image brightness. However, the overlap method is one of the rough analysis methods [32], and we performed an additional analysis to verify the differences of the LRR TH s.

Bayesian Estimation Analysis
The psychophysical analysis is very useful to find out the threshold levels, but has a limit when analyzing their statistical significance. Thus, we additionally performed a Bayesian estimation (BEST). As the psychophysical results provide the value with the posterior distribution for LRR TH , a comparison of the posterior distributions was performed among the various methods of the BEST analysis [30,33]. This method is based on the premise that different random samples obtained from the two different groups will show different trends because of random variation [33]. If two random samples are repeatedly compared, the distribution of the difference between two samples will be derived. Figure 10 shows two example results. The horizontal axis indicates the difference, and the black dashed line and blue solid line denote the zero point and the 95% highest density interval (HDI). If two groups have a very similar data distribution, the value of the difference between two random samples would be most frequently zero, as shown in Figure 10a. If not, the histogram results would be skewed to the left or right sides, as shown in Figure 10b. Consequently, the degree of skew in the histogram is related to the similarity of the two distributions. In this study, the distribution of the differences was computed using Markov chain Monte Carlo sampling [34] with a sample size of 50,000. We took the 95% HDI as a criterion, and concluded that there was no significant difference if the 95% HDI included zero. The psychophysical analysis is very useful to find out the threshold levels, but has a limit when analyzing their statistical significance. Thus, we additionally performed a Bayesian estimation (BEST). As the psychophysical results provide the value with the posterior distribution for LRRTH, a comparison of the posterior distributions was performed among the various methods of the BEST analysis [30,33]. This method is based on the premise that different random samples obtained from the two different groups will show different trends because of random variation [33]. If two random samples are repeatedly compared, the distribution of the difference between two samples will be derived. Figure  10 shows two example results. The horizontal axis indicates the difference, and the black dashed line and blue solid line denote the zero point and the 95% highest density interval (HDI). If two groups have a very similar data distribution, the value of the difference between two random samples would be most frequently zero, as shown in Figure 10a. If not, the histogram results would be skewed to the left or right sides, as shown in Figure 10b. Consequently, the degree of skew in the histogram is related to the similarity of the two distributions. In this study, the distribution of the differences was computed using Markov chain Monte Carlo sampling [34] with a sample size of 50,000. We took the 95% HDI as a criterion, and concluded that there was no significant difference if the 95% HDI included zero.  Figure 11 shows the differences between the posterior distributions. Firstly, let us see the results compared with C (i.e., T-C, C-B, L-C, and C-R). In most results, it was observed that the distributions of the same comparison conditions had the same skew direction as the distribution. For example, the results of C-B and C-R were skewed to the left and the right, respectively. However, there was no result where the 95% HDI excluded zero. LRRTH seemed to be affected by the gaze position, but we considered it a negligible level. Next, in the comparison between the symmetrical gaze positions, T-B and L-R, mixed results were observed. In the case of the symmetrical gaze position, it was predicted that there would be no difference, because the degree of darkening was the same. The results of L-R were in line with our forecast, whereas the results of T-B were not. However, these results showed that the 95% HDI included zero like the other results, so we decided that the difference of the trends was within an allowable error. Therefore, we conclude that, under the condition of the FoV of 41.6° × 24.1°, LRRTH did not depend on the gaze position significantly.  Figure 11 shows the differences between the posterior distributions. Firstly, let us see the results compared with C (i.e., T-C, C-B, L-C, and C-R). In most results, it was observed that the distributions of the same comparison conditions had the same skew direction as the distribution. For example, the results of C-B and C-R were skewed to the left and the right, respectively. However, there was no result where the 95% HDI excluded zero. LRR TH seemed to be affected by the gaze position, but we considered it a negligible level. Next, in the comparison between the symmetrical gaze positions, T-B and L-R, mixed results were observed. In the case of the symmetrical gaze position, it was predicted that there would be no difference, because the degree of darkening was the same. The results of L-R were in line with our forecast, whereas the results of T-B were not. However, these results showed that the 95% HDI included zero like the other results, so we decided that the difference of the trends was within an allowable error. Therefore, we conclude that, under the condition of the FoV of 41.6 • × 24.1 • , LRR TH did not depend on the gaze position significantly.  Figure 12 shows the comparison results for the image brightness conditions. If image brightness affects LRRTH, the distribution of the differences between AL70 and AL50 will be more skewed than for the other distributions. The obtained results, however, show that it did not affect it. The skew patterns were erratic, regardless of image brightness. Only one feature was commonly observed in all results, namely that the 95% HDI includes zero. The results clearly show that there was no significant correlation between LRRTH and image brightness. Because the experimental conditions were more strictly controlled in this study, as mentioned above, we suggest that LRRTH could be independent of image brightness.

Performance Evaluation for Power-Saving
The total dissipated power (TDP) of the OLED display is given by [35].
where i and j denote the horizontal and vertical indices of a pixel, respectively. N and M denote the numbers of the horizontal and vertical pixels, respectively. R, G, and B denote the RGB levels of the pixel (i, j). wR, wG, and wB, are the weighting coefficients and γ is the gamma value. They are panel-dependent coefficients. The used values of wR, wG, and wB and γ were 70, 115, and 154 and 2.2, respectively [4,35].  Figure 12 shows the comparison results for the image brightness conditions. If image brightness affects LRR TH , the distribution of the differences between AL70 and AL50 will be more skewed than for the other distributions. The obtained results, however, show that it did not affect it. The skew patterns were erratic, regardless of image brightness. Only one feature was commonly observed in all results, namely that the 95% HDI includes zero. The results clearly show that there was no significant correlation between LRR TH and image brightness. Because the experimental conditions were more strictly controlled in this study, as mentioned above, we suggest that LRR TH could be independent of image brightness.  Figure 12 shows the comparison results for the image brightness conditions. If image brightness affects LRRTH, the distribution of the differences between AL70 and AL50 will be more skewed than for the other distributions. The obtained results, however, show that it did not affect it. The skew patterns were erratic, regardless of image brightness. Only one feature was commonly observed in all results, namely that the 95% HDI includes zero. The results clearly show that there was no significant correlation between LRRTH and image brightness. Because the experimental conditions were more strictly controlled in this study, as mentioned above, we suggest that LRRTH could be independent of image brightness.

Performance Evaluation for Power-Saving
The total dissipated power (TDP) of the OLED display is given by [35].
where i and j denote the horizontal and vertical indices of a pixel, respectively. N and M denote the numbers of the horizontal and vertical pixels, respectively. R, G, and B denote the RGB levels of the pixel (i, j). wR, wG, and wB, are the weighting coefficients and γ is the gamma value. They are panel-dependent coefficients. The used values of wR, wG, and wB and γ were 70, 115, and 154 and 2.2, respectively [4,35].

Performance Evaluation for Power-Saving
The total dissipated power (TDP) of the OLED display is given by [35].
where i and j denote the horizontal and vertical indices of a pixel, respectively. N and M denote the numbers of the horizontal and vertical pixels, respectively. R, G, and B denote the RGB levels of the pixel (i, j). w R , w G , and w B , are the weighting coefficients and γ is the gamma value. They are panel-dependent coefficients. The used values of w R , w G , and w B and γ were 70, 115, and 154 and 2.2, respectively [4,35]. Based on the TDP, we computed the ratio of power saving (P SAVED ) as follows: where TDP ORG and TDP TH represent the TDPs of the original image and that adopting peripheral dimming with LRR TH , respectively. Table 3 describes the P SAVED values for each condition. On average, the peripheral dimming technique reduced power consumption by 11.5%. The differences of P SAVED depending on the gaze positions were within 3%. The obtained P SAVED values of the AL50, AL60, and AL70 conditions were 11.6%, 12.2%, and 10.9%, respectively. Interestingly, the resulting P SAVED values were very similar, even for different image brightness conditions. To investigate if P SAVED was independent of image brightness, we applied the peripheral dimming with different LRR to additional images with different lightness [27] and computed P SAVED , as shown in Figure 13. LRRs of 0.3, 0.4, and 0.5%/degree were applied while fixing the gaze position to the center of the image. The resolution of the images was 1920 × 1080. As shown in Figure 13, the P SAVED values remained almost constant under the same LRR, regardless of the average lightness of the images. We believe that the P SAVED was only dependent on LRR because the peripheral dimming technique decreased the lightness by a ratio instead of an absolute value. Considering the average of LRR TH s is about 0.4%/degree, we concluded that the peripheral dimming technique reduced the average power consumption by about 12-14%, while maintaining a good perceptual image quality. Based on the TDP, we computed the ratio of power saving (PSAVED) as follows: where TDPORG and TDPTH represent the TDPs of the original image and that adopting peripheral dimming with LRRTH, respectively. Table 3 describes the PSAVED values for each condition. On average, the peripheral dimming technique reduced power consumption by 11.5%. The differences of PSAVED depending on the gaze positions were within 3%. The obtained PSAVED values of the AL50, AL60, and AL70 conditions were 11.6%, 12.2%, and 10.9%, respectively. Interestingly, the resulting PSAVED values were very similar, even for different image brightness conditions. To investigate if PSAVED was independent of image brightness, we applied the peripheral dimming with different LRR to additional images with different lightness [27] and computed PSAVED, as shown in Figure 13. LRRs of 0.3, 0.4, and 0.5%/degree were applied while fixing the gaze position to the center of the image. The resolution of the images was 1920 × 1080. As shown in Figure 13, the PSAVED values remained almost constant under the same LRR, regardless of the average lightness of the images. We believe that the PSAVED was only dependent on LRR because the peripheral dimming technique decreased the lightness by a ratio instead of an absolute value. Considering the average of LRRTHs is about 0.4%/degree, we concluded that the peripheral dimming technique reduced the average power consumption by about 12-14%, while maintaining a good perceptual image quality. Peripheral dimming can be applied well to virtual reality (VR) head-mounted display (HMD) device. It requires a higher resolution and faster refresh rates for a more immersive experience, which results in more power consumption [36][37][38][39]. Moreover, it is likely to utilize cloud computing for image rendering in the near future, by virtue of cloud VR [40][41][42]. Currently, the display accounts for 7-17% of the total power of a VR device [43][44][45]. However, the display accounts for about 30% of the total power of a cloud VR system. Peripheral dimming can be applied well to virtual reality (VR) head-mounted display (HMD) device. It requires a higher resolution and faster refresh rates for a more immersive experience, which results in more power consumption [36][37][38][39]. Moreover, it is likely to utilize cloud computing for image rendering in the near future, by virtue of cloud VR [40][41][42]. Currently, the display accounts for 7-17% of the total power of a VR device [43][44][45]. However, the display accounts for about 30% of the total power of a cloud VR system. Considering 14% of the maximum power saving, our proposed method will save over 5% of the overall system power.

Discussion
In this paper, we investigated the effect of the gaze position and image brightness on the peripheral dimming technique. Furthermore, we obtained the result that the proposed technique could reduce the power consumption of the display panel by about 12-14%. In this study, however, the field of view (FoV) was limited to 41.6 • × 24.1 • because of the given monitor size and the viewing distance for proper operation of the eye tracker. As the technique reduces the lightness depending on the viewing angle, the power saving efficiency became higher where the distance from the gaze position was further. The larger the display size, the more the power saved. A wide FoV is indispensable for a more immersive experience of VR devices. Thus, larger displays are preferred. Therefore, our proposed method can save more power from the VR headset with a wider FoV.
In our previous work, we had observed that LRR TH is inversely proportional to the AL of the video. However, this trend was not observed in this study. For most gaze conditions, LRR TH for AL70 was the smallest, but LRR TH for AL60 was larger than that for AL50. In addition, the CIs also considerably overlapped. It seems that LRR TH might hardly be related to the AL of the images. In the previous experiment, three full-color videos with different contents were used, whereas monochromatic videos with the same contents were used in this experiment. Because the experimental environment in this study was more strictly controlled, although the two results conflict with each other, we conclude that the results obtained in this study are reliable. Thus, it is considered that image brightness in itself is hardly correlated to LRR TH . We speculate that there are veiled factors other than image brightness that have a complex effect on LRR TH , and that correlation was observed in the previous study. Further study should be performed to solve this issue.
The results show that the peripheral dimming technique can be simply applied with a constant dimming level while tracking the user's gaze. These findings demonstrate the universal applicability and usefulness of the peripheral dimming technique. In addition, the technique can save the power consumption constantly by 12-14%, without degradation of the perceptual image quality. The power consumption in a self-luminous display, such as an organic light-emitting diode display, is proportional to its luminance. Thus, the technique would help to reduce power more effectively when the display consumes power heavily. We believe that it is an attractive low-power technique for a head-mounted display device with an integrated eye tracker.  Informed Consent Statement: Written informed consent was obtained from all participants involved in the study.