This experiment utilized the equipment (model: NirSmart-3000K) from HuiChuang Medical. The equipment comprises a head cap with 14 channels, a functional imaging module, and a computer with NirSmart and NirSpark software. The device has a sampling rate of 20 Hz, features 730 nm and 850 nm spectral illumination, and provides high-precision brain oxygen analysis. Figure 2 illustrates the spatial distribution of light sources, light sensors, and channels in the 3D brain model. In an fNIRS system, a channel refers to the region between a pair of light sources and light sensors. The light emitted by the source passes through the cortical tissue and is then received by the light sensor, and this entire process is referred to as the measurement of one channel. In the figure, red raised points represent the emission light sources, blue raised points represent the light sensors, yellow raised points represent the channels, and the dark-colored area represents the detectable region. There are six light sources (S), 5 light sensors (D), and 14 channels. The arrangement of the channels follows the international standard 10–20 system.

The experimental protocol was implemented via a computer with E-prime software, providing stimulus images and event markers to the NirSmart software. Stimuli were presented on a 23-inch Samsung 3D monitor (model: S23A950D) with a resolution of 1,920 × 1,080 pixels, featuring 2D/3D switching functionality and paired with 3D glasses. The display was connected to an NVIDIA GeForce GTX 1080 graphics card. We used a PR-715 spectroradiometer to measure and calibrate the displayed colors. The lookup table (LUT) method was used to obtain brightness values corresponding to digital input and the luminance and chromaticity of the display's center point. The CIE XYZ values of the black point of the 3D display were 0.247/0.241/0.467, the CIE-1931 chromaticity (x, y) of the white point was (0.274, 0.280), and the chromaticities (x, y) of red, green and blue channels were (0.617, 0.333), (0.330, 0.616) and (0.152, 0.067), respectively.

The experiment was conducted in a darkroom to minimize other factors (mainly ambient light). Participants were instructed to minimize physical movement during the experiment to reduce motion artifacts that could affect the near-infrared imaging data. According to the International Telecommunication Union standard (38) participants sit approximately 860 millimeters from the screen. Figure 3 shows the experimental setup and environment.

Twelve graduate students were recruited as participants for this experiment, with an age range of 24–26 years and mean age of 25 years. All participants had normal color vision (assessed using Dvorine Color Plates, 2nd ed.), normal stereoscopic vision (tested with Random Dot Stereoacuity), and normal or corrected visual acuity. They were all non-experts and had not worked with stereo vision. Before the experiment began, each participant signed an informed consent form, which adhered to the ethical standards of the Declaration of Helsinki (21).

The stimulus images were generated using specially developed C++ software (Figure 4). The generated images have 3,840 × 1,080 pixels, with participants wearing 3D glasses to receive images of 1,920 × 1,080 pixels per eye (left and right). These images consisted of a centrally displayed colored circular patch with a visual angle of 2° on a black background. The colors of patches were selected from the CIELAB color space, with the luminance fixed at L^* = 30. The color values for the circular patches were chosen along the a^* (red-green) axis, and the specific values are provided in Table 2. The color remains constant during the presentation, with the color input to the left eye always being green and the color input to the right eye always being red. The selection of these color samples is based on previous research by Xiong et al. (22), which demonstrated that these color combinations effectively induce binocular color fusion and rivalry in most individuals with normal vision. Based on the different color values selected along the red/green axis, two types of stimulus images were created: binocular color fusion on red/green direction (FoRG) and binocular color rivalry on red/green direction (RoRG). FoRG and RoRG can be considered as two objective conditions. When the left and right eyes receive different colors, a larger color difference induces binocular color rivalry, while a smaller color difference induces binocular color fusion. To minimize or eliminate the effects of disparity cues, a gray rectangular frame was added to the stimulus images as a zero-disparity reference, based on the study by Chen et al. (23). Disparity cues can evoke additional depth perception, which may alter the brain's integration of binocular images and, in turn, affect the perception of color fusion or rivalry. Since participants might experience potential small disparities due to equipment calibration or the characteristics of the visual stimuli, we provided a zero-disparity reference to avoid interference with the results. The zero-disparity reference ensures the spatial alignment of the images presented to both eyes, reducing or eliminating the potential effects of disparity cues on the perception of color fusion and rivalry.

Each participant underwent one session of experiment 1 and experiment 2. Each session did not exceed 15 min, including explanations and instructions given to the participants. In the experiments, a Mid-Gray field image was used to mitigate visual aftereffects and reduce visual fatigue. The procedure for experiment 1 was as follows: (1) Present a 90-s Mid-Gray field image; (2) Present a 90-s FoRG image; (3) Present a 90-s Mid-Gray field image; (4) Present a 90-s RoRG image; (5) Present another 90-s Mid-Gray field image. The purpose of Experiment 1 was to study the overall functional connectivity strength of the PFC under three conditions: no binocular color stimulus (gray field), binocular color fusion, and binocular rivalry. Geng et al. (24) found that functional connectivity strength stabilizes and becomes reproducible in fNIRS signals after 1 min of data collection. Therefore, we chose a longer stimulus presentation duration (90 s) and presented each stimulus only once to avoid any potential impact on data reliability due to insufficient stimulus presentation time. During the experiment, participants were instructed to sit still in a chair and focus on the center of the screen to ensure they received the physical stimuli presented by the 3D display monitor. Figure 5 illustrates the stimulus presentation sequence for experiment 1.

Experiment 2 consisted of eight trials, each following the sequence below: (1) Presentation of a Mid-Gray field image for 10 s; (2) Random presentation of FoRG image/RoRG image for 10 s; (3) Presentation of a Mid-Gray field image for 10 s; (4) Presentation of FoRG image/RoRG image for 10 s (if FoRG was presented in step 2, RoRG is presented this time, and vice versa); (5) Presentation of a Mid-Gray field image for 10 s. The focus of Experiment 2 was to identify key regions that distinguish between color fusion and rivalry, which required faster repeated trials to capture more diverse brain activity patterns. The duration of each stimulus presentation was set to 10 s in a similar study (25). Thus, we chose a shorter stimulus presentation duration (10 s) with each stimulus repeated eight times to maximize data collection efficiency while minimizing the potential for visual fatigue and other nonspecific effects caused by prolonged stimulation. For this experiment, data were collected during the presentation of the stimulus images (FoRG and RoRG). Each of the 12 participants underwent this experiment once. During the experiment, participants were instructed to sit in a chair and focus on the center of the screen. When participants perceived binocular color rivalry, they were asked to press the “A” key on the keyboard. After pressing “A,” the stimulus continued to be presented until the end of the 10-s stimulus duration. Simultaneously, the data acquisition software Nirsmart recorded a tag (value = 1). This tag was used to calculate the participants' reaction time (RT), aiding in the collection of behavioral data. By analyzing the reaction time, we can further investigate the behavioral characteristics of binocular color fusion and integrate these data with brain activity data (fNIRS signals) to gain deeper insights into the neural mechanisms of binocular visual phenomena. Figure 6 illustrates the stimulus presentation sequence for experiment 2.

We performed four steps of preprocessing on the collected fNIRS data:

By systematically applying these preprocessing steps, we improved the quality of the fNIRS data, ensuring the reliability of subsequent analyses. All of the preprocessing steps mentioned above were carried out using the NirSpark software. Raw data can be downloaded at: https://doi.org/10.6084/m9.figshare.27330858.

The data from Experiment 1 was primarily used for brain network analysis. Functional Connectivity (FC) is an important measure used to evaluate the temporal coordination of activities between different brain regions. Unlike anatomical connectivity, FC reflects functional relationships, providing insights into the interactions between various brain areas. Studying FC is essential for understanding the brain's functional organization, modes of information processing, and neural mechanisms under different tasks or stimuli. Changes in functional connectivity patterns have been associated with cognitive processes and neurological disorders (26).

The Pearson correlation coefficient is a commonly used method for quantifying the linear relationship between two time series (27). Functional connectivity analysis is typically used to calculate the correlation between blood oxygen level-dependent signals from different brain regions, thereby assessing the synchrony and strength of functional connectivity (28). This method has also been successfully applied in fNIRS research to construct functional connectivity networks.

Given the time series data of two brain regions X = {x₁, x₂, …, x_n} and Y = {y₁, y₂, …, y_n}, the Pearson correlation coefficient r_XY is calculated as:

Where ∑i=1n(xi- X¯)(yi- Y¯) is the covariance between X and Y, reflecting the extent to which both signals deviate from their respective means simultaneously.∑i=1n(xi - X¯)2 and ∑i=1n(yi-Y¯)2 are the standard deviations of X and Y, respectively, used to normalize the covariance. By calculating the Pearson correlation coefficients between all channels, we can construct a functional connectivity matrix R:

In Equation 3, r_ij represents the functional connectivity strength between the i−th and j−th channels. Sum all the selected correlation coefficients r_ij and divide by the number of coefficients N to obtain the mean functional connectivity strength r¯ :

The data from experiment 2 were analyzed using a generalized linear model (GLM). GLM is a statistical method widely used to analyze fNIRS and fMRI data. Its core principle lies in constructing a design matrix to describe the effect of experimental stimuli on brain function signals and using a regression model to estimate the neural responses under different experimental conditions. By incorporating a standard Hemodynamic Response Function (HRF), GLM not only captures signal changes due to neural activity but also reflects the time-delay characteristics of the hemodynamic response, thereby providing a more accurate depiction of the physiological reactions of the brain to specific stimuli. The basic formula for GLM is as follows:

WhereY represents the observed fNIRS signal (changes in oxyhemoglobin concentration). X is the design matrix, which includes the experimental stimulus events and other potential confounding factors. β represents the regression coefficients to be estimated, which indicate the response strength of the brain under different experimental conditions. ε denotes the residuals, representing unexplained noise or error.

The GLM involves convolving the design matrix X with a standard HRF to describe the brain's response to stimuli accurately. The HRF is a function that describes the hemodynamic response following neural activity and is often modeled as a double gamma function:

In Equation 5, t represents time, starting from the point when the stimulus occurs. a₁ and b₁ are the shape and scale parameters for the positive peak, which describe the initial increase in blood flow following neural activity. a₂ and b₂ are the shape and scale parameters for the negative peak, which describe the dip during the recovery phase of blood flow. c is the scaling factor that controls the amplitude of the negative peak. Γ(a) is the gamma function used for normalization purposes.

To control the false positive rate caused by multiple comparisons, this study adopted the False Discovery Rate (FDR) correction method. FDR correction dynamically adjusts the significance threshold to effectively control the false discovery rate (i.e., the proportion of false positives among all significant results), making it particularly suitable for multi-channel and multi-condition brain imaging studies. The Benjamini-Hochberg method was used to correct all p-values in this study. The specific steps include: first, all p-values are sorted in ascending order; second, for each test, a critical value is calculated based on the significance level α (set to 0.05), the total number of tests m, and the rank i:

Then, the largest p-value p_(i) that satisfies p_(i) ≤ p_critical is identified, and this p_(i) and all smaller p-values are considered significant. Compared to the traditional Bonferroni correction, FDR correction is more flexible, effectively controls the false discovery rate, and retains higher statistical power, making it suitable for large-scale multiple comparison studies.

The Friedman test is a non-parametric method used to analyze the differences among three or more conditions in repeated measures data. It serves as a non-parametric alternative to repeated measures ANOVA, particularly suitable for cases where the data do not follow a normal distribution or contain outliers. The principle of the Friedman test is based on analyzing ranked data instead of directly using the raw data. For each subject, the measurements under multiple conditions are ranked, and the ranks are summed. These rank sums are then compared to determine whether significant differences exist among the conditions. The formula for calculating its test statistic is:

n represents the number of subjects, k is the number of conditions, R_j is the rank sum for condition j. The null hypothesis (H₀) assumes that the median values across all conditions are equal. By calculating the test statistic χF2 and comparing it to the chi-squared distribution with k−1 degrees of freedom, the significance level (P-value) is determined. If the P-value is less than the chosen significance level (0.05), the null hypothesis is rejected, indicating significant differences among the conditions.

The Wilcoxon Signed-Rank Test is a non-parametric statistical method used to compare the differences between two paired datasets. Compared to the paired t-test, the Wilcoxon test does not require assumptions about data distribution, making it particularly suitable for small sample sizes or data that deviate from normality, and it is more robust to outliers. The test procedure includes: first, calculating the differences between paired data d_i = X_i−Y_i; then, ranking the absolute values of the differences and assigning ranks (Ranks), followed by calculating the positive rank sum W⁺ and negative rank sum W⁻ based on the sign of the original differences. The test statistic W is defined as the smaller of the two rank sums:

Based on W and the sample size n, the p-value is calculated to determine significance. In Experiment 1, the Wilcoxon Signed-Rank Test was used to compare brain functional connectivity strengths across the Mid-Gray, FoRG, and RoRG conditions; in Experiment 2, it was applied to compare the GLM results of the same channels (a total of 14 channels) under the FoRG and RoRG conditions.

To evaluate the statistical capability of the experimental design with the current sample size, this study conducted a post-hoc power analysis. Power analysis is used to assess the ability of a statistical test to correctly reject the null hypothesis (H0) when a true effect exists. After applying the FDR correction, the significance level for post-hoc power analysis can remain at 0.05 because the purpose of power analysis is to evaluate the capability of the statistical test rather than to control the false positive rate in multiple comparisons. The effect size is calculated using Cohen's d formula:

Where Mean Difference represents the mean difference between two conditions, and Standard Deviation represents the standard deviation of the differences. The formula for Power is:

β represents the probability of a Type II error, which is the failure to detect a true effect (failure to reject H₀). In this study, the statistical power was calculated based on the sample size (12 participants), a significance level (α = 0.05), and the effect size (d).

The statistical analysis in this study was conducted using Python.

Table 3 presents the mean brain functional connectivity strength values for each participant under the conditions of a Mid-Gray field image, binocular color fusion image, and binocular color rivalry image stimulation. Bold values indicate the mean brain functional connectivity strength under the FoRG image condition, and these bolded values represent the highest connectivity strength among the three conditions (Mid-Gray field, FoRG, and RoRG). Figure 7 presents each participant's mean brain functional connectivity strength using a bar chart. The data from Table 3, after calculation, yielded the following Standard Deviation (SD): Mid-Gray field = 0.0675, FoRG = 0.1746, RoRG = 0.1300. The data under all three conditions are relatively stable, with the Mid-Gray field condition showing the greatest stability.

In this study, the Friedman test was used to evaluate whether there were significant overall differences among the three conditions (Mid-Gray, FoRG and RoRG). The test results: Statistic (χF2) = 24, P-value=0.00001, indicating that there were statistically significant differences among the three conditions overall. Additionally, the post-hoc statistical power of the Friedman test was calculated to be 0.88, demonstrating that the experiment had a high power and was effective in detecting significant differences among the conditions. We further conducted pairwise comparisons among the three conditions using the Wilcoxon Signed-Rank Test with FDR correction. The results are as follows: (1) FoRG and RoRG: Statistic = 0, corrected p-value = 0.00049, indicating a significant difference. (2) Mid-Gray Field and FoRG: Statistic = 0, corrected p-value = 0.00049, indicating a significant difference. (3) Mid-Gray Field and RoRG: Statistic = 0, corrected p-value = 0.00049, indicating a significant difference. In the Wilcoxon Signed-Rank Test, a statistic of 0 means that the differences in the data are entirely in one direction, with no differences in the opposite direction. This indicates that the group differences are very strong and consistent.

Binocular color visual stimulation involves two primary processing modes: binocular color fusion and binocular color rivalry. These stimuli require coordinated cooperation between both eyes to integrate or compete with color information, resulting in complex visual experiences. This process engages multiple brain regions working in collaboration, and the increase in functional connectivity strength reflects the brain's efficient coordination in processing complex binocular visual information. Experimental results demonstrate that functional connectivity strength under binocular color visual stimulation conditions is significantly higher than under the Mid-Gray field condition. This indicates that in visual tasks requiring binocular coordination to process color information, the brain's functional connectivity becomes more active and robust. The Mid-Gray field represents a low-stimulation or basic visual state. Its functional connectivity strength is relatively low, reflecting the baseline activity level of the brain in the absence of specific visual tasks. Further experimental results reveal that the mean functional connectivity strength is highest under binocular color fusion, followed by binocular color rivalry, and lowest under the Mid-Gray field condition. This finding indicates that binocular color visual stimulation significantly enhances collaboration and integration between brain regions. Specifically, binocular color fusion exhibits a more pronounced increase in functional connectivity strength compared to binocular color rivalry, suggesting that the fusion process better facilitates cooperation and information integration among brain regions.

Additionally, the experiment observed considerable individual differences in functional connectivity strength under each condition. For example, P6 demonstrated the highest functional connectivity strength under both binocular color fusion and the Mid-Gray field conditions, while P7 exhibited lower connectivity strength across all conditions. These differences may be attributed to variations in participants' brain structure, functional state, or sensitivity to the stimuli. Despite these individual differences, the overall trend was consistent: all participants exhibited the highest mean functional connectivity strength under binocular color fusion stimulation and the lowest under the Mid-Gray field condition. This finding further highlights that binocular color fusion stimulation can significantly activate inter-regional cooperation in the brain, enhancing its ability to process complex visual information.

This study analyzes the behavioral data (reaction time) collected from Experiment 2. Reaction Time (RT) was calculated as the difference between the time of the stimulus image presentation and the time when the “A” key was pressed. All participants made accurate judgments, responding only during the presentation of RoRG stimuli and not during the presentation of FoRG stimuli. This demonstrates that the subjective experiences elicited by binocular color rivalry and fusion are fundamentally different, and there is no mutual transformation between the two. Table 4 presents the reaction times, mean reaction times, and standard deviations for each participant in response to eight random binocular color rivalry image stimuli in a single experiment. Figure 8 visually illustrates the mean reaction times and standard deviations for participants responding to binocular color rivalry stimuli. Despite some individual differences, all participants' responses met the experimental requirements.

All participants' reaction times fell within the 10-s window of stimulus presentation. This observation indicates that all participants were able to accurately perceive the binocular color rivalry stimuli within the designated timeframe. It also confirms that the subjective experiences of binocular fusion and rivalry stimuli are distinct, enabling participants to make accurate judgments. P4 and P7 exhibited longer mean reaction times, ~3.79 s and 5.64 s, respectively. This may indicate slower responses during the task, potentially due to differences in color sensitivity, attention, or perceptual factors. In contrast, P3, P2, and P8 demonstrated shorter mean reaction times, close to 1 s, suggesting higher levels of focus and color sensitivity. All participants completed the task accurately, demonstrating their ability to effectively distinguish between the subjective experiences of binocular color fusion and rivalry stimuli. This result indicates that these two types of stimuli elicit entirely different perceptual experiences, enabling participants to make clear and precise judgments. The ability to differentiate between these conditions shows that the experimental design successfully presented robust and distinguishable visual stimuli, further validating the reliability of the experimental methodology and the robustness of the results. This distinction between binocular color fusion and rivalry stimuli proves that the perceptual and cognitive mechanisms involved in processing these two types of conditions are fundamentally different.

Table 5 presents the brain activation analysis results (β-value) for FoRG, while Table 6 provides the brain activation analysis results (β-value) for RoRG. Based on Tables 5, 6, Figures 8, 9 were created. Figure 9 shows the mean β-value across 14 channels under the two conditions, Through Figure 9, it is clearly evident that FoRG induces more neural activation in the prefrontal cortex compared to RoRG. Figure 10 presents the level of brain activation following the GLM analysis. Figure 10a shows the results under the binocular color fusion condition, where a large proportion of the area is shaded in purple, indicating high levels of brain activation. Figure 10b displays the results under the binocular color rivalry condition, where most areas are shown in blue, suggesting relatively low levels of brain activation. The higher level of activation under binocular color fusion, indicated by more extensive purple regions, suggests that the brain actively integrates the visual inputs from both eyes, which is a complex perceptual task. Conversely, the lower activation level under binocular color rivalry, predominantly shown by blue regions, indicates that fewer brain areas are activated. It implies that the brain processes a relatively more straightforward task with lower activation demands during the rivalry condition.

After GLM analysis, the data under binocular color fusion and rivalry conditions were analyzed using the Wilcoxon Signed-Rank Test. Since both fusion and rivalry stimuli were tested on the same group of participants, the results for the two conditions are paired, making the Wilcoxon Signed-Rank Test an appropriate choice. This test is used to determine whether the two stimulation conditions have a significantly different impact on brain function. To ensure the accuracy of the test, the FDR correction method was applied. Table 7 presents the test statistic and corrected P-value for all channels, indicating the significance of the results for each channel. Among all the channels, CH12, CH13, and CH14 exhibit statistically significant differences (corrected P < 0.05), suggesting significant changes in brain activation between binocular color fusion and rivalry stimuli in these channels. Figure 11 shows that the corrected P-values for channels CH12, CH13, and CH14 are below 0.05, highlighting the notable activation differences in these channels under binocular color fusion vs. rivalry conditions. Post-hoc power analysis was conducted for the three channels with significant differences, and the results are as follows: (1) CH12: Effect size(d) = 1.09, Power = 0.92. (2) CH13: Effect size(d) = 1.28, Power = 0.98. (3) CH14: Effect size(d) = 1.35, Power = 0.98. The results of the power analysis indicate that the experimental design demonstrates high efficiency for these three channels. Given the current sample size and effect strength, the reliability of the test results is relatively high. These results are unlikely to be affected by insufficient sample size or inadequate experimental sensitivity.