A quantitative measurement of dichoptic color difference thresholds related to binocular luster across various luminance

Abstract

Gloss perception, a crucial visual ability, poses computational challenges for human and machine vision when estimating surface glossiness. The Dichoptic Color Difference Threshold (DCDT) is a quantitative metric to assess the minimal discernible color variation in binocular luster perception. In this study, we investigated the relationship between binocular luster and color hue, color difference, and luminance factors by quantifying and measuring DCDTs under binocular equivalent luminance conditions. Additionally, we fitted a quadratic logarithmic function model to describe the association between binocular luster and luminance factors. The experiments and data analysis presented in this article demonstrate that luminance significantly influences binocular luster. These research findings provide robust support for luster reproduction in three-dimensional system design.

How to Cite this Article

Su, J., Guan, H., & Chen, Z. (2026). A quantitative measurement of dichoptic color difference thresholds related to binocular luster across various luminance. i-Perception, 17(2), 1–17. https://doi.org/10.1177/20416695261427982

Introduction

Surface gloss is an appearance attribute, but binocular luster is a cue to the visual perception of surface gloss. Binocular luster is usually described as having a graphite-like or metallic quality (Brewster, 1855; Dove, 1851). Some researchers have further highlighted the metallic properties of tin or lead (Wendt & Faul, 2022a). Additionally, other researchers have reported that individuals often associate this sensation with glass or crystal-like appearances (Kiesow, 1920; Oppel, 1857; Rood, 1861). A prominent characteristic of binocular luster is its inherent instability, often described as a “fluctuating silvery sheen” (Howard, 1995).

When different colors are presented to the left and the right eyes, with increasing color differences between the two eyes, the observer will experience the stages of binocular color fusion and binocular color rivalry (Malkoc & Kingdom, 2012). Binocular color fusion and rivalry are often thought to be two sides of the same coin. However, there exists a stage between fusion and rivalry; as one increases a between-eye difference in color from zero, a threshold is reached when the binocular image appears slightly glossy, or shimmery. It is considered that the between-eye difference is just detectable, but there is no perceptual alternation, which is defined as the Dichoptic Color Difference Threshold (DCDT). When the binocular color difference exceeds the DCDT, the brain can simultaneously generate binocular luster while performing binocular color fusion. This point occurs at a much smaller binocular difference in color from that required to elicit an impression of rivalry—the Binocular Color Rivalry Threshold, but it is a form of local rivalry.

Current research on the impact of luminance on binocular luster primarily centers on the luminance contrast between interocular target color blocks. This is because, according to conflict theory, the origin of binocular luster effects is largely attributed to neural conflicts arising from interocular luminance contrasts. Czepluch (1976) and Sheedy and Stocker (1984) used the ratio of the luminance of the target patches, $L_{\min }/L_{\max }$ , as a measure of the luster threshold. Czepluch (1976) found that regardless of the fixed luminance level when tested at several levels between 20 and 320 cd/m², luster was detected when the luminance ratio $L_{\min }/L_{\max }$ was approximately 0.7 (corresponding to a Michelson contrast of 0.18). For luminance ratios below 0.35, that is, Michelson contrasts greater than 0.48, binocular rivalry was found to dominate the perceptual experience. Sheedy and Stocker (1984) used simple incremental center-surround stimuli. The threshold ratios ( $L_{\min }/L_{\max }$ ) of two of the three subjects varied between 0.2 and 0.3, while the third subject's threshold was slightly lower, with the ratio ranging from 0.4 to 0.6. The inconsistency between these two studies indicates that the luminance ratio based on the absolute luminance of the color patches is a rather inappropriate measurement standard and cannot represent the relevant input variables of the visual system. However, Wendt and Faul (2019) found in their threshold experiments that a relatively low proportion of stimuli with consistent contrast polarity can also be completely judged as lustrous, especially when the target color blocks all decrease in luminance relative to the surroundings.

Since binocular luster is a kind of high-level vision, it must be affected by various low-level visual features. Wendt et al. (2008) demonstrated that the existence of highlight disparity enhances the authenticity and intensity of perceived glossiness. Stimuli with strong highlight disparity require less objective glossiness to evoke the same intensity of perceived gloss than those without strong highlight disparity. Wendt et al. (2010) found that disparity, motion, and color information are conducive to enhancing the constancy of gloss matches. The visual system can utilize these three information sources either separately or in combination. Wendt and Faul (2017) found that minor changes in the structure of the light field can cause significant changes in perceived gloss, and the degree of overlap of nearby highlights also affects perceived gloss. They further concluded that increasing the complexity of the geometric structure of the illumination may reduce gloss constancy. Additionally, it was found that shape also has an impact on perceived gloss, with a decrease in curvature leading to a reduction in gloss. Wendt and Faul (2018) further discovered through experiments that the color information of the light source contributes to gloss constancy: if the light sources have significantly different colors, the performance of gloss constancy is much better than when all light sources have the same color, and the highlights can be grouped based on the cause of the light source color. Motion information from object rotation does not have such an effect, but it can slightly increase the overall perception of gloss.

In stereoscopic vision, under the condition of equal luminance between the eyes, binocular color difference is an important clue to reproduce binocular luster. It can provide evidence for exploring the mechanism of color processing in human vision. Wendt et al. (2008) proved that binocular luminance difference accompanied by binocular disparity can significantly enhance the gloss perception of the surface. Still, since binocular disparity cues in the stereoscopic display need to be obtained by equal luminance information, they conflict with each other. Binocular color difference can be used to express the surface gloss of an object on three-dimensional (3D) display devices without being accompanied by a specular reflection pattern, and a simple image with a binocular color difference provided a similar surface appearance impression to a real object that has a same binocular color difference (Jung et al., 2013). Mausfeld et al. (2014) also found that glossy surface appearances can be elicited through simple image configurations that lack texture or specular highlights. Stereoscopic luster cannot be adequately explained solely by the binocular luminance conflict. In a comparable binocular fusion experiment, it was demonstrated that the process of perceiving two hues to produce a third hue occurs within the retina. This finding contributes to further experimental investigation into how the human visual system processes color information and visual stimuli (Dai et al., 2024).

The purpose of this article is to investigate the effects of color hue, color difference, and luminance on binocular luster perception to further explore the processing mechanisms of the human brain for color information. The aim is to address the following: (1) the influence of color information (including hue and chroma) on binocular luster perception; (2) the range of color differences that elicit binocular luster; (3) quantitative analysis of binocular luster perception influenced by luminance factors under interocular equivalent luminance conditions. Its primary innovations lie in quantification and modeling, with the main contribution being improvements and quantitative extensions to prior research (e.g., Jung et al., 2013; Mausfeld et al., 2014).

Method

Apparatus and Test Material

The color stimulation for the experiment was provided by a Samsung 3D display (S23A950D) with a two-dimensional (2D)/3D switching function. The observer is required to wear specific 3D switching glass to enable the left and the right eyes to view different color stimuli in time, and the crosstalk levels of this switching glass is 0.95% for the left eye and 1.08% for the right eye. To avoid the effect of viewing distance on the experimental results, the observers viewed the stimulus at a distance of 800 mm from the 3D display (ITU-R BT. 500, 2012). The experiment was conducted in a dark room with all participants having consistent lighting conditions, and the “black” on the LCD in the darkened room was 0.6354cd/m². The apparatus and viewing environment are shown in Figure 1. The parameters of the display are shown in Supplemental Table S1, the screen refresh rate is 120 Hz, and the display is connected to the computer (processor: Intel Core 2 Duo CPU, processing speed: 3 GHz, RAM:4GB, operating system: Microsoft Windows 10, Graphics card: NVIDIA GeForce GTX 1080, display digital number N = 8 bits).To accurately control the colors presented in the experiment, the spectral radiometer PR-715 of the American Photo Research Company was calibrated for the spectral emission function (Chen et al., 2019a). By looking up the table to obtain the color value of the digital input, taking into account the effect of black dots on accuracy, the conversion between RGB values and CIE XYZ values will be more accurate (Shi et al., 2007). The measured CIE XYZ value of the black dot of this display was 0.6124/0.6354/1.105. The chromaticity coordinates of the white point and red, green, and blue channels are shown in Supplemental Table S1.

Figure 1.

(a) Apparatus and (b) viewing environment.

Observers

Fifteen young adults aged between 20 and 35 were selected to participate in the experiment (ITU-R BT. 500, 2012). Among them, seven were female and eight male students. All of them passed the vision and color vision tests, and all of them showed naked-eye color vision and naked-eye stereoscopic vision. This experiment conforms to the standards stipulated in the Declaration of Helsinki (Association, 2009). They have read and signed the informed consent form and can withdraw from the experiment at any time.

Stimulation

The color gamut of the display is represented by a dashed triangle in the CIE 1976 uniform chromaticity scale diagram. Under equal luminance conditions between the left and the right eyes, we uniformly selected three sampled points within the color gamut of the display to measure the DCDTs, as shown in Figure 2(a). We sampled neighbors along the straight lines in five directions from the origin point, as shown in Figure 2(b). The directions consisted of (Chen et al., 2019b):

Three color directions red (R), green (G), and blue (B) and

Three directions representing an equiangular division between R and G, G and B, and B and R, respectively.

Figure 2.

(a) The three sampled points in the CIE 1976 chromaticity diagram were selected through our experiment. The dashed triangle represents the LCD color gamut used in our experiments. (b) The neighbor selection scheme for three sampled points. Neighbor points are evenly selected along five directions for each sampled point.

These three sample points were selected because they are positioned near the white spot on the CIE1976 chromaticity diagram or lie on a straight line. When sampling points are selected in five directions from these points, the experiment can demonstrate a wider variety of color hues, resulting in a more representative color gamut range and enhanced universal applicability. The sampling step of the sample point is 0.005. The neighbor points were selected in the LCD color gamut. The maximum number of neighbor points for each of the three points is 42. To measure the DCDTs under different luminance levels, the luminance (Y) settings for the left and the right eyes on the display were set at five levels: 6, 10, 14, 18, and 22 cd/m². During the experiment, the luminance was displayed randomly, and the luminance of the left and the right eyes remained consistent. Due to the limitation of the display color gamut, all sampled points were selected in five directions, and the number of selected neighbor points on each line varied according to the specific requirements. Each sampled point was selected with a total of 42 neighbor points. A total of 629 stimuli were used (three sampled points, each with 42 neighbor points per sampled point, and five luminance levels, one of which falls outside the display gamut), and each stimulus was randomly repeated 10-fold. At the No.1 sampled point, a total of 2090 trials were recorded due to the limitation of the color gamut of the display, and the other two sampled points each recorded 2100 trials. Therefore, a total of 6290 trials were recorded for a single observer.

The stimuli for the left and the right eyes displayed on the screen are generated and controlled by specially written C# software. As shown in Figure 3, the color stimulus is composed of two solid annular rings on a black background. To match the size of the foveal central pit of the human eye, the size of the central chromatic patch is 2 degrees, and the size of the annular ring around the central chromatic patch is 4 degrees. The rectangular box in the upper left corner was used to interact with the observer, remained binocularly visible throughout the experiment, and was used to ask the observer about his perception. The experimental interface designs gray rectangular frames as zero disparity reference planes and sets the disparity of the annular stimulation to zero to avoid the influence of depth perception on the experimental results (Xiong et al., 2021). The left central chromatic patch is filled with the colors of sampled points, and the annular ring around the central chromatic patch is filled with the colors of selected neighbor points and presented to the observer's left eye. The right central chromatic patch and peripheral annulus are both filled with the colors of sampled points and presented to the observer's right eye.

Figure 3.

Example of a stimulus used in our experiment ([a] for the left eye and [b] for the right eye). The central chromatic patch size is 2 degrees and the annular ring around the central chromatic patch size is 4 degrees.

Procedure

The experiment was entirely controlled by software. The stimuli were left on the screen until the subject responded, and subjects were encouraged to respond within 2 s. A clue is, “Can you feel the outer ring ‘lustrous’?” It was a forced choice. The central chromatic patch is a matte contrast, while the lustrous outer ring makes it easier for observers to perceive the metal quality, lustrous sensation, and transparent medium. Before the experiment, the experimenter will furnish the participants with examples of stimuli to be utilized, thereby ensuring that they are thoroughly acquainted with the perceptual characteristics of luster perception and familiar with the experimental procedures. If the observer presses the “Y” key on the keyboard, it indicates the observer can perceive the gloss. If the observer presses the “N” key on the keyboard, the observer cannot perceive it. The experimental results were automatically recorded in a program document after each sampled color and all its surrounding neighbor colors were traversed for all luminance levels.

The observation process for all trials was lengthy and induced visual fatigue. Thus, the observations were divided into several tests consisting of several 30min sessions. The observation was stopped immediately when the observer sensed any visual fatigue.

Results and Discussion

Calculation of the Dichoptic Color Difference Threshold

We recorded the number of “lustrous” responses to 629 stimuli in 15 observers. Statistical standard deviation and box diagram method were used to analyze the reliability of the experimental data, and outliers were eliminated. Numerical analysis is provided in the Supplemental document. Figure 4 shows examples of the proportions of lustrous perception of the No.1 sampled point in Figure 2. The abscissa represents the Euclidean distance from the sampled point in the $u^{\mathrm{\prime }}{v}^{\mathrm{\prime }}$ chromaticity diagram. Each psychometric function illustrates the proportions of neighboring points along a specific direction that was sampled. We designated $p(\text{\%})$ as 50% to define the DCDT, which was estimated through linear interpolation between two adjacent points near the 50% lustrous level (Ikeda & Sagawa, 1979). The DCDT was computed in the following manner:

$$u_f^{\mathrm{\prime }}=u_i^{\mathrm{\prime }}+(u_{i-1}^{\mathrm{\prime }}-u_i^{\mathrm{\prime }}){\displaystyle \frac{50-p_i}{p_{i-1}-p_i}}$$

(1)

$$v_f^{\mathrm{\prime }}=v_i^{\mathrm{\prime }}+(v_{i-1}^{\mathrm{\prime }}-v_i^{\mathrm{\prime }}){\displaystyle \frac{50-p_i}{p_{i-1}-p_i}}$$

(2)

Figure 4.

A sample of proportions of lustrous perception in five neighbor's directions from No. 1 point ([a] red direction, [b] green direction, [c] blue direction, [d] red-green direction, and [e] red-blue direction). The abscissa represents the Euclidean distance from the point $(u^{\mathrm{\prime }}=0.2,v^{\mathrm{\prime }}=0.3)$ . $p(\text{\%})$ indicates the proportions of lustrous perception. Observer: LS.

where $u_i^{\mathrm{\prime }}$ and $v_i^{\mathrm{\prime }}$ represent the first neighboring chromaticity point with proportions of lustrous perception below 50%, and $p_i$ the proportions of lustrous perception at point i. Additionally, $u_f^{\mathrm{\prime }}$ and $v_f^{\mathrm{\prime }}$ indicate the lustrous chromaticity point for the DCDT, while $u_{i-1}^{\mathrm{\prime }}$ and $v_{i-1}^{\mathrm{\prime }}$ refer to the first neighboring chromaticity point with proportions of lustrous perception above 50%, and $p_{i-1}$ denotes the proportions of lustrous perception at the point $(i-1)$ . For example, the DCDT was calculated for the red direction in Figure 4(a) using formulas (1) and (2), with $p_i=40,p_{i-1}=70$ , resulting in corresponding values of ( $u_i^{\mathrm{\prime }}=0.2036,v_i^{\mathrm{\prime }}=0.3034)$ and ( $u_{i-1}^{\mathrm{\prime }}=0.2072,$ , $v_{i-1}^{\mathrm{\prime }}=0.3069)$ . The calculated DCDT values were found to be $(u_f^{\mathrm{\prime }}=0.2048,v_f^{\mathrm{\prime }}=0.3046)$ . Similarly, in Figure 4(b) to (e), the DCDTs were determined as follows: for the green direction $(u_f^{\mathrm{\prime }}=0.1972,v_f^{\mathrm{\prime }}=0.3096)$ ; for the blue direction $(u_f^{\mathrm{\prime }}=0.1992,v_f^{\mathrm{\prime }}=0.2870)$ ; for the red-green direction $(u_f^{\mathrm{\prime }}=0.2045,v_f^{\mathrm{\prime }}=0.3169)$ ; and for the red-blue direction $(u_f^{\mathrm{\prime }}=0.2058,v_f^{\mathrm{\prime }}=0.2973)$ .

However, when the proportion of lustrous perception does not exceed 50%, linear interpolation is not applicable. Therefore, we employ a psychometric function to model the probability accurately (Chen et al., 2014):

$$p_i=\sum _{n=0}^N{a}_n(ln{x}_i{)}^n$$

(3)

where $p_i$ represents the proportions of lustrous perception for the neighboring colors in a sampled line direction and $x_i$ the Euclidean distance between the sampled color and its neighbor; the fundamental function $lnx$ is based on Weber–Fechner's law to determine the proportions of lustrous perception; the power series expansion of $lnx$ characterizes these proportions as multi-items scales; with a total of $(N+1)$ items; $a_n$ represents the coefficient for each item, which can be obtained by fitting a psychometric function. By varying different values of N, regression analysis was conducted to identify the optimal coefficient (denoted as $a_n$ ) and evaluate goodness-of-fit using the coefficient of determination ( $R^2$ ).

We employs the CV value (coefficient of variation) to quantify the dispersion of individual differences in threshold ranges among observers. As the ratio of standard deviation to mean, it reflects the degree of data dispersion relative to its mean. The CV values for sample points 1, 2, and 3 range from 0.19 to 0.67, 0.17 to 0.60, and 0.37 to 0.72, respectively. Figure 5 further demonstrates significant variations in threshold ranges across observers, highlighting substantial variability in gloss perception—a finding consistent with the research results of Wendt and Faul (2022a).

Figure 5.

The CV values of individual differences in DCDTs threshold range under varying luminance and neighbor selection direction conditions ([a] No.1 point, [b] No. 2 point, and [c] No. 3 point). CV= coefficient of variation; DCDT= Dichoptic Color Difference Threshold.

Scatter Plots of Dichoptic Color Difference Thresholds

Based on the results of the proportions of lustrous perception, we obtained the DCDTs in all directions for each sampled point under different luminance, as shown in Supplemental Table S2. The scatter plots drawn on a standard uniform chromaticity diagram are shown in Figure 6. It can be seen that the DCDTs are not equal in each color direction and tend to decrease with increasing luminance.

Figure 6.

Scatter plots of the Dichoptic Color Difference Thresholds for three sampled points in different luminance and color directions ([a] No.1 point, [b] No. 2 point, and [c] No. 3 point).

To understand whether different hues and luminance have statistical significance for the DCDTs, we performed a two-way analysis of variance (ANOVA). Quantitative analysis was conducted to determine whether different color direction and luminance had significant effects on the DCDT. In Supplemental Table S3, $SS$ is the sum of squares, $DF$ the degree of freedom, total $DF$ is the number of observations minus one, $MS$ is the mean square error for each change source or $SS/DF$ , F statistic is the ratio of mean square errors, the P value is the probability that an observed outcome will occur if the null hypothesis holds.

The P-values calculated for the color direction and luminance factors of the three sampled points were all found to be below 0.05, as shown in Supplemental Table S3. These results indicate significant differences in the DCDTs for different color directions and luminance, as evidenced by the significant differences observed between the column averages. The impact of varying color directions and luminance factors on the DCDTs at the three sampled points is illustrated in Figure 7. As depicted in Figure 7, it can be observed that the DCDTs vary with changes in color direction and luminance. Specifically, at the first sampled point, larger DCDTs were found in the green (G) and red-green (R-G) directions, while smaller DCDTs were observed in the red (R) and red-blue (R-B) directions. Similarly, at the second sampled point, larger DCDTs were identified in the blue (B) and red-green (R-G) directions, whereas smaller DCDTs were noted in the red (R) and red-blue (R-B) directions. Lastly, at the third sampled point, larger DCDTs were detected in the blue (B) direction compared to smaller ones seen in the red (R) direction.

Figure 7.

The Dichoptic Color Difference Thresholds of three sampled points correspond to color direction and luminance factors ([a] No.1 point, [b] No. 2 point, and [c] No. 3 point).

Quantification of the Dichoptic Color Difference Thresholds

The proportions of lustrous perception obtained from the results above can be represented by ellipses, which depict the shape of the chromaticity points of the DCDTs (Jung et al., 2011). The fitting formula for this ellipse is provided as follows:

$${\displaystyle \frac{{[(u^{\mathrm{\prime }}-C_1)\cos \theta +(v^{\mathrm{\prime }}-C_2)\sin \theta ]}^2}{a^2}+{\displaystyle \frac{{[-(u^{\mathrm{\prime }}-C_1)\sin \theta +(v^{\mathrm{\prime }}-C_2)\cos \theta ]}^2}{b^2}=1}}$$

(4)

Where the semi-minor and semi-major axes of the center point $(C_1,C_2)$ are represented by a and b, respectively, while $\theta$ represents the rotation angle of the ellipse. Nonlinear regression fitting was employed to obtain the parameters of the ellipses. Additionally, we assessed the goodness-of-fit statistics for the nonlinear regressions: sum of squares due to error (SSE) and R-squared value (Ler et al., 2010; Rosin, 2000). Supplemental Table S4 presents a summary of parameter estimates and goodness-of-fit statistics for ellipses at three sampled points under varying luminance conditions.

The ellipses in Figure 8 represent the DCDTs for each of the three sampled chromaticity points under varying luminance levels, plotted on a consistent scale. Figure 8(d) illustrates an overall sample plot of the resulting DCDTs at different luminance levels on the CIE 1976 chromaticity diagram. It is important to note that these DCDTs were modeled using ellipses with shapes and rotation directions similar to MacAdam ellipses, which are used to represent just-noticeable differences in chromaticity (Kentridge et al., 2012; Wada et al., 2014). The semi-minor axis aligns with $u^{\mathrm{\prime }}$ axis, while the semi-major axis aligns with the $v^{\mathrm{\prime }}$ axis for each ellipse fitted by three sampled points under different luminance levels. Furthermore, these ellipses exhibit similarities in shape and rotation direction.

Figure 8.

The ellipses that quantify the DCDT for each of the three sampled chromaticity points under different luminance ([a] No. 1, [b] No. 2, [c] No. 3, and [d] a resulting sample plot of the DCDTs plotted on the CIE 1976 chromaticity diagram, Y = 6). DCDT= Dichoptic Color Difference Thresholds.

Figure 8(a) to (c) represents the DCDTs of the three sampled points that are different under different luminance. The semi-minor axis of the ellipses ranged from 0.00791 to 0.01683 in the Euclidean distance in the $u^{\mathrm{\prime }}{v}^{\mathrm{\prime }}$ chromaticity diagram, while the semi-major axis ranged from 0.02455 to 0.03746. The average value of a is 0.01242, and the average value of b is 0.03746.

Model Fitting

The average curve shape of the DCDTs for the three sampled points as a function of luminance is depicted in Figure 9. The solid circle curve shown in the figure represents the average DCDT values of the three sampled points as a function of luminance. It can be seen from the figure that with the increase in luminance, the DCDT gradually decreases. The trend of decrease is more apparent when the luminance increases from 6 to 10cd/m² and from 18 to 22 cd/m², while the trend of decline is relatively flat between 10 to 18cd/m².

Figure 9.

The average curve shape of the Dichoptic Color Difference Thresholds for the three sampled points as a function of luminance.

Using the psychometric function (3), as N increases, $R^2$ approaches 1. To avoid redundancy, we select $N=2$ . At this time, the $R^2=0.94$ , and the $SSE$ is 1.08842E-6. The DCDT (D), as a function of luminance factor (Y), yields a quadratic logarithmic function model:

$$D=0.05251+(-0.02178)*\ln (Y)+0.00334*(\ln (Y){)}^2$$

(5)

According to the quadratic logarithmic function model (6), the relationship between D and Y is shown in Figure 10.

Figure 10.

The relationship between D (the dichoptic color difference threshold) and Y (the luminance factor).

Discussion

Binocular luster has been proven to be a cue to the visual perception of surface gloss. However, the visual attribute of surface gloss also includes other important cues, such as specular gloss, haze and distinctness-of-image, to mention only a few, which all play a role in the visual impression of surface gloss. In this study, the theme is that color hue, color difference, and luminance factors might exert a considerable influence on binocular luster. For instance, even without specular reflection, binocular color differences can give rise to a sense of surface gloss, which is a highly typical phenomenon. The findings from the “Calculation of the Dichoptic Color Difference Threshold” section reveal that binocular color difference cues enhanced the lustrous perception of object surfaces. However, it is essential to note that this lustrous perception is only evoked within a specific range of values. The findings in the “Scatter plots of Dichoptic Color Difference Thresholds” and the “Quantification of the Dichoptic Color Difference Thresholds” sections suggest that the perceptual color difference plays a crucial role in determining the DCDT. It can be inferred that perceptual color difference primarily determines the DCDT for color stimuli. The increase in binocular luminance also has an impact on DCDT. So, under the circumstances of stereoscopic display, binocular luster, as a high-level visual phenomenon, is likely to be influenced by various low-level visual features such as luminance and binocular color difference.

The findings from the “Model Fitting” section demonstrate the DCDT can be effectively represented as an ellipse within the chromaticity diagram. Specifically, it is the subjective perception of color differences that influences the intensity of the lustrous perception rather than the actual tonal distance encompassed by the overall color difference. For instance, while the combination of yellow and purple produces only a relatively weak lustrous effect, the pairing of red and green generates a more vivid and pronounced lustrous experience. Ikeda and Sagawa (1979) previously reported that, in the CIE1960 $uv$ chromaticity diagram, the color fusion threshold of the white point $(u=0.1864,v=0.3196)$ was depicted by a circle with an approximate radius of 0.0792. Jung et al. (2011) on the other hand, found that for binocular color fusion thresholds of nonspectral colors in the $u^{\mathrm{\prime }}{v}^{\mathrm{\prime }}$ chromaticity diagram, the semi-minor axis of the ellipse ranges from 0.0415 to 0.0923 and the semi-major axis ranges from 0.0640 to 0.1560. Chen et al.’s (2019b) study revealed that as disparity increases from −120 to +120 arc minutes, ellipses were employed to quantify color fusion limits within the chromaticity diagram; here, axis values ranged between 0.017 and 0.145 $\mathrm{\Delta }{E}_{u^{\mathrm{\prime }}{v}^{\mathrm{\prime }}}$ . Our measured DCDTs are considerably smaller than those obtained for binocular color fusion thresholds mentioned above, which aligns well with our initial hypothesis.

The findings presented in the “Discussion” section further confirm that luminance affects the DCDT, which in turn indirectly affects the lustrous perception. In this article, we develop a quantitative model to analyze the relationship between the luminance factor and the intensity of binocular luster. The DCDT reported in this study was measured under the equivalent luminance condition between the two eyes. This approach facilitates the reproduction of binocular luster by leveraging binocular disparity cues, which are critical for depth perception and stereoscopic display applications. In stereoscopic display, the human visual system primarily relies on luminance information within an image to match corresponding left and right points, thereby obtaining disparity cues and generating depth perception (Lu & Fender, 1972). Specifically, luminance information serves as the primary signal for object depth perception. Stereoscopic matching can be achieved as long as the binocular stimuli of the corresponding points exhibit equal luminance levels. Although color information (including hue and chroma) plays a role in simple or monocular contour recognition, it does not contribute significantly to detecting stereoscopic contours. Therefore, to reproduce the surface gloss perception in a stereo display by utilizing binocular difference cues, the most effective approach is to implement color difference modulation while ensuring, to the greatest extent possible, the luminance consistency of corresponding points between the left and the right images for accurate depth perception.

Binocular luster, a visual phenomenon characterized by the perception of glossy appearance when conflicting binocular information is presented to the two eyes (e.g., different color signals), serves as a critical perceptual correlate in 3D display and vision modeling by providing a direct link between binocular disparity processing and the human perception of surface properties. In 3D displays, which aim to replicate the binocular cues that drive binocular luster arises when the visual system receives inconsistent signals from the two eyes—for instance, when a display presents slightly different color difference for corresponding image regions in the left and the right eye views. This inconsistency triggers a perceptual response where the brain interprets the conflicting binocular input as a glossy quality surface, because the visual system resolves the color different by attributing the discrepancy to light reflection properties rather than spatial depth. This makes binocular luster a valuable marker for evaluating the realism of 3D displays.

Currently, it is widely acknowledged that the visual system processes information hierarchically. Following Palmer's “independent hierarchical model,” wherein color/shape and depth information are processed along the distinct pathways (Palmer, 1999), color and shape signals are initially captured by the Cone photoreceptors in the Retina through light absorption. These signals subsequently traverse the Lateral Geniculate Nucleus (LGN) of the thalamus before reaching the primary visual cortex (V1) within the occipital lobe. From there, the processing continues through the V2 and V4 stages of the visual cortex. The three types of cone cells serve as the theoretical foundation for the “Trichromatic Theory.” At the same time, the opponent processing in the LGN forms the basis of the “Opponent Color Theory.” Consequently, the “Stage Theory” provides a unifying framework that integrates these two theories. Nonlinear interactive processing in V1 and V2 enhances color contrast and facilitates tone perception, whereas V4 is responsible for color constancy under varying lighting conditions (Conway, 2009). This study reveals that binocular luster is influenced by color information and luminance, further supporting the notion that, from the perspective of the “hierarchical model,” binocular color difference luster perception should be integrated with depth information, potentially located at the V2 and V4 levels, or beyond. This conclusion has also been corroborated by other studies. For instance, a functional magnetic resonance imaging study conducted by Sun et al. (2016) demonstrated that both the higher dorsal regions (e.g., hMT+/V5, V7, VIPS, DIPSM, and DIPSA) and the higher ventral regions, such as V4 and LO, are involved in the processing of binocular luster information. This indicates that these regions extend well beyond the structures in the early visual cortex, which are traditionally considered responsible for detecting interocular conflicts. In this study, we observed that the DCDT decreases as luminance increases. This indicates that the intensity of binocular luster rises with increased luminance, consistent with the findings of the interocular conflict model proposed by Wendt and Faul (2022b, 2024) and its color variant. The model they introduced is grounded in the assumption that binocular luster arises from neuronal conflicts between the ON and OFF visual pathways. Consequently, an increase in binocular luminance necessarily results in a higher level of interocular conflict, thereby enhancing the intensity of binocular luster.

The measured DCDTs and luminance-dependent research findings provide critical constraints and insights for advancing computational and neural models of luster perception. The interaction between DCDTs and luminance dependence reveals higher-order integration rules in binocular luster. The systematic variation of DCDTs with luminance indicates that color cues and luminance cues are not processed independently. These discoveries challenge models solely based on luminance contrast, supporting instead a hybrid framework that dynamically weights color and luminance signals according to ambient lighting conditions. The contrast discrimination model proposed by Georgeson et al. (2016) can be extended by introducing luminance-adjusted chromatic contrast terms to capture this interaction. Meanwhile, Sun et al.’s (2016) hierarchical neural model requires integration of luminance-dependent receptive field size to explain how pixel intensity variations under different illumination levels affect neural responses to luster perception. Although the lustrous perception is relatively weak, numerous studies have demonstrated that it can be induced by color stimulation when all stimulus elements are equally luminance (e.g., Dove, 1851; Jennings & Kingdom, 2016; Jung et al., 2013; Malkoc & Kingdom, 2012; Wendt & Faul, 2019; Yoonessi & Kingdom, 2009). Notably, Wendt and Faul (2024) further revealed that binocular luster elicited by equal-luminance color stimulation relies on a mechanism analogous to that observed in noncolor conditions.

Conclusions

This article quantitatively measures the dichoptic color difference thresholds of three sampled points in the CIE1976 uniform chromaticity diagram at different luminance using a 3D display platform, and the results are represented as a series of ellipses.

It is the subjective perception of color differences that influences the intensity of the lustrous perception rather than the actual tonal distance encompassed by the overall color difference.

From the fitted quadratic logarithmic function model, it can be seen that the dichoptic color difference threshold is proportional to the logarithmic value of the luminance factor. The increase in luminance follows a geometric series, while the dichoptic color difference threshold increases with an arithmetic series. The relationship between the two is nonlinear compression. When the luminance increases, the dichoptic color difference threshold decreases.

From the perspective of the “hierarchical model,” binocular luster should be integrated with depth information, potentially located at the V2 and V4 levels or beyond. This study offers additional evidence supporting the mechanism of neural conflict in binocular luster.

In addition, we hope that the quantification of lustrous perception will be used in various applications such as stereo displays and binocular vision systems. There, we can present a more realistic visual experience, including the lustrous perception of the surface. This will help optimize stereoscopic display technology to provide more lifelike visual effects. This means that engineers can leverage binocular luster to encode surface properties: by intentionally introducing controlled luminance and color disparities in regions meant to appear glossy, displays can simulate the natural binocular cues that humans use to perceive gloss, enhancing the immersive quality of virtual environments. Similarly, in vision modeling, incorporating binocular luster as a perceptual correlate allows for more accurate simulations of how the brain constructs a coherent 3D scene from binocular inputs, integrating material properties into a unified perception.

Supplemental Material

sj-docx-1-ipe-10.1177_20416695261427982 - Supplemental material for A quantitative measurement of dichoptic color difference thresholds related to binocular luster across various luminance

Supplemental material, sj-docx-1-ipe-10.1177_20416695261427982 for A quantitative measurement of dichoptic color difference thresholds related to binocular luster across various luminance by Jiawei Su, Huiting Guan and Zaiqing Chen in i-Perception