Human perception becomes difficult in the event of binocular color fusion when the color difference presented for the left and right eyes exceeds a certain threshold value, known as the binocular color fusion limit. This paper discusses the binocular color fusion limit for non-spectral colors within the color gamut of a conventional LCD 3DTV. We performed experiments to measure the color fusion limit for eight chromaticity points sampled from the CIE 1976 chromaticity diagram. A total of 2480 trials were recorded for a single observer. By analyzing the results, the color fusion limit was quantified by ellipses in the chromaticity diagram. The semi-minor axis of the ellipses ranges from 0.0415 to 0.0923 in terms of the Euclidean distance in the u’v´ chromaticity diagram and the semi-major axis ranges from 0.0640 to 0.1560. These eight ellipses are drawn on the chromaticity diagram.
©2011 Optical Society of America
Starting with the recent success of the stereoscopic three-dimensional (3D) cinema industry, stereoscopic 3D content services are the subject of great interest from many industries, including the 3D broadcasting industry. However, one of the main bottlenecks preventing the proliferation of stereoscopic 3D services into the mass market is the concern over visual fatigue and visual discomfort that can be induced at various stages, including stereo shooting and 3D production, coding and transmission, and rendering on stereoscopic displays .
In stereopsis, binocular asymmetry may be one of the causes of visual fatigue and visual discomfort. Human perception becomes difficult in the event of binocular fusion when the level of asymmetries exceeds a certain limit [2,3]. There are three categories of the binocular asymmetries: luminance asymmetry, chromaticity asymmetry, and structure asymmetry . Specifically, nonfused impressions in dichoptic color viewing have been reported as color rivalry or superimposition . Color rivalry is a periodic alternation of the image in each eye occurring in either the spatial or temporal domain. Superimposition appears as simultaneous perception of both colors.
There is a great need to investigate and quantitatively determine the chromatic fusion limit in dichoptic viewing. This quantitative fusion limit can be used for various applications to provide users with comfortable viewing, such as an automatic stereo analyzer to guide content creators for the creation of visually comfortable stereoscopic contents, manufacturing guidelines to create safe optical instruments, image safety guidelines for users who watch 3DTV, and automatic content adaptation to reduce the level of visual discomfort [6–8].
Ikeda et al. studied the color fusion limits of spectral colors and white light [4,5]. Their experiments were conducted to determine the wavelength difference that initiated color rivalry. The color fusion limit was quantified as a function of the wavelength for the spectral colors. The wavelengths of the stimuli ranged from 500 to 660 nm. Seventeen sample points were subjectively examined to find the color fusion limit. These points were presented for the right eye. In addition, each point for the right eye was coupled with ten neighboring wavelengths for the left eye. The results of the wavelength difference ranged from 10 to 50 nm with a minimum value near 480 nm and 580 nm and a maximum value at the spectral extremes . They also reported the color fusion limit for white point as a circle with a radius of about 0.0792 in the CIE 1960 uv chromaticity diagram . However, their works were limited to spectral colors and white light.
As 3DTV has spread, it is necessary to measure how color differences between left and right images of non-spectral colors as well as spectral colors initiate color rivalry. In particular, the color fusion limit of non-spectral colors needs to be measured in the color gamut of 3DTV. Thus far, no attempt has been made to measure the color fusion limit for non-spectral colors.
In this paper, we measure the binocular color fusion limit for non-spectral colors within the color gamut of a conventional LCD (Liquid Cristal Display) 3DTV. The color fusion limit is measured for eight chromaticity points, covering the entire area in the standard CIE 1976 u´v´ chromaticity diagram. In order to check the consistency of our measurements with the results of a previous study, the color fusion limit for a white point was compared to that in a previous study . For eight chromaticity points, over two thousand trials were recorded for a single observer. It takes very long time to observe all stimuli, and the long observation time necessary for the asymmetrical visual stimuli can induce visual fatigue such as eye strain. To limit this investigation to reasonable proportions, it was considered that only a single trichromat would cover all eight chromaticity points to complete this investigation. And four selected chromaticity points were tested by an author to confirm the results of the trichromat. The experimental results show the color fusion limit represented in terms of the Euclidean distance along straight lines in the chromaticity diagram. We quantify the color fusion limit of each point through the use of ellipses, as shown in the color differences obtained by Macadam’s experiment . These results were tabulated and then drawn on a standard chromaticity diagram.
The rest of this paper is organized as follows. In section 2, we describe the experimental method used for the measurement of the color fusion limit. Experimental results are presented in section 3, illustrating the color fusion limit plotted in the CIE 1976 uniform chromaticity scale diagram. Finally, section 4 concludes this paper.
2.1 Apparatus and test material
The apparatus for the present experiments was a calibrated stereoscopic monitor manufactured by Redrover (true3Di®). It consisted of two 40” TFT-LCD displays by Samsung Electronics (LTA400HA07®) and a half mirror. The stereoscopic 3D monitor exploited the linear polarization technique. The viewers watched stereoscopic stimuli upon wearing polarized glasses. The viewing distance was 1.5m. Figure 1 shows the apparatus used in our experiment. Table 1 summarizes the specifications of the LCD display. The brightness and chromaticity were measured at the center point of the monitor using a spectroradiometer (Minolta CS-1000®). The crosstalk levels of the stereoscopic 3D monitor were 0.75% for the left eye and 0.27% for the right eye [14,15]. Both crosstalk levels were as low as visibility threshold of about 1 to 2%, as reported in previous literature .
We uniformly sampled the points in the CIE 1976 uniform chromaticity scale diagram. Figure 2 shows all eight sample points in the CIE 1976 chromaticity diagram, where we measured the color fusion limit. The numbers in Fig. 2 indicate the sample numbers to be observed for the color fusion limit and the triangle represents the color gamut of the LCD display used in our experiments. In the experiments, the colors of the sampled points were presented for the right eye.
To prepare the stimuli for the left eye, which were coupled with the stimulus given for the right eye, we sampled neighbors along the straight lines of six directions from the origin point given for the right eye. The six directions consisted of:
- • Three main directions to the red (R), green (G), and blue (B) primaries.
- • Three sub-directions representing an equiangular division between R and G, G and B, and B and R, respectively.
Seven chromaticity points were sampled along each line while uniformly increasing the distance from the origin points for the right eye. Figure 3 illustrates examples of the neighbor selection scheme for the No. 3 and No. 5 points in Fig. 2. The sampling step size is 0.02. Here, the neighbor points were selected from inside of the color gamut of the LCD display. Consequently, the maximum number of neighbor points for each of the eight points for the right eye is 42 (= 6 directions x 7 neighbor points).
We should note that as more samples are examined, more accurate information is obtained to quantify the color fusion limit. In our experiments, however, we compromised regarding the number of stimulus samples to prevent the number of observations from becoming too large for an observer. There were 248 stimuli overall for each of the eight chromaticities: 23 for No. 1, 30 for No. 2, 35 for No. 3, 25 for No. 4, 36 for No. 5, 37 for No. 6, 33 for No. 7, and 29 for No. 8 (see Table 3 and Table 4 in Appendix).
In our experiments, the sample points along each chromaticity vector did not exactly sit on straight lines as shown in Fig. 3. This was mainly due to the LCD monitor calibration. In the conventional LCD color-calibration techniques that exploit gamma correction or tone response correction with look up Tables [16,17], calibrated monitor output included calibration error, which was not negligible for our measurement of the color fusion limit. As such, we utilized a direct measurement method by constructing a mapping table between RGB and tri-stimulus values:
- 1) We directly measured a set of candidate points in the entire chromaticity diagram. In order to construct the mapping table, first we prepared a set of u'v' values sampled with the step size of 0.005 (i.e., an intended precision of our measurement) in the entire area of the CIE 1976 diagram. Second, the u'v' values (sampled with the step size of 0.005), constrained at a brightness level of 10cd/m2, were transformed to RGB values using gamma correction functions with the gamma values estimated in our monitor calibration. Third, the transformed RGB values were inputted into the left and right LCD monitors, respectively. Finally, the u'v' chromaticity and luminance values for each input were measured using a spectroradiometer (Minolta CS-1000®) attached to polarized glasses in front of camera lens. The mapping table between RGB and tri-stimulus values was constructed using the directly measured values. All procedure was automatically performed by a third-party software program.
- 2) Among the candidate points in the mapping table, we selected the nearest points to the points on straight lines. The nearest points were used for visual stimuli in our experiment. As a result, Table 3 and Table 4 in Appendix show the u', v', and luminance values of all the visual stimuli. The average u'v' difference between the sample points on straight lines and the nearest points in the mapping table was 0.003 in the Euclidean distance. The colorimetric errors were negligible as low as the intended precision (i.e., 0.005) of our measurement for the color fusion limits.
We used a black background and a circular object filled with the sampled colors. The binocular disparity was zero, indicating no depth perception. Figure 4 shows an example of a stimulus. It consists of different colors for the left and right eyes.
In the experiments, the test field size had a visual angle of 2° and a brightness level of 10 cd/m2. The background intensity was 0.05 cd/m2 and the viewing duration was 15 seconds. Many studies have been conducted to investigate the characteristics related to the dependency on binocular color fusion and rivalry . Hovis provided a useful review of these dependencies on binocular color fusion . He concluded that color fusion was more likely to occur with a visual field size smaller than 1°. Ikeda and Sagawa also reported that the fusion increased as the size increased to 45´ and then stayed constant up to 1°20′ . Based on this preliminary observation, they used a 1° visual field size in their experiments on wavelength differences. However, Ikeda and Nakashima pointed out that the variance between observers was not small as a consequence of a small field size, 1° . Thus, they employed larger field sizes of 2° and 10° in their subsequent experiments. From their observations, the wavelength difference values at 2° were somewhat larger than those in a 10° visual field. Color fusion becomes more stable when the absolute luminance of the stimulus is lowered. Qin et al. studied the wavelength difference limit with the four brightness levels of 3 cd/m2, 7.5 cd/m2, 15 cd/m2 and 30 cd/m2 . They showed that the fusion limit becomes smaller as the brightness level increases. Color fusion is more stable with a dark background than with a white background . It is also known that as the viewing duration increases, color fusion becomes more stable. Researchers generally agree that color fusion is more stable with a viewing duration of 3 to 15 seconds . Ikeda and Sagawa also reported that the degree of rivalry increased to 15 seconds and stayed constant up to 25 seconds . From these earlier reports, we designed the experimental parameters for our stimulus.
For the right eye, a sample point was randomly chosen from among the eight sample points depicted in Fig. 2. For the left eye, its neighboring different chromaticity points were presented. An observer was exposed to the stimulus for 15 seconds and reported either fused or nonfused by a forced choice method during a resting time of 10 seconds. After the observations of all neighboring chromaticities were performed, the observations were repeated ten times in a random order . After the ten observations for each pair of the left and right stimuli, the observer chose another sample point for the right eye.
A total of 2480 (= 248 stimuli x 10 observations) trials were recorded for a single observer. The observation process for all of the stimuli was lengthy and induced visual fatigue. Thus, the observations were divided into several test sessions consisting of several 30-min sessions. The observations were stopped immediately when the observer sensed any visual fatigue. The test was conducted under approval from the KAIST Institutional Review Board (IRB).
Based on the results derived from all the observations, the percentage of fused perceptions was calculated for each pair of stimuli. 50 percent of fused perceptions were then used as the color fusion limit . Furthermore, the color fusion limit was quantified as ellipses for the eight sample points in the chromaticity diagram.
3. Results and discussion
The overall results of the observations by a single observer, DH, are presented in Tables 3 and 4 in Appendix. Figure 5 shows three examples of the percentage of fused perceptions, p(%), at the chromaticity point (u´=0.15, v´=0.55) represented by the No. 1 point in Fig. 2 and Table 3. The abscissa represents the Euclidean distance from the point in the u’v´ chromaticity diagram. Each psychometric function shows the percentages for the neighbors in a line of the direction sampled for the left eye. We selected a 50% fused level as the color fusion limit. As indicated in , the fusion points were estimated by using linear interpolation between two adjacent points near the 50% of fused level. The fusion points were calculated as follows:Fig. 5(a) and Table 3. Using Eq. (1) and Eq. (2), the color fusion limit was computed as (u'f=0.2456, v'f=0.5434) for the red direction. Similarly, from the observed psychometric function in Fig. 5(b) and Fig. 5(c), the color fusion limits were interpreted as (u'f=0.1588, v'f=0.4727) for the blue direction, and (u'f=0.2204, v'f=0.4793) for the blue-red direction. Figure 6 shows another example of the percentage of fused perceptions at the No. 6 point (u´=0.3, v´=0.4). In the same way, the chromaticity points of the color fusion limits were obtained as follows: (u'f=0.3710, v'f=0.4585) for the red direction, (u'f = 0.3057, v'f = 0.4952) for the red-green direction, (u'f = 0.2500, v'f=0.4431) for the green direction, (u'f=0.2462, v'f=0.3925) for the green-blue direction, and (u'f=0.2577, v'f=0.3170) for the blue direction, respectively.
Based on the results of the percentage of fused perceptions, we observed that the shape of the chromaticity points of the color fusion limit could be represented by ellipses. To confirm the shape of the color fusion limit, four additional neighboring directions from the No. 3 point were tested. The four additional directions also represented an equiangular division between the five directions from the No. 3 point. Thus, a total of nine chromaticity points of the color fusion limit were measured for the No. 3 point. For the nine chromaticity points, the sums of square errors in the regression of the ellipse and circle were 0.3912 and 0.4311, respectively. From the above observations, we modeled the color fusion limit using a set of ellipses . This can be defined as18, 19]. The SSE, also called the residual sum of squares, was measured by the sum of squared algebraic distances as follows:18]. The fitting of an ellipse was realized by minimizing the sum of squared algebraic distances. As for iterative estimation algorithm, “Levenberg-Marquardt” method was adopted for the purpose of estimating the nonlinear function. The iterations were stopped when a convergence criterion was reached. The convergence criterion used was 1.0e −8. For the ellipse represented in Fig. 7(a) , C 1 was 0.15, C 2 was 0.55, a was 0.0707, b was 0.1049, and θ was 62.0273 degrees, respectively. The standard errors of the regression are 0 for a, 0 for b, and 0.0189 for θ. Also, for the goodness-of-fit statistics for the nonlinear regress, the SSE was 3.76e −07 and R-squared value was 1.
Figure 7 and Fig. 8 represent the ellipses that quantify the color fusion limit for each of the eight chromaticity points. All of the ellipses are plotted in the same scale. Table 2 summarizes the estimated parameter values and the goodness-of-fit statistics of the ellipses for the eight points. Figure 9 represents the overall results of the color fusion limit plotted on the CIE 1976 chromaticity diagram. For clarity, the plots are downscaled to one third of their actual lengths. In summary, the semi-minor axis, a, of the ellipses ranges from 0.0415 to 0.0923 in terms of the Euclidean distance in the u’v´ chromaticity diagram, whereas the semi-major axis, b, ranges from 0.0640 to 0.1560. The average of the a values is 0.0641 and the average of the b values is 0.1054.
The color fusion limit is not modeled as equal-sized circles in the standard uniform chromaticity diagram. It should be noted that the color fusion limit is modeled by a set of ellipses whose shapes and directions of rotation are similar to those of MacAdam ellipses for the just-noticeable differences of chromaticity [9,11]. For example, the ellipse for the No. 1 point has an elongated shape along the direction of the second and fourth quadrants in the u’v´ plane (see Fig. 7(a)). The ellipse for the No. 4 point has an oval shape with the major radius along the u´ axis (see Fig. 8(b)). The ellipse for the No. 8 point has an elongated shape along the v´ axis (see Fig. 8(f)). The ellipses of the other points also look similar in terms of their shape and direction of rotation. However, we cannot directly compare the two ellipses, as the observed points of the color fusion limit are different from those of the color difference; moreover, the MacAdam ellipses transformed to the u´v´ chromaticity diagram are not ellipses in a strict mathematical sense (their shapes closely resemble those of ellipses) .
To check the consistency of our measurement with the result of a previous study, we also compared our results with the results of a white point. Ikeda et al.  reported that the color fusion limit for a white point (u=0.1864, v=0.3196) was obtained in the form of a circle with a radius of about 0.0792 in the CIE 1960 uv chromaticity diagram. For the comparison, the color fusion limit was measured along the lines of the red and blue directions from the white point. The color fusion limits, as represented in the Euclidean distance from the white point in the CIE 1960 uv plane, were 0.0833 for the red direction and 0.0673 for the blue direction. Both values were close to Ikeda’s result of 0.0792.
Furthermore, one of the present authors, YJ, made observations to confirm the above results of the color fusion limit obtained from DH’s observations. As mentioned earlier, only four important chromaticity points were tested to avoid undue visual fatigue. The four points were the three points near the R, G, and B primaries (No. 1, No. 4, and No. 8) and one point near the center of the chromaticity diagram (No. 5). We observed that DH’s curves did not significantly differ from those of YJ. The average differences of the color fusion limits, represented in the Euclidean distance in the u´v´ plane, were 0.0124 for the No. 1 point, 0.0023 for the No. 4 point, 0.0132 for the No. 5 point, and 0.0108 for the No. 8 point, respectively. The average difference of the color fusion limits for the four points was 0.0102 in terms of the u’v´ distance. The data for the two observers indicate that their color sensitivity and stereo vision are not different. In clinical tests, the two observers had normal color vision and normal stereo vision: Visual acuities for DH and YJ were 20/25 and 20/20, respectively, in the Snellen chart. Both had normal color vision according to the Ishihara test. In the Farnsworth-Munsell 100-hue arrangement test, the total error scores for DH and YJ were 7 and 0, respectively. A zero score indicates the perfect arrangement of colors, and a large total error score indicates a high number of color misplacements . Both had very low score, that is, high color acuity. Moreover, both had stereo acuity of 40 seconds of arc in the Titmus stereo fly test.
In addition, a better fit may be searched for the observed psychometric functions instead of linear interpolation as in Figs. 5 and 6. To investigate the fitting of psychometric functions, we fitted the observed psychometric function with a logistic function . In order to compare the difference between the use of linear interpolation and the fitting of a logistic function, we measured the Euclidean distance between the color fusion limits obtained by two methods. The average difference value of the color fusion limits was 0.0028 for all the eight chromaticity points. Consequently, the difference in the fitting results was not much to affect the measurement of color fusion limits.
Previous research investigated the binocular color fusion limit for spectral colors, represented as the wavelength difference. However, an investigation of the color fusion limit for non-spectral colors has not been done thus far. Hence, we conducted a quantitative investigation of the color fusion limit for non-spectral colors. The measurements were made at eight chromaticity points on the standard CIE 1976 chromaticity diagram. For the eight chromaticity points, the results of the color fusion limit were represented as a series of ellipses. The semi-minor axis of the ellipses ranged from 0.0415 to 0.0923 in the Euclidean distance in the u’v´ chromaticity diagram while the semi-major axis ranged from 0.0640 to 0.1560. The shapes and directions of rotation of the ellipses were similar to those of MacAdam ellipses for the just-noticeable differences of chromaticity.
We expect that our quantification of the color fusion limit will be utilized for various applications, such as an automatic stereo analyzer to guide content creators in the creation of visually comfortable stereoscopic contents, safety guidelines for watching 3DTV, and stereoscopic video quality metrics.
A male volunteer, Mr. DH Kim, participated in the observations. The authors acknowledge his interest and patience.
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