The application of stereoscopic display, virtual reality, and head-mounted devices requires research on binocular properties of the human vision system (HVS). Threshold measurement is one method to investigate the characteristics of visual perception. At the same time, there are some color vision phenomena related to binocular vision systems that cannot be explained. One of the phenomena is called hue cancellation, which can also occur in binocular vision. Thus, it is called binocular hue cancellation and is a special phenomenon in binocular color fusion. Currently, most studies on binocular color fusion focus on the reproduction of glossiness in binocular color fusion, quantitative measurement of the thresholds of binocular color fusion, and the distinction between binocular color fusion and rivalry. However, as far as we know, no particular studies on binocular hue cancellation have been reported. To investigate the color vision mechanism of this particular phenomenon, we design a psychophysical experiment. We also investigate the opposite color directions and hue cancellation thresholds within the binocular color fusion that can perceive gray in the CIELAB color space and represent the experimental results in the LMS, Macleod-Boynton, and DKL color spaces respectively to provide experimental data for exploring the visual properties of HVS and the mechanism of binocular color.

We research a Samsung 3D display (S23A950D) with 2D/3D switching capability, requiring the observer to wear specific 3D switching glasses to obtain binocular vision. Eight opposite color directions are selected at 22.5° intervals in the isoluminance plane of CIELAB color space, and color stimulus sample pairs are selected at equal intervals in each direction (Fig. 4). The experiment is conducted among five college students between the ages of 22 and 25 with normal vision, and each of them experiences at least 19800 color stimuli. We carry out the experiment in a dark room and first employ the adjustment method to determine the opposite color directions in which the binocular hue cancellation phenomenon could occur and the initial values of the binocular hue cancellation thresholds. Then the limit method is adopted to accurately determine the binocular hue cancellation thresholds.

The experimental results show that binocular hue cancellation phenomenon could occur only when red-green (R-G), yellow-blue (Y-B), and yellow green-purple (YG-P) color pairs are combined (Fig. 6). The binocular hue cancellation thresholds of the five observers are expressed in the CIELAB, LMS, Macleod-Boynton, and DKL color spaces respectively. In the CIELAB color space, the range of binocular hue cancellation thresholds in the R-G color direction is 11.36-13.58, with a mean value of 13.03, and the range of thresholds in the Y-B direction is 8.14-10.07, with a mean value of 9.25. The range of thresholds in the YG-P direction is 11.26-15.55, with a mean value of 13.02. Among them, the Y-B combination has the smallest threshold, and the average thresholds of the R-G and YG-P combinations are almost equal (Table 2). After exchanging the colors viewed by the left and right eyes, the obtained binocular hue cancellation thresholds are similar, which indicates that the dominant eye does not affect the binocular hue cancellation phenomenon. Five observers are largely different in thresholds of the YG-P direction, and one of them has much smaller thresholds in the R-G direction than the others, showing individual differences in the binocular hue cancellation phenomenon (Fig. 7). In the LMS color space, the six color directions are uniformly distributed and almost divide the L-M plane into six equal parts. The color directions in the L-M plane and the L-S plane are symmetric about the S axis, and the thresholds in the L-M plane are shown as a straight line parallel to the S axis (Fig. 8). In the Macleod-Boynton chromaticity diagram, the binocular hue cancellation thresholds of six colors are close to the white point, indicating the saturation of the colors which can produce the binocular hue cancellation phenomenon is low (Fig. 9). In DKL space, the direction of YG-P overlaps with the cardinal direction S-(L+M), while the directions of R-G, Y-B, and the cardinal direction L-M are not close to each other (Fig. 10).

The binocular hue cancellation phenomenon is investigated through a visual psychophysics experimental method. The results show that the particular phenomenon can only occur in three color directions of red-green, yellow-blue, and yellow green-purple, which means observers can only perceive gray in the three directions. There are individual differences in binocular hue cancellation thresholds of the five observers, but the thresholds in the yellow-blue direction are all minimal. Because the study on visual mechanisms is strongly related to the choice of color space, the binocular hue cancellation thresholds of the five observers are expressed in the color spaces of CIELAB, LMS, Macleod-Boynton, and DKL respectively. The binocular hue cancellation directions are more uniformly distributed in LMS, Macleod-Boynton, and DKL color space approximately in six equal parts, implying the specificity of these six hues. The binocular hue cancellation threshold occupies only a small range in Macleod-Boynton color space, thus indicating that the binocular hue cancellation phenomenon not only occurs in the three color directions but also occupies only a small range within the color range that can be perceived by the human visual system.