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As a fundamental metric of human visual system (HVS), contrast sensitivity function (CSF) is typically measured by sinusoidal gratings at the detection of thresholds for psychophysically defined cardinal channels: luminance, red-green, and blue-yellow. Chromatic CSF, which is a quick and valid index to measure human visual performance and various retinal diseases in two-dimensional (2D) space, can not be directly applied into the measurement of human stereo visual performance. And no existing perception model considers the influence of chromatic CSF of inclined planes on depth perception in three-dimensional (3D) space. The main aim of this research is to extend traditional chromatic contrast sensitivity characteristics to 3D space and build a model applicable in 3D space, for example, strengthening stereo quality of 3D images. This research also attempts to build a vision model or method to check human visual characteristics of stereo blindness. In this paper, CRT screen was clockwise and anti-clockwise rotated respectively to form the inclined planes. Four inclined planes were selected to investigate human chromatic vision in 3D space and contrast threshold of each inclined plane was measured with 18 observers. Stimuli were isoluminant blue-yellow sinusoidal gratings. Horizontal spatial frequencies ranged from 0.05 to 5 c/d. Contrast sensitivity was calculated as the inverse function of the pooled cone contrast threshold. According to the relationship between spatial frequency of inclined plane and horizontal spatial frequency, the chromatic contrast sensitivity characteristics in 3D space have been modeled based on the experimental data. The results show that the proposed model can well predicted human chromatic contrast sensitivity characteristics in 3D space.
© 2016 Optical Society of America
1. Introduction
The contrast sensitivity is a measure of fundamental spatio-chromatic properties of HVS. It is typically measured by the detection of thresholds for the psychophysically defined cardinal channels: luminance, red-green, and blue-yellow. Thus, for the luminance channel, the detection thresholds for chromatically neutral stimuli-sinusoidal gratings of a certain spatial frequency are measured and the sensitivity is expressed as an inverse of the detection threshold. Researchers pay much attention to investigate human chromatic visual characteristics [1–9]. Vander Horst and Bouman [10] confirmed, as also Granger [11], that the chrominance CSF has low-pass. Kelly [12] provided an incomplete set of chrominance CSF by using isoluminant red-green gratings. Mullen [13], as also Vander Horst and Bouman [10], presented measurements for red-green and blue-yellow gratings. There are also evidences in the animal world, which indicates the spatial tuning of achromatic and chromatic vision [14,15].
Besides, the effects of luminance contrast on stereo acuity have also been investigated in a number of researches [16–28], and some of them payed additional attention to the effects of chromatic contrast [24]. The consensus of these researches is that stereo acuity improves with increasing chromatic or luminance contrast, providing that the stimulus is processed by ”first-order” stereopsis mechanisms [24, 25, 29]. There is a disagreement over the exact slope of the dependence, but a power-law relationship with a fractional exponent normally provides a reasonable fit for intermediate contrasts. Then Simmons [30] took the behavior at extreme contrast into the fitting process by allowing the fitted curve to asymptote, and provided a more complete description of the data without having to resort to the arbitrary ”kneepoint” determination, which was a necessary component of piecewise linear fits. Therefore, interactions between chromatic- and luminance-contrast sensitive stereopsis mechanisms were proposed.
However, there were few researches which directly applied contrast sensitivity to blue-yellow gratings to 3D space, and CSF of inclined planes to blue-yellow gratings in 3D space was barely considered. Most researches took the binocular disparity as the basis, and so far, no existing perception model considers the influence of chromatic CSF of inclined planes on depth perception in 3D space. Intuitively, according to corresponding model of inclined planes, visual perception quality of inclined planes in 3D space will be strengthened. What’s more, as we all know, some people may be blind to the third dimensional sight, which means stereo blindness, and what they see are flat surfaces. This research also tries to build a vision model or method to check this type visual characteristic. Chromatic CSF, which is a quick and valid index to measure human visual performance and various retinal diseases in 2D space, can not be directly applied to measure the stereo visual performance. Based on the problems mentioned above, we extend traditional chromatic contrast sensitivity test method to 3D space. In our research, we focus on the inclined planes that are not parallel to human face in 3D space. To get more knowledge on human chromatic vision in 3D space, we have clockwise and anti-clockwise rotated the CRT monitor, and select four inclined planes to investigate human chromatic contrast sensitivity.
2. Method
2.1. Subjects
18 healthy observers (28±2 years old) with normal acuity participated in the study. The observers were required to view the gratings monocularly with the other eye occluded. The experiment was undertaken with the understanding and written consent of each subject.
2.2. Apparatus
The stimuli was displayed on a 2D displayed CRT color monitor, with 120Hz frame rate and 1024×768 pixels, which was connected to a graphics card (Cambridge Research Systems, VSG 2/5) in a generic PC. This graphics card has over 14 bits of contrast resolution and is specialized for the measurement of visual thresholds. The gamma nonlinearity of the output luminance was corrected in look-up tables using a Cambridge Research Systems Optical photometer. The spectral outputs of the red, green, and blue phosphors of the monitor were calibrated using a PhotoResearch PR-645 SpectraScan spectroradiometer. The CIE-1931 chromaticity coordinates of the red, green, and blue phosphors were (x = 0.631, y = 0.340), (x = 0.299, y = 0.611), and (x = 0.147, y = 0.073), respectively. The background was achromatic with a mean luminance of 34 cd/m2 at the screen center.
2.3. Color space
Stimuli were represented in a 3D cone-contrast space [31, 32], and for each cone type, every axis was defined by the incremental stimulus intensity to a given stimulus which was normalized by the intensity of the fixed white background, respectively. Cone excitations for the L–, M–, and S–cones were calculated using the cone fundamentals of Smith and Pokorny [33]. A linear transform was calculated to specify the required phosphor contrasts of the monitor for given cone contrasts. Postreceptoral luminance and red-green cone-opponent mechanisms were modeled as linear combinations of cone contrast responses and were isolated by using achromatic (L + M + S) and isoluminant red-green (L − aM) cardinal stimuli, where a is a numerical constant obtained at isoluminance. Stimulus contrast is defined as the vector length in cone contrast units (CC):
where LC, MC, and SC represent the L, M, and S Weber cone-contrast fractions in relation to the L–, M–, and S–cone values of the achromatic background. This metric differs from the conventional luminance contrast by a factor of . For each spatial and temporal frequency, the isolation of the red-green mechanism at isoluminance was estimated by a minimum motion task [34], in which the perceived minimum motion was measured based on the average of at least 10 settings.2.4. Stimuli
Visual stimuli consisting horizontal blue-yellow equiluminant gratings was displayed in 180° phase reversal at 6Hz temporal frequency. Horizontal spatial frequencies ranged from 0.05 to 5 c/d. A central cross (1° of visual field) was used for fixation. Eight contrast levels were used for each spatial frequency. Chromaticities were at the highest contrast: for red, u9 = 0.288, v9 = 0.480; for green, u9 = 0.150, v9 = 0.480; for blue, u9 = 0.219, v9 = 0.420; for yellow, u9 = 0.219, v9 = 0.540. Stimuli were displayed against a background of the same mean luminance (34.3cd/m2) and chromaticity (u9 = 0.219, v9 = 0.480).
2.5. Procedure
In this paper, thresholds were measured using a two-interval forced-choice staircase procedure, a ”2-down, 1-up” weighted staircase with audio feedback. Presentation intervals were 500 ms each, separated by 500 ms. Subjects responded with a button-press when the test stimulus appeared. A reversal was defined when the subject responded incorrectly after a minimum of two consecutive correct responses. Each staircase terminated after six reversals. After the first reversal, stimulus contrast was raised by 25% following one incorrect response and lowered by 12.5% following two consecutive correct responses. For any given staircase session, the number of total trials fluctuated between approximately 35 and 65. The threshold value was calculated as the arithmetic mean of the last five reversals of the staircase.
Firstly, based on the traditional experiment condition, the observers were instructed to sit 60 cm far from the monitor with their face parallel to the screen in a dimly lit room (shown in Fig. 1(a)). The right eye was patched, and the left eye was used for measurements. For each grating and spatial frequency, the stimulus was first shown at the highest contrast. Horizontal spatial frequencies used in our experiments ranged from 0.05 to 5 c/d. The final results were the average across 18 subjects. Then the screen was clockwise and anti-clockwise rotated with 15° interval angles respectively, and clockwise rotating was shown in Fig. 1(b). Four inclined planes were selected and the tests were repeated.
Fig. 1 (a) Traditional experiment condition. (b) Experiment condition when the screen is clockwise rotated with inclined angle θ.
3. Results
3.1. Theory analysis
Define the spatial frequency of the inclined plane as fθ (shown in Fig. 2(a)) and horizontal spatial frequency as fu. Take the clockwise rotate direction as an example. When human in front of plane 1 observes inclined plane 2, owing to the existence of inclined angle θ, the projection from inclined plane 2 to plane 1 is cosθ times the length of plane 2, and the number of the gratings per degree subtended at the eye is also cosθ times that of the original. Therefore, the relationship between fθ and fu can be established according to the concept of the spatial frequency, shown in Eq. (2).
Fig. 2 (a) Geometric scheme when the screen is clockwise rotated with inclined angle θ. (b) Geometric scheme of the anti-clockwise rotated CRT screen.
Besides, based on the geometric symmetry, the relationship between spatial frequency of inclined plane in anti-clockwise orientation (shown in Fig. 2(b)) and horizontal spatial frequency fu is the same as Eq. (2).
3.2. Data analysis
Figure 3 shows contrast sensitivity to the chromatic stimuli based on the average results of all observers. Solid dots indicates clockwise measured data by grating test system. Open circles are anti-clockwise measured data. For each inclined plane, contrast sensitivity is low-pass function both in the clockwise and anti-clockwise direction. The measured data of clockwise direction are similar with those of anti-clockwise direction, which demonstrate that contrast sensitivity characteristics of human eyes have the nature of geometric symmetry. All data of inclined planes in clockwise direction are shown in Fig. 4.
Fig. 3 Measured data of each inclined plane. Solid dots are clockwise measured data; Open circles represent anti-clockwise measured data. Seven spatial frequencies are shown as marked. Each subgraph represents a fixed inclined angle with 15° interval.
Figure 4 indicates that contrast sensitivity to blue-yellow gratings varies from different inclined planes, and each curve has similar low-pass characteristics. The contrast sensitivity increases with the inclined angles at the same spatial frequency. All curves are practically independent of spatial frequency up to 0.3 and start to decrease between 0.3 and 1 c/d. The drop point of each inclined plane gradually moves back with the increasing inclined angle. At high spatial frequency, contrast sensitivity decreases rapidly, and the decent speed is reduced with the increase of inclined angle.
Then we applied linear interpolation method to compute more data and obtained the surface of human eyes’ contrast sensitivity characteristics to blue-yellow gratings in 3D space (shown in Fig. 5).
Fig. 5 (a) The surface of contrast sensitivity characteristics to blue-yellow gratings in 3D space. (b) The vertical view of (a).
4. Model
Based on the analysis above, also the previous work [13] [35], we used a low-pass function to quantify the measured data of each inclined plane, defined as A(fθ, θ), shows in Eq. (3).
Here, a, b, c, d and e are constant parameters, fθ is the spatial frequency. Based on the above measured data, all inclined planes are fitted with a low-pass function, shown in Eq. (4)–Eq. (8): From Eq. (4) to Eq. (8), it can be seen that a, b, d and e of each inclined plane are similar, while parameter c is different obviously. The trend of c is similar to cosine curve shown in Fig. 6(a). The comparison between values of c and cosine curve shown in Fig. 6(b).Fig. 6 (a) Parameter c of each inclined plane. (b) The comparison between normalized values of c and cosine values. Four inclined angles are shown as marked (0°, 15°, 30°, 45° and 60°).
By constantly revised all parameters, we fitted the final model of contrast sensitivity to blue-yellow gratings as Eq. (9). fθ is the spatial frequency (unit:c/d) and θ is the inclined angle (uint:degree).
The contrast sensitivity to blue-yellow gratings of each inclined plane obtained from the model are show in Fig. 7, and also clockwise measured data. It reveals that the model proposed in this paper is consistent with characteristics of human color vision. Its surface scheme and the vertical view are shown in Fig. 8, and the two subgraphs have great similarity with Fig. 5, which further confirms the validity of the proposed model.
5. Conclusion
In this paper, traditional CSF has been extended into 3D space. Four inclined planes were selected to investigate human stereo chromatic vision. Contrast sensitivity to blue-yellow gratings was measured based on subjective tests, and the threshold was calculated as the inverse function of the pooled cone contrast threshold. According to the relationship between inclined spatial frequency and horizontal spatial frequency, a well fitted model was built up. Experimental results show that the proposed model can effectively describe human spatial sensitivity characteristics to blue-yellow gratings in 3D space.
Acknowledgments
This research is partially supported by the National Natural Science Foundation of China (No.61471260 and No.61271324), and Program for New Century Excellent Talents in University (NCET-12-0400).
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