Resolution of Temporal-Multiplexing and Spatial-Multiplexing Stereoscopic Televisions

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  • ABSTRACT

    Stereoscopic (S3D) displays present different images to the two eyes. Temporal multiplexing and spatial multiplexing are two common techniques for accomplishing this. We compared the effective resolution provided by these two techniques. In a psychophysical experiment, we measured resolution at various viewing distances on a display employing temporal multiplexing, and on another display employing spatial multiplexing. In another experiment, we simulated the two multiplexing techniques on one display and again measured resolution. The results show that temporal multiplexing provides greater effective resolution than spatial multiplexing at short and medium viewing distances, and that the two techniques provide similar resolution at long viewing distance. Importantly, we observed a significant difference in resolution at the viewing distance that is generally recommended for high-definition television.


  • KEYWORD

    Stereoscopic 3D displays , Spatial multiplexing , Temporal multiplexing , Resolution

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  • [FIG. 1.] Three methods of stereo image presentation in spatial multiplexing [5, 6]. Same-line allocation uses the same rows from each eye’s image. Alternate-line allocation recruits rows from each eye’s image in an alternating fashion. Both-line allocation uses two rows from the left and right eyes’ images to generate one row in the stereo image.
    Three methods of stereo image presentation in spatial multiplexing [5, 6]. Same-line allocation uses the same rows from each eye’s image. Alternate-line allocation recruits rows from each eye’s image in an alternating fashion. Both-line allocation uses two rows from the left and right eyes’ images to generate one row in the stereo image.
  • [FIG. 2.] Stimuli for the visual acuity task. The stimuli followed the design criteria for the most widely used clinical visual acuity test [11]. Letter height was five times letter stroke width. Letter width was four times stroke width. Spacing between letters was two times letter width. Three randomly chosen letters were presented on each trial.
    Stimuli for the visual acuity task. The stimuli followed the design criteria for the most widely used clinical visual acuity test [11]. Letter height was five times letter stroke width. Letter width was four times stroke width. Spacing between letters was two times letter width. Three randomly chosen letters were presented on each trial.
  • [FIG. 3.] Schematic of the algorithm used by the spatially multiplexed TV. The middle panel (yellow) shows image data sent to the TV. Black squares represent black pixels in the image data, and bright squares represent white pixels in the image data. The pixel rows are numbered from 1 to 9 so that the reader can keep track of odd and even rows. The left (pink) and right (green) panels show the displayed images presented to the left and right eyes respectively. For the left eye, the first frame presents image data from the odd rows to the odd rows in the display; the second frame presents image data from the even rows to the odd rows in the display. The x’s indicate rows that are not seen by the left eye, due to the polarization of the eyewear. The two frames are temporally averaged by the visual system to create the apparent image, labeled “time average of frames 1 & 2.” The situation is the same for the right eye, except that the image data are delivered to even rows. Note that the images displayed to the left and right eyes are identical, except that the right-eye image is one pixel row lower on the display screen.
    Schematic of the algorithm used by the spatially multiplexed TV. The middle panel (yellow) shows image data sent to the TV. Black squares represent black pixels in the image data, and bright squares represent white pixels in the image data. The pixel rows are numbered from 1 to 9 so that the reader can keep track of odd and even rows. The left (pink) and right (green) panels show the displayed images presented to the left and right eyes respectively. For the left eye, the first frame presents image data from the odd rows to the odd rows in the display; the second frame presents image data from the even rows to the odd rows in the display. The x’s indicate rows that are not seen by the left eye, due to the polarization of the eyewear. The two frames are temporally averaged by the visual system to create the apparent image, labeled “time average of frames 1 & 2.” The situation is the same for the right eye, except that the image data are delivered to even rows. Note that the images displayed to the left and right eyes are identical, except that the right-eye image is one pixel row lower on the display screen.
  • [Table 1.] Letter sizes presented at the four viewing distances
    Letter sizes presented at the four viewing distances
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  • [FIG. 4.] Psychometric data from one subject in one condition. Proportion of correct letter identification is plotted as a function of letter stroke width. Black squares indicate the data, and the black curve is the Gaussian function that best fits those data. The red square is the estimate of effective resolution. The error bar indicates the 95% confidence interval for the estimate.
    Psychometric data from one subject in one condition. Proportion of correct letter identification is plotted as a function of letter stroke width. Black squares indicate the data, and the black curve is the Gaussian function that best fits those data. The red square is the estimate of effective resolution. The error bar indicates the 95% confidence interval for the estimate.
  • [FIG. 5.] Effective resolution for temporal and spatial multiplexing. Effective resolution is plotted as a function of viewing distance in units of screen height (H) for the two types of multiplexing. The data have been averaged across subjects. Asterisks indicate statistically significant differences (p<0.01, paired t-test, two-tailed).
    Effective resolution for temporal and spatial multiplexing. Effective resolution is plotted as a function of viewing distance in units of screen height (H) for the two types of multiplexing. The data have been averaged across subjects. Asterisks indicate statistically significant differences (p<0.01, paired t-test, two-tailed).
  • [FIG. 6.] Apparatus in Experiment 2. A CRT was used to present both eyes’ images. The left half of the screen presented the left eye’s image and the right half the right eye’s image. Four front-surface mirrors created the stereoscopic view at the appropriate distance. The orientations of mirrors were adjusted so that the optical and vergence distances to the images always matched.
    Apparatus in Experiment 2. A CRT was used to present both eyes’ images. The left half of the screen presented the left eye’s image and the right half the right eye’s image. Four front-surface mirrors created the stereoscopic view at the appropriate distance. The orientations of mirrors were adjusted so that the optical and vergence distances to the images always matched.
  • [Table 2.] Letter Sizes in Experiment 2
    Letter Sizes in Experiment 2
  • [FIG. 7.] Effective resolution for simulated temporal and spatial multiplexing. Effective resolution is plotted as a function of viewing distance in screen heights (H) for temporal multiplexing, spatial multiplexing with alternate-line allocation, and spatial multiplexing with both-line allocation. The data have been averaged across subjects. Asterisks indicate statistically significant differences (p<0.01, paired t-test, two-tailed).
    Effective resolution for simulated temporal and spatial multiplexing. Effective resolution is plotted as a function of viewing distance in screen heights (H) for temporal multiplexing, spatial multiplexing with alternate-line allocation, and spatial multiplexing with both-line allocation. The data have been averaged across subjects. Asterisks indicate statistically significant differences (p<0.01, paired t-test, two-tailed).
  • [FIG. 8.] Visual processing of a scene presented on a display, at short viewing distance (upper panel) and long viewing distance (lower panel). The displayed images are identical in the two cases. The central lobe in the leftmost plot at the bottom of each panel is the signal from the original scene. The side lobes are aliases, due to sampling and displaying. From the viewer’s eye, the image subtends a larger angle at short viewing distance and a smaller angle at long distance. As a result, the amplitude spectrum is respectively narrower and wider at those distances (second plots from left). Then the images undergo optical and neural filtering, which we represent by multiplication with the CSF (third plots from left), yielding the amplitude spectra of the image after early visual processing (fourth plots from left). The aliases are still present at the short viewing distance, but have been filtered out at the long distance.
    Visual processing of a scene presented on a display, at short viewing distance (upper panel) and long viewing distance (lower panel). The displayed images are identical in the two cases. The central lobe in the leftmost plot at the bottom of each panel is the signal from the original scene. The side lobes are aliases, due to sampling and displaying. From the viewer’s eye, the image subtends a larger angle at short viewing distance and a smaller angle at long distance. As a result, the amplitude spectrum is respectively narrower and wider at those distances (second plots from left). Then the images undergo optical and neural filtering, which we represent by multiplication with the CSF (third plots from left), yielding the amplitude spectra of the image after early visual processing (fourth plots from left). The aliases are still present at the short viewing distance, but have been filtered out at the long distance.
  • [FIG. 9.] Sampling and display process. The original image goes through antialiasing and sampling. The antialiasing filter in the second panel is a cubic-convolution interpolation kernel. Sampling is represented in the third panel. In the spatial domain, this is equivalent to multiplying by an impulse-train function with a period of 1/fs. In the frequency domain, it is equivalent to convolving with an impulse-train function with period fs. The sampled information is presented on a display with finite pixel size. In the spatial domain, this is equivalent to convolving the sampled information with a rectangular function whose extent is the same as a pixel on the display. In the frequency domain, it is equivalent to multiplying by the Fourier transform of the rectangular function.
    Sampling and display process. The original image goes through antialiasing and sampling. The antialiasing filter in the second panel is a cubic-convolution interpolation kernel. Sampling is represented in the third panel. In the spatial domain, this is equivalent to multiplying by an impulse-train function with a period of 1/fs. In the frequency domain, it is equivalent to convolving with an impulse-train function with period fs. The sampled information is presented on a display with finite pixel size. In the spatial domain, this is equivalent to convolving the sampled information with a rectangular function whose extent is the same as a pixel on the display. In the frequency domain, it is equivalent to multiplying by the Fourier transform of the rectangular function.
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  • [FIG. 10.] Simulation of appearance without discrete sampling. The target image, which is the letter ‘A’, is 10×8 arcmin. The middle panel is the simulated appearance in the spatial domain. The right panel is the appearance in the frequency domain.
    Simulation of appearance without discrete sampling. The target image, which is the letter ‘A’, is 10×8 arcmin. The middle panel is the simulated appearance in the spatial domain. The right panel is the appearance in the frequency domain.
  • [FIG. 11.] Simulation of temporal multiplexing. From left to right are the target image presented on the display, its appearance in the spatial domain, and its appearance in the frequency domain. From top to bottom are the results for pixel sizes of 2, 1, and 0.5 arcmin.
    Simulation of temporal multiplexing. From left to right are the target image presented on the display, its appearance in the spatial domain, and its appearance in the frequency domain. From top to bottom are the results for pixel sizes of 2, 1, and 0.5 arcmin.
  • [FIG. 12.] Simulation of spatial multiplexing. From left to right are the target image presented on the display, its appearance in the spatial domain, and its appearance in the frequency domain. From top to bottom are results for pixel sizes of 2, 1, and 0.5 arcmin.
    Simulation of spatial multiplexing. From left to right are the target image presented on the display, its appearance in the spatial domain, and its appearance in the frequency domain. From top to bottom are results for pixel sizes of 2, 1, and 0.5 arcmin.