Characterization of 3-D Gray-to-Gray Crosstalk with a Matrix of Lightness Differences

Stereoscopic televisions, which are mainly striped-retarder displays with passive glasses or time-sequential displays with active glasses, are emerging in the consumer market.  3-D crosstalk is an important characteristic that defines the quality of these displays.  A new crosstalk metric is proposed that uses an intuitive matrix representation with perceptually relevant lightness-difference values instead of the single percentage value that is often used.

by Hans Van Parys, Kees Teunissen, and Aleksandar Ševo

STEREOSCOPIC TVs are becoming commonplace in the consumer market.  Available models are usually striped-retarder displays with passive glasses or time-sequential displays with active glasses.  The most important characteristic in defining the quality of 3-D image perception, and therefore the quality of the user experience, is inter-ocular crosstalk.  The use of a good characterization method for crosstalk is crucial to enable direct comparison of the performance of 3-D TVs and technologies.  This means a characterization method that is well-defined and easy to measure, calculate, and interpret.  Only with a good characterization method can the performance of different stereoscopic displays be compared and insight be gained as to the source and nature of crosstalk, which will, in turn, lead to improvements in 3-D performance.

Different 3-D crosstalk formulas are proposed in the literature.^1-3  A commonly used crosstalk definition is discussed in more detail in the next paragraph.  The shortcomings of this characterization are shown, and a better characterization method is derived in the following paragraphs.

Commonly Used 3-D Crosstalk Characterization

A 3-D crosstalk characterization commonly used in the industry today is provided in the equation below.  It is based on the combination of white and black test images for the left and right views (see Fig. 1) when the luminance is measured through, for instance, the left lens of the 3-D glasses.⁴ The equation below assumes “identical” behavior for left and right views.

in which L_M,N is the measured luminance with M in the observed and N in the unobserved image. M and N can be white (W) or black (B).

However, this formula has several severe drawbacks, especially for the characterization of time-sequential 3-D LCDs.  First of all, the characterization of 3-D crosstalk with only one number does not make sense for many 3-D display types: 3-D crosstalk can be heavily dependent on the applied gray levels, and, as such, also on the image content.  This has already been noticed and concluded by, for instance, Shestak et al.³ and Barkowsky et al.⁵

A second drawback is that white-to-black and black-to-white crosstalk are mixed into one formula.  This makes the interpretation of the result less than obvious.  Moreover, it becomes problematic when L_W,B is higher than L_W,W – this is possible in time-sequential 3-D displays: with L_W,B in the nominator, the crosstalk will decrease with higher L_W,B, although more crosstalk will be visible.  An improvement can be made here by replacing L_W,B with L_W,W.

Finally, Xia et al.⁶ found a poor correlation between perceived crosstalk and crosstalk as determined by several crosstalk equations.  In particular, the white-to-black crosstalk (see, e.g., Fig. 2) is much more visible than the black-to-white crosstalk, although the crosstalk percentage values could be identical. This clearly demonstrates the necessity for a perceptually relevant characterization method.

Fig. 2:  The image at the far right shows the effect of visible crosstalk.

A New Method for 3-D Crosstalk Characterization

A proposed measurement setup is shown in Fig. 3.  A luminance meter is directed perpendicularly toward the center on the display surface.  The 3-D glasses are mounted in front of the luminance meter with the meter measuring through one of the lenses.  The glasses should be mounted in a position similar to what their position would be if a person was wearing them to watch the 3-D display.

Fig. 3:  This measurement setup includes a stereoscopic display, 3-D glasses, and a luminance meter directed perpendicularly toward the display and measuring through one of the lenses of the glasses.

During the measurement, a range of test patterns are rendered on the display and for each test pattern, the luminance is measured through the glasses.  These test patterns are generated with different combinations of two gray levels for the left- and the right-eye image as shown in Fig. 4 (left).

Conventionally, only the four combinations of full black (B) and full white (W) are measured.  Especially for the time-sequential 3-D LCDs, this leads to an incomplete characterization.  For these displays, the crosstalk is strongly dependent on the particular combination of gray levels for both eyes, due to intrinsic properties of LCDs and response-time compensation technologies.  Thorough characterization of time-sequential 3-D displays may require as many as 17 gray values per view.  This leads to a 17 × 17 measurement grid containing 289 cells.  However, for convenience, we will restrict the examples in this paper to a 9 × 9 measurement grid.

Interpretation of the Measurement Grid

The measurement grid in Fig. 4 (right) shows the luminance values as recorded by the luminance meter.  In this example, the applied gray values (in the gamma-corrected domain) on an 8-bit scale are 0, 32, 64, 96, 128, 160, 192, 224, and 255.  The value of 0 corresponds to full black and 255 to full white.  In the grid, the rows correspond to the values of the unobserved right-eye image and the columns to the values of the observed left-eye image.  Obviously, the measurement grid could also have been measured for the right-eye image as the observed image and the left-eye image as the unobserved image.  For most stereoscopic systems, however, the obtained measurement grid would be the same.

Fig. 4:  At left are test images for the left eye (observed image) and the right eye (unobserved image); at right is a measurement grid for the combination of left-eye (observed image) and right-eye (unobserved image) gray levels.

In the upper left corner, we find the level when full black is applied to both images (left and right view), so this number could be called the “black offset,” and it can have multiple origins in the display as well as in the measurement setup.  In the lower right corner, we find the full-white level.

On the diagonal, we find the luminance values for the observed left-eye image when the left and right images have equal gray levels.  So, on the diagonal we find per definition the crosstalk-free luminance values for the applied gray levels, or in other words, the “target luminance levels.”

When the system is crosstalk free, i.e., when the observed image is not influenced by the unobserved image, the luminance values should be constant down every column because in theory the gray level of the unobserved image (right eye in this example) should have no impact on the gray-level measured from the observed image (left eye in this example).  That would represent a case of no crosstalk at all.  In this example, this is apparently not the case; in some cells, the luminance is higher than the luminance on the diagonal.  In other cells, it is lower.

Conversion to a Lightness Value

Instead of calculating crosstalk numbers by subtracting and dividing luminance values, we will first perform a conversion to a “lightness value.”  This step will make the resulting crosstalk figure more perceptually uniform.

To do this, we first subtract the “black offset” and normalize on the full-white luminance level.  Then we apply the lightness formula from the CIELab colorspace.⁷  We propose to use a scale factor of 255 (8-bit equivalent) instead of 100, as this makes the formula more intuitive for engineers working with image processing: the results can be interpreted as 8-bit (gamma-corrected) gray values.  Besides, the scale factor of 255 better suits the rounding used in the last step of the procedure.

For any cell on coordinate r,c (where r is unobserved image and c is observed image) on the measurement grid, the conversion from luminance to 8-bit normalized lightness values (0..255) is expressed by the following formula:

where Y_r,c is the luminance in each cell as measured by the luminance meter, L_r,c is the corresponding lightness, Y_0,0 is the “black offset,” and Y_N,N is the full-white level.  As an alternative, a simplified formula with a pure power law could also be used:

The exponent 1/γ can be discussed.  We propose to use 1/2.2 because, although 1/2.4 is a closer match to the overall CIELab function, 1/2.2 is a better match where it matters most, i.e., for low light values.

The conversion of the luminance grid to a lightness grid is shown in Fig. 5 (left).  This conversion can be interpreted as follows.  The numbers show what lightness is perceived for any combination of gray-level values for the observed and unobserved image.  Again, on the diagonal we find the “target lightness” for the columns.  The difference between a cell’s lightness and the target lightness of its column can be qualified as the visible crosstalk.  Therefore, to construct the final crosstalk grid, we subtract from the value in every cell the value on the diagonal in the same column and round the result to the nearest integer.

As a consequence, the result will show zeros on the diagonal, and this fits with our previous observation that there is no visible crosstalk for combinations on the diagonal, per definition.  Please notice that with our 8-bit representation, rounding leaves enough precision for practical applications and makes interpretation faster.

An additional enrichment is a small modification on the sign: for all cells above the diagonal, we will invert the sign.  This will give a consistent relationship between the sign of the crosstalk number and the direction of crosstalk: a positive number will always denote a type of crosstalk that has its luminance level between the observed and unobserved luminance levels (see the equation below).

Finally, the crosstalk grid can be made even more intuitive by applying a bipolar color map.  For example, in Fig. 5 (right), crosstalk with a positive number obtains a blue color, crosstalk with a negative number obtains a red color, and crosstalk-free cells are black.  The more crosstalk, the more saturated the color.  The result is a gray-to-gray crosstalk grid in a perceptually uniform lightness domain that can be interpreted quickly, without the necessity for a three-dimensional graph.

Fig. 5:  At left is a measurement grid converted to lightness. A final crosstalk representation as a grid of lightness differences appears at right.

The bipolar color map in Table 1 is inspired by a submission in the Matlab Central File Exchange⁸ and describes the exact color mapping.  In Table 1, a color value of one is the maximum value for that color.  Outside the range of [-64, 64] colors are clipped to the values for -64 or 64.  The colors for crosstalk numbers in between those mentioned in the table are linearly interpolated.

Interpretation of the Crosstalk Grid

Contrary to crosstalk percentages, the lightness-difference-based crosstalk numbers have a more perceptually intuitive meaning.  The conversion to lightness makes the result an approximation for perceptual uniformity.  The absolute value of the crosstalk number is a measure of the visibility of the crosstalk – it denotes how many “gamma-corrected gray-level values” (on an 8-bit scale) the crosstalk is away from the target level.

In the lower left corner of the grid, we find the white-to-black crosstalk, generally the most dominant crosstalk factor in the display, and in many other 3-D characterization methods the only crosstalk number that is focused upon.

The sign of a crosstalk number denotes the direction of crosstalk.  Striped-retarder stereoscopic displays will generally only show positive crosstalk numbers.  This type of crosstalk is due to leakage of the light intended for one view into the other view.  In time-sequential stereoscopic displays, however, crosstalk with a negative number is also present.  The origin of this is “overcompensated” crosstalk or so-called “overshoots”.

This method could be seen as a simplification of the method using the DICOM standard and the concept of just-noticeable differences (JNDs) as proposed by Teunissen et al.⁹  This is shown in Fig. 6, where a comparison is made between the two methods.  The middle grid shows the ΔJNDs calculated from the same luminance measurements and adapted with the sign and color conventions as proposed here.  In the right grid, the ΔJNDs are scaled for equal numbers on white-to-black crosstalk.  The similarity between lightness differences and (scaled) ΔJNDs is clearly visible.  This observation supports the correspondence between our measured crosstalk values (Fig. 6, left) and the (relative) severity of the perceived crosstalk.

Fig. 6:  Above are comparisons of the lightness differences (left) with ΔJNDs (middle) and scaled ΔJNDs (right).

The relationship between the level of measured crosstalk and acceptability is not straightforward.  The concept of JND, as introduced by Teunissen et al.,⁹ does provide an answer if crosstalk is just visible (JND = 1), perceptible (JND ≥ 3), or easily visible (JND ≥ 10).  However, this is calculated for the most critical case, e.g., a white bar on a black background.  For natural images, this critical pattern may not occur or if it occurs, may even be unnoticed.  Also, motion in the image may draw attention away from crosstalk.  Finally, some image impairments remain unnoticed until someone points them out.  After that, those impairments may become unacceptable, while they initially were unnoticed.

A New Way of Looking at Crosstalk

We presented a new method of crosstalk characterization that is suited for all types of stereoscopic displays and is particularly useful for time-sequential stereoscopic displays.  The result is a matrix of gray-to-gray crosstalk numbers to be interpreted as corresponding gray-level offset or lightness-based difference values.  This representation is a good approximation for perceptual uniformity and clearly shows visibility differences in perceived crosstalk for different gray-level transitions.  It allows a quick calculation and analysis of the complete crosstalk behavior of a stereoscopic display device.  Although there are no clear guidelines for crosstalk in terms of acceptability, system developers may strive for lightness difference values less than 5.

References

¹A. J. Woods, “Understanding Crosstalk in Stereoscopic Displays,” Keynote Presentation at the 3DSA (Three-Dimensional Systems and Applications) Conference, Tokyo, Japan, May 2010.

²A. Abileah, “3-D Displays: Technologies and Testing Methods,” J. Soc. Info. Display 19/11, 749–763 (2011).

³S. Shestak, et al., “Measuring the Gray-to-Gray Crosstalk in a LCD Based Time-Sequential Stereoscopic Displays,” SID Symposium Digest Tech Papers 41, 132–135 (2010).

⁴J.-C. Liou, K. Lee, F.-G. Tseng, J.-F. Huang, W.-T. Yen, and W.-L. Hsu, “Shutter Glasses Stereo LCD with a Dynamic Backlight,” Proc. SPIE, Stereoscopic Displays and Applications XX 7237, 72370X (2009).

⁵M. Barkowsky et al., “Crosstalk Measurements of Shutter Glasses 3-D Displays,” SID Symposium Digest Tech. Papers 42, 812–815 (2011).

⁶Z. Xia, X. Li, Y Cui, L Chen, and K. Teunissen, “Perceptual Correspondence of Gray-to-Gray Crosstalk Equations for Stereoscopic Displays,” Proc. IDW/AD ’12, 581–584 (2012).

⁷Colorimetry, 3rd edition. CIE 15:2004. ISBN 978-3-901906-33-6.

⁸G. Ridgway, “Bipolar Colormap,” submission in the Matlab Central File Exchange, 04 Dec 2009.

⁹K. Teunissen et al., “Perceptually Relevant Characterization of Stereoscopic Displays,” SID Symposium Digest Tech Papers 42, 994–997 (2011). •