Evaluating Display Device Performance
Dear Gary: In the “Calibration Equipment Shootout” article in Issue 79, December 2003 of Widescreen Review, the three manufacturers of color measuring systems were discussing a way to evaluate display devices using a number that Mark Hunter of Milori, Inc. called “total xy distance to the goal.” However, the interview didn’t go into much detail on what exactly that phrase refers to, or how it is calculated. Can you clarify?
Ryan Richelieu, San Dimas, California
Video Technical Editor Greg Rogers Comments:
In the interview, Editor Gary asked if there was a single value metric that would describe how accurately a display’s gray scale tracked the D65 reference target. As I’ve explained in past reviews and in this column, Correlated Color Temperature (CCT) is insufficient to adequately describe the color of gray because there are an infinite number of points on the CIE x,y diagram that all have the same CCT, but are different colors of gray. Let’s examine this a little closer before I answer your question, and Gary’s. The original concept of color temperature describes the color of the light emitted when carbon is heated to extreme temperatures. At 5000K (degrees Kelvin) the color is perceived as a reddish shade of white. At 10000K it appears as a bluish shade of white. As the temperature of carbon is changed, the color of the emitted light can be plotted on a CIE x,y Chromaticity diagram as a curved line near the center of the Spectral Locus. This is known as the Planckian Locus, or the black-body curve. White (or gray) hues are assigned a Correlated Color Temperature value that is equal to the color temperature of the white they most closely resemble on the black-body curve. Hence, many different shades of white with the same CCT lie along lines that cross the black-body curve in a roughly vertical direction. These are known as iso-thermal lines. The white reference standard for video is called D65, and it has a CCT of 6504K (usually rounded off to 6500K). But more importantly, D65 has a unique CIE (x, y) value of (0.3127, 0.3290) that lies slightly above the black-body curve. Other shades of white on the same iso-thermal line also have the same 6500K correlated color temperature, but appear greenish as they get farther above the black-body curve, and become more of a magenta hue as they are located farther below the curve. This is the reason that Correlated Color Temperature is inadequate to describe the color of white. Any competent professional calibrator knows that it is crucial to adjust the gray scale to match the x,y value of D65 as closely as possible, and it is insufficient to just maintain a color temperature close to 6500K. This prompted Gary to ask if there is a better single value metric that indicates how closely a gray scale color matches the color of D65. In the interview, it was suggested that a possible metric would be the distance from each gray scale x,y value to the D65 x,y reference. That distance is simply the square root of the sum of the x and y distances each squared. D = sqrt ( (x - 0.3127)^2 + (y - 0.3290)^2 ). The problem with this simple metric is that the CIE x,y color space is perceptually non-uniform. Two gray colors may be the same distance from D65, but lie in different directions from D65. In that case, they will have the same value of D, but one may be perceived as a different shade of gray than D65, while the other may appear to be virtually the same as D65. In other words, the x,y distance metric is not the best indicator of how closely a gray color matches D65. Fortunately, a better solution exists. The CIE x,y chromaticity can be transformed into a more perceptually uniform color space. There have been many attempts to find the “best” transformation and none are perfect. Two uniform color spaces are recommended by the CIE, the1976 CIELUV and 1976 CIELAB uniform color spaces. Both are about equally uniform (or non-uniform), but the CIELUV space has some advantages for video display analysis, so it will be used here. The x and y values are converted into u’ and v’ values using a simple mathematical transform. The distance from D65 (also transformed into u’v’) is computed using normalized values of u’ and v’. The resulting value is known as dE (delta-E). The dE value provides a measure of the perceptual difference between two colors; in this case a gray scale color and the D65 white reference. The dE value also takes into account differences in Lightness (brightness) when they exist. The u’v’ transform is straightforward: u’ = 4x / (-2x + 12y + 3) and v’ = 9y / (-2x + 12y + 3) For a D65 white reference, and no difference in Lightness, dE simplifies to: dE = 1300 * sqrt ( (u’ - 0.1978)^2 + (v’ - 0.4683)^2 ) A dE value of about 3 corresponds to 1 JND (Just Noticeable Difference) unit. A dE value of 1 may be barely perceptible to some observers, but most viewers don’t see a color difference unless dE is about 3. (A JND unit corresponds to a 75% probability that an observer will see a difference in multiple viewings.) I hadn’t planned to include dE with the color temperature data until there was time to write an article explaining the concept. But thanks to your letter, and Gary’s timely question, we’ve covered the basics right here. Contributing Editor Bill Cushman also introduces the concept of dE in his review of the JVC DLA-HX1U in this Issue 80. Compare the Color Temperature table from his review to the table of dE values here. Note that these dE values do not compare the gray scale colors relative to each other, nor do they indicate any color error direction, which can often be inferred from the color temperature data, which we will still publish. On a related note, I have tried to make chromaticity diagrams a familiar tool for conveying color accuracy, which led me to publish the more common CIE x,y diagrams. But I will soon switch to the CIE u’v’ Chromaticity diagram, which depicts color errors in the more perceptually uniform u’v’ color space. That diagram will look a bit different, but it will more accurately reflect the way we perceive color errors. We will continue to plot both the primary and complementary colors versus the appropriate video standards, because the complementary colors reveal the critically important color decoding accuracy.
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