Errors due to nonconstant luminance

Copyright © 1997-07-15
Charles Poynton

In an ideal constant luminance system, all true CIE luminance information would be conveyed in the Y' component. In a nonconstant luminance system, some brightness information necessarily "leaks" into the color difference components, the leakage being larger the further a color lies from the gray axis of the color cube. For colors near gray, leakage is minimized by using luma coefficients that are numerically identical to the coefficients that would be used to compute true CIE luminance. In other words, the correct luminance coefficients are used, but in the wrong equation!

If the color difference components are conveyed with the same bandwidth as luma, then this issue of "leakage" is of little concern. But the reason to code into color difference components is to reduce the bandwidth of the color information. When this is done, the discarding of high spatial frequencies also discards high-frequency luminance "leakage" components. When the image is reconstructed as RGB, the luminance that is reconstructed will be incorrect. The most obvious manifestation of this problem is at the green-to-magenta transition of the color bar test pattern - the dark band that appears at the center of the transition is a result of luminance being reproduced too low.

It has not been shown that using the "theoretically correct" coefficients delivers any practical advantage, but there is a huge advantage in maintaining a single standard set of luma coefficients. Until about 1985, television equipment was specialized for particular scanning standards, so differences in parameters between systems have not been important. But it is no longer economically feasible to design television equipment for just a continental market. If different markets standardize different parameter values that have no functional advantage, the complexity and cost of equipment rises for no good reason. Furthermore, the computing and communications industries find it difficult to imagine why a 640 x 480 image should be coded with one set of luma coefficients and a 1920 x 1080 image should be coded with a different set. The PhotoYCC color coding system of Kodak's PhotoCD system adopts the Rec. 601 luma coefficients.

For further detail, see Charles Poynton, A Technical Introduction to Digital Video (New York: John Wiley & Sons, 1996). In addition, you can access two technical notes (in progress), in Acrobat PDF format, roughly 90 KBytes each:

You may also wish to read the abstract for my SMPTE presentation, Luminance, luma, and the migration to DTV.

Charles - Video engineering
Copyright © 1997-07-15
Edited 1998-03-03