The term luminance is widely misused in video. See Relative luminance, on page 258, and Appendix A, YUV and luminance considered harmful, on page 567.

Video systems convey colour image data using one component that approximates lightness, and two other components that represent colour, absent lightness. In Colour science for video, on page 287, I will detail how luminance can be formed as a weighted sum of linear RGB values each of which is proportional to optical power. A colour scientist uses the term constant luminance to refer to this sum being constant. Transmitting a single component from which relative luminance can be reconstructed is the principle of constant luminance. Preferably a nonlinear transfer function acts on that component to impose perceptually uniform coding.

Standard video systems do not strictly adhere to that principle; instead, they implement an engineering approximation. The colour scientist’s weighted sum of linear RGB is not computed. Instead, a nonlinear transfer function is applied to each linear-light RGB component individually, then a weighted sum of the nonlinear gamma-corrected R’G’B’ components forms what I call luma. (Many video engineers carelessly call this quantity luminance.) In standard video systems, luma is encoded using the theoretical RGB weighting coefficients of colour science, but in a block diagram different from the one a colour scientist would expect: In video, gamma correction is applied before the matrix, instead of the colour scientist’s preference, after.

Historically, transmission of a single component representative of greyscale enabled compatibility with “black-and-white” television. Human vision has poor acuity for colour compared to luminance. Placing “black-and-white” information into one component

The term “monochrome” is sometimes used instead of “greyscale.” However, in classic computer graphics terminology monochrome refers to bilevel (1-bit) images or display systems, so I avoid that term.

Applebaum, Sidney (1952), “Gamma correction in constant luminance color television systems,” in Proc. IRE, 40 (11): 1185–1195 (Oct.).

enables chroma subsampling to take advantage of vision’s low acuity for chroma in order to reduce data rate (historically, bandwidth) in the two other components. In colour imaging, it is sensible to code a “black- and-white” component even if “black-and-white” compatibility isn’t required (for example, in JPEG).

I’ve been placing “black-and-white” in quotes. At the invention of television, the transmitted signal represented greyscale, not just black and white: Then, and now, greyscale would be a better term.

Historical video literature refers to the “signal representing luminance” or the “luminance signal” or the “luminance component.” All of these terms were once justified; however, they are now dangerous: To use the term “luminance” suggests that relative luminance (Y) can be decoded from that component. However, without strict adherence to the principle of constant luminance, luminance cannot be decoded from the greyscale component alone: Two other components (typically CB and CR) are necessary.

In this chapter, I will explain why and how all current video systems depart from the principle of constant luminance. If you are willing to accept this departure from theory as a fact, then you may safely skip this chapter, and proceed to Introduction to luma and chroma, on page 121, where I will introduce how the luma and colour difference signals are formed and subsampled.

The principle of constant luminance

Ideally, the so-called monochrome component in colour video would mimic a greyscale system: Relative luminance would be computed as a properly weighted sum of (linear-light) R, G, and B tristimulus values, according to the principles of colour science that are explained in

Transformations between RGB and CIE XYZ, on page 307. At the decoder, the inverse matrix would reconstruct linear R, G, and B tristimulus values:

electron gun of a historical CRT display introduces a power function having an exponent of about 2.4:

Figure 10.5 The CRT transfer function

R G B