Figure 10.8 Simplified decoder

the combination of the two has no net effect. Both functions can be dropped from the decoder:

-1 2.4

[P ]

Television engineers who are uneducated in colour science often mistakenly call luma (Y’) by the name luminance and denote it by the unprimed symbol Y. This leads to great confusion, as I explain in Appendix A, on page 567.

Figure 10.9 represents the basic signal flow for all video systems; it will be elaborated in later chapters.

Luma

The rearranged flow diagram of Figure 10.9 is not mathematically equivalent to the arrangement of

Figures 10.1 through 10.4! In Figure 10.9, the encoder’s matrix does not operate on (linear-light) tristimulus signals, and relative luminance is not computed. Instead, a nonlinear quantity – denoted luma and symbolized Y’ – is computed and transmitted. Luma involves an engineering approximation: The system no longer adheres strictly to the principle of constant luminance (though it is often mistakenly claimed to do so).

In the rearranged encoder, we no longer use CIE L* to optimize for perceptual uniformity; instead, we use the inverse of the CRT’s inherent transfer function.

A 0.42-power function accomplishes approximately perceptually uniform coding, and reproduces tristimulus values proportional to those in the original scene.

The following chapter, Picture rendering, explains that the 0.42 value must be altered in a normal scene to

Figure 10.12 Y’ and CB/CR waveforms at the greenmagenta transition of SD colourbars are shown, following idealized 4:2:2 chroma subsampling. The luma waveform is plotted in grey; CB and CR share the same waveform, plotted in magenta. The transition rate (rise time) of the CB and CR components is half that of luma.

Figure 10.13 Luminance waveform at the green-magenta transition of colourbars is shown in the solid line. The dashed line reflects luminance in a hypothetical true constantluminance system.

Figure 10.14 Failure to adhere to constant luminance is evident in the dark band in the green-magenta transition of colourbars. The dark band is found upon displaying any colourbar signal that has been subject to chroma subsampling.

the relative luminance traverses the chroma pathways. Figure 10.12 above shows the idealized Y’CBCR waveforms at the green-magenta transition of colourbars, with 4:2:2 chroma subsampling. Figure 10.13 shows, in the solid line, the luminance that results after conventional decoding. Subsampling not only removes detail from the colour components, it removes detail from the “leaked” relative luminance. We have to ask, “What’s lost?” The departure from theory is apparent in the dark band appearing between the green and magenta colour bars of the standard video test pattern, depicted in Figure 10.14 in the margin.

With conventional video coding, in areas where luminance detail is present in saturated colours, relative luminance is incorrectly reproduced: relative luminance is reproduced too dark, and saturation is reduced. This inaccurate conveyance of high-frequency

Livingston, Donald C. (1954), “Reproduction of luminance detail by NTSC color television systems,” in Proc. IRE 42 (1): 228–234.

luminance is the price that must be paid for lack of strict adherence to the principle of constant luminance. Such “Livingston” errors are perceptible by experts, but they are very rarely noticeable – let alone objectionable – in normal imagery.

To summarize signal encoding in video systems: First, a nonlinear transfer function, gamma correction, comparable to a square root, is applied to each of the linear R, G, and B tristimulus values to form R’, G’, and B’. Then, a suitably weighted sum of the nonlinear components is computed to form the luma signal (Y’). Luma approximates the lightness response of vision. Colour difference components blue minus luma (B’-Y’) and red minus luma (R’-Y’) are formed. (Luma, B’-Y’, and R’-Y’ can be computed from R’, G’, and B’ simultaneously, through a 3× 3 matrix.) The colour difference components are then subsampled (filtered), using one of several schemes – including 4:2:2, 4:1:1, and 4:2:0 – to be described starting on page 124.

This chapter has outlined how, in the development of NTSC, an engineering approximation to constant luminance was adopted rather than “true” constant luminance. This engineering decision has served spectacularly well, and has been carried into component video systems (SD and HD), and into modern compression systems such as JPEG, MPEG, and H.264.

Since about 2000, the majority of television receivers have incorporated digital signal processing that obviates the engineering argument made in 1950: The two nonlinear functions of Figure 10.6 could today be easily be implemented by lookup tables. Some purists believe that in the modern age we should abolish the approximation, and adopt the correct theoretical approach. However, the video infrastructure of SD and HD is built on Figure 10.9 (or with chroma subsampling,

Figure 10.11). It seems unreasonable to change the block diagram of video, and impose a huge conversion burden, unless substantial benefit can be shown.

I appreciate the theoretical argument; however, I am unaware of any significant benefit that would result from such a change, so I argue that we should not change the block diagram of video.