Owing to the dependence of the optimum end-to-end power function upon viewing conditions, there here ought to be a user control for rendering intent – perhaps even replacing brightness and contrast – but there isn’t!

the display primaries must be the same as – or at least very similar to – the interchange primaries.

The transfer functions of the decoder (or the CRT) are intertwined with gamma correction. As explained on page 115, an end-to-end power function having an exponent of about 1.2 is appropriate for typical television acquired at studio lighting levels and viewed at 100 nt in a dim surround. The encoder of Figure 28.8 imposes a 0.5-power function; the decoder of

Figure 28.9 imposes a 2.4-power function. The product of these implements the end-to-end power function. If the native EOCF of a display device differs from that of a CRT, then decoding should include a transfer function that is the composition of a 2.4-power function and the inverse transfer function of the display device.

When viewing a rather bright display (say 320 nt) in an average surround (say 20%), a 1.1 end-to-end power is appropriate; a 2.2-power EOCF (like that of sRGB) is appropriate. When viewing in a dark (0%) surround,

a 1.3 end-to-end power is appropriate; a 2.6-power EOCF (like that of digital cinema) is appropriate.

If the display primaries match the interchange primaries, the decoder’s 3× 3 tristimulus matrix is not needed. If a display has primaries not too different from the interchange primaries, then it may be possible to compensate the primaries by applying a 3× 3 matrix in the nonlinear domain. But if the primaries are quite different, it will be necessary to apply the transform between primaries in the tristimulus domain; see Transforms among RGB systems, on page 309.

Figure 28.10 Luma/colour difference flavors

SD and HD luma chaos

Although the concepts of Y’PBPR and Y’CBCR coding are identical in SD and HD, the BT.709 standard established a new set of luma coefficients for HD. That set differs dramatically from the luma coefficients for SD specified in BT.601. There are now two flavors of Y’CBCR coding, as suggested by Figure 28.10 in the margin;

I denote the flavors 601Y’CBCR for SD, and 709Y’CBCR for HD. Similarly, there are two flavors of Y’PBPR for analog systems, 601Y’PBPR for SD, and 709Y’PBPR for HD.

In my view, it is extremely unfortunate that different coding was adopted: Image coding and decoding now depend on whether the picture is small (conventional

It’s sensible to use the term colourbar test signal (or pattern) instead of colourbar test image, because the signal is standardized, not the image.

Table 28.1 luma coefficients, EOCF, and primary chromaticities for video decoding and display circa 2011 are summarized. Encoding in all systems should be accomplished through forming R’G’B’ values that yield the intended image appearance in the reference display and viewing conditions. For SD, there is no effective standard for either the reference EOCF or the viewing conditions. For HD, BT.1886 standardizes the reference EOCF, but not the viewing conditions.

video, SD) or large (HD); that dependence erodes the highly useful concept of resolution-independent production in the Y’CBCR 4:2:2 and 4:2:0 domains. In my opinion, HD should have been standardized with the BT.601 luma coefficients. With things as they stand, the smorgasbord of colour-encoding parameters makes accurate image interchange extremely difficult. The situation is likely to get worse with time, not better.

Table 28.1 above summarizes the standards for primary chromaticities, transfer functions, and luma coefficients that are either implicit or explicit in several SD and HD standards. When video is converted among these standards, appropriate processing should be performed in order to preserve the intended colour.

The colourbar test signal is standardized in the R’G’B’ domain, without any reference to primaries, transfer function, or luma coefficients. The colours of the bars depend upon which primary chromaticities are in use; the luma and colour difference levels of the bars depend upon which luma coefficients are in use. When colour conversions and standards conversions are properly performed, the colours and levels of the colourbar test signal will change!

Video uses the symbols U and V to represent certain colour difference components. The CIE defines the pairs [u, v], [u’, v’], and [u*, v*]. All of these pairs represent chromatic or chroma information, but they are all numerically and functionally different. Video [U, V] components are neither directly based upon, nor superseded by, any of the CIE colour spaces.

Component video

Various scale factors are applied to the basic colour difference components B’-Y’ and R’-Y’ for different applications. In the previous chapter, I introduced luma and colour difference coding; in this chapter, I will detail the following coding systems:

•B’-Y’, R’-Y’ components form the numerical basis for all the other component sets; otherwise, they are not directly used.

•PBPR components are used for component analog video (including analog interfaces in devices such as

DVD players and set-top boxes).

•CBCR components as defined in BT.601 and BT.709 are used for component digital video, including studio

video, DV, MPEG, and H.264.

•“Full-swing” (or “full-range”) CBCR components are used in JPEG/JFIF.

•UV components are used for composite NTSC or PAL, as described in UV components, in Chapter 5 of

Composite NTSC and PAL: Legacy Video Systems.

•IQ components were historically used for composite NTSC until about 1970, as described in Chapter 4, NTSC Y’IQ system, of Composite NTSC and PAL: Legacy Video Systems.

Y’UV and Y’IQ are intermediate quantities toward the formation of composite NTSC, PAL, and S-video. Neither Y’UV nor Y’IQ has a standard component interface, and neither is appropriate when the components are kept separate. Unfortunately, the Y’UV nomenclature has come to be used rather loosely, and some people use Y’UV to denote any scaling of B’-Y’ and R’-Y’.

For a discussion of primary chromaticities, see page 290.

The coding systems described in this chapter can be applied to various RGB primary sets – EBU 3213, SMPTE RP 145 (or potentially even BT.709). BT.601 does not specify primary chromaticities: SMPTE RP 145 primaries are implicit in 480i SD, and EBU 3213 primaries are implicit in 576i SD. However, virtually all of modern consumer receivers interpret content – whether SD or HD – according to BT.709 primaries. As I write, program content created in North America is mastered with SMPTE primaries (contrary to the spirit and letter of ITU-R, SMPTE, and ATSC standards) and content created in Europe is mastered to EBU primaries. However, all of this content is displayed in the consumer domain using BT.709 primaries. We look forward to the day when content creators actually master using the BT.709 colour space.

The equations for [Y’, B’-Y’, R’-Y’], Y’PBPR, and Y’CBCR can be based upon either the BT.601 luma coefficients of SD or the BT.709 coefficients of HD. The equations and figures of this chapter are based upon the BT.601 coefficients. Unfortunately, the luma coefficients that have been standardized for HD are different from those of BT.601. Concerning the HD luma coefficients, see BT.709 luma on page 346; for details of HD colour difference components, see the following chapter, Component video colour coding for HD, on page 369.

Chroma components are properly ordered B’-Y’ then R’-Y’; or PB then PR; or CB then CR. Blue associates with U, and red with V; U and V are ordered alphabetically. The subscripts in CBCR and PBPR are often written in lowercase. In my opinion, this compromises readability, so I write them in uppercase. The B in CB serves as a tag, not a variable, so I set it in Roman type (that is, upright, not italic). Authors with great attention to detail sometimes “prime” CBCR and PBPR to indicate their nonlinear origin, but no standard or deployed image coding system has employed linear-light colour differences, nor would that be sensible for perceptual reasons, so I omit the primes.