OECF

R

G

B

Figure 28.4 Conventional luma/colour difference encoder. Numerical coefficients here are for SD; unfortunately, different coefficients were standardized for HD.

Figure 28.4 shows a time delay element in the luma path. Luma is delayed by a time interval equal to the transit delay of chroma through the chroma bandlimiting filters.

Eq 28.1 BT.601 Y’PBPR encoding matrix (for SD)

For the derivation of this matrix, and a more precise expression, see PBPR components for SD, on page 359.

Conventional luma/colour difference coding

I explained constant luminance on page 107. True constant luminance coding remains an intriguing possibility, but at present all video systems use nonconstant luminance coding, which I will now describe.

A conventional luma/colour difference encoder is shown in Figure 28.4 above. First, a nonlinear transfer function is applied to each of the red, green, and blue linear (tristimulus) components. Then luma is formed as a weighted sum of gamma-corrected R’, G’, and B’ components. B’-Y’ and R’-Y’ colour difference components are formed by subtraction; in Figure 28.4, scaling to analog PB and PR components is indicated. Finally, the colour difference components are lowpass filtered.

The highlight rectangle in Figure 28.4 groups together the weighted adder that forms luma with the pair of colour difference subtractors; the combination is equivalent to matrix multiplication by the 3× 3 matrix P shown in Equation 28.1 in the margin. The numerical values used in Equation 28.1, in Figure 28.4, and in subsequent figures in this chapter all reflect the BT.601 luma coefficients used in SD. Unfortunately, the coefficients for HD are different, as I will describe in Component video colour coding for HD, on page 369.

Figure 28.5 illustrates a conventional luma/colour difference decoder. In a digital decoder, the colour difference (chroma) components are horizontally (and,

R’

R

G

B

Eq 28.2 BT.601 Y’PBPR decoding matrix (for SD)

in some applications, spatially) interpolated; in an analog decoder, no circuitry is required to perform this function. Luma is added to the colour difference components to reconstruct nonlinear blue and red components. A weighted sum of luma, blue, and red is then formed to reconstruct the nonlinear green component.

The blue and red colour difference adders and the weighted adder that recovers green, all enclosed by the highlight rectangle in Figure 28.5, can be considered together as multiplication by the 3× 3 matrix P-1 shown in Equation 28.2. These values are for SD; the matrix for HD is different.

To produce linear-light tristimulus components, all three components are subject to the inverse transfer function sketched at the right with dashed outlines. Usually, a decoder is used with a CRT that has an intrinsic 2.4-power function, or with some other display that incorporates a 2.4-power function; in either case, the transfer function need not be explicitly computed.

Luminance and luma notation

In Luminance from red, green, and blue, on page 258, I described how relative (linear-light) luminance,

See Appendix A, YUV and luminance considered harmful, on page 567.

Figure 28.6 Luminance and luma notation is necessary because different primary chromaticity sets, different luma coefficients, and different component scale factors are in use. Unity scaling suffices for components in this chapter; in succeeding chapters, other scale factors will be introduced.

proportional to intensity, can be computed as an appropriately weighted sum of RGB.

In video, the luminance of colour science isn’t computed. Instead, we compute a nonlinear quantity luma as a weighted sum of nonlinear (gammacorrected) R’G’B’. The weights – or luma coefficients – are related to the luminance coefficients. The luma coefficients specified in BT.601 have been ubiquitous for SD, but new and different weights have been introduced in HD standards. In my opinion, the luma coefficients need not and should not have been changed for HD: Complexity is added to upconversion and downconversion in studio and consumer equipment, for no improvement in performance or quality.

Television standards documents historically used the prime symbol (’) – often combined with the letter E for voltage – to denote a component that incorporates gamma correction. For example, E’R historically denoted the gamma-corrected red channel. Gamma correction is nowadays so taken for granted in video that the E and the prime symbol are usually elided. This has led to much confusion among people attempting to utilize video technology in other domains.

The existence of several standard sets of primary chromaticities, the introduction of new coefficients, and continuing confusion between luminance and luma all beg for a notation to distinguish among the many possible combinations. In the absence of any standard notation, I was compelled to invent my own.

Figure 28.6 below sketches the notation that I use. The base symbol is Y, R, G, or B. The subscript denotes the standard specifying the chromaticities of the primaries

601219Y709’

Figure 28.7 Typesetting Y’CBCR is a challenge! Luma coefficient set, scaling, and chromaticities are set out as in

Figure 28.6. The prime should always be present, to distinguish luma from the luminance of colour science. C is appropriate for digital signals, P for analog. Subscripts B and R serve as tags, not variables: They should be in roman type, not italics. B comes before R.

Figure 28.6.

Luma details; see

C for digital, P for analog

601219Y709’ CBCR