In video, codeword (or codepoint) refers to a combination of three integer values such as [R’, G’, B’] or [Y’, CB, CR].

RGB and R’G’B’ colour cubes

Red, green, and blue tristimulus (linear light) primary components, as detailed in Colour science for video, on page 287, can be considered to be the coordinates of a three-dimensional colour space. Coordinate values between zero and unity define the unit cube of this space, as sketched at the top of Figure 28.1 opposite. Linear-light coding is used in CGI, where physical light is simulated. However, as I explained in the previous chapter, Gamma in video, 8-bit linear-light coding exhibits poor perceptual performance: 12 or 14 bits per component are necessary to achieve excellent quality. The best perceptual use is made of a limited number of bits by using nonlinear coding that mimics the nonlinear lightness response of human vision. As introduced on page 27, and detailed in Chapter 27 Gamma, on page 315, in video, JPEG, MPEG, computing, digital still photography, and in many other domains a nonlinear transfer function is applied to RGB tristimulus signals to give nonlinearly coded (gamma-corrected) components, denoted with prime symbols: R’G’B’. Excellent image quality is obtained with 10-bit nonlinear coding with a transfer function similar to that of BT.709 or sRGB.

In PC graphics, 8-bit nonlinear coding is common: Each of R’, G’, and B’ ranges from 0 through 255, inclusive, following the quantizer transfer function sketched in Figure 4.1, on page 37. The resulting R’G’B’ cube is sketched at the bottom of Figure 28.1 opposite. A total of 224 colours – that is, 16,777,216 colours – are representable. Not all of them can be distinguished visually; not all are perceptually useful; but they are all colours. Studio video uses headroom and footroom, as explained in Studio-swing (footroom and headroom), on page 42: 8-bit R’G’B’ has 219 codes between black and white, for a total of 2203 or 10,648,000 codewords.

The drawback of conveying R’G’B’ components of an image is that each component requires relatively high spatial resolution: Transmission or storage of a colour image using R’G’B’ components requires a capacity three times that of a greyscale image. Human vision has considerably less spatial acuity for colour information than for lightness. Owing to the poor colour acuity of vision, a colour image can be coded into a wideband

Here the term colour difference refers to a signal formed as the difference of two gamma-corrected colour components. In other contexts, the term can refer to

a numerical measure of the perceptual distance between two colours.

I introduced interface offsets on page 44.

monochrome component representing lightness, and two narrowband components carrying colour information, each having substantially less spatial resolution than lightness. In analog video, each colour channel has bandwidth typically one-third that of the monochrome channel. In digital video, each colour channel has half the data rate (or data capacity) of the monochrome channel, or less. There is strong evidence that the human visual system forms an achromatic channel and two chromatic colour-difference channels at the retina.

Green dominates luminance: Between 60% and 70% of luminance comprises green information. Signal-to- noise ratio is maximized if the colour signals on the other two components are chosen to be blue and red. The simplest way to “remove” lightness from blue and red is to subtract it, to form a pair of colour difference (or loosely, chroma) components.

The monochrome component in colour video could have been based upon the luminance of colour science (a weighted sum of R, G, and B). Instead, as I explained in Constant luminance, on page 107, luma is formed as a weighted sum of R’, G’, and B’, using coefficients similar or identical to those that would be used to compute luminance. Expressed in abstract terms, luma ranges 0 to 1. Colour difference components B’-Y’ and R’-Y’ are bipolar; each ranges nearly ±1.

In component analog video, B’-Y’ and R’-Y’ are scaled to form PB and PR components. In abstract terms, these range ±0.5. Figure 28.2 shows the unit R’G’B’ cube transformed into luma [Y’, PB, PR]. (Various interface standards are in use; see page 359.) In component digital video, B’-Y’ and R’-Y’ are scaled to form CB and CR components. In 8-bit Y’CBCR prior to the application of the interface offset, the luma axis of

Figure 28.2 would be scaled by 219, and the chroma axes by 112.

Once colour difference signals have been formed, they can be subsampled to reduce bandwidth or data capacity, without the observer’s noticing, as I will explain in Chroma subsampling, revisited, on page 347.

REFERENCE WHITE

Mg

0+0.5

PB AXIS

REFERENCE BLACK

Izraelevitz, David, and Joshua L. Koslov (1982), “Code utilization for component-coded digital video,” in Tomorrow’s Television

(Proc. 16th Annual SMPTE Television Conference): 22–30.

It is evident from Figure 28.2 that when R’G’B’ signals are transformed into the Y’PBPR space of analog video, the unit R’G’B’ cube occupies only part of the volume of the unit Y’PBPR cube: Only 1⁄4 of the Y’PBPR volume corresponds to R’G’B’ values all between 0 and 1. Consequently, Y’PBPR exhibits a loss of signal-to- noise ratio compared to R’G’B’. However, this disadvantage is offset by the opportunity to subsample.

In a legal signal, no component exceeds its reference excursion. Signal combinations that are R’G’B’-legal are termed valid. Signals within the Y’PBPR unit cube are Y’PBPR-legal. However, about 3⁄4 of these combinations correspond to R’G’B’ combinations outside the R’G’B’ unit cube: Although legal, these Y’PBPR combinations are invalid – that is, they are R’G’B’-illegal.

In digital video, we refer to codewords instead of combinations. There are about 2.75 million valid codewords in 8-bit Y’CBCR, compared to 10.6 million in 8-bit studio R’G’B’. If R’G’B’ is transcoded to 8-bit Y’CBCR , then transcoded back to R’G’B’, the resulting R’G’B’ cannot have any more than 2.75 million colours.

CBCR components are comparable to PBPR components, but have codeword values ranging ±112 on the 8-bit scale instead of abstract values ranging ±0.5.

In Figure 28.2, the Y’PBPR cube is portrayed off-axis. Figure 28.3 shows three orthographic views of the R’G’B’ prism in Y’PBPR-space. The luma axis, denoted Y’, ranges 0 to 1. The chroma axes are annotated with both [B’-Y’, R’-Y’] scaling (where the components range ±0.886 and ±0.701, respectively), and PBPR scaling (where the components both range ±0.5). The extent of the volume of Y’PBPR space that lies outside the R’G’B’ prism is apparent. The emergent xvYCC system, to be described, uses Y’CBCR codewords outside the unit R’G’B’ prism – that is, formerly “invalid” codewords – to convey wide-gamut colour.