Component video

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Y’=0.0722. The B’-Y’ component reaches its negative maximum at yellow (B’-Y’ =-0.9278). Analogously, the extrema of R’-Y’ occur at red and cyan at values ±0.7874 (see Figure 30.1 above). These are inconvenient values for both digital and analog systems. The 709Y’PBPR and 709Y’CBCR systems to be described both employ versions of [Y’, B’-Y’, R’-Y’] that are scaled to place the extrema of the component values at more convenient values.

To obtain [Y’, B’-Y’, R’-Y’], from R’G’B’, for BT.709 luma coefficients, use this matrix equation:

PBPR components for BT.709 HD

If two colour difference components are to be formed having excursions identical to luma, then PB and PR colour difference components are used. For BT.709 luma, the equations are these:

These scale factors limit the excursion of each colour difference component to the range ±0.5 with respect to unity luma excursion: 0.0722 in the first expression above is the luma coefficient of blue, and 0.2126 in the second is for red. At an HD analog interface, luma ranges from 0 mV (black) to 700 mV (white), and PB and PR analog components range ±350 mV. Figure 30.2 above shows a plot of the [PB, PR] plane.

Expressed in matrix form, the B’-Y’ and R’-Y’ rows of Equation 30.1 are scaled by 0.5⁄0.9278 and 0.5⁄0.7874. To encode from R’G’B’ where reference black is zero and reference white is unity:

The inverse, decoding matrix is this:

CBCR components for BT.709 HD

709Y’CBCR coding is used in component digital HD equipment. In 8-bit systems, luma has an excursion of 219. Colour differences CB and CR are coded in 8-bit

offset binary form, with excursions of ±112. The [CB, CR] plane of HD is plotted in Figure 30.3.

In 8-bit systems, a luma offset of +16 is added at the interface, placing black at code 16 and white at code 235; an offset of +128 is added to CB and CR, yielding a range of 16 through 240 inclusive. (Following the convention of the previous chapter, in the equations to follow I write the offset terms in colour.) HD standards provide for 10-bit components, and 10-bit studio video equipment is commonplace. In a 10-bit interface, the 8-bit interface levels and prohibited codes are maintained; the extra two bits are appended as least-signifi- cant bits to provide increased precision.

To form 709Y’CBCR from [Y’, B’-Y’, R’-Y’] components in the range [0…+1], use these equations:

To obtain 709Y’CBCR from R’G’B’ ranging 0 to 1, scale the rows of the matrix in Equation 30.3 by the factors