Nonlinear red, green, blue (R’G’B’)

The BT.601 luma coefficients were computed using the technique that I explained in Luminance coefficients, on page 306, using the historical NTSC primaries and white point of 1953; see Table 3.2, on page 25 of Composite NTSC and PAL: Legacy Video Systems.

The mismatch between the primaries and the luma coefficients of SD has little practical significance; however, the mismatch of luma coefficients between SD and HD has great practical significance!

BT.601 luma

The following luma equation is standardized in BT.601 for SD, and also applies to JPEG/JFIF (in computing) and Exif (in digital still photography):

As mentioned a moment ago, the E and prime symbols originally used for video signals have been elided over the course of time, and this has led to ambiguity of the Y symbol between colour science and television.

The coefficients in the luma equation are based upon the sensitivity of human vision to each of the RGB primaries standardized for the coding. The low value of the blue coefficient is a consequence of saturated blue colours having low lightness. The luma coefficients are also a function of the white point, or more properly, the chromaticity of reference white.

In principle, luma coefficients should be derived from the primary and white chromaticities. The BT.601 luma coefficients of Equation 28.5 are the same as those established in 1953 by the NTSC from the primaries and white point then in use. Primaries actually used in consumer displays changed a few years after the adoption of NTSC. The primaries in use for 480i SD today are approximately those specified in SMPTE RP 145; the primaries in use for 576i SD are approximately those specified in EBU Tech. 3213. (These primary sets are slightly different; both sets very nearly match the primaries of BT.709.) Despite the change in primaries, the luma coefficients for SD video – both 480i and 576i – have remained unchanged from the values that were established in 1953. As a consequence of the change in primaries, the luma coefficients in SD no longer theoretically match the primaries. The mismatch has little practical significance.

BT.709 luma

International agreement on BT.709 was achieved in 1990 on the basis of “theoretically correct” luma coefficients derived from the BT.709 primaries:

I use T1-1 to denote the encoding “linear matrix,” to conform to the notation of Luminance coefficients, on page 306.

Interchange primaries are also called transmission primaries.

a 3× 3 matrix that transforms tristimulus signals from the image capture primaries to the interchange primaries. (This is the “linear matrix” built into the camera.) Similarly, a decoder may be required to drive a display whose primaries are different from the interchange primaries; at the output of the decoder, it may be necessary to insert a 3× 3 matrix that transforms from the interchange primaries to the image display primaries. (See page 309.)

Figure 28.8 above summarizes luma/colour difference encoding. If image data originated in linear XYZ components, a 3× 3 matrix transform (T1-1) would be applied to obtain linear RGB having chromaticities and white reference of the interchange primaries. For BT.709 interchange primaries standard for SD and HD, the matrix would be that of Equation 26.9, on

page 308. More typically, image data originates in some device-dependent space that I denote R1G1B1, and the 3× 3 “linear matrix” transform (T1-1) is determined by the camera designer. See the sequence of Figures 26.3 through 26.8, starting on page 300, and the accompanying text and captions, to gain an appreciation for how such a matrix might be crafted. Practical cameras do not have spectral sensitivities that are linear combinations of the CIE colour matching functions, so they are not properly characterized by chromaticities. Nonetheless, once a linear matrix to a set of interchange primaries has been chosen, Equation 26.10 can be used to derive equivalent sensor primaries (the “taking primaries”).

Figures 28.8 and 28.9 show 3× 3 matrix transforms being used for two distinctly different tasks.

When someone hands you a 3× 3, you have to ascertain

whether it is linearly or nonlinearly related to light power.

Once the linear matrix has been applied, each of the components is subject to a nonlinear transfer function (gamma correction) that produces nonlinear R’G’B’.

These components are transformed through a 3× 3 matrix (P), to obtain luma and colour difference components Y’CBCR or Y’PBPR. (This matrix depends upon the luma coefficients in use, and upon colour difference scale factors.) Then, if necessary, a chroma subsampling filter is applied to obtain subsampled colour difference components; luma is subject to a compensating delay.

A decoder uses the inverse operations of the encoder, in the opposite order, as sketched in

Figure 28.9. In a digital decoder, the chroma interpolation filter reconstructs missing chroma samples; in an analog decoder, no explicit operation is needed. The 3× 3 colour difference matrix (P-1) reconstructs nonlinear red, green, and blue primary components. The transfer functions restore the primary components to their linear-light tristimulus values. Finally, the tristimulus 3× 3 matrix (T2) transforms from the primaries of the interchange standard to the primaries implemented in the display device.

When a decoder is intimately associated with a CRT display, the decoder’s transfer function is performed by the nonlinear voltage-to-luminance relationship intrinsic to the CRT: No explicit operations are required for this step. However, to exploit this transfer function,