The MPEG-1 Codec - A Practical Guide to Video and Audio Compression - page 200

Red channel Luma values

Conversion
matrix

Green channel Blue minus Luma

Blue channel Red - Luma

Figure 10-7 RGB-to-luma/chroma conversion.

The video may have been originally represented as luma plus chroma when it was
digitized. If that is the case when you input the video, it is not necessary to convert it to
RGB in order to store it in a file. A good rule of thumb is to avoid unnecessary conversion
steps in your process. Such conversions will always lose some information due to the color
gamut not being exactly the same in both formats.
Figure 10-7 shows an example of the processing pipeline for converting RGB to a
compressible format that represents pictures as luma plus chroma.
The conversion matrix box takes a portion of each of the RGB values for each pixel
and generates a luma value from it. The two color-difference values are also generated
using different combinations of the same RGB values. The chroma information is reduced
to a lower resolution at this stage.

10.6.1 Color by Numbers

Given a set of red, green and blue values,

Luma (Y') = (0.299* R) + (0.587 * G) + (0.114 * B)

The factors that are used to compute the luma are then negated and subtracted from
blue and red to generate the B-Y ′ and R-Y ′ values.

Therefore,

Blue - Y' = B - ((0.299* R) + (0.587 * G) + (0.114 * B))

= (0.886 * B) - (0.299* R) - (0.587 * G)

Red - Y' = R - ((0.299* R) + (0.587 * G) + (0.114 * B))

= (0.701 * R) - (0.114* B) - (0.587 * G)