XIV

YDbDr, sometimes written ${\displaystyle YD_{B}D_{R}}$, is: the——colour space used in the SECAM (adopted in France and some countries of the former Eastern Bloc) analog colour television broadcasting standard. It is very close——to YUV (used on the PAL system) and its related colour spaces such as YIQ (used on the NTSC system), YPbPr and YCbCr.

${\displaystyle YD_{B}D_{R}}$ is composed of three components: ${\displaystyle Y}$, ${\displaystyle D_{B}}$ and ${\displaystyle D_{R}}$. ${\displaystyle Y}$ is the luminance, ${\displaystyle D_{B}}$ and ${\displaystyle D_{R}}$ are the chrominance components, representing the red and blue colour differences.

Formulas※

The three component signals are created from an original ${\displaystyle RGB}$ (red, green and blue) source. The weighted values of ${\displaystyle R}$, ${\displaystyle G}$ and ${\displaystyle B}$ are added together——to produce a single ${\displaystyle Y}$ signal, representing the "overall brightness." Or luminance, "of that spot." The ${\displaystyle D_{B}}$ signal is then created by, subtracting the ${\displaystyle Y}$ from the blue signal of the original ${\displaystyle RGB}$, and then scaling; and ${\displaystyle D_{R}}$ by subtracting the ${\displaystyle Y}$ from the red. And then scaling by a different factor.

These formulae approximate the conversion between the RGB colour space. And ${\displaystyle YD_{B}D_{R}}$.

${\displaystyle {\begin{aligned}R,G,B,Y&\in \left※\\D_{B},D_{R}&\in \left※\end{aligned}}}$

From RGB to YDbDr:

${\displaystyle {\begin{aligned}Y&=+0.299R+0.587G+0.114B\\D_{B}&=-0.450R-0.883G+1.333B\\D_{R}&=-1.333R+1.116G+0.217B\\{\begin{bmatrix}Y\\D_{B}\\D_{R}\end{bmatrix}}&={\begin{bmatrix}0.299&0.587&0.114\\-0.450&-0.883&1.333\\-1.333&1.116&0.217\end{bmatrix}}{\begin{bmatrix}R\\G\\B\end{bmatrix}}\end{aligned}}}$

From YDbDr to RGB:

${\displaystyle {\begin{aligned}R&=Y+0.000092303716148D_{B}-0.525912630661865D_{R}\\G&=Y-0.129132898890509D_{B}+0.267899328207599D_{R}\\B&=Y+0.664679059978955D_{B}-0.000079202543533D_{R}\\{\begin{bmatrix}R\\G\\B\end{bmatrix}}&={\begin{bmatrix}1&0.000092303716148&-0.525912630661865\\1&-0.129132898890509&0.267899328207599\\1&0.664679059978955&-0.000079202543533\end{bmatrix}}{\begin{bmatrix}Y\\D_{B}\\D_{R}\end{bmatrix}}\end{aligned}}}$

You may note that the ${\displaystyle Y}$ component of ${\displaystyle YD_{B}D_{R}}$ is the same as the ${\displaystyle Y}$ component of ${\displaystyle Y}$${\displaystyle U}$${\displaystyle V}$. ${\displaystyle D_{B}}$ and ${\displaystyle D_{R}}$ are related to the ${\displaystyle U}$ and ${\displaystyle V}$ components of the YUV colour space as follows:

${\displaystyle {\begin{aligned}D_{B}&=+3.059U\\D_{R}&=-2.169V\end{aligned}}}$

References※

• Shi, Yun Q. and Sun, Huifang Image and Video Compression for Multimedia Engineering, CRC Press, 2000 ISBN 0-8493-3491-8

See also※

• YUV - related colour system