# YDbDr

An image along with its ${\displaystyle Y}$, ${\displaystyle D_{B}}$ and ${\displaystyle D_{R}}$ components.

YDbDr, sometimes written YDBDR, is the colour space used in the SECAM analog terrestrial colour television broadcasting standard, which is used in France and some countries of the former Eastern Bloc. It is very close to YUV (PAL) and its related colour spaces such as YIQ (NTSC), YPbPr and YCbCr.

YDbDr 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 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 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 YDbDr.

{\displaystyle {\begin{aligned}R,G,B,Y&\in \left[0,1\right]\\D_{B},D_{R}&\in \left[-1.333,1.333\right]\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 YDbDr is the same as the ${\displaystyle Y}$  component of YUV. ${\displaystyle D_{B}}$  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}}}

There is also a variety of the PAL broadcasting standard, PAL-N, that uses the YDbDr colour space.

## References

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