YDbDr

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 ${\displaystyle YD_{B}D_{R}}$ .

${\displaystyle {\begin{aligned}R,G,B,Y&\in \left[0,1\right]\\D_{B},D_{R}&\in \left[-1.333,1.333\right]\end{aligned}}}$ 

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 ${\displaystyle YD_{B}D_{R}}$  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:

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

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

• YUV - related colour system