YDbDr, sometimes written ${\displaystyle YD_{B}D_{R))$, is the colour space[1] used in the SECAM (adopted in France and some countries of the former Eastern Bloc) analog colour television broadcasting standard.[2][3][4] 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.[5][6]

${\displaystyle YD_{B}D_{R))$ 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.[7]

## 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[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))}

## References

1. ^ Issues in Electronic Circuits, Devices, and Materials: 2011 Edition. ScholarlyEditions. 2012-01-09. p. 1146. ISBN 978-1-4649-6373-5.
2. ^ RECOMMENDATION ITU-R BT.470-6 - CONVENTIONAL TELEVISION SYSTEMS (PDF). ITU-R. 1998.
3. ^ Shi, Yun-Qing; Sun, Huifang (2019-03-07). Image and Video Compression for Multimedia Engineering: Fundamentals, Algorithms, and Standards, Third Edition. CRC Press. ISBN 978-1-351-57864-6.
4. ^ Dorf, Richard C. (2018-10-03). Circuits, Signals, and Speech and Image Processing. CRC Press. ISBN 978-1-4200-0308-6.
5. ^ Hoang, Dzung Tien; Vitter, Jeffrey Scott (2002-02-21). Efficient Algorithms for MPEG Video Compression. Wiley. ISBN 978-0-471-37942-3.
6. ^ Shum, Heung-Yeung; Chan, Shing-Chow; Kang, Sing Bing (2008-05-26). Image-Based Rendering. Springer Science & Business Media. ISBN 978-0-387-32668-9.
7. ^ ASC, David Stump (2021-11-18). Digital Cinematography: Fundamentals, Tools, Techniques, and Workflows. Routledge. ISBN 978-0-429-88901-1.
• Shi, Yun Q. and Sun, Huifang Image and Video Compression for Multimedia Engineering, CRC Press, 2000 ISBN 0-8493-3491-8