YDbDr explained

YDbDr, sometimes written

YD _{BD} _{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]} YD _{BD} _{R} is composed of three components: Y , D _{B} and D _{R} . Y is the luminance, D _{B} and D _{R} are the chrominance components, representing the red and blue colour differences.^[7]

Formulas

The three component signals are created from an original

RGB (red, green and blue) source. The weighted values of R , G and B are added together to produce a single Y signal, representing the overall brightness, or luminance, of that spot. The D _{B} signal is then created by subtracting the Y from the blue signal of the original RGB , and then scaling; and D _{R} by subtracting the Y from the red, and then scaling by a different factor.

These formulae approximate the conversion between the RGB colour space and

YD _{BD} _{R} .\begin{align} R, G, B, Y &\in \left[ 0 , 1 \right]\\ D _{B,} D _{R} &\in \left[ -1 . 333 , 1 . 333 \right]\end{align}

From RGB to YDbDr:

\begin{align} Y & = +0 . 299 R +0 . 587 G +0 . 114 B\\ D _{B} & = -0 . 450 R -0 . 883 G +1 . 333 B\\ D _{R} & = -1 . 333 R +1 . 116 G +0 . 217 B\\ \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{align}

From YDbDr to RGB:

\begin{align} R & = Y +0 . 000092303716148 D _{B} -0 . 525912630661865 D _{R\\ G} & = Y -0 . 129132898890509 D _{B} +0 . 267899328207599 D _{R\\ B} & = Y +0 . 664679059978955 D _{B} -0 . 000079202543533 D _{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{align}

You may note that the

Y component of YD _{BD} _{R} is the same as the Y component of Y U V . D _{B} and D _{R} are related to the U and V components of the YUV colour space as follows:\begin{align} D _{B} & = + 3 . 059 U\\ D _{R} & = - 2 . 169 V\end{align}

References

• Shi, Yun Q. and Sun, Huifang Image and Video Compression for Multimedia Engineering, CRC Press, 2000

See also

• YUV - related colour system

Notes and References

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