# YDbDr

An image along with its $Y$, $D_B$ and $D_R$ components.

YDbDr, sometimes written YDBDR, is the colour space used in the SÉCAM 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 - $Y$, $D_B$ and $D_R$. $Y$ is the luminance, $D_B$ and $D_R$ are the chrominance components, representing the red and blue colour differences.

## 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 YDbDr.

\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 +0.217B\\ \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{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 YDbDr is the same as the $Y$ component of YUV. $D_B$ 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}

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