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# YDbDr

YDbDr is the colour space used in the SÉCAM colour television broadcasting standard, which is used in France and some countries of the former Eastern Bloc. It is very close to YUV and its related colour spaces such as YIQ, YPbPr and YCbCr.

YDbDr is composed of three components - Y, Db and Dr. Y is the luminance, and Db and Dr are the chrominance components (representing the red and blue colour differences).

## Formulas

The Y, Db and Dr 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 Db signal is then created by subtracting the Y from the blue signal of the original RGB, and then scaling; and Dr 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.

$R, G, B, Y in left\left[0, 1 right\right]$
$Db in left\left[-1.333, 1.333 right\right]$
$Dr in left\left[-1.333, 1.333 right\right]$
From RGB to YDbDr:
$Y =$ $0.299R$ $+0.587G$ $+0.114B$
$Db =$ $-0.450R$ $-0.883G$ $+1.333B$
$Dr =$ $-1.333R$ $+1.116G$ $+0.217B$
From YDbDr to RGB:
$R =$ $Y$ $+0.000092303716148Db$ $-0.525912630661865Dr$
$G =$ $Y$ $-0.129132898890509Db$ $+0.267899328207599Dr$
$B =$ $Y$ $+0.664679059978955Db$ $-0.000079202543533Dr$
Or, using a matrix representation:

$begin\left\{bmatrix\right\} Y Db Dr end\left\{bmatrix\right\} = begin\left\{bmatrix\right\} 0.299 & 0.587 & 0.114 -0.450 & -0.883 & 1.333 -1.333 & 1.116 & 0.217 end\left\{bmatrix\right\} begin\left\{bmatrix\right\} R G B end\left\{bmatrix\right\}$

$begin\left\{bmatrix\right\} R G B end\left\{bmatrix\right\} = begin\left\{bmatrix\right\} 1 & 0.000092303716148 & -0.525912630661865 1 & -0.129132898890509 & 0.267899328207599 1 & 0.664679059978955 & -0.000079202543533 end\left\{bmatrix\right\} begin\left\{bmatrix\right\} Y Db Dr end\left\{bmatrix\right\}$

You may note that the Y component of YDbDr is the same as the Y component of YUV. Db and Dr are related to the U and V components of the YUV colour space as follows:

$Db =$ $+ 3.059U$
$Dr =$ $- 2.169V$
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