Editing YDbDr (section)

== Formulas ==
The three component signals are created from an original <math>RGB</math> (red, green and blue) source. The weighted values of <math>R</math>, <math>G</math> and <math>B</math> are added together to produce a single <math>Y</math> signal, representing the overall brightness, or luminance, of that spot. The <math>D_B</math> signal is then created by subtracting the <math>Y</math> from the blue signal of the original <math>RGB</math>, and then scaling; and <math>D_R</math> by subtracting the <math>Y</math> from the red, and then scaling by a different factor.

These formulae approximate the conversion between the [[RGB color model|RGB]] colour space and <math>YD_BD_R</math>.

:<math>\begin{align}
R, G, B, Y &\in \left[ 0, 1 \right]\\
D_B, D_R &\in \left[ -1.333, 1.333 \right]\end{align}</math>

'''From RGB to YDbDr:'''
:<math>\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}</math>

'''From YDbDr to RGB:'''
:<math>\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}</math>

You may note that the <math>Y</math> component of <math>YD_BD_R</math> is the same as the <math>Y</math> component of <math>Y</math><math>U</math><math>V</math>. <math>D_B</math> and <math>D_R</math> are related to the <math>U</math> and <math>V</math> components of the [[YUV#SDTV with BT.601|YUV]] colour space as follows:
:<math>\begin{align}
D_B &= + 3.059 U\\
D_R &= - 2.169 V\end{align}</math>