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 +0.217B\\ \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 YD_BD_R 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} == See also ==