YDbDr

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 +0.217B\ \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}

References

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

References

1. (2012-01-09). "Issues in Electronic Circuits, Devices, and Materials: 2011 Edition". ScholarlyEditions.
2. (1998). "Recommendation ITU-R BT.470-6 - Conventional Television Systems". ITU-R.
3. (2019-03-07). "Image and Video Compression for Multimedia Engineering: Fundamentals, Algorithms, and Standards, Third Edition". CRC Press.
4. Dorf, Richard C.. (2018-10-03). "Circuits, Signals, and Speech and Image Processing". CRC Press.
5. (2002-02-21). "Efficient Algorithms for MPEG Video Compression". Wiley.
6. (2008-05-26). "Image-Based Rendering". Springer Science & Business Media.
7. ASC, David Stump. (2021-11-18). "Digital Cinematography: Fundamentals, Tools, Techniques, and Workflows". Routledge.