YDbDr

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Short description: Colour space used in the SECAM analog color TV standard
An image along with its [math]\displaystyle{ Y }[/math], [math]\displaystyle{ D_B }[/math] and [math]\displaystyle{ D_R }[/math] components.

YDbDr, sometimes written [math]\displaystyle{ YD_BD_R }[/math], is the colour space[1] used in the SECAM (adopted in France and some countries of the former Eastern Bloc) and PAL-N (adopted in Argentina, Paraguay and Uruguay) analog colour television broadcasting standards.[2][3][4] It is very close to YUV (used on the PAL system) and its related colour spaces such as YIQ (used on the NTSC system), YPbPr and YCbCr.[5][6]

[math]\displaystyle{ YD_BD_R }[/math] is composed of three components: [math]\displaystyle{ Y }[/math], [math]\displaystyle{ D_B }[/math] and [math]\displaystyle{ D_R }[/math]. [math]\displaystyle{ Y }[/math] is the luminance, [math]\displaystyle{ D_B }[/math] and [math]\displaystyle{ D_R }[/math] are the chrominance components, representing the red and blue colour differences.[7]

Formulas

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

These formulae approximate the conversion between the RGB colour space and [math]\displaystyle{ YD_BD_R }[/math].

[math]\displaystyle{ \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]\displaystyle{ \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]\displaystyle{ \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]\displaystyle{ Y }[/math] component of [math]\displaystyle{ YD_BD_R }[/math] is the same as the [math]\displaystyle{ Y }[/math] component of [math]\displaystyle{ Y }[/math][math]\displaystyle{ U }[/math][math]\displaystyle{ V }[/math]. [math]\displaystyle{ D_B }[/math] and [math]\displaystyle{ D_R }[/math] are related to the [math]\displaystyle{ U }[/math] and [math]\displaystyle{ V }[/math] components of the YUV colour space as follows:

[math]\displaystyle{ \begin{align} D_B &= + 3.059 U\\ D_R &= - 2.169 V\end{align} }[/math]

References

  1. ↑ (in en) Issues in Electronic Circuits, Devices, and Materials: 2011 Edition. ScholarlyEditions. 2012-01-09. pp. 1146. ISBN 978-1-4649-6373-5. https://books.google.com/books?id=R6VBtXAIi7oC&dq=YDbDr&pg=PA1146. 
  2. ↑ RECOMMENDATION ITU-R BT.470-6 - CONVENTIONAL TELEVISION SYSTEMS. ITU-R. 1998. https://www.itu.int/dms_pubrec/itu-r/rec/bt/R-REC-BT.470-6-199811-S!!PDF-E.pdf. 
  3. ↑ Shi, Yun-Qing; Sun, Huifang (2019-03-07) (in en). Image and Video Compression for Multimedia Engineering: Fundamentals, Algorithms, and Standards, Third Edition. CRC Press. ISBN 978-1-351-57864-6. https://books.google.com/books?id=DkqMDwAAQBAJ&dq=YDbDr&pg=PT43. 
  4. ↑ Dorf, Richard C. (2018-10-03) (in en). Circuits, Signals, and Speech and Image Processing. CRC Press. ISBN 978-1-4200-0308-6. https://books.google.com/books?id=N05sBgAAQBAJ&dq=YDbDr&pg=SA18-PA3. 
  5. ↑ Hoang, Dzung Tien; Vitter, Jeffrey Scott (2002-02-21) (in en). Efficient Algorithms for MPEG Video Compression. Wiley. ISBN 978-0-471-37942-3. https://books.google.com/books?id=AT8fAQAAIAAJ&q=YDbDr. 
  6. ↑ Shum, Heung-Yeung; Chan, Shing-Chow; Kang, Sing Bing (2008-05-26) (in en). Image-Based Rendering. Springer Science & Business Media. ISBN 978-0-387-32668-9. https://books.google.com/books?id=93J3Z96ZVwoC&dq=YDbDr&pg=PA208. 
  7. ↑ ASC, David Stump (2021-11-18) (in en). Digital Cinematography: Fundamentals, Tools, Techniques, and Workflows. Routledge. ISBN 978-0-429-88901-1. https://books.google.com/books?id=A1I_EAAAQBAJ&dq=YDbDr&pg=PA75. 
  • Shi, Yun Q. and Sun, Huifang Image and Video Compression for Multimedia Engineering, CRC Press, 2000 ISBN:0-8493-3491-8

See also



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