Editing YDbDr

{{Short description|Colour space used in the SECAM analog color TV standard}}

[[File:YDbDr components.jpg|right|thumb|An image along with its <math>Y</math>, <math>D_B</math> and <math>D_R</math> components.]]

'''YDbDr''', sometimes written <math>YD_BD_R</math>, is the [[colour space]]<ref>{{cite book |url=https://books.google.com/books?id=R6VBtXAIi7oC&dq=YDbDr&pg=PA1146 |title=Issues in Electronic Circuits, Devices, and Materials: 2011 Edition |date=2012-01-09 |publisher=ScholarlyEditions |isbn=978-1-4649-6373-5 |pages=1146 |language=en}}</ref> used in the [[SECAM]] (adopted in [[France]] and some countries of  the former [[Eastern Bloc]]) analog colour [[television]] broadcasting standard.<ref name=":0">{{cite book |url=https://www.itu.int/dms_pubrec/itu-r/rec/bt/R-REC-BT.470-6-199811-S!!PDF-E.pdf |title=Recommendation ITU-R BT.470-6 - Conventional Television Systems |publisher=ITU-R |year=1998}}</ref><ref>{{cite book |last1=Shi |first1=Yun-Qing |url=https://books.google.com/books?id=DkqMDwAAQBAJ&dq=YDbDr&pg=PT43 |title=Image and Video Compression for Multimedia Engineering: Fundamentals, Algorithms, and Standards, Third Edition |last2=Sun |first2=Huifang |date=2019-03-07 |publisher=CRC Press |isbn=978-1-351-57864-6 |language=en}}</ref><ref>{{cite book |last=Dorf |first=Richard C. |url=https://books.google.com/books?id=N05sBgAAQBAJ&dq=YDbDr&pg=SA18-PA3 |title=Circuits, Signals, and Speech and Image Processing |date=2018-10-03 |publisher=CRC Press |isbn=978-1-4200-0308-6 |language=en}}</ref> It is very close to [[Y′UV|YUV]] (used on the [[PAL]] system) and its related colour spaces such as [[YIQ]] (used on the [[NTSC]] system), [[YPbPr]] and [[YCbCr]].<ref>{{cite book |last1=Hoang |first1=Dzung Tien |url=https://books.google.com/books?id=AT8fAQAAIAAJ&q=YDbDr |title=Efficient Algorithms for MPEG Video Compression |last2=Vitter |first2=Jeffrey Scott |date=2002-02-21 |publisher=Wiley |isbn=978-0-471-37942-3 |language=en}}</ref><ref>{{cite book |last1=Shum |first1=Heung-Yeung |url=https://books.google.com/books?id=93J3Z96ZVwoC&dq=YDbDr&pg=PA208 |title=Image-Based Rendering |last2=Chan |first2=Shing-Chow |last3=Kang |first3=Sing Bing|author3-link=Sing Bing Kang |date=2008-05-26 |publisher=Springer Science & Business Media |isbn=978-0-387-32668-9 |language=en}}</ref>

<math>YD_BD_R</math> is composed of three components: <math>Y</math>, <math>D_B</math> and <math>D_R</math>. <math>Y</math> is the [[Luma (video)|luminance]], <math>D_B</math> and <math>D_R</math> are the [[chrominance]] components, representing the [[R-Y|red]] and [[B-Y|blue colour differences]]<!--from Y-->.<ref>{{cite book |last=ASC |first=David Stump |url=https://books.google.com/books?id=A1I_EAAAQBAJ&dq=YDbDr&pg=PA75 |title=Digital Cinematography: Fundamentals, Tools, Techniques, and Workflows |date=2021-11-18 |publisher=Routledge |isbn=978-0-429-88901-1 |language=en}}</ref>

== 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>

== See also ==
* [[Y′UV#SDTV_with_BT.470|YUV]] - related colour system

== References ==
{{reflist}}

* Shi, Yun Q. and Sun, Huifang ''Image and Video Compression for Multimedia Engineering'', CRC Press, 2000 {{ISBN|0-8493-3491-8}}

{{Color space}}

[[Category:Color space]]