View source for ColorBars theory

Description of encoded colour-bar<sup>[http://en.wikipedia.org/wiki/SMPTE_color_bars]</sup> signals according to the 4:2:2 level of Recommendation ITU-R BT.601 and ITU-R BT.709. Those are described in Rec. ITU-R BT.801-1<sup>[http://www.itu.int/rec/R-REC-BT.801/en]</sup> and Rec. ITU-R BT.1927).

filter: [[ColorBars|ColorBars and ColorBarsHD]]

== SMPTE color bars ==

[[File:SMPTE_Color_Bars-320x240.png]]

The SMPTE color bars - RGB [16,235] (Rec.601 coefficients, 75% intensity)

From left to right, 75% colorbars consists of the following colors (given in normalized colorspace rgb [0,1]):

{| border="1"
|-
! color
! RGB
|-
| 75% white
| (0.75, 0.75, 0.75)
|-
| 75% yellow
| (0.75, 0.75, 0)
|-
| 75% cyan
| (0, 0.75, 0.75)
|-
| 75% green
| (0, 0.75, 0)
|-
| 75% magenta
| (0.75, 0, 0.75)
|-
| 75% red
| (0.75, 0, 0)
|-
| 75% blue
| (0, 0, 0.75)
|}

Black and white in this colorspace are given by

{| border="1"
|-
! color
! RGB
|-
| 100% white
| (1, 1, 1)
|-
| black
| (0, 0, 0)
|}


In the SMPTE color bars the top two-thirds of the image consists of seven colorbars and below them, seven shorter bars or boxes. When a television receiver or monitor is properly adjusted and set to filter out all colors except for blue, there is no visible distinction between the bars and the boxes beneath them, and you should see four solid blue bars like this:

[[File:SMPTE_Color_Bars-320x240-blue_only.png]]

If the colors are mis-adjusted, you may see a visible break in the bars like this:

[[File:SMPTE_Color_Bars-320x240-blue_only-bad.png]]


The bottom section contains a pattern called the Pluge<sup>[http://en.wikipedia.org/wiki/Picture_line-up_generation_equipment]</sup>, which is used to set up monitor black levels<sup>[http://www.spearsandmunsil.com/portfolio/setting-the-brightness-control-2]</sup>


== 100/0/75/0 bars using Rec.601 coefficients ==

==== Y,Cb,Cr [16,235] ====

{| border="1"
|-
! color
! YCbCr
! hex
|-
| gray
| 104,128,128
| b48080
|-
| 75% white
| 180,128,128
| b48080
|-
| yellow
| 168,44,136
| a82c88
|-
| cyan
| 145,147,44
| 91932c
|-
| green
| 133,63,52
| 853f34
|-
| magenta
| 63,193,204
| 3fc1cc
|-
| red
| 51,109,212
| 336dd4
|-
| blue
| 28,212,120
| 1cd478
|-
| 100% white
| 235,128,128 
| eb8080
|-
| black
| 16,128,128 
| 108080
|}

==== R,G,B [16,235] ====
 yellow: 
 R = 0.75*219 + 16 = 180.25 = 180
 G = 0.75*219 + 16 = 180.25 = 180
 B = 0*219 + 16 = 16

{| border="1"
|-
! color
! RGB
! hex
|-
| gray
| 104,104,104 
| b4b4b4
|-
| 75% white
| 180,180,180 
| b4b4b4
|-
| yellow
| 180,180,16 
| b4b410
|-
| cyan
| 16,180,180 
| 10b4b4
|-
| green
| 16,180,16 
| 10b410
|-
| magenta
| 180,16,180 
| b410b4
|-
| red
| 180,16,16 
| b41010
|-
| blue
| 16,16,180 
| 1010b4
|-
| 100% white
| 235,235,235 
| ebebeb
|-
| black
| 16,16,16 
| 101010
|}

== 100/0/100/0 bars using Rec.601 coefficients ==

==== Y,Cb,Cr [16,235] ====

{| border="1"
|-
! color
! YCbCr
! (hex)
|-
| light grey
| 180,128,128 
| b48080
|-
| yellow
| 210,16,146 
| d21092
|-
| cyan
| 170,166,16 
| aaa610
|-
| green
| 145,54,34 
| 913622
|-
| magenta
| 106,202,222 
| 6acade
|-
| red
| 81,90,240 
| 515af0
|-
| blue
| 41,240,110 
| 29f06e
|-
| white
| 235,128,128 
| eb8080
|-
| black
| 16,128,128 
| 108080
|}


==== R,G,B [16,235] ====

{| border="1"
|-
! color
! RGB
! (hex)
|-
| light grey
| 178,178,178 
| b2b2b2
|-
| yellow
| 235,235,16 
| ebeb10
|-
| cyan
| 16,235,235 
| 10ebeb
|-
| green
| 16,235,16 
| 10eb10
|-
| magenta
| 235,16,235 
| eb10eb
|-
| red
| 235,16,16 
| eb1010
|-
| blue
| 16,16,235 
| 1010eb
|-
| white
| 235,235,235 
| ebebeb
|-
| black
| 16,16,16 
| 101010
|}


==== the pluge using Rec.601 coefficients ====

todo: fix (see http://forum.videohelp.com/threads/377237-Purple-green-VHS?p=2435970&viewfull=1#post2435970, and check code of Colorbars again)

-4/0/4 IRE levels: ...

+Q/-I levels:

 100% * 20IRE / 92.5IRE = 21.6216% = 0.2162 
(include reference to 20IRE ...)

The components iq can be obtained by rotating vu 33 degrees poyton - eq.33 (Poyton wrong; det!=1, or am I too drunk?), that is
 Q = V*cos(Pi*33/180) + U*sin(Pi*33/180)
 I = - V*sin(Pi*33/180) + U*cos(Pi*33/180)

and thus
 V = Q*cos(Pi*33/180) - I*sin(Pi*33/180)
 U = Q*sin(Pi*33/180) + I*cos(Pi*33/180)

The components vu can be obtained from B-Y and R-Y in the following way poyton - eq.33:
 V = 0.492*(B-Y_601)
 U = 0.877*(R-Y_601)
 +Q: Q=0.2162, I=0, Y=0

 0.492*(B-Y_601) = Q*cos(Pi*33/180) - I*sin(Pi*33/180) = 0.2162*cos(Pi*33/180) = 0.1813
 0.877*(R-Y_601) = Q*sin(Pi*33/180) + I*cos(Pi*33/180) = 0.2162*sin(Pi*33/180) = 0.1178

 Y_601 = 0
 R-Y_601 = 0.1178/0.877 = 0.1343 => R = 0.1343
 B-Y_601 = 0.1813/0.492 = 0.3685 => B = 0.3685

 G = (Y_601 - Kr*R - Kb*B)/Kg = (0 - 0.299*0.1343 - 0.114*0.3685)/0.587 = -0.1400
 Cb_601 = (B - Y_601)/(1-Kb) = 0.4159
 Cr_601 = (R - Y_601)/(1-Kr) = 0.1742

thus for ycbcr [16,235]: 
 y = 16, 
 cb = 112*0.4159+128 = 175, 
 cr = 112*0.1742+128 = 148

and for rgb [16,235]: 
 r = 219*0.1343+16 = 45, 
 g = 219*(-0.1400)+16 = -15, 
 b = 219*0.3685+16 = 97

 -I: q=0, i=-0.2162, Y=0 

 0.492*(B-Y_601) = Q*cos(Pi*33/180) - I*sin(Pi*33/180) = 0.2162*sin(Pi*33/180) = 0.1178
 0.877*(R-Y_601) = Q*sin(Pi*33/180) + I*cos(Pi*33/180) = -0.2162*cos(Pi*33/180) = -0.1813

 Y_601 = 0
 R-Y_601 = -0.1813/0.877 = -0.2067 => R = -0.2067
 B-Y_601 = 0.1178/0.492 = 0.2394 => B = 0.2394
 
 G = (Y_601 - Kr*R - Kb*B)/Kg = (0 - 0.299*(-0.2067) - 0.114*0.2394)/0.587 = 0.0588
 Cb_601 = (B - Y_601)/(1-Kb) = 0.2701
 Cr_601 = (R - Y_601)/(1-Kr) = -0.2949
 
thus for ycbcr [16,235]: 
 y = 16, 
 cb = 112*0.2701+128 = 158, 
 cr = 112*(-0.2949)+128 = 95
 
and for rgb [16,235]: 
 r = 219*(-0.2067)+16 = -29, 
 g = 219*0.0588+16 = 29, 
 b = 219*0.2394+16 = 68

While ycbcr is a valid color, the corresponding rgb value is not, since r is negative. Instead of rounding it to zero, the luminance is highered to make red zero (this is done in in AviSynth v2.57). As a consequence the green for the +Q signal is also positive. This way the phase of the YIQ signal is preserved. r is zero for R = -16/219 = -0.0731, and thus Y_601 = -0.0731+0.2067 = 0.1336. It follow that:
 +Q: Q=0.2162, I=0, Y=0.1336

 R = 0.1343 + 0.1336 = 0.2679
 B = 0.3685 + 0.1336 = 0.5021
 G = -0.1400 + 0.1336 = -0.0064
 
and thus for rgb [16,235]:
 r = 219*0.2679+16 = 75, 
 b = 219*0.5021+16 = 126, 
 g = 219*(-0.0064)+16 = 15

 -I: Q=0, I=-0.2162, Y=0.1336

 R = -0.2067 + 0.1336 = -0.0731
 B = 0.2394 + 0.1336 = 0.3730
 G = 0.0588 + 0.1336 = 0.1924
 
and thus for rgb [16,235]: 
 r = 219*(-0.0731)+16 = 0, 
 b = 219*0.3730+16 = 98, 
 g = 219*0.1924+16 = 58

..........................
ycbcr the same?
..........................

 +Q = ycbcr{16, 175, 148} = hex ycbcr{10, AD, 94}
 -I = ycbcr{16, 158, 95} = hex ycbcr{10, 9E, 5F}

 +Q = rgb{75, 15, 126} = hex rgb{4B, 0F, 7E}
 -I = rgb{0, 58, 98} = hex rgb{0, 3A, 62}

== 100/0/75/0 bars using Rec.709 coefficients ==

==== Y,Cb,Cr [16,235] ====

{| border="1"
|-
! color
! YCbCr
! (hex)
|-
| light grey
| 180,128,128 
| b48080
|-
| yellow
| 168,44,136 
| a82c88
|-
| cyan
| 145,147,44 
| 91932c
|-
| green
| 134,63,52 
| 863f34
|-
| magenta
| 63,193,204 
| 3fc1cc
|-
| red
| 51,109,212 
| 336dd4
|-
| blue
| 28,212,120 
| 1cd478
|-
| white
| 235,128,128 
| eb8080
|-
| black
| 16,128,128 
| 108080
|}


== 100/0/100/0 bars using Rec.709 coefficients ==

==== Y,Cb,Cr [16,235] ====

{| border="1"
|-
! color
! YCbCr
! (hex)
|-
| light grey
| 180,128,128 
| b48080
|-
| yellow
| 219,16,138 
| db108a
|-
| cyan
| 188,154,16 
| bc9a10
|-
| green
| 173,42,26 
| ad1a2a
|-
| magenta
| 78,214,230 
| 4ed6e6
|-
| red
| 63,102,240 
| 3f66f0
|-
| blue
| 32,240,118 
| 20f076
|-
| white
| 235,128,128 
| eb8080
|-
| black
| 16,128,128 
| 108080
|}


==== the pluge using Rec.709 coefficients ====

 -4,0,+4 IRE: same as 1c.
 
 +Q: q=0.2162, i=0, y=0 -I: q=0, i=-0.2162, y=0
 
 +Q = ycbcr{16, 172.4, 145.7} = hex ycbcr{10, AC, 92} -I = ycbcr{16, 156.8, 98.6} = hex ycbcr{10, 9D, 63}
 
 +Q: q=0.2162, i=0, y=0.134 (makes red zero for -I) -I: q=0, i=-0.2162, y=0.134 (makes red zero for -I)
 
 +Q = rgb{74.8, 17.2, 125.9} = hex rgb{4B, 11, 7E} -I = rgb{0, 53.5, 97.6} = hex rgb{0, 36, 62}


Looking at Poynton again:

http://www.poynton.com/notes/colour_and_gamma/ColorFAQ.html

It says that YUV is derived (defined is a better word) from Y_601,B-Y_601,R-Y_601. So, it's not derived from Y_709. To compute the corresponding YCbCr for Rec.709 one should do the following:

 YUV->RGB->YCbCr (Rec.709)

But i guess that's only possible after "correcting RGB (raising luma with 13.4%)". The uncorrected (negative) RGB values are used to do this.

References:

* [http://en.wikipedia.org/wiki/SMPTE_color_bars SMPTE Color Bars]
* [http://www.itu.int/rec/R-REC-BT/recommendation.asp?lang=en&parent=R-REC-BT.801 Rec. ITU-R BT.801-1] (Rec.601 coefficients)
* [http://www.itu.int/rec/R-REC-BT/recommendation.asp?lang=en&parent=R-REC-BT.1729 Rec. ITU-R BT.1729] (Rec.709 coefficients)
* http://en.wikipedia.org/wiki/Color_bars
* todo: see links in http://forum.doom9.org/showthread.php?p=795723#post795723

[[Category:Advanced topics]]