ColorBars theory

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SMPTE color bars

filter: ColorBars ...

Description of encoded colour-bar 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) and Rec. ITU-R BT.18..).

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

In the SMPTE color bars the top two-thirds of the image consists of seven colorbars. ... Rec.601 75%, later Rec.709 at 100%. Below those seven bars a combination of blue, magenta, cyan, and white boxes is given. When a television receiver is set to filter out all colors except for blue, these boxes, combined with the of color bars, are used to properly adjust the color controls. If they are properly adjusted, there is no visible distinction between the bars and the boxes, and you should see four solid blue bars. The bottom section of the test pattern is called the pluge ... is used to ...

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

light grey (0.75,0.75,0.75)
yellow (1,1,0)
cyan (0,1,1)
green (0,1,0)
magenta (1,0,1)
red (1,0,0)
blue (0,0,1)

black and white are given by

white (1,1,1)
black (0,0,0)

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

Y,Cb,Cr [16,235]

As an example, consider the color yellow (0.75,0.75,0) (the used color conversions can be found here: Color conversions):

yellow:

Y = Kr*R + Kg*G + Kb*B = 0.75*(0.299 + 0.587)*219 + 16 = 0.6645*219 + 16 = 161.53 = 162

Cb = (B-Y)/(1-Kb) = (0 - 0.6645)/(1-0.114)*112 + 128 = -0.75*112 + 128 = 44

Cr = (R-Y)/(1-Kr) = (0.75 - 0.6645)/(1-0.299)*112 + 128 = 0.1220*112 + 128 = 141.66 = 142

color YCbCr
light grey 180,128,128 (b48080)
yellow 162,44,142 (a22c8e)
cyan 131,156,44 (839c2c)
green 112,72,58 (70483a)
magenta 84,184,198 (54b8c6)
red 65,100,212 (4164d4)
blue 35,212,114 (23d472)

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

color RGB
light grey 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)

white: 235,235,235 (ebebeb)

black: 16,16,16 (101010)

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

Y,Cb,Cr [16,235]

color YCbCr
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]

color RGB
light grey 235,235,235 (ebebeb) (white !!!)
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

-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]

color YCbCr
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 (1,1,1): 235,128,128 (eb8080)

black (0,0,0): 16,128,128 (108080)

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

Y,Cb,Cr [16,235]

color YCbCr
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:

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