ColorBars theory

Revision as of 01:07, 13 April 2015 (view source) Raffriff42 (Talk | contribs) (add mis-adjusted color bars image) ← Older edit		Revision as of 16:57, 6 March 2016 (view source) Admin (Talk | contribs) (→‎the pluge using Rec.601 coefficients) Newer edit →
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	==== the pluge using Rec.601 coefficients ====		==== 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: ...		-4/0/4 IRE levels: ...
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	+Q = rgb{75, 15, 126} = hex rgb{4B, 0F, 7E}		+Q = rgb{75, 15, 126} = hex rgb{4B, 0F, 7E}
	-I = rgb{0, 58, 98} = hex rgb{0, 3A, 62}		-I = rgb{0, 58, 98} = hex rgb{0, 3A, 62}
−
	== 100/0/75/0 bars using Rec.709 coefficients ==		== 100/0/75/0 bars using Rec.709 coefficients ==

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Revision as of 16:57, 6 March 2016

Description of encoded colour-bar^[1] 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^[2] and Rec. ITU-R BT.1927).

filter: ColorBars and ColorBarsHD

Contents 1 SMPTE color bars 2 100/0/75/0 bars using Rec.601 coefficients 2.1 Y,Cb,Cr [16,235] 2.2 R,G,B [16,235] 3 100/0/100/0 bars using Rec.601 coefficients 3.1 Y,Cb,Cr [16,235] 3.2 R,G,B [16,235] 3.3 the pluge using Rec.601 coefficients 4 100/0/75/0 bars using Rec.709 coefficients 4.1 Y,Cb,Cr [16,235] 5 100/0/100/0 bars using Rec.709 coefficients 5.1 Y,Cb,Cr [16,235] 5.2 the pluge using Rec.709 coefficients

SMPTE color bars

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]):

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

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:

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

The bottom section contains a pattern called the Pluge^[3], which is used to set up monitor black levels^[4]

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	(hex)
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	(hex)
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	(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]

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]

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]

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:

• SMPTE Color Bars
• Rec. ITU-R BT.801-1 (Rec.601 coefficients)
• 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