一、 公式：基于BT.601-6
BT601 CbCr 的坐标图（量化后）： （横坐标为u，纵坐标为v，左下角为原点）
通过坐标图我们可以看到UV并不会包含整个坐标系，而是呈一个旋转了一定角度的八边形, U越大蓝色越蓝，V越大，红色越红。
名词解释：
**量化后**: Y~[16,235] Cb ~[16-240] Cr~[16-240] 量化就是让通过线性变换让Y 或 U 或V 处于一定的范围内， 比如让Y 【0,1】变到 Y' (16,235) 就这样来实行： Y' = Y* （235-16）/(1-0) + 16 即 Y' = 219*Y + 16
**未量化**: Y~ [0,1] U,V~[-0.5,0.5]
**YUV 和 YCbCr的区别**： YUV是模拟型号， 取值范围为Y~[0-1] U/V~[-0.5, 0.5] , YCbCr 是数字信号， 取值范围为 Y ~[16, 235] UV~[16, 240]
**关于为什么要量化？ **
以下是维基百科摘抄的一段， 意思是量化是为了解决滤波后的过冲现象，
Y′ values are conventionally shifted and scaled to the range [16, 235] (referred to as studio swing or "TV levels") rather than using the full range of [0, 255] (referred to as full swing or "PC levels"). This practice was standardized in SMPTE-125M in order to accommodate signal overshoots ("ringing") due to filtering. The value 235 accommodates a maximal black-to-white overshoot of 255 − 235 = 20, or 20 / (235 − 16) = 9.1%, which is slightly larger than the theoretical maximal overshoot (Gibbs phenomenon) of about 8.9% of the maximal step. The toe-room is smaller, allowing only 16 / 219 = 7.3% overshoot, which is less than the theoretical maximal overshoot of 8.9%. This is why 16 is added to Y′ and why the Y′ coefficients in the basic transform sum to 220 instead of 255.[9]U and V values, which may be positive or negative, are summed with 128 to make them always positive, giving a studio range of 16–240 for U and V. (These ranges are important in video editing and production, since using the wrong range will result either in an image with "clipped" blacks and whites, or a low-contrast image.)
关于如何判断图像是否经过量化？
在完全黑画面的时候打印出图像的Y数据， 如果Y=16左右 说明Y经过量化 ，如果Y=0左右 说明Y未经过量化
以下具体为各种转换公式
1.小数形式,未量化 ( U~[-0.5-0.5] , R~[0,1] ), 其中RGB 是经过Gamma 变换后的非线性信号
R = Y + 1.4075 * V;
G = Y - 0.3455 * U - 0.7169*V;
B = Y + 1.779 * U;
Y = 0.299*R + 0.587*G + 0.114*B;
U = (B-Y)/1.772;
V = (R-Y)/1.402;
或写为：
Y = 0.299*R + 0.587*G + 0.114*B;
U = -0.169*R - 0.331*G + 0.5 *B ;
V = 0.5 *R - 0.419*G - 0.081*B;
2.整数形式（减少计算量）未量化 R，G，B~[0,255] U，V~[-128,128]
R= Y + ((360 * (V - 128))>>8) ;
G= Y - (( ( 88 * (U - 128) + 184 * (V - 128)) )>>8) ;
B= Y +((455 * (U - 128))>>8) ;
Y = (77*R + 150*G + 29*B)>>8;
U = ((-44*R - 87*G + 131*B)>>8) + 128;
V = ((131*R - 110*G - 21*B)>>8) + 128 ;
3. 量化后的公式( Y~(16,235) U/V ~(16,240) ) 量化 ( I420 , YUV422 用改公司转换即可 )
[Y,U,V,1]T= M[R,G,B,1]T其中 M =
[ 0.2568, 0.5041, 0.0979, 16
-0.1479, -0.2896, 0.4375, 128
0.4375, -0.3666, -0.0709, 128,
0, 0, 0, 1 ]
[R,G,B,1]T = M[Y,U,V,1]T M =
1.1644 0 1.6019 -223.5521
1.1644 -0.3928 -0.8163 136.1381
1.1644 2.0253 0 -278.0291
0.0000 0.0000 0.0000 1.0000
由此可以得到红色的YUV分量 YUV = ( 81,91,240 )
4 量化后的公式写成整数的形式（减小计算量） ( Y~(16,235) U/V ~(16,240) )
yuv --> rgb
R = (298*Y + 411 * V - 57344)>>8
G = (298*Y - 101* U - 211* V+ 34739)>>8
B = (298*Y + 519* U- 71117)>>8
rgb --> yuv
Y= ( 66*R + 129*G + 25*B)>>8 + 16
U= (-38*R - 74*G + 112*B)>>8 +128
V= (112*R - 94*G - 18*B)>>8 + 128
5. YUV量化 与 非量化 互转
YUV 量化 转 非量化
Y=(Y'-16 )*255/219 ;
U=(U'-128)*128/112;
V=(V'-128)*128/112;
YUV 量化 转 非量化 U~(-128-127) -----> U~(16-240)
Y' = ((219*Y)>>8) + 16;
U' = ((219*U)>>8) + 128;
V' = ((219*V)>>8) + 128;
6. YV12 转RGB （这个有待考证。。！！）
R = Y + 1.370705 * ( V - 128 ) ; // r分量值
G = Y - 0.698001 * ( U - 128 ) - 0.703125 * (V - 128) // g分量值
B = Y + 1.732446 * ( U - 128 ); // b分量值
J420 ->RGB
R = Y - V * -1.40200
G = Y - U * 0.34414 - V * 0.71414
B = Y - U * -1.77200
=>
[RGB,1]T = M [YUV,1]T
[YUV, 1]T = M-1 * [RGB,1]
M =
1.0000 0.0000 1.3707 -175.4502
1.0000 -0.6980 0.0000 89.3441
1.0000 1.7324 0.0000 -221.7531
0.0000 0.0000 0.0000 1.0000
M-1 =
0.0000 0.7128 0.2872 -0.0000
0.0000 -0.4114 0.4114 128.0000
0.7296 -0.5200 -0.2095 128.0000
0.0000 0.0000 0.0000 1.0000
7. 矩阵形式（BT601）：
矩阵形式
量化前
[Y,U,V]T= M[R,G,B]T 其中 M = 0.299 , 0.587, 0.114, -0.169, - 0.331, 0.5, 0.5, - 0.419 - 0.081
[R,G,B]T= M[Y,U,V]T 其中 M = 1 0 1.4017 1 -0.3437 -0.7142 1 1.7722 0
量化后
[Y,U,V,1]T= M[R,G,B,1]T 其中 M = [ 0.2568, 0.5041, 0.0979, 16 -0.1479, -0.2896, 0.4375, 128 0.4375, -0.3666, -0.0709, 128, 0, 0, 0, 1 ]
[R,G,B,1]T = M[Y,U,V,1]T M = 1.1644 0 1.6019 -223.5521 1.1644 -0.3928 -0.8163 136.1381 1.1644 2.0253 0 -278.0291 0.0000 0.0000 0.0000 1.0000
量化后的公式写成整数形式
[Y,U,V,1]T= (M[R,G,B,1]T)>>8其中 M = 66, 129, 25, 4096, -38, -74, 112, 32768, 112, -94, -18, 32768, 0, 0, 0, 256
[R,G,B,1]T = (M[Y,U,V,1]T)>>8 M = 298, 0, 410, -57229, 298, -101, -209, 34851, 298, 518, 0, -71175, 0, 0, 0, 256
二、Rec2020 (BT2020) 下的YUV与RGB转换公式
BT2020 UV 的坐标图（量化后）： （横坐标为u，纵坐标为v，左下角为原点）
通过坐标图我们可以看到UV不同于BT601协议，该uv代表的颜色范围更大，该颜色范围呈一个不规则八边形。
1. BT2020 文档上的公式
即：
Y = 0.2627*R + 0.6780*G + 0.0593*B;
U = -0.1396*R - 0.3604*G + 0.5*B;
V = 0.5*R - 0.4598*G -0.0402*B;
矩阵形式
量化前
[Y,U,V]T= M[R,G,B]T 其中 M = 0.2627 0.6780 0.0593 , -0.1396 -0.3604 0.5000, 0.5000 -0.4598 -0.0402
[R,G,B]T= M[Y,U,V]T 其中 M = 1.0000 -0.0000 1.4746 1.0000 -0.1645 -0.5713 1.0000 1.8814 -0.0001
量化后
[Y,U,V,1]T= M[R,G,B,1]T 其中 M = 0.2256, 0.5823, 0.05093, 16, -0.1222, -0.3154, 0.4375, 128 , 0.4375, -0.4023, -0.0352, 128, 0,0,0,1
[R,G,B,1]T = M[Y,U,V,1]T M =1.1644, 0, 1.6853, -234.3559, 1.1644, -0.1881, -0.6529, 89.0206, 1.1646, 2.1501, 0.0000, -293.8542, 0.0000, 0.0000, 0.0000, 1.0000
量化后的公式写成整数形式
[Y,U,V,1]T= (M[R,G,B,1]T)>>8其中 M = 58, 149, 13, 4096, -31, -81, 112, 32768, 112, -103, -9, 32768, 0, 0, 0, 256
[R,G,B,1]T = (M[Y,U,V,1]T)>>8 M = 298, 0, 431, -59995, 298, -48, -167, 22789, 298, 550, 0, -75227, 0, 0, 0, 256
2. BT601 转 BT2020
_Y = (256*Y - 32*U -30*V+ 7826)>>8;
_U = (258*U +17*V - 2208)>>8;
_V = (22*U + 264*V - 3369)>>8;
3. bt2020 转bt601
YUV_601 = M*[Y,U,V,1]T
M=[
1.0000 0.1157 0.1037 -28.0756
0.0000 0.9951 -0.0602 8.3197
-0.0000 -0.0835 0.9767 13.6686
0.0000 0.0000 0.0000 1.0000
]
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