【YUV】【1】YUV颜色空间与RGB颜色空间的相互转换公式

本文仅对YUV与RGB颜色空间的两种相互转换方式做简单说明，并指出常用方式。

第一种方式：

$$RGB\to YUV\{\begin{array}{l}Y=0.257R+0.504G+0.098B+16\\ U=-0.148R-0.291G+0.439B+128\\ V=0.439R-0.368G-0.071B+128\end{array}$$ $$YUV\to RGB\{\begin{array}{l}R=1.164(Y-16)+1.596(V-128)\\ G=1.164(Y-16)-0.391(U-128)-0.813(V-128)\\ B=1.164(Y-16)+2.018(U-128)\end{array}$$  其中RGB以及YUV取值范围分别为:
$$R/G/B\in [0,255],Y\in [16,235],U/V\in [16,240]$$若超出取值范围，则直接截断处理。

  当前方式出自$KeithJack$的书$<<VideoDemystified>>(ISBN1-8787-7-09-4)$，$OpenCV$采用的$YUV\to RGB$的整型系数转换公式正是基于当前方式。

  将公式中的$YUV$和 $RGB$的取值范围以线性方式统一到$\text{[}0,255\text{]}:$
$$RGB\to YUV\{\begin{array}{l}Y=\left(0.257R+0.504G+0.098B+16-16\right)\ast \frac{255}{235-16}\\ =0.2992R+0.5868G+0.1141B\\ U=\left(-0.148R-0.291G+0.439B+128-16\right)\ast \frac{255}{240-16}\\ =-0.1685R-0.3313G+0.4998B+127.5\\ V=\left(0.439R-0.368G-0.071B+128-16\right)\ast \frac{255}{240-16}\\ =0.4998R-0.4189G-0.0808B+127.5\end{array}$$ $$YUV\to RGB\{\begin{array}{l}R=1.164\left(\frac{235-16}{255}Y+16-16\right)+1.596\left(\frac{240-16}{255}V+16-128\right)\\ =0.9997Y+1.402V-178.520=0.9997Y+1402(V-127.4979)\\ G=1.164\left(\frac{235-16}{255}Y+16-16\right)-0.391\left(\frac{240-16}{255}U+16-128\right)-0.813\left(\frac{240-16}{255}V+16-128\right)\\ =0.9997Y-0.3435U+43.792-0.7142V+91.056\\ =0.9997Y-0.3435(U-127.4846)-0.7142(V-127.4937)\\ B=1.164\left(\frac{235-16}{255}Y+16-16\right)+2.018\ast \left(\frac{240-16}{255}+16-128\right)\\ =0.9997Y+1.7727U-226.016=0.9997Y+1.7727(U-127.4982)\end{array}$$

第二种方式：

$$RGB\to YUV\{\begin{array}{l}Y=0.299R+0.587G+0.114B\\ U=-0.169R-0.331G+0.500B=0.564(B-Y)\\ V=0.500R-0.419G-0.081B=0.713(R-Y)\end{array}$$ $$YUV\to RGB\{\begin{array}{l}R=Y+1.403V\\ G=Y-0.344U-0.714V\\ B=Y+1.770U\end{array}$$  其中RGB以及YUV取值范围分别为:
$$R/G/B\in [0,1],Y\in [0,1],U/V\in [-0.5,0.5]$$   当前方式出自$CCIR601$。

  将公式中的$YUV$和 $RGB$的取值范围以线性方式统一到$\text{[}0,255\text{]}:$
$$RGB\to YUV\{\begin{array}{l}Y=255(0.299\frac{R}{255}+0.587\frac{G}{255}+0.114\frac{B}{255})\\ =0.299R+0.587G+0.114B\\ U=255(-0.169\frac{R}{255}-0.331\frac{G}{255}+0.5008\frac{B}{255})+255\ast 0.5\\ =-0.169R-0.331G+0.5008B+128\\ V=255(0.500\frac{R}{255}-0.419\frac{G}{255}-0.081\frac{B}{255})+255\ast 0.5\\ =0.500R-0.419G-0.081B+128\end{array}$$ $$YUV\to RGB\{\begin{array}{l}R=255\left(\frac{Y}{255}+1.403\left(\frac{V}{255}-0.5\right)\right)\\ =Y+1403(V-128)\\ G=255\left(\frac{Y}{255}-0.344\left(\frac{U}{255}-0.5\right)-0.714\left(\frac{V}{255}-0.5\right)\right)\\ =Y-0.344(U-128)-0.714(V-128)\\ B=255\left(\frac{Y}{255}+1.770\left(\frac{U}{255}-0.5\right)\right)\\ =Y+1.770(U-128)\end{array}$$

常用方式：

  将$RGB$以及$YUV$的取值范围都缩放到$\text{[}0,255\text{]}$之后的常用公式为：
$$RGB\to YUV\{\begin{array}{l}Y=0.299R+0.587G+0.114B\\ U=-0.169R-0.331G+0.5008B+128\\ V=0.500R-0.419G-0.081B+128\end{array}$$ $$YUV\to RGB\{\begin{array}{l}R=Y+1.403(V-128)\\ G=Y-0.343(U-128)-0.714(V-128)\\ B=Y+1.770(U-128)\end{array}$$