RGB与YUV色彩空间的相互转换 - 代码先锋网 (2024)

原理

RGB与YUV空间的对应关系

根据电视原理的相关知识可知，RGB与的YUV对应关系为：
$\begin{cases}Y= 0.299\ R &+ 0.587\ G &+ 0.114\ B \\U= -0.1684\ R &- 0.3316\ G &+ 0.5\ B &= 0.564\ (B-Y) \\V= 0.5\ R &- 0.4187\ G &- 0.0813\ B &= 0.713\ (R-Y) \\\end{cases}\tag{1}$⎩⎪⎨⎪⎧​Y=0.299RU=−0.1684RV=0.5R​+0.587G−0.3316G−0.4187G​+0.114B+0.5B−0.0813B​=0.564(B−Y)=0.713(R−Y)​(1)
其中，为了使色差信号的动态范围控制在[-0.5, 0.5]，需要进行量化前的归一化处理，需要引入数字色差信号的压缩系数（分别为0.564与0.713）。

量化电平的分配

参考：《现代电视原理》7.4.2节：视频信号量化电平的分配

在进行8 bit量化时，需要在上下两端留出一定的余量，作为信号超越动态范围的保护带。具体地：

• 对于亮度信号，在256级的上端留出20级，下端留出16级作为余量，即Y的动态范围为16—235；
• 对于两个色差信号，在256级的上端留出15级，下端留出16级作为余量，即U、V的动态范围为16—240。

根据码电平数字表达式
$量化等级={\rm{int}}\left\{ \dfrac{Q_{\max}-Q_{\min}}{模拟电平最大值-模拟电平最小值}\times 对应的数字电平公式+0电平对应得量化等级 \right\} \tag{2}$量化等级=int{模拟电平最大值−模拟电平最小值Qmax​−Qmin​​×对应的数字电平公式+0电平对应得量化等级}(2)
可知
$\begin{cases}Y' = {\rm int}\left\{\dfrac {235-16}{0.5-(-0.5)}Y+16 \right\}\\U' = {\rm int}\left\{\dfrac {240-16}{1-0}U+128 \right\}\\V' = {\rm int}\left\{\dfrac {240-16}{1-0}V+128 \right\}\end{cases}\tag{3}$⎩⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎧​Y′=int{0.5−(−0.5)235−16​Y+16}U′=int{1−0240−16​U+128}V′=int{1−0240−16​V+128}​(3)
其中，

• ${\rm int}$int表示向下取整；
• $Y'$Y′、$U'$U′、$V'$V′为数字量化电平，$Y$Y、$U$U、$V$V为归一化的模拟电平（$Y\in [0,1]$Y∈[0,1]，$U,V\in [-0.5,0.5]$U,V∈[−0.5,0.5]）；
• 考虑到色差信号有负值，需要将原来的0值对应到128，故加上128。

由于读取的RGB文件已经进行了8 bit的量化（RGB三个分量范围均为0—255），所以要对公式$(2)$(2)进行修正，先将$Y$Y映射到-0.5—0.5，$U$U、$V$V映射到0—1：
$\begin{cases}Y' = {\rm int}\left\{ \dfrac {219}{255}Y+16 \right\}\\U' = {\rm int}\left\{ \dfrac {224}{255}U+128 \right\}\\V' = {\rm int}\left\{ \dfrac {224}{255}V+128 \right\}\end{cases}\tag{4}$⎩⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎧​Y′=int{255219​Y+16}U′=int{255224​U+128}V′=int{255224​V+128}​(4)
带入$(1)$(1)式，得：
$\begin{cases}Y= \dfrac {66R + 129G + 25B}{255} + 16 \\U= \dfrac{-38R - 74G + 112B}{255} +128 \\V= \dfrac{112R - 94G - 18B}{255} + 128\end{cases}\tag{5}$⎩⎪⎪⎪⎪⎨⎪⎪⎪⎪⎧​Y=25566R+129G+25B​+16U=255−38R−74G+112B​+128V=255112R−94G−18B​+128​(5)

为了提高计算机的计算效率且不会造成过大的误差，在程序中使用>> 8来代替除以255的计算。

将$(5)$(5)式写为矩阵形式：
$\begin{bmatrix}Y \\ U \\ V\end{bmatrix}= \dfrac {1}{255}\begin{bmatrix}66 & 129 & 25 \\-38 & -74 & 112 \\112 & -94 & -18\end{bmatrix}\begin{bmatrix}R \\ G \\ B\end{bmatrix}+\begin{bmatrix}16 \\ 16 \\ 128\end{bmatrix}\tag{6}$⎣⎡​YUV​⎦⎤​=2551​⎣⎡​66−38112​129−74−94​25112−18​⎦⎤​⎣⎡​RGB​⎦⎤​+⎣⎡​1616128​⎦⎤​(6)

并记$\boldsymbol A= \begin{bmatrix}66 & 129 & 25 \\-38 & -74 & 112 \\112 & -94 & -18\end{bmatrix}$A=⎣⎡​66−38112​129−74−94​25112−18​⎦⎤​。

反解，得：
$\begin{bmatrix}R \\ G \\ B\end{bmatrix}= 255\boldsymbol A^{\rm T}\begin{bmatrix}Y-16 \\ U-16 \\ V-128\end{bmatrix}\tag{7}$⎣⎡​RGB​⎦⎤​=255AT⎣⎡​Y−16U−16V−128​⎦⎤​(7)
整理得：

R = (298 * Y + 411 * V - 57344) >> 8;G = (298 * Y - 101 * U - 211 * V + 34739) >> 8;B = (298 * Y + 519 * U - 71117) >> 8;

main函数的命令行参数

main函数实际上具有两个形参，int argc和char* argv[]。虽然很多情况下是缺省的，但在例如涉及文件的操作中，使用命令行参数可以为编程提供一定的便利。

设置方法如下：在Visual Studio中，依次点击菜单栏中的项目→项目属性，在项目属性页的配置属性菜单下，点击“调试”。通过浏览文件夹的方式设置工作目录，并在命令参数中输入n个字符串（以空格分隔）。

命令行参数的设置

这些字符串将会自动传递给argv，作为其第1至n个元素（第0个元素为"项目名.exe"），而argc的值为n+1。

源代码

declarations.h

#pragma oncevoid rgb2yuv(FILE*, int, int, int, unsigned char*, unsigned char*, unsigned char*, unsigned char*);void yuv2rgb(FILE*, int, int, int, unsigned char*, unsigned char*, unsigned char*, unsigned char*);void errorData(int, unsigned char*, char* []);

rgb2yuv.cpp

#include <iostream>#include "declarations.h"int rgb66[256], rgb129[256], rgb25[256];int rgb38[256], rgb74[256], rgb112[256];int rgb94[256], rgb18[256];void rgbLookupTable(){for (int i = 0; i < 256; i++){rgb66[i] = 66 * i;rgb129[i] = 129 * i;rgb25[i] = 25 * i;rgb38[i] = 38 * i;rgb74[i] = 74 * i;rgb112[i] = 112 * i;rgb94[i] = 94 * i;rgb18[i] = 18 * i;}}void rgb2yuv(FILE* yuvFile, int rgbSize, int w, int h, unsigned char* rgbBuf, unsigned char* yBuf, unsigned char* uBuf, unsigned char* vBuf){unsigned char* uBuf444 = NULL;// 下采样前的U分量缓冲区unsigned char* vBuf444 = NULL;// 下采样前的V分量缓冲区uBuf444 = new unsigned char[rgbSize / 3];// 4:4:4格式vBuf444 = new unsigned char[rgbSize / 3];int pxNum = w * h;// RGB to YUV (4:4:4)for (int i = 0; i < pxNum; i++)// i为图像像素序号{unsigned char r = rgbBuf[3 * i + 2];// RGB图像第i个像素的R分量unsigned char g = rgbBuf[3 * i + 1];// RGB图像第i个像素的G分量unsigned char b = rgbBuf[3 * i];// RGB图像第i个像素的B分量//yBuf[i] = ((66 * r + 129 * g + 25 * b) >> 8) + 16;//uBuf444[i] = ((-38 * r - 74 * g + 112 * b) >> 8) + 128;//vBuf444[i] = ((112 * r - 94 * g - 18 * b) >> 8) + 128;rgbLookupTable();// 使用查找表，提高运算效率yBuf[i] = ((rgb66[r] + rgb129[g] + rgb25[b]) >> 8) + 16;uBuf444[i] = ((-rgb38[r] - rgb74[g] + rgb112[b]) >> 8) + 128;vBuf444[i] = ((rgb112[r] - rgb94[g] - rgb18[b]) >> 8) + 128;}// 4:4:4 to 4:2:0for (int i = 0; i < h; i += 2){for (int j = 0; j < w; j += 2){uBuf[i / 2 * w / 2 + j / 2] = uBuf444[i * w + j];vBuf[i / 2 * w / 2 + j / 2] = vBuf444[i * w + j];}}delete[]uBuf444;delete[]vBuf444;fwrite(yBuf, sizeof(unsigned char), rgbSize / 3, yuvFile);fwrite(uBuf, sizeof(unsigned char), rgbSize / 12, yuvFile);fwrite(vBuf, sizeof(unsigned char), rgbSize / 12, yuvFile);}

yuv2rgb.cpp

#include <iostream>#include "declarations.h"int yuv298[256], yuv411[256];int yuv101[256], yuv211[256];int yuv519[256];void yuvLookupTable(){for (int i = 0; i < 256; i++){yuv298[i] = 298 * i;yuv411[i] = 411 * i;yuv101[i] = 101 * i;yuv211[i] = 211 * i;yuv519[i] = 519 * i;}}void yuv2rgb(FILE* rgbFile, int yuvSize, int w, int h, unsigned char* yBuf, unsigned char* uBuf, unsigned char* vBuf, unsigned char* rgbBuf){unsigned char* uBuf444 = new unsigned char[yuvSize * 2 / 3];// 还原成4:4:4的U分量缓冲区unsigned char* vBuf444 = new unsigned char[yuvSize * 2 / 3];// 还原成4:4:4的V分量缓冲区int pxNum = w * h;// 图像中的总像素数// 4:2:0 to 4:4:4for (int i = 0; i < h / 2; i++)// i控制行{for (int j = 0; j < w / 2; j++)// j控制列{uBuf444[2 * i * w + 2 * j] = uBuf[i * w / 2 + j];uBuf444[2 * i * w + 2 * j + 1] = uBuf[i * w / 2 + j];uBuf444[2 * i * w + 2 * j + w] = uBuf[i * w / 2 + j];uBuf444[2 * i * w + 2 * j + w + 1] = uBuf[i * w / 2 + j];vBuf444[2 * i * w + 2 * j] = vBuf[i * w / 2 + j];vBuf444[2 * i * w + 2 * j + 1] = vBuf[i * w / 2 + j];vBuf444[2 * i * w + 2 * j + w] = vBuf[i * w / 2 + j];vBuf444[2 * i * w + 2 * j + w + 1] = vBuf[i * w / 2 + j];}}// YUV (4:4:4) to RGBfor (int i = 0; i < pxNum; i++){// 中间变量均使用int型，以保证足够的精度，防止溢出int y = yBuf[i];// YUV图像第i个像素的Y分量int u = uBuf444[i];// YUV图像第i个像素的U分量（4:4:4）int v = vBuf444[i];// YUV图像第i个像素的V分量（4:4:4）int r;int g;int b;yuvLookupTable();//r = (298 * y + 411 * v - 57344) >> 8;// 还原的RGB图像的R分量r = (yuv298[y] + yuv411[v] - 57344) >> 8;// 还原的RGB图像的R分量if (r < 0)r = 0;// 修正if (r > 255)r = 255;//g = (298 * y - 101 * u - 211 * v + 34739) >> 8;// 还原的RGB图像的G分量g = (yuv298[y] - yuv101[u] - yuv211[v] + 34739) >> 8;// 还原的RGB图像的G分量if (g < 0)g = 0;if (g > 255)g = 255;//b = (298 * y + 519 * u - 71117) >> 8;// 还原的RGB图像的B分量b = (yuv298[y] + yuv519[u] - 71117) >> 8;// 还原的RGB图像的B分量if (b < 0)b = 0;if (b > 255)b = 255;rgbBuf[3 * i + 2] = (unsigned char)r;// 还原的RGB图像的R分量rgbBuf[3 * i + 1] = (unsigned char)g;// 还原的RGB图像的G分量rgbBuf[3 * i] = (unsigned char)b;// 还原的RGB图像的B分量}delete[]uBuf444;delete[]vBuf444;fwrite(rgbBuf, sizeof(unsigned char), yuvSize * 2, rgbFile);}

errorData.cpp

#include <iostream>#include "declarations.h"using namespace std;void errorData(int yuvSize, unsigned char* rgbBuf, char* argv[]){FILE* rgbOriFile = NULL;// 原始RGB图像文件指针FILE* errorFile = NULL;// 误差数据文件指针const char* rgbOriName = argv[1];// 原始RGB图像文件名const char* errorName = argv[4];// 误差数据文件名// 打开文件if (fopen_s(&rgbOriFile, rgbOriName, "rb") == 0){cout << "Successfully opened " << rgbOriName << "." << endl;}else{cout << "Failed to open " << rgbOriName << "." << endl;exit(0);}if (fopen_s(&errorFile, errorName, "w") == 0){cout << "Successfully opened " << errorName << "." << endl;}else{cout << "Failed to open " << errorName << "." << endl;exit(0);}unsigned char* rgbOriBuf = new unsigned char[yuvSize * 2];fread(rgbOriBuf, sizeof(unsigned char), yuvSize * 2, rgbOriFile);// 将误差数据输出到csv文件fprintf(errorFile, "Pixel,B Error,G Error,R Error\n");for (int i = 0; i < yuvSize * 2 / 3; i++){fprintf(errorFile, "%d,%d,%d,%d\n", i, (int)abs(rgbBuf[3 * i] - rgbOriBuf[3 * i]), (int)abs(rgbBuf[3 * i + 1] - rgbOriBuf[3 * i + 1]), (int)abs(rgbBuf[3 * i + 2] - rgbOriBuf[3 * i + 2]));}delete[]rgbOriBuf;fclose(rgbOriFile);fclose(errorFile);}

main.cpp

#include <iostream>#include "declarations.h"using namespace std;int main(int argc, char* argv[]){FILE* rgbOriFilePtr = NULL;// 原RGB图像的文件指针FILE* yuvFilePtr = NULL;// YUV图像的文件指针FILE* rgbRecFilePtr = NULL;// 复原的RGB文件的文件指针const char* rgbOriFileName = argv[1];// 原RGB图像文件名const char* yuvFileName = argv[2];// YUV图像文件名const char* rgbRecFileName = argv[3];// 复原RGB图像文件名int width = 256;// 图像宽int height = 256;// 图像高int rgbFileSize;// RGB图像总字节数int yuvFileSize;// YUV图像总字节数unsigned char* rgbOriBuffer = NULL;// 原RGB图像缓冲区unsigned char* yBuffer = NULL;// Y分量缓冲区unsigned char* uBuffer = NULL;// U分量缓冲区unsigned char* vBuffer = NULL;// V分量缓冲区unsigned char* rgbRecBuffer = NULL;// 复原RGB图像缓冲区// 打开文件if (fopen_s(&rgbOriFilePtr, rgbOriFileName, "rb") == 0){cout << "Successfully opened " << rgbOriFileName << "." << endl;}else{cout << "Failed to open " << rgbOriFileName << "." << endl;exit(0);}if (fopen_s(&yuvFilePtr, yuvFileName, "wb+") == 0){cout << "Successfully opened " << yuvFileName << "." << endl;}else{cout << "Failed to open " << yuvFileName << "." << endl;exit(0);}if (fopen_s(&rgbRecFilePtr, rgbRecFileName, "wb") == 0){cout << "Successfully opened " << rgbRecFileName << "." << endl;}else{cout << "Failed to open " << rgbRecFileName << "." << endl;exit(0);}// 计算原RGB图像总字节数fseek(rgbOriFilePtr, 0L, SEEK_END);rgbFileSize = ftell(rgbOriFilePtr);rewind(rgbOriFilePtr);cout << "The space that " << rgbOriFileName << " accounts for is " << rgbFileSize << " Bytes = " << rgbFileSize / 1024 << " kB." << endl;yuvFileSize = rgbFileSize / 2;// 建立缓冲区rgbOriBuffer = new unsigned char[rgbFileSize];yBuffer = new unsigned char[rgbFileSize / 3];uBuffer = new unsigned char[rgbFileSize / 12];// 4:2:0格式vBuffer = new unsigned char[rgbFileSize / 12];rgbRecBuffer = new unsigned char[rgbFileSize];fread(rgbOriBuffer, sizeof(unsigned char), rgbFileSize, rgbOriFilePtr);// RGB图像读入缓冲区rgb2yuv(yuvFilePtr, rgbFileSize, width, height, rgbOriBuffer, yBuffer, uBuffer, vBuffer);yuv2rgb(rgbRecFilePtr, yuvFileSize, width, height, yBuffer, uBuffer, vBuffer, rgbRecBuffer);errorData(yuvFileSize, rgbRecBuffer, argv);delete[]rgbOriBuffer;delete[]yBuffer;delete[]uBuffer;delete[]vBuffer;delete[]rgbRecBuffer;fclose(rgbOriFilePtr);fclose(yuvFilePtr);fclose(rgbRecFilePtr);}

实验结果与误差分析

down.rgb

down_transformed.yuv

down_recoverd.rgb

以上三张图分别是原RGB图像、通过RGB转换的YUV图像和通过YUV复原的RGB图像。对比第1、3张图，几乎通过肉眼分辨不出差别。为了量化误差，在程序中，利用errorData函数计算了两张RGB图像各像素的三个分量的误差，并输出到了csv文件中。

由于在C++中进行数据分析与可视化并不方便，考虑到数据量较大，因而采用R进行分析。

在R中分别作出boxplot和直方图：

errorData <- read.csv("errorData.csv")b.error <- errorData[, 2]g.error <- errorData[, 3]r.error <- errorData[, 4]boxplot(r.error, g.error, b.error, horizontal = TRUE, names = c("R Error", "G Error", "B Error"), col = c("coral2", "palegreen1", "skyblue1"))hist(r.error, freq = FALSE, xlab = "Pixel", ylab = "Frequency of R Error", col = "coral2")hist(g.error, freq = FALSE, xlab = "Pixel", ylab = "Frequency of G Error", col = "palegreen1")hist(b.error, freq = FALSE, xlab = "Pixel", ylab = "Frequency of B Error", col = "skyblue1")

可以再求出各分量误差的Empirical CDF：

> ecdf.r.error <- ecdf(r.error)> ecdf.g.error <- ecdf(g.error)> ecdf.b.error <- ecdf(b.error)> ecdf.r.error(5)[1] 0.9351196> ecdf.g.error(5)[1] 0.9855804> ecdf.b.error(5)[1] 0.8774567

图表显示，该色度空间的转换不能做到100%的准确。误差来源可能有：

• 由于从4:4:4的RGB图像转换为4:2:0的YUV图像时，舍弃掉了3/4的色度信息，因而在还原为YUV文件时是无法还原出舍弃部分的色度信息的；
• 在进行色彩空间转换的公式推导时，使用了移位运算代替了除法运算，并且在计算过程中存在四舍五入；
• 在YUV向RGB的转换时，存在部分数据溢出。

但R、G、B分量分别有93.5%、98.6%、87.8%的像素误差小于等于5，因而该算法的色彩空间转换的误差并不大；由于人眼对色度的敏感度远高于对亮度的敏感度，误差也在人眼的分辨能力之外。