颜色空间系列4: RGB和YDbDr颜色空间的转换及优化算法

来源：互联网发布：大数据相关期刊编辑：程序博客网时间：2024/05/16 14:11

颜色空间系列代码下载链接：http://files.cnblogs.com/Imageshop/ImageInfo.rar （同文章同步更新）

YDbDr颜色空间和YCbCr颜色空间类似，其和RGB空间之间的相互转换公式里取http://en.wikipedia.org/wiki/YDbDr 所描述的。

RGB转为YDbDr为：

$\begin{align}Y &= +0.299 R +0.587 G +0.114 B\\D_B &= -0.450 R -0.883 G +1.333 B\\D_R &= -1.333 R +1.116 G +0.217B\\\begin{bmatrix} Y \\ D_B \\ D_R \end{bmatrix} &=\begin{bmatrix} 0.299 & 0.587 & 0.114 \\ -0.450 & -0.883 & 1.333 \\ -1.333 & 1.116 & 0.217 \end{bmatrix}\begin{bmatrix} R \\ G \\ B \end{bmatrix}\end{align}$ （1）

对应的YDbDr转换为RGB的公式为：

$\begin{align}R &= Y +0.000092303716148 D_B -0.525912630661865 D_R\\G &= Y -0.129132898890509 D_B +0.267899328207599 D_R\\B &= Y +0.664679059978955 D_B -0.000079202543533 D_R\\\begin{bmatrix} R \\ G \\ B \end{bmatrix} &=\begin{bmatrix} 1 & 0.000092303716148 & -0.525912630661865 \\1 & -0.129132898890509 & 0.267899328207599 \\1 & 0.664679059978955 & -0.000079202543533 \end{bmatrix}\begin{bmatrix} Y \\ D_B \\ D_R \end{bmatrix}\end{align}$ （2）

由式（1）可知Y的范围是[0,255],Db的范围是[-1.333*255,1.333*255],Dr的范围亦为[-1.333*255,1.333*255]。

为了使Db,Dr的变换量程也为255-0大小，需要将上述Db/Dr压缩1.333*2倍，即将各系数处理（ 1.333*2），得到新的转换：　

　　　[Y ]　　　[0.2990　　-0.1688 　　-0.5000 ] [R]
　　 [Db]　=　 [0.5870 -0.3312 　　 0.4186 ] [G]　　　　　　
　　　[Dr]　　　 [0.1140 0.5000 　　 0.0814 ] [B]

对应的逆变换可用matlab求上述矩阵的逆阵即可：

　　　[R]　　　[ 1.000000000000000 0.000246081707249 -1.402083073344533 ] [Y]
　　 [G]　=　 [ 1.000000000000000 -0.344268308442098 0.714219609001458 ] [Db]　　　　　　
　　　[B]　　　 [ 1.000000000000000 1.772034373903893 -0.000211153981059 ] [Dr]

理论上 YDbDr和RGB之间的转换时完全无损可逆的。不过如果YDbDr采用byte类型表达会有一定的精度损失。

附上最终的代码供大家参考：

    sealed unsafe class RGBYDbDr    {        //const float YDbDrYRF = 0.299F;              // RGB转YDbDr的系数(浮点类型）        //const float YDbDrYGF = 0.587F;        //const float YDbDrYBF = 0.114F;        //const float YDbDrDbRF = -0.450F;        //const float YDbDrDbGF = -0.883F;        //const float YDbDrDbBF = 1.333F;        //const float YDbDrDrRF = -1.333F;        //const float YDbDrDrGF = 1.116F;        //const float YDbDrDrBF = 0.217F;        //const float RGBRYF = 1.00000F;            // YDbDr转RGB的系数(浮点类型）        //const float RGBRDbF = 0.000092303716148F;        //const float RGBRDrF = -0.525912630661865F;        //const float RGBGYF = 1.00000F;        //const float RGBGDbF = -0.129132898890509F;        //const float RGBGDrF = 0.267899328207599F;        //const float RGBBYF = 1.00000F;        //const float RGBBDbF = 0.664679059978955F;        //const float RGBBDrF = -0.000079202543533F;        const float YDbDrYRF = 0.299F;              // RGB转YDbDr的系数(浮点类型）        const float YDbDrYGF = 0.587F;        const float YDbDrYBF = 0.114F;        const float YDbDrDbRF = -0.1688F;        const float YDbDrDbGF = -0.3312F;        const float YDbDrDbBF = 0.5F;        const float YDbDrDrRF = -0.5F;        const float YDbDrDrGF = 0.4186F;        const float YDbDrDrBF = 0.0814F;        const float RGBRYF = 1.00000F;            // YDbDr转RGB的系数(浮点类型）        const float RGBRDbF = 0.0002460817072494899F;        const float RGBRDrF = -1.402083073344533F;        const float RGBGYF = 1.00000F;        const float RGBGDbF = -0.344268308442098F;        const float RGBGDrF = 0.714219609001458F;        const float RGBBYF = 1.00000F;        const float RGBBDbF = 1.772034373903893F;        const float RGBBDrF = 0.0002111539810593343F;        const int Shift = 20;        const int HalfShiftValue = 1 << (Shift - 1);        const int YDbDrYRI = (int)(YDbDrYRF * (1 << Shift) + 0.5);         // RGB转YDbDr的系数(整数类型）        const int YDbDrYGI = (int)(YDbDrYGF * (1 << Shift) + 0.5);        const int YDbDrYBI = (int)(YDbDrYBF * (1 << Shift) + 0.5);        const int YDbDrDbRI = (int)(YDbDrDbRF * (1 << Shift) + 0.5);        const int YDbDrDbGI = (int)(YDbDrDbGF * (1 << Shift) + 0.5);        const int YDbDrDbBI = (int)(YDbDrDbBF * (1 << Shift) + 0.5);        const int YDbDrDrRI = (int)(YDbDrDrRF * (1 << Shift) + 0.5);        const int YDbDrDrGI = (int)(YDbDrDrGF * (1 << Shift) + 0.5);        const int YDbDrDrBI = (int)(YDbDrDrBF * (1 << Shift) + 0.5);        const int RGBRYI = (int)(RGBRYF * (1 << Shift) + 0.5);              // YDbDr转RGB的系数(整数类型）        const int RGBRDbI = (int)(RGBRDbF * (1 << Shift) + 0.5);        const int RGBRDrI = (int)(RGBRDrF * (1 << Shift) + 0.5);        const int RGBGYI = (int)(RGBGYF * (1 << Shift) + 0.5);        const int RGBGDbI = (int)(RGBGDbF * (1 << Shift) + 0.5);        const int RGBGDrI = (int)(RGBGDrF * (1 << Shift) + 0.5);        const int RGBBYI = (int)(RGBBYF * (1 << Shift) + 0.5);        const int RGBBDbI = (int)(RGBBDbF * (1 << Shift) + 0.5);        const int RGBBDrI = (int)(RGBBDrF * (1 << Shift) + 0.5);public static void ToYDbDr(byte* From, byte* To, int Length = 1)        {            if (Length < 1) return;            byte* End = From + Length * 3;            int Red, Green, Blue;            while (From != End)            {                Blue = *From; Green = *(From + 1); Red = *(From + 2);                // 无需判断是否存在溢出，因为测试过整个RGB空间的所有颜色值，无颜色存在溢出                *To = (byte)((YDbDrYRI * Red + YDbDrYGI * Green + YDbDrYBI * Blue + HalfShiftValue) >> Shift);         // YDbDr和YUV的Y相同                *(To + 1) = (byte)(128 + ((YDbDrDbRI * Red + YDbDrDbGI * Green + YDbDrDbBI * Blue + HalfShiftValue) >> Shift));                     *(To + 2) = (byte)(128 + ((YDbDrDrRI * Red + YDbDrDrGI * Green + YDbDrDrBI * Blue + HalfShiftValue) >> Shift));                     From += 3;                To += 3;            }        }        public static void ToRGB(byte* From, byte* To, int Length = 1)        {            if (Length < 1) return;            byte* End = From + Length * 3;            int Red, Green, Blue;            int Y, Db, Dr;            while (From != End)            {                Y = *From; Db = *(From + 1) - 128; Dr = *(From + 2) - 128;                Red = Y + ((RGBRDbI * Db + RGBRDrI * Dr + HalfShiftValue) >> Shift);                Green = Y + ((RGBGDbI * Db + RGBGDrI * Dr + HalfShiftValue) >> Shift);                Blue = Y + ((RGBBDbI * Db + RGBBDrI * Dr + HalfShiftValue) >> Shift);                if (Red > 255) Red = 255; else if (Red < 0) Red = 0;                if (Green > 255) Green = 255; else if (Green < 0) Green = 0;                    if (Blue > 255) Blue = 255; else if (Blue < 0) Blue = 0;                *To = (byte)Blue;                                                             *(To + 1) = (byte)Green;                *(To + 2) = (byte)Red;                From += 3;                To += 3;            }        }    }

　　由于有些转换系数很小，建议Shift 常数取值不得小于10，否则会有更多的损失。

照例附上一些效果：

原图：

YDbDr综合效果图：

Y通道图：

Db通道：

Dr通道：

分类: [09] 图像颜色空间,[03] 图像算法优化

标签: RGB, YDbDr, 颜色空间。

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