颜色空间系列4: RGB和YDbDr颜色空间的转换及优化算法

超、凢脫俗 2022-03-28 07:24 295阅读 0赞

颜色空间系列代码下载链接：[http://files.cnblogs.com/Imageshop/ImageInfo.rar][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][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\}][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\}][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：

![15200915-82525b50a964418abca754895b083473.jpg][]

YDbDr综合效果图：

![15200943-bcaa4bfa14984fa398e60dbac9f52ccd.jpg][]

Y通道图：

![15200959-bfbe49cdd72a45f1b1538e7f4ec5c438.jpg][]

Db通道：

![15201015-5db3e6f294a949c7aef4b10b68258738.jpg][]

Dr通道：

![15201029-aa5da106064e4978b428daf331d16e48.jpg][]

[http_files.cnblogs.com_Imageshop_ImageInfo.rar]: http://files.cnblogs.com/Imageshop/ImageInfo.rar
[http_en.wikipedia.org_wiki_YDbDr]: http://en.wikipedia.org/wiki/YDbDr
[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]: /images/20220328/c5a78c028ef04bdbb5c660af6cd24bbb.png
[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]: /images/20220328/e21c5a46225f47e4be820519dc9ca3b0.png
[15200915-82525b50a964418abca754895b083473.jpg]: /images/20220328/7ee868053dfc4e749fae314250308fe8.png
[15200943-bcaa4bfa14984fa398e60dbac9f52ccd.jpg]: /images/20220328/34d6a2f9a908463e9ddd2de03d2fe4e8.png
[15200959-bfbe49cdd72a45f1b1538e7f4ec5c438.jpg]: /images/20220328/4a581d3a683c4a53b9caa1cde2f47a7a.png
[15201015-5db3e6f294a949c7aef4b10b68258738.jpg]: /images/20220328/ed78ee1b69714a4c990d12184120a635.png
[15201029-aa5da106064e4978b428daf331d16e48.jpg]: /images/20220328/d5fb9621f8fa4b1d83485cc2b3f65fae.png