# Exploring Image Decolorization: Methods, Implementations, and Performance Assessment
## 3 Decolorization Methods
### Basic Methods
\right], \tag{2}\]  
\[X_{R}=\frac{x_{R}}{y_{R}},\quad Y_{R}=1,\quad Z_{R}=\frac{(1-x_{R}-y_{R})}{y_{R}}, \tag{3}\]  
\[X_{G}=\frac{x_{G}}{y_{G}},\quad Y_{G}=1,\quad Z_{G}=\frac{(1-x_{G}-y_{G})}{y_{G }}, \tag{4}\]  
\[X_{B}=\frac{x_{B}}{y_{B}},\quad Y_{B}=1,\quad Z_{B}=\frac{(1-x_{B}-y_{B})}{y_{ B}}, \tag{5}\]  
\[X_{W}=\frac{x_{W}}{y_{W}},\quad Y_{W}=1,\quad Z_{W}=\frac{(1-x_{W}-y_{W})}{y_{ W}}, \tag{6}\]  
\[\left[ \begin{array}{c}S_{R}\\ S_{G}\\ S_{B}\end{array} \right]=\left[ \begin{array}{ccc}X_{R}&X_{G}&X_{B}\\ Y_{R}&Y_{G}&Y_{B}\\ Z_{R}&Z_{G}&Z_{B}\end{array} \right]^{-1}\left[ \begin{array}{c}X_{W}\\ Y_{W}\\ Z_{W}\end{array} \right], \tag{7}\]  
\[Y=S_{R}R+S_{G}G+S_{B}B. \tag{8}\]  
Here, \(X_{W}\), \(Y_{W}\), and \(Z_{W}\) are the XYZ values of the reference white point and \(S_{R}\), \(S_{G}\), and \(S_{B}\) are the luminous coefficients (or scaling factors) for the R, G, and B components that represent the contribution of color channel to the overall luminance. Table 1 provides the chromaticity coordinates for color primaries in the SDTV (Rec. 601 [17]), HDTV (Rec. 709 [18]), and UHDTV (Rec. 2020 [19]) systems. Due to differences in these chromaticity coordinates across video standards, each standard uses a unique equation for calculating the luminance component Y, based on the specific color primaries of the system. The first widely used equation for the luminance component in SDTV color systems was based on the color primaries defined by the NTSC standard, where the reference white is specified as the CIE Standard Illuminant C. Using Equations (1)-(8), the conversion from the RGB to XYZ color space for the SDTV system can be performed, providing the luminance component that is given by \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline \multirow{2}{*}{**System**} & \multicolumn{3}{c}{**Reference**} & \multicolumn{3}{c}{**Chromaticity Coordinates of Primary Colors**} \\ \cline{2-9}  & \(x_{W}\) & \(y_{W}\) & \(x_{R}\) & \(y_{R}\) & \(x_{G}\) & \(y_{G}\) & \(x_{B}\) & \(y_{B}\) \\ \hline SDTV & 0.31 & 0.316 & 0.67 & 0.33 & 0.21 & 0.71 & 0.14 & 0.08 \\ \hline HDTV & 0.313 & 0.329 & 0.64 & 0.33 & 0.30 & 0.60 & 0.15 & 0.06 \\ \hline UHDTV & 0.313 & 0.329 & 0.708 & 0.292 & 0.170 & 0.797 & 0.131 & 0.046 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Chromaticity coordinates of color primaries in SDTV, HDTV and UHDTV system. \[Y=0.299R+0.587G+0.114B. \tag{9}\]  
This equation weights the RGB values according to the human visual system's sensitivity, with green having the highest weight as the human eye is most sensitive to green light. Red contributes less, and blue contributes the least, as the eye is less sensitive to those colors. A schematic representation of the basic image decolorization method using the SDTV coefficients is shown in Figure 2.  
However, with the advent of HDTV and modern display technologies, new standards were developed, such as the Rec. 709 standard for HDTV [18]. This new standard introduced slightly different RGB primaries and a new reference white point (D65 instead of Illuminant C), shown in Table 1. The Rec. 709 primaries are also valid for a sRGB color system and, therefore, for many PC monitors. Following the same procedure as for SDTV, the equation for Y can be derived as follows:  
\[Y=0.2126R+0.7152G+0.0722B. \tag{10}\]  
The slightly lower contribution from blue means that bright, colorful scene, especially those rich in red tones and green tones, appear more luminous and saturated, resulting in a more visually dynamic image. The color primaries for UHDTV, as defined by the Rec. 2020 standard [19], differ significantly from those used in SDTV and HDTV. Using a similar approach the equations for Y in the UHDTV system can be derived as follows:  
\[Y=0.2627R+0.6780G+0.0593B. \tag{11}\]  
The updated luminance formula ensures that bright areas of the image appear extremely vivid without losing detail, while dark areas retain depth and clarity.