# Exploring Image Decolorization: Methods, Implementations, and Performance Assessment
## 3 Decolorization Methods
### Basic Methods  
In image processing, color spaces are essential for representing and manipulating colors in a standardized way. Here are some common color spaces used:  
1. RGB (Red, Green, Blue): The most widely used color space, especially in digital images and displays. Colors are represented as combinations of red, green, and blue primary colors. 2. HSV (Hue Saturation Value): This color space is often used in image processing for tasks that involve human perception of color. It separates the color information (hue) from intensity (value) and colorfulness (saturation). 3. LAB (CIE L*s*b*, CIELAB): A perceptually uniform color space, meaning small changes in the values correspond to small changes in perceived color. The L component represents lightness, while a* and b* represent color dimensions. 4. YUV: This space separates luminance (Y) from chrominance (U and V) and allows manipulation of brightness and color independently, which is key for efficient encoding and filtering. For image decolorization, YUV and CIE L*a*b* are particularly suitable. The L channel and the Y channel both produce a decolorized image, but they do so in different ways depending on the color space they come from and how they handle light and color. In video and imaging systems, RGB color primaries are represented mathematically through chromaticity coordinates, typically denoted as x, y, and z. These chromaticity coordinates specify the precise color properties of each primary color in each system and vary across different television standards defined by the International Telecommunication Union (ITU):  
* SDTV (Standard Definition Television) uses chromaticity coordinates originally defined by the analog NTSC (National Television System Committee) system, which are applied consistently in digital SDTV systems, independent of variations within SDTV standards [17],
* HDTV (High Definition Television) uses coordinates that are adapted for higher-resolution differing from those of SDTV [18],
* UHDTV (Ultra High Definition Television) uses an even further refined set of chromaticity coordinates optimized for the expanded color range and detail in ultra-high-definition content [19]. Each system's specific chromaticity coordinates ensure accurate color reproduction by defining reference points for R, G, and B. These coordinates are part of the CIE XYZ color space, developed by the Commission Internationale de l'Eclairage (CIE) in 1931 to create a device-independent system aligned with human vision. The CIE XYZ space is derived from RGB via a linear transformation matrix specific to the RGB primaries used. X corresponds to the red/green region, Y to luminance, and Z to the blue/yellow region [31]. The chromaticity coordinates \(x\), \(y\), and \(z\) represent the proportions of color primaries that produce various hues. The color gamut of any RGB system forms a triangle in the CIE 1931 xy chromaticity diagram. The CIE RGB primaries, shown in Figure 1, are defined as monochromatic stimuli with specific wavelengths: red at 700 nm, green at 546.1 nm, and blue at 435.8 nm [31]. In the CIE XYZ color space, the Y component represents the human visual system's sensitivity to light and defines luminance, while X and Z do not contribute. Y can generate a grayscale image from RGB components and serves as a basis for other color spaces like YUV and LAB. Figure 1: Color triangle of CIE RGB primary colors on the CIE 1931 xy chromaticity diagram. When the chromaticity coordinates of the color primaries \((x_{R},y_{R})\), \((x_{G},y_{G})\), \((x_{B},y_{B})\) are known together with the reference white coordinates \((x_{W},y_{W})\), conversion from RGB to XYZ is given by [32]:  
\[\left[ \begin{array}{c}X\\ Y\\ Z\end{array} \right]=\left[M\right]\left[ \begin{array}{c}R\\ G\\ B\end{array} \right], \tag{1}\]  
\[\left[M\right]=\left[ \begin{array}{ccc}S_{R}X_{R}&S_{G}X_{G}&S_{B}X_{B}\\ S_{R}Y_{R}&S_{G}Y_{G}&S_{B}Y_{B}\\ S_{R}Z_{R}&S_{G}Z_{G}&S_{B}Z_{B}\end{array}