Color quantization represents an image using a fraction of its original number of colors while only minimally losing its visual quality. The $k$-means algorithm is commonly used in this context, but has mostly been applied in the machine-based RGB colorspace composed of the three primary colors. However, some recent studies have indicated its improved performance in human perception-based colorspaces. We investigated the performance of $k$-means color quantization at four quantization levels in the RGB, CIE-XYZ, and CIE-LUV/CIE-HCL colorspaces, on 148 varied digital images spanning a wide range of scenes, subjects and settings. The Visual Information Fidelity (VIF) measure numerically assessed the quality of the quantized images, and showed that in about half of the cases, $k$-means color quantization is best in the RGB space, while at other times, and especially for higher quantization levels ($k$), the CIE-XYZ colorspace is where it usually does better. There are also some cases, especially at lower $k$, where the best performance is obtained in the CIE-LUV colorspace. Further analysis of the performances in terms of the distributions of the hue, chromaticity and luminance in an image presents a nuanced perspective and characterization of the images for which each colorspace is better for $k$-means color quantization.

翻译：色彩量化技术使用原始色彩数量的一部分来表示图像，同时仅最小化地损失其视觉质量。$k$-means算法在此领域被广泛应用，但主要应用于由三原色构成的机器感知RGB色彩空间。然而，近期一些研究表明该算法在基于人类感知的色彩空间中性能有所提升。我们在RGB、CIE-XYZ以及CIE-LUV/CIE-HCL色彩空间中，针对涵盖广泛场景、主体与拍摄条件的148幅多样化数字图像，研究了$k$-means色彩量化在四种量化级别下的性能表现。通过视觉信息保真度（VIF）指标对量化图像质量进行数值评估，结果显示：在大约半数情况下，$k$-means色彩量化在RGB空间表现最佳；而在其他情况，尤其是较高量化级别（$k$）下，CIE-XYZ色彩空间通常表现更优。也存在部分情况，特别是在较低$k$值时，最佳性能出现在CIE-LUV色彩空间。进一步从图像色调、色度与亮度分布的角度分析性能表现，为不同色彩空间在$k$-means色彩量化中的适用场景提供了细致入微的视角与特征描述。