Optimized $k$-means color quantization of digital images in machine-based and human perception-based colorspaces

TL;DR

This study compares the effectiveness of $k$-means color quantization across different colorspaces (RGB, CIE-XYZ, CIE-LUV) on diverse images, revealing that the optimal colorspace varies with quantization level and image characteristics.

Contribution

It provides a comprehensive analysis of $k$-means color quantization performance in multiple colorspaces, highlighting conditions where each colorspace yields better image quality.

Findings

RGB space often yields best results at lower quantization levels.

CIE-XYZ space generally outperforms others at higher quantization levels.

Performance varies based on image hue, chromaticity, and luminance distributions.

Abstract

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.