Statistical Colour Quantization for Minimum Distortion

Abstract

Colour quantization for frame buffer displays, a basic computer graphics technique for efficient use of colours, is statistically a large scale clustering process and it poses a difficult discrete optimization problem. Many heuristic color quantization algorithms were proposed [7, 12, 22, 24] but they all suffer from various degrees of non-adaptability to the colour statistics of input images. In this article we will introduce an adaptive colour image quantization algorithm that outperforms existing algorithms in subjective image quality and in least square approximation sense. The new algorithm eliminates many current suboptimal treatments of colour quantization such as a prequantization of discarding few lower bits of RGB values, restricted cuts orthogonal to RGB axes, partition criteria based on population or marginal distributions rather than variance minimization. A constrained global optimization scheme is incorporated into a divide-and-conquer clustering process to minimize quantization distortion. The time and space complexities of the new algorithm are O(N log K) and O(N), where N is the number of pixels in the image and K is the number of colours in quantized image.