A color quantization algorithm based on minimization of modified L_p norm error in a CIELAB space

摘要

Color quantization algorithms are used to select a small number of colors that can accurately represent the content of a particular image. In this research, we introduce a novel color quantization algorithm which is based on the minimization of a modified L_p norm rather than the more traditional L_2 norm associated with mean square error (MSE). We demonstrate that the L_p optimization approach has two advantages. First, it distributes the colors more uniformly over the regions of the image; and second, the norm's value can be used as an effective criterion for selecting the minimum number of colors necessary to achieve accurate representation of the image. One potential disadvantage of the modified L_p norm criteria is that it could increase the computation of the associated clustering methods. However, we solve this problem by introducing a two stage clustering procedure in which the first stage (pre-clustering) agglomerates the full set of pixels into a relatively large number of discrete colors; and the second stage (post-clustering) performs modified L_p norm minimization using the reduced number of discrete colors resulting from the pre-clustering step. The number of groups used in the post-clustering is then chosen to be the smallest number that achieves a selected threshold value of the normalized L_p norm. This two-stage clustering process dramatically reduces computation by merging together colors before the computationally expensive modified L_p norm minimization is applied.