彩色图像颜色量化问题的求解方法

针对K-means聚类算法在彩色图像颜色量化问题中对初始条件依赖性较强而易陷入局部最优的缺点，以及传统智能优化算法在寻优时只考虑了种群层内个体的相互竞争而忽略种群层间相互协作的问题，提出了一种基于K-means的金字塔结构演化策略（PES）彩色图像量化算法。首先，将K-means聚类算法中的聚类损失函数作为新算法的适应度函数；其次，运用PES对色彩进行种群初始化、分层、探索、加速以及聚类等操作；最后，利用新算法对4幅标准彩色测试图像进行不同色彩量化级的量化。实验结果表明，所提算法能够改善K-means聚类算法以及传统智能算法的上述缺陷，在类内均方误差评判准则下，图像的平均失真率比基于PES的算法低12.25%，比差分进化算法低15.52%，比粒子群优化（PSO）算法低58.33%，比K-means算法低15.06%，且随着色彩量化级的减少，算法量化后的图像失真率比其他算法降低更多，此外，算法量化图像的视觉效果优于其他算法。

Method for solving color images quantization problem of color images

For the color quantization problem of color images, the K-means clustering algorithm has strong dependence on initial conditions and is easy to fall into local optimum, and the traditional intelligent optimization algorithms only consider the mutual competition between individuals in the population layer and ignores the mutual cooperation between the population layers. To solve the problems, a K-means-based PES (Pyramid Evolution Strategy) color image quantization algorithm was proposed. Firstly, the clustering loss function in K-means clustering algorithm was used as the fitness function of the new algorithm; secondly, PES was used for the population initialization, layering, exploration, acceleration and clustering of the colors; finally, the new algorithm was used to quantify four standard color test images at different color quantization levels. The experimental results show that the proposed algorithm can improve the defects of the K-means clustering algorithm and the traditional intelligent algorithm. Under the criterion of intra-class mean squared error, the average distortion rate of the image quantized by the new algorithm is 12.25% lower than that quantized by the PES-based algorithm, 15.52% lower than that quantized by the differential evolution algorithm, 58.33% lower than that quantized by the Particle Swarm Optimization (PSO) algorithm, 15.06% lower than that quantized by the K-means algorithm; and the less the color quantization levels, the more the image distortion rate reduced quantized by the new algorithm than that quantized by other algorithms. In addition, the visual effect of the image quantized by the proposed algorithm is better than that quantized by other algorithms.