Differential evolution algorithm (DE) is one of the novel stochastic optimization methods. It has a better performance in the problem of the color image quantization, but it is difficult to set the parameters of DE for users. This paper proposes a color image quantization algorithm based on self-adaptive DE. In the proposed algorithm, a self-adaptive mechanic is used to automatically adjust the parameters of DE during the evolution, and a mixed mechanic of DE and -means is applied to strengthen the local search. The numerical experimental results, on a set of commonly used test images, show that the proposed algorithm is a practicable quantization method and is more competitive than -means and particle swarm algorithm (PSO) for the color image quantization. 1. Introduction Color image quantization, one of the common image processing techniques, is the process of reducing the number of colors presented in a color image with less distortion [1]. The main purpose of color quantization is reducing the use of storage media and accelerating image sending time [2]. Color image quantization consists of two essential phases. The first one is to design a colormap with a smaller number of colors (typically 8–256 colors [3]) than that of a color image. The second one is to map each pixel in the color image to one color in the colormap. Most of the color quantization methods focus on creating an optimal colormap. For being an NP-hard problem, it is not feasible to find the optimal colormap without a prohibitive amount of time [4]. To address this problem, researchers have applied several stochastic optimization methods, such as GA and PSO. In particular, the literature [5–8] has compared the color image quantization algorithm using PSO (PSO-CIQ) and several other well-known color image quantization methods. The experimental results show that PSO-CIQ has higher performance. Differential evolution algorithm (DE) [9–11] is a population-based heuristic search approach. DE has been applied to the classification for gray images [12–14]. In the literature [12–14], DE and PSO show similar performance. However, due to simple operation, litter parameters, and fast convergence, DE is the better choice to use than PSO [12]. However, few researches have been done for using DE to solve the color image quantization. This paper applies DE to solve the color image quantization. However, the performance of DE is decided by two important parameters, the scaling factor and the crossover rate CR. In practice, it is difficult to set the two parameters. For this difficulty, this paper
J.-P. Braquelaire and L. Brun, “Comparison and optimization of methods of color image quantization,” IEEE Transactions on Image Processing, vol. 6, no. 7, pp. 1048–1052, 1997.
F. Alamdar, Z. Bahmani, and S. Haratizadeh, “Color quantization with clustering by F-PSO-GA,” in Proceedings of the IEEE International Conference on Intelligent Computing and Intelligent Systems (ICIS '10), vol. 3, pp. 233–238, October 2010.
M. G. Omran, A. P. Engelbrecht, and A. Salman, “A color image quantization algorithm based on Particle Swarm Optimization,” Soft Computing in Multimedia Processing, vol. 29, no. 3, pp. 261–269, 2005.
Q. Sa, X. Liu, X. He, and D. Yan, “Color image quantization using particle swarm optimization,” Journal of Image and Graphics, vol. 12, no. 9, pp. 1544–1548, 2007 (Chinese).
X. Zhou, Q. Shen, and J. Wang, “Color quantization algorithm based on particle swarm optimization,” Microelectronics and Computer, vol. 25, no. 3, pp. 51–54, 2009 (Chinese).
Y. Xu and Z. Jiang, “A K-mean color image quantization method based on particle swarm optimization,” Journal of Northwest University, vol. 42, no. 3, 2012 (Chinese).
F. Alamdar, Z. Bahmani, and S. Haratizadeh, “Color quantization with clustering by F-PSO-GA,” in Proceedings of the IEEE International Conference on Intelligent Computing and Intelligent Systems (ICIS '10), pp. 233–238, October 2010.
R. Storn and K. Price, “Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces,” Journal of Global Optimization, vol. 11, no. 4, pp. 341–359, 1997.
Y. Shen, M. Li, and H. Yin, “A novel differential evolution for numerical optimization,” International Journal of Advancements in Computing Technology, vol. 4, no. 4, pp. 24–31, 2012.
H. Li and J. Tang, “Improved differential evolution with local search,” Journal of Convergence Information Technology, vol. 7, no. 4, pp. 197–204, 2012.
M. G. H. Omran, A. P. Engelbrecht, and A. Salman, “Differential evolution methods for unsupervised image classification,” in Proceedings of the IEEE Congress on Evolutionary Computation (IEEE CEC '05), pp. 966–973, September 2005.
S. Das and A. Konar, “Automatic image pixel clustering with an improved differential evolution,” Applied Soft Computing Journal, vol. 9, no. 1, pp. 226–236, 2009.
Q. Su, Z. Huang, and Z. Hu, “Binarization algorithm based on differential evolution algorithm for gray images,” ICNC-FSKD, vol. 6, pp. 2624–2628, 2012.
J. Brest, S. B. Bo？kovi？, V. ？ume, and M. S. Mau？ec, “Performance comparison of self-adaptive and adaptive differential evolution algorithms,” Soft Computing, vol. 11, no. 7, pp. 617–629, 2007.
J. Brest, V. ？umer, and M. S. Mau？ec, “Self-adaptive differential evolution algorithm in constrained real-parameter optimization,” in Proceedings of the IEEE Congress on Evolutionary Computation (CEC '06), pp. 215–222, July 2006.
S.-C. Cheng and C.-K. Yang, “A fast and novel technique for color quantization using reduction of color space dimensionality,” Pattern Recognition Letters, vol. 22, no. 8, pp. 845–856, 2001.