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In recent years, various image encryption algorithms based on chaos-based image cryptosystems have been proposed. In this paper, a design of the compound one-dimensional chaotic function by coupling piecewise nonlinear chaotic map and nearest-neighboring coupled-map lattices (NCML) suggests self-adaptive color image encryption. The coupling and nonlinear structure of the compound chaotic function enhances cryptosystem security. The self-adaptive color image encryption is carried out by using one half of the image data for encryption of the other half of the image recursively. The salient features of the proposed image encryption scheme are high security level, high sensitivity, high speed and large key space. In order to generate the initial conditions and parameters of the chaotic function of one half of the image, 192-bit-long external secret key and the other half of the image data are used. The results of several experimental, statistical analysis and key sensitivity tests for color images have shown the high performance on the sensitivity, speed and security of the proposed algorithm.