From the viewpoint of optimal image contrast measure, a kind of optimization mathematical models and its enhanced methods are proposed for image enhancement by histogram equalization.For the shortcoming of low operation efficiency of optimal contrast image enhancement method by linear programming, the gray level mapping optimization mathematical model for classical histogram equalization is established to improve its mathematical theory. The improved gray level mapping optimization models for histogram equalization are constructed by means of weighted geometry averaging in order to avoid the shortcoming of classical histogram equalization. The good properties of its optimal solution for gray level mapping optimization models are discussed, and the classical and adjustable histogram equalization methods are regarded as special cases of the proposed optimization mathematical models for image enhancement. Experimental results show that the optimization model of histogram equalization is reasonable and can obtain satisfactory image enhancement effect.To some extent,it is more universal than classical and adjustable histogram equalization methods.%从图像最优对比度出发,提出直方图均衡化的一类最优化数学模型及其增强方法.针对线性规划求解基于最优对比度的图像增强法效率极低的不足,首先对传统直方图均衡化方法建立灰度级映射的最优化数学模型；其次提出了传统直方图均衡化的一种改进型灰度级映射最优化模型；最后探讨了灰度级映射最优化模型解具有的性质,以及传统直方图均衡化和可调直方图均衡化可视为本文方法的特例.实验结果表明,本文所提出直方图均衡化的一类最优化模型是合理的且能获得满意的增强效果,相比传统直方图均衡化和可调直方图均衡化方法更具普适性.
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