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.