An image pixel based variational model for histogram equalization

Abstract

In this paper, we develop an image pixel based histogram equalization model for image contrast enhancement. The approach is to propose a variational model containing an energy functional to adjust the pixel values of an input image directly so that the resulting histogram can be redistributed to be uniform. This idea is different from existing histogram equalization algorithms where a histogram based on the input image is constructed, a mapping is determined to output a uniform histogram and then the pixel values of the input image are adjusted based on the mapping. In the variational model, a mean brightness term is incorporated to preserve the brightness of the input image, and a geometry constraint can also be added to keep the geometry structure of the input image. Theoretically, the existence of the minimizer of the proposed model, and the convergence of the proposed algorithm are given. Experimental results are reported to demonstrate that the performance of the proposed model are competitive with the other testing histogram equalization methods for several testing images.