Histogram equalization (HE) is the one of the simplest and most effective methods for contrast enhancement. It can automatically define the gray-level mapping function based on the distribution of gray-level included in the image. However, since HE does not use a spatial feature included in the input image, HE fails to produce satisfactory results for broad range of low-contrast images. The differential gray-level histogram (DH), which is contained edge information of the input image, was defined and the differential gray-level histogram equalization (DHE) has been proposed. The DHE shows better enhancement results compared to HE for many kinds of images. In this paper, we propose a generalized histogram equalization (GHE) including HE and DHE. In GHE, the histogram is created using the power of the differential gray-level, which includes the spatial features of the image. In HE, the mean brightness of the enhancement image cannot be controlled. On the other hand, GHE can control the mean brightness of the enhancement image by changing the power, thus, the mean brightness of the input image can be perfectly preserved while maintaining good contrast enhancement.