We present an adaptive contrast enhancement method based on the generalized histogram, which is obtained by relaxing the restriction of using the integer count. For each pixel, the integer count 1 allocated to a pixel is split into the fractional count and the remainder count. The generalized histogram is generated by accumulating the fractional count for each intensity level and distributing the remainder count uniformly throughout the intensity levels. The intensity mapping function, which determines the contrast gain for each intensity level, is derived from the generalized histogram. Since only the fractional part of the count allocated to each pixel is used for increasing the contrast gain of its intensity level, the amount of contrast enhancement is adjusted by varying the fractional count according to regional characteristics. The proposed scheme produces visually more pleasing results than the conventional histogram equalization.