In this paper, a novel neighborhood metric of histogram equalization (HE) algorithm for contrast enhancement is presented. We present a refinement of HE using neighborhood metrics with a general framework which orders pixels based on a sequence of sorting functions which uses both global and local information to remap the image greylevels. We tested a novel sorting key with the suggestion of using the original image greylevel as the primary key and a novel neighborhood distinction metric as the secondary key, and compared HE using proposed distinction metric and other HE methods such as global histogram equalization (GHE), HE using voting metric and HE using contrast difference metric. We found that our method can preserve advantages of other metrics, while reducing drawbacks of them and avoiding undesirable over-enhancement that can occur with local histogram equalization (LHE) and other methods.