We present a refinement of histogram equalization which uses both global and local information to remap the image greylevels. Local image properties, which we generally call neighborhood metrics, are used to subdivide histogram bins that would be otherwise indivisible using classical histogram equalization (HE). Choice of the metric influences how the bins are subdivided, affording the opportunity for additional contrast enhancement. We present experimental results for two specific neighborhood metrics and compare the results to classical histogram equalization and local histogram equalization (LHE). We find that our methods can provide an improvement in contrast enhancement versus HE, while avoiding undesirable over-enhancement that can occur with LHE and other methods. Moreover, the improvement over HE is achieved with only a small increase in computation time.