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Contrast enhancement is important and useful for consumer electronics. One widely accepted contrast enhancement method is global histogram equalization (GHE), which achieves comparatively better performance on almost all types of image but sometimes causes excessive visual deterioration. We propose a new extension of bi-histogram equalization called Bi-Histogram Equalization with Neighborhood Metric (BHENM). BHENM consists of two stages. First, large histogram bins that cause washout artifacts are divided into sub-bins using neighborhood metrics; the same intensities of the original image are arranged by neighboring information. In the second stage, the histogram of the original image is separated into two sub-histograms based on the mean of the histogram of the original image; the sub-histograms are equalized independently using refined histogram equalization, which produces flatter histograms. In an experimental trial, BHENM simultaneously preserved the brightness and enhanced the local contrast of the original image.