Image Contrast Enhancement based Sub-histogram Equalization Technique without Over-equalization Noise
The paper is not really well written, so it's not surprising that you're having a hard time. These are a few hints to guide you:


the authors try to do some mode detection on the image brightness histogram in order to segment it between common values in the image (= high density in their terminology) and rare values in the image (= low density);
in order to segment the histogram, they fix a window width (i.e., a number of bin of the histogram), apply this window over all possible positions in the histogram and sum the populations of the bins inside the window ($Eq. (7)$). This gives the density of a histogram bin (or equivalently of a brightness level);
their segmentation process consists then in going from the peaks of the histogram and merging neighbouring bins into it as long as the difference between the border bin and its neighbour (= the momentary change) is less than the average of the momentary changes in the region.