if you have way too many pixels with gray level 123 (let's
say 500,000 of them) and you want to reduce it (say to 100,000 pixels
with gray level 123) then you're going to have to pick 400,000 of
those pixels and assign them to a new gray level(s). The questions to
ask are *which* 400,000 (of the 500,000 pixels total) are you going to
reassign.
CLAHE stands for Contrast Limited Adaptive Histogram Equalization, and as the acronym suggests the method is adaptive. Basic adaptive histogram equalization operates in blocks (that may or may not overlap depending on the implementation) and the neighborhood of a pixel (in the block) defines the statistics (histogram) that govern how the pixel value is mapped to a new value. With the contrast limited version you have in addition to neighborhood size and number of input and output bins in histogram one more parameter defining the contrast limits for the mapping. So the answer for the question "which pixels" - depends on the neighborhood (size and values) of the pixel and the set clipping parameter values (in addition to the binning size of the histogram). If more detailed answer is sought I suggest to study some of the freely available implementations around the net...
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