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I'm on histogram equalization process. I have quite well understood the math but i don't understand why an histogram on bimodal image fails in image enhancement and what techniques can be used in this case (some kind of local/adaptive histogram?).

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Yes it is true. A simple histogram equalization may fail for certain image intensity distributions. In your case there are some bins with excessive number of pixels. For other methods, try for example gamma and contrast corrections.

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In this case, you can decompose your image into a set of (overlapping) image patches, apply equalization for each patch and merge the results. You can find more information about this approach by searching for adaptive histogram equalization algorithms (CLAHE for example).

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It's not a bimodality, it's a dominance of a background that turns out to be "enhanced" by algorithm. Find out how to select only the region of interest for processing. Heavy median filtering + thresholding should do the trick in your case.

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