No, it doesn't do correlations. What is does is to linearly map one intensity region into another. So you could do the first row of your equalization plots because they are linear, but not any on the bottom row because they aren't linear. You could do the ones on the bottom row with intlut().
How about doing it all over with adapthisteq() or imadjust()? If you want just the box, then you're going to have to extract it, enhance the contrast with something like imadjust() and then write it back - at least that's one way.
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