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Given Histogram A and B. Modify histogram of A as given by histogram of B

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To obtain histogram specification, we apply the inverse transform by comparing equalized image (a) and image (b).

We get

$1\to3 \\ 3\to4\\ 5\to5 \\ 6\to6 \\ 7\to7$

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Hence the final result is shown and we conclude that histogram (a) has been equalized and mapped in such a way that it resembles the histogram (b). This is histogram specification.

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