To accomplish the equalization effect, the remapping should be the cumulative distribution function (cdf) (more details, refer to Learning OpenCV). For the histogram
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, its cumulative distribution
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This is pdfTeX, Version 3.1415926-1.40.10 (TeX Live 2009/Debian)
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is:
System Message: WARNING/2 (H^{'}(i) = \sum_{0 \le j < i} H(j))
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This is pdfTeX, Version 3.1415926-1.40.10 (TeX Live 2009/Debian)
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LaTeX2e <2009/09/24>
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To use this as a remapping function, we have to normalize
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This is pdfTeX, Version 3.1415926-1.40.10 (TeX Live 2009/Debian)
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LaTeX2e <2009/09/24>
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such that the maximum value is 255 ( or the maximum value for the intensity of the image ). From the example above, the cumulative function is: