histogram.slides.printing

# I sometimes we may want to do nonlinear contrast

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I Sometimes we may want to do nonlinear contrast enhancement automatically . I Basic idea: choose to allocate the most output levels to the sections of the input range that occur most frequently. I Look at the histogram of the input signal. I If we properly allocate our output levels proportional to the frequency of occurrence for our input levels, the histogram of the output should be uniform. I This process is known as histogram equalization .

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Level Operations (Part 2) Histogram Equalization Histogram Equalization: Examples
Level Operations (Part 2) Histogram Equalization From Histograms to Probabilities Can convert from the histogram (counting values) to probabilities (percentages) by just dividing by the area: p ( r ) = H ( r ) Area This produces a probability density function .

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Level Operations (Part 2) Histogram Equalization Implementation - Continuous s = Z r 0 p ( w ) dw where I r is the input level I s is the corresponding output level I p is the probability density function (normalized histogram) of the input signal I w is a dummy variable of integration Produces a value 0 s 1, which you then can scale linearly to the desired output range.
Level Operations (Part 2) Histogram Equalization Histogram Equalization (Discrete Values) Using discrete greylevel values and the histogram directly: s = 1 Area r X w = 0 H ( w ) !

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• Winter '08
• Morse,B
• Probability distribution, Probability theory, Histogram, Density estimation, Histogram equalization

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