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I have two normalized histograms which are normalized to area 1. They have different bin widths and forms. They only thing which they have in common is their area which is 1. Can someone explain me how I can evaluate the area overlap of these histograms?

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Two of the most famous approaches to compare 2 normalized histogram $Q_i$ and $P_i$ where $i$ is the bin number $i=1:d$ are as followed:

  1. Histogram Intersection $~~~s_{IS} = \sum_i min(P_i,Q_i)$
  2. ChebyChev X2 $~~~d_{sq-chi} = \sum_i \frac{(P_i-Q_i)^2}{(P_i+Q_i)}$

where 1 is a "similarity metric" and 2 is a "distance metric". Refer to Cha's Survey for more examples on similarity and distance metrics.

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