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How to obtain a quantitative measure of the difference between histograms? 

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A quantitative measure of the difference between histograms can be obtained using multi-dimensional test statistics . This approach allows for the estimation of the statistical difference between two histograms by calculating the "significance of deviation" . By constructing a number of clones (rehistograms) of the observed histograms, the distinguishability of the histograms can be estimated . Another method involves calculating a similarity score between two histograms based on a subset of bins, which are independently selected for each image . Additionally, a distance function can be used to measure distances between histograms, and a statistical test can be constructed to determine the statistical significance of these distances . Hidden Markov models (HMMs) can also be associated with sets of histograms to capture both the bin values and visual shapes of the histograms, providing a similarity rate for comparison .

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The paper proposes using hidden Markov models (HMMs) to capture both the bin values and visual shapes of histograms, and then calculates the similarity rate between these HMMs to obtain a quantitative measure of the difference between histograms.
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The paper proposes an approach based on the notion of "significance of deviation" to estimate the statistical difference between histograms. It uses multi-dimensional test statistics and constructs rehistograms to estimate the distinguishability of the histograms.
The paper proposes an approach for obtaining a quantitative measure of the difference between histograms using multi-dimensional test statistics and the construction of rehistograms.
The paper describes calculating a similarity score between two histograms, which represents a quantitative measure of the difference between the histograms.

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