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medpy.metric.image.mutual_information(i1, i2, bins=256)[source]

Computes the mutual information (MI) (a measure of entropy) between two images.

MI is not real metric, but a symmetric and nonnegative similarity measures that takes high values for similar images. Negative values are also possible.

Intuitively, mutual information measures the information that i1 and i2 share: it measures how much knowing one of these variables reduces uncertainty about the other.

The Entropy is defined as:

\[H(X) = - \sum_i p(g_i) * ln(p(g_i)\]

with \(p(g_i)\) being the intensity probability of the images grey value \(g_i\).

Assuming two images \(R\) and \(T\), the mutual information is then computed by comparing the images entropy values (i.e. a measure how well-structured the common histogram is). The distance metric is then calculated as follows:

\[MI(R,T) = H(R) + H(T) - H(R,T) = H(R) - H(R|T) = H(T) - H(T|R)\]

A maximization of the mutual information is equal to a minimization of the joint entropy.


i1 : array_like

The first image.

i2 : array_like

The second image.

bins : integer

The number of histogram bins (squared for the joined histogram).


mutual_information : float

The mutual information distance value between the supplied images.



If the supplied arrays are of different shape.