Hutchinson metric

In mathematics, the Hutchinson metric otherwise known as Kantorovich metric is a function which measures "the discrepancy between two images for use in fractal image processing" and "can also be applied to describe the similarity between DNA sequences expressed as real or complex genomic signals".

[1][2] Consider only nonempty, compact, and finite metric spaces.

denote the space of Borel probability measures on

, with the embedding associating to

the point measure

δ

μ

is the smallest closed subset of measure 1.

is Borel measurable then the induced map associates to

μ

Then the Hutchinson metric is given by where the

is taken over all real-valued functions

with Lipschitz constant

δ

is an isometric embedding of

is Lipschitz then

is Lipschitz with the same Lipschitz constant.