In mathematics, the Hutchinson metric, otherwise known as the 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".

Consider only nonempty, compact, and finite metric spaces. For such a space ${\displaystyle X}$, let ${\displaystyle P(X)}$ denote the space of Borel probability measures on ${\displaystyle X}$, with

the embedding associating to ${\displaystyle x\in X}$ the point measure ${\displaystyle \delta _{x}}$. The support ${\displaystyle |\mu |}$ of a measure in ${\displaystyle P(X)}$ is the smallest closed subset of measure 1.

If ${\displaystyle f:X_{1}\rightarrow X_{2}}$ is Borel measurable then the induced map

associates to ${\displaystyle \mu }$ the measure ${\displaystyle f_{*}(\mu )}$ defined by

for all ${\displaystyle B}$ Borel in ${\displaystyle X_{2}}$.

Then the Hutchinson metric is given by

where the ${\displaystyle \sup }$ is taken over all real-valued functions ${\displaystyle u}$ with Lipschitz constant ${\displaystyle \leq \!1.}$