Hutchinson metric
In mathematics, the Hutchinson 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 a space, let denote the space of Borel probability measures on, with
the embedding associating to the point measure. The support of a measure in P is the smallest closed subset of measure 1.
If
is Borel measurable then the induced map
associates to the measure defined by
for all Borel in.
Then the Hutchinson metric is given by
where the is taken over all real-valued functions u with Lipschitz constant
Then is an isometric embedding of into, and if
is Lipschitz then
is Lipschitz with the same Lipschitz constant.
