Group actions, homomorphisma, and matching: a general framework
M. Miller and L Younes
This paper constructs metrics on
the space of images I subject to
group actions G.
The groups studied include the finite dimensional
matrix groups and their products,
as well as the infinite dimensional
diffeomorphisms examined by Trouv\'e, or Duipuis, Grenander and Miller.
Left-invariant metrics are defined
on the product G X I,
thus allowing the generation of transformations of the background
geometry as well as the image values.
Examples of the application of
such metrics are presented for rigid object matching with
and without signature variation, curves and volume matching,
and structural generation in which
image values are change supporting notions such as tissue creation
in carrying one image to another.
