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.

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