Group Actions, Homeomorphisms, and Matching: A General Framework

@article{Miller2004GroupAH,
  title={Group Actions, Homeomorphisms, and Matching: A General Framework},
  author={Michael I. Miller and Laurent Younes},
  journal={International Journal of Computer Vision},
  year={2004},
  volume={41},
  pages={61-84}
}
This paper constructs metrics on the space of images I defined as orbits under group actions G. The groups studied include the finite dimensional matrix groups and their products, as well as the infinite dimensional diffeomorphisms examined in Trouvé (1999, Quaterly of Applied Math.) and Dupuis et al. (1998). Quaterly of Applied Math. Left-invariant metrics are defined on the product G × I thus allowing the generation of transformations of the background geometry as well as the image values… 
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