The Euler-Poincare theory of Metamorphosis

@article{Holm2008TheET,
  title={The Euler-Poincare theory of Metamorphosis},
  author={Darryl D. Holm and Alain Trouv{\'e} and Laurent Younes},
  journal={ArXiv},
  year={2008},
  volume={abs/0806.0870}
}
In the pattern matching approach to imaging science, the process of ``metamorphosis'' is template matching with dynamical templates. Here, we recast the metamorphosis equations of into the Euler-Poincare variational framework of and show that the metamorphosis equations contain the equations for a perfect complex fluid \cite{Ho2002}. This result connects the ideas underlying the process of metamorphosis in image matching to the physical concept of order parameter in the theory of complex fluids… 
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