The Momentum Map Representation of Images

@article{Bruveris2011TheMM,
  title={The Momentum Map Representation of Images},
  author={Martins Bruveris and François Gay‐Balmaz and Darryl D. Holm and Tudor S. Ratiu},
  journal={Journal of Nonlinear Science},
  year={2011},
  volume={21},
  pages={115-150}
}
This paper discusses the mathematical framework for designing methods of Large Deformation Diffeomorphic Matching (LDM) for image registration in computational anatomy. After reviewing the geometrical framework of LDM image registration methods, we prove a theorem showing that these methods may be designed by using the actions of diffeomorphisms on the image data structure to define their associated momentum representations as (cotangent-lift) momentum maps. To illustrate its use, the momentum… 
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