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Related Experiment Videos

Soliton dynamics in computational anatomy.

Darryl D Holm1, J Tilak Ratnanather, Alain Trouvé

  • 1Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA. dholm@lanl.gov

Neuroimage
|October 27, 2004
PubMed
Summary
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Computational anatomy uses geodesic deformations to model anatomical structures. A new momentum map formulation reveals landmarks and outlines as solutions to the EPDiff equation, enabling novel data representation.

Area of Science:

  • Computational anatomy
  • Differential geometry
  • Image analysis

Background:

  • Anatomical structures are modeled using geodesic deformations in computational anatomy.
  • Landmarks and image outlines are singular solutions to the geodesic EPDiff equation.

Purpose of the Study:

  • To present a canonical Hamiltonian formulation for singular solutions of the EPDiff equation.
  • To establish an isomorphism between image landmarks/outlines and soliton solutions.

Main Methods:

  • Utilizing a recently discovered momentum map for singular EPDiff solutions.
  • Applying canonical Hamiltonian formulation.
  • Establishing an isomorphism between anatomical data and soliton solutions.

Main Results:

Related Experiment Videos

  • A complete parameterization of landmarks using canonical positions and momenta.
  • Demonstration of an isomorphism between image landmarks/outlines and singular soliton solutions of the EPDiff equation.

Conclusions:

  • The momentum map offers a new dynamical paradigm for computational anatomy.
  • This framework provides a novel data representation for anatomical images.