Soliton Dynamics in Computational Anatomy

Details Soliton Dynamics in Computational Anatomy Soliton Dynamics in Computational Anatomy

2004-11-05

arxiv.org/abs/nlin/0411014v1

NeuroImage Vol 23, S170-178, 2004

Nonlinear Sciences

Exactly Solvable and Integrable Systems

published in NeuroImage

Scientific paper

10.1016/j.neuroimage.2004.07.017

Computational anatomy (CA) has introduced the idea of anatomical structures being transformed by geodesic deformations on groups of diffeomorphisms. Among these geometric structures, landmarks and image outlines in CA are shown to be singular solutions of a partial differential equation that is called the geodesic EPDiff equation. A recently discovered momentum map for singular solutions of EPDiff yields their canonical Hamiltonian formulation, which in turn provides a complete parameterization of the landmarks by their canonical positions and momenta. The momentum map provides an isomorphism between landmarks (and outlines) for images and singular soliton solutions of the EPDiff equation. This isomorphism suggests a new dynamical paradigm for CA, as well as new data representation.

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