title: Soliton dynamics in computational anatomy.
abstract: 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.
authors.affiliation: Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA. dholm@lanl.gov
authors.forename: Darryl D
authors.initials: DD
authors.lastname: Holm
authors.forename: J Tilak
authors.initials: JT
authors.lastname: Ratnanather
authors.forename: Alain
authors.initials: A
authors.lastname: Trouvé
authors.forename: Laurent
authors.initials: L
authors.lastname: Younes
mesh_terms: D000465:Algorithms; D000715:Anatomy / Q000706:statistics & numerical data*; D019295:Computational Biology / Q000706:statistics & numerical data*; D006624:Hippocampus / Q000033:anatomy & histology / Q000502:physiology; D006801:Humans; D007091:Image Processing, Computer-Assisted; D025341:Principal Component Analysis