Campuses:

Soliton Dynamics in Computational Anatomy

Thursday, April 6, 2006 - 9:00am - 10:00am
EE/CS 3-180
Darryl Holm (Los Alamos National Laboratory)
Computational Anatomy (CA) introduces the idea that shapes
may be transformed into each other by geodesic deformations on
groups of diffeomorphisms. In particular, the
template matching approach involves Riemannian metrics on the
tangent space of the diffeomorphism group and employs their
projections onto specific landmark shapes, or image spaces. A
singular momentum map provides an isomorphism between
landmarks (and outlines) for images and singular soliton
solutions of the geodesic equation. This isomorphism suggests a
new dynamical paradigm for CA, as well as a new data
representation.

The main references for this talk are

Soliton Dynamics in Computational Anatomy,


D. D. Holm, J. T. Ratnanather, A. Trouvé, L. Younes,
http://arxiv.org/abs/nlin.SI/0411014


Momentum Maps and Measure-valued Solutions for the EPDiff
Equation,

D. D. Holm and J. E. Marsden, In The Breadth
of Symplectic and Poisson Geometry, A Festshrift for Alan
Weinstein
, 203-235,Progr. Math., 232,
J.E. Marsden and T.S. Ratiu, Editors, Birkhäuser Boston, Boston, MA, 2004. Also at http://arxiv.org/abs/nlin.CD/0312048

D. D. Holm and M. F. Staley, Interaction Dynamics
of Singular Wave Fronts
, at Martin Staley's website, under
Recent Papers at http://cnls.lanl.gov/~staley/
MSC Code: 
35C08