Un-reduction

Abstract

This paper provides a full geometric development of a new technique called un-reduction, for dealing with dynamics and optimal control problems posed on spaces that are unwieldy for numerical implementation. The technique, which was originally concieved for an application to image dynamics, uses Lagrangian reduction by symmetry in reverse. A deeper understanding of un-reduction leads to new developments in image matching which serve to illustrate the mathematical power of the technique.

25 pages, revised version

References in corpus (4)

• An overview of the Riemannian metrics on spaces of curves using the Hamiltonian approach
• Invariant higher-order variational problems
• Almost local metrics on shape space of hypersurfaces in n-space
• Lagrange-Poincare field equations

Cited by in corpus (5)

• A novel formulation of point vortex dynamics on the sphere: geometrical and numerical aspects
• On the coupling between an ideal fluid and immersed particles
• $G$-Strands on symmetric spaces
• Un-reduction in field theory, with applications
• Un-Reduction of Systems of Second-Order Ordinary Differential Equations