Un-reduction

Martins Bruveris; David C. P. Ellis; Darryl D. Holm; François Gay-Balmaz

doi:10.3934/jgm.2011.3.363

Article Contents

2011, Volume 3, Issue 4: 363-387. Doi: 10.3934/jgm.2011.3.363

This issue Previous Article Preface Next Article Sobolev metrics on shape space of surfaces

Un-reduction

1.
Department of Mathematics, Imperial College London, London, SW7 2AZ
2.
Department of Mathematics, Imperial College London, London SW7 2AZ
3.
Laboratoire de Météorologie Dynamique, Ecole Normale Supérieure de Paris, 75005 Paris

Received: December 2010

Revised: November 2011

Published: December 2011

Abstract / Introduction Related Papers Cited by

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 conceived 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.

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Mathematics Subject Classification: 37K05, 37K65.

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