Jacobi fields in groups of diffeomorphisms and applications
Top Cited Papers
- 15 February 2007
- journal article
- research article
- Published by American Mathematical Society (AMS) in Quarterly of Applied Mathematics
- Vol. 65 (1) , 113-134
- https://doi.org/10.1090/s0033-569x-07-01027-5
Abstract
This paper presents a series of applications of the Jacobi evolution equations along geodesics in groups of diffeomorphisms. We describe, in particular, how they can be used to perform implementable gradient descent algorithms for image matching, in several situations, and illustrate this with 2D and 3D experiments. We also discuss parallel translation in the group, and its projection on shape manifolds, and focus in particular on an implementation of these equations using iterated Jacobi fields.Keywords
This publication has 19 references indexed in Scilit:
- Metamorphoses Through Lie Group ActionFoundations of Computational Mathematics, 2005
- Computing Large Deformation Metric Mappings via Geodesic Flows of DiffeomorphismsInternational Journal of Computer Vision, 2005
- Local Geometry of Deformable TemplatesSIAM Journal on Mathematical Analysis, 2005
- Soliton dynamics in computational anatomyNeuroImage, 2004
- On the Metrics and Euler-Lagrange Equations of Computational AnatomyAnnual Review of Biomedical Engineering, 2002
- The Euler–Poincaré Equations and Semidirect Products with Applications to Continuum TheoriesAdvances in Mathematics, 1998
- Gaussian random fields on sub-manifolds for characterizing brain surfacesPublished by Springer Nature ,1997
- Deformable templates using large deformation kinematicsIEEE Transactions on Image Processing, 1996
- An integrable shallow water equation with peaked solitonsPhysical Review Letters, 1993
- The fundamental equations of a submersion.The Michigan Mathematical Journal, 1966