Jacobi fields in groups of diffeomorphisms and applications

DOI10.1090/S0033-569X-07-01027-5zbMath1128.53040WikidataQ125791386 ScholiaQ125791386MaRDI QIDQ5424298

Laurent Younes

Publication date: 5 November 2007

Published in: Quarterly of Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

Jacobi fieldsgroups of diffeomorphismsshape analysisdeformable templatesimage deformations

Mathematics Subject Classification ID

Related Items (25)

Constrained $H^1$-Regularization Schemes for Diffeomorphic Image Registration ⋮ Registration of anatomical images using paths of diffeomorphisms parameterized with stationary vector field flows ⋮ Geometry of Image Registration: The Diffeomorphism Group and Momentum Maps ⋮ Metric Spaces of Shapes and Geometries Constructed from Set Parametrized Functions ⋮ Efficient representation in spaces of plane curves ⋮ A Fanning Scheme for the Parallel Transport along Geodesics on Riemannian Manifolds ⋮ Numerical accuracy of ladder schemes for parallel transport on manifolds ⋮ A reparameterisation based approach to geodesic constrained solvers for curve matching ⋮ Diffeomorphic 3D image registration via geodesic shooting using an efficient adjoint calculation ⋮ The TPS direct transport: a new method for transporting deformations in the size-and-shape space ⋮ A Comparative Study of Different Variants of Newton--Krylov PDE-Constrained Stokes-LDDMM Parameterized in the Space of Band-Limited Vector Fields ⋮ A Lagrangian Gauss--Newton--Krylov Solver for Mass- and Intensity-Preserving Diffeomorphic Image Registration ⋮ Constrained diffeomorphic shape evolution ⋮ Geodesics, parallel transport \& one-parameter subgroups for diffeomorphic image registration ⋮ Geodesic regression and the theory of least squares on Riemannian manifolds ⋮ Image Extrapolation for the Time Discrete Metamorphosis Model: Existence and Applications ⋮ Registration of Multiple Shapes using Constrained Optimal Control ⋮ Analysing `simple' image registrations ⋮ Combining the band-limited parameterization and semi-Lagrangian Runge-Kutta integration for efficient PDE-constrained LDDMM ⋮ Efficient parallel transport of deformations in time series of images: from Schild's to pole ladder ⋮ Diffeomorphic metric landmark mapping using stationary velocity field parameterization ⋮ PDE-constrained optimization in medical image analysis ⋮ Transport of relational structures in groups of diffeomorphisms ⋮ CLAIRE: A Distributed-Memory Solver for Constrained Large Deformation Diffeomorphic Image Registration ⋮ An Inexact Newton--Krylov Algorithm for Constrained Diffeomorphic Image Registration

Uses Software

• LDDMM

Cites Work

• The Euler-Poincaré equations and semidirect products with applications to continuum theories
• Metamorphoses through Lie group action
• The fundamental equations of a submersion
• An integrable shallow water equation with peaked solitons
• Variational problems on flows of diffeomorphisms for image matching
• Computational anatomy: an emerging discipline
• Local Geometry of Deformable Templates
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