Shape analysis via gradient flows on diffeomorphism groups

DOI10.1088/1361-6544/aca73cOpenAlexW4313260919MaRDI QIDQ5061383

Carl-Joar Karlsson, Tracey Balehowsky, Klas Modin

Publication date: 12 January 2023

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2203.13346

zbMATH Keywords

Sobolev spacesgradient flowdiffeomorphismsnonlinear analysispartial differential equationsimage registrationshape analysis

Mathematics Subject Classification ID

Computing methodologies for image processing (68U10) Groups of diffeomorphisms and homeomorphisms as manifolds (58D05) Initial value problems for nonlinear first-order PDEs (35F25)

Related Items (2)

The Toda flow as a porous medium equation ⋮ Convergence of the vertical gradient flow for the Gaussian Monge problem

Uses Software

• LDDMM

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The basic geometry of the manifold of Riemannian metrics and of its quotient by the diffeomorphism group
• A multiscale theory for image registration and nonlinear inverse problems
• The breadth of symplectic and Poisson geometry. Festschrift in honor of Alan Weinstein
• A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem
• Semi-invariant Riemannian metrics in hydrodynamics
• Lie-Poisson methods for isospectral flows
• Geodesic warps by conformal mappings
• Geometry of the Madelung transform
• Generalized Hunter-Saxton equations, optimal information transport, and factorization of diffeomorphisms
• The momentum map representation of images
• Spaces of Riemannian metrics
• Sur la géométrie différentielle des groupes de Lie de dimension infinite et ses applications à l'hydrodynamique des fluides parfaits
• Groups of diffeomorphisms and the motion of an incompressible fluid
• Computing large deformation metric mappings via geodesic flows of diffeomorphisms
• On completeness of groups of diffeomorphisms
• Landmark matching via large deformation diffeomorphisms
• Diffeomorphic Density Matching by Optimal Information Transport
• Geometry of Image Registration: The Diffeomorphism Group and Momentum Maps
• The inverse function theorem of Nash and Moser
• THE RIEMANNIAN MANIFOLD OF ALL RIEMANNIAN METRICS
• An integrable shallow water equation with peaked solitons
• Variational problems on flows of diffeomorphisms for image matching
• Geometric hydrodynamics and infinite-dimensional Newton’s equations
• Shapes and diffeomorphisms

This page was built for publication: Shape analysis via gradient flows on diffeomorphism groups