Shape analysis via gradient flows on diffeomorphism groups
arXiv:2203.13346 · doi:10.1088/1361-6544/aca73c
Abstract
We study a gradient flow on Sobolev diffeomorphisms for the problem of image registration. The energy functional quantifies the effect of transforming a template to a target, while also penalizing deformation of the metric tensor. The main result is well-posedness of the flow. We also give a geometric description of the gradient in terms of the momentum map.
arXiv comment18 pages, 1 figure
References in corpus (10)
- An integrable shallow water equation with peaked solitons
- The momentum map representation of images
- Lie-Poisson methods for isospectral flows
- Geometric hydrodynamics and infinite-dimensional Newton's equations
- Diffeomorphic density matching by optimal information transport
- Generalised Hunter-Saxton equations, optimal information transport, and factorisation of diffeomorphisms
- A Multiscale Theory for Image Registration and Nonlinear Inverse Problems
- Geometry of the Madelung transform
- Semi-invariant Riemannian metrics in hydrodynamics
- Geodesic Warps by Conformal Mappings