Shape analysis via gradient flows on diffeomorphism groups

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.

18 pages, 1 figure

References in corpus (1)

• Geometric hydrodynamics and infinite-dimensional Newton's equations

Cited by in corpus (1)

• Convergence of the vertical Gradient flow for the Gaussian Monge problem