Shape analysis via gradient flows on diffeomorphism groups

• We study a Riemannian 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 non-isometric deformations. The main result is well-posedness of the flow. We also give a geometric description of the gradient in terms of the momentum map.

Ämnesord

NATURVETENSKAP  -- Matematik -- Beräkningsmatematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Computational Mathematics (hsv//eng)

NATURVETENSKAP  -- Matematik -- Matematisk analys (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Mathematical Analysis (hsv//eng)

Nyckelord

Sobolev spaces

Primary 58D05

diffeomorphisms

shape analysis

68U10

Secondary 35F25

gradient flow

image registration

partial differential equations

nonlinear analysis

Publikations- och innehållstyp

art (ämneskategori)

ref (ämneskategori)