Shape analysis via gradient flows on diffeomorphism groups
Journal article, 2023
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.
Sobolev spaces
Primary 58D05
diffeomorphisms
shape analysis
68U10
Secondary 35F25
gradient flow
image registration
partial differential equations
nonlinear analysis
Author
Tracey Balehowsky
University of Calgary
Carl-Joar Karlsson
Chalmers, Mathematical Sciences, Analysis and Probability Theory
University of Gothenburg
Klas Modin
Chalmers, Mathematical Sciences, Applied Mathematics and Statistics
University of Gothenburg
Nonlinearity
0951-7715 (ISSN)
Vol. 36 2 862-877Geometric analysis and applications to microbe ecology
Swedish Research Council (VR) (2018-03873), 2019-01-01 -- 2022-12-31.
Geometric numerical methods for computational anatomy
Swedish Research Council (VR) (2017-05040), 2018-01-01 -- 2021-12-31.
Subject Categories
Computational Mathematics
Mathematical Analysis
DOI
10.1088/1361-6544/aca73c