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) 13616544 (eISSN)

Vol. 36 2 862-877

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Subject Categories

Computational Mathematics

Mathematical Analysis

DOI

10.1088/1361-6544/aca73c

More information

Created

3/16/2023