Shape analysis via gradient flows on diffeomorphism groups

2022/03/24 by Tracey Balehowsky, Balehowsky, Tracey, Carl-Joar Karlsson +3
Mathematics · Medicine · #35F25 #58D05 #68U10 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals #Medical Imaging Techniques and Applications

paper · pdf · doi:10.48550/arxiv.2203.13346

openalex publication_date 2022/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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