Diffeomorphic image matching with left-invariant metrics
Schmah, Tanya; Risser, Laurent; Vialard, François-Xavier (2015), Diffeomorphic image matching with left-invariant metrics, in Dong Eui Chang, Darryl D. Holm, George Patrick, Tudor Ratiu, Geometry, Mechanics, and Dynamics. The Legacy of Jerry Marsden, Springer : Berlin Heidelberg, p. 373-392. 10.1007/978-1-4939-2441-7_16
External document linkhttps://arxiv.org/abs/1401.3609v1
Book titleGeometry, Mechanics, and Dynamics. The Legacy of Jerry Marsden
Book authorDong Eui Chang, Darryl D. Holm, George Patrick, Tudor Ratiu
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Abstract (EN)The geometric approach to diffeomorphic image registration known aslarge deformation by diffeomorphic metric mapping(LDDMM) is based on a leftaction of diffeomorphisms on images, and a right-invariant metric on a diffeomor-phism group, usually defined using a reproducing kernel. We explore the use ofleft-invariant metrics on diffeomorphism groups, based on reproducing kernels de-fined in the body coordinates of a source image. This perspective, which we callLeft-LDM, allows us to consider non-isotropic spatially-varying kernels, which canbe interpreted as describing variable deformability of the source image. We alsoshow a simple relationship between LDDMM and the new approach, implying thatspatially-varying kernels are interpretable in the same way in LDDMM. We con-clude with a discussion of a class of kernels that enforce a soft mirror-symmetryconstraint, which we validate in numerical experiments on a model of a lesionedbrain.
Subjects / Keywordslarge deformation by diffeomorphic metric mapping; diffeomorphic image
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