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Pré-Publication, Document De Travail Année : 2014

Diffeomorphic image matching with left-invariant metrics

Résumé

The geometric approach to diffeomorphic image registration known as "large deformation by diffeomorphic metric mapping" (LDDMM) is based on a left action of diffeomorphisms on images, and a right-invariant metric on a diffeomorphism group, usually defined using a reproducing kernel. We explore the use of left-invariant metrics on diffeomorphism groups, based on reproducing kernels defined in the body coordinates of a source image. This perspective, which we call Left-LDM, allows us to consider non-isotropic spatially-varying kernels, which can be interpreted as describing variable deformability of the source image. We also show a simple relationship between LDDMM and the new approach, implying that spatially-varying kernels are interpretable in the same way in LDDMM. We conclude with a discussion of a class of kernels that enforce a soft mirror-symmetry constraint, which we validate in numerical experiments on a model of a lesioned brain.

Dates et versions

hal-00940049 , version 1 (31-01-2014)

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Tanya Schmah, Laurent Risser, François-Xavier Vialard. Diffeomorphic image matching with left-invariant metrics. 2014. ⟨hal-00940049⟩
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